THE LOCAL LIMIT OF GLOBAL GYROKINETIC SIMULATIONS
CANDY J; WALTZ RE; DORLAND W
2003-10-01
OAK-B135 Global gyrokinetic simulations of turbulence include physical effects that are not retained in local flux-tube simulations. nevertheless, in the limit of sufficiently small {rho}* (gyroradius compared to system size) it is expected that a local simulation should agree with a global one (at the local simulation radius) since all effects that are dropped in the local simulations are expected to vanish as {rho}* {yields} 0. In this note, global simulations of a well-established test case are indeed shown to recover the flux-tube limit at each radius.
Global gyrokinetic simulations with strong flows
NASA Astrophysics Data System (ADS)
Collier, J. D.; McMillan, B. F.; Robinson, J. R.
2016-11-01
We report on the investigation of strong toroidal rotation effects in a global tokamak code, ORB5. This includes the implementation of a strong flow gyrokinetic Lagrangian, allowing a complete treatment of centrifugal and Coriolis effects in the laboratory frame. In order to consistently perform the linear analysis in this system, an axisymmetric gyrokinetic equilibrium distribution function is defined using the constants of motion: we show it corresponds to the standard choice in the local limit and is close to the neoclassical solution in the banana regime. The energy and momentum transport equations are presented in an analogous form to those for the weak flow system. Linear studies of Ion Temperature Gradient (ITG) modes in rotating plasmas are performed to determine how the global effects interact with the effects of strong rotation. We also determine the geodesic acoustic mode dispersion with respect to plasma rotation rate in this gyrokinetic model and compare it to MHD theory.
Global Gyrokinetic Simulation Model for Laboratory Magnetosphere
NASA Astrophysics Data System (ADS)
Xie, Hua-Sheng; Ou, Wei-Ke; Zhang, Yi; Du, Shi-Kang; Huang, Zi-Cong; Li, Bo
2016-10-01
A global gyro-kinetic particle-in-cell code (GKD) is developed to study the micro-instabilties driven turbulent transport for magnetic dipole configuration. This configuration is relevant to several experiment devices, such as LDX at MIT, CTX at Columbia University and HDX at Harbin Institute of Technology. The major electrostatic drift instability in this system is entropy mode, which can be unstable even when ideal interchange mode is stable. For comparison, we also show the nonlinear results in Z-pinch and linear results with benchmark to linear eigenvalue solution.
Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments
Wang, W.X.; Lin, Z.; Tang, W.M.; Lee, W.W.; Ethier, S.; Lewandowski, J.L.V.; Rewoldt, G.; Hahm, T.S.; Manickam, J.
2006-01-01
A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Global gyrokinetic simulations of microturbulence for TCV-relevant plasmas
NASA Astrophysics Data System (ADS)
Merlo, G.; Brunner, S.; Coda, S.; Huang, Z.; Sauter, O.; Villard, L.; Görler, T.; Jenko, F.; Told, D.; Camenen, Y.; Marinoni, A.
2015-11-01
Due to significant global effects, in smaller-sized tokamaks such as TCV local (flux-tube) microturbulence simulations are unable to fully reproduce experimental transport levels. We will therefore present results obtained with the global version of the gyrokinetic code GENE aiming at addressing two observations made on TCV. 1) Effect of negative triangularity: it has been experimentally demonstrated that half the heating power is required to maintain the same electron temperature profile when the sign of triangularity of the Last Closed Flux Surface is reversed from δ=0.4 to -0.4 . Local simulations fail at reproducing both the actual transport level and positive/negative δ flux ratio. Therefore global simulations have been carried out with the aim of recovering the experimental results. 2) GAM physics: a complete multi-diagnostic characterization of the Geodesic Acoustic Mode has been reported from TCV. In particular the dependency of frequency, radial location and wave vector on plasma parameters have been experimentally investigated. Global runs modeling these TCV conditions will be discussed and simulations compared to experiments with the help of synthetic diagnostics.
Global gyrokinetic ion temperature gradient turbulence simulations of ITER
NASA Astrophysics Data System (ADS)
Villard, L.; Angelino, P.; Bottino, A.; Brunner, S.; Jolliet, S.; McMillan, B. F.; Tran, T. M.; Vernay, T.
2013-07-01
Global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence in an ideal MHD ITER equilibrium plasma are performed with the ORB5 code. The noise control and field-aligned Fourier filtering procedures implemented in ORB5 are essential in obtaining numerically healthy results with a reasonable amount of computational effort: typical simulations require 109 grid points, 109 particles and, despite a particle per cell ratio of unity, achieve a signal to noise ratio larger than 50. As compared with a circular concentric configuration with otherwise similar parameters (same ρ* = 1/720), the effective heat diffusivity is considerably reduced for the ITER MHD equilibrium. A self-organized radial structure appears, with long-lived zonal flows (ZF), modulating turbulence heat transport and resulting in a corrugated temperature gradient profile. The ratio of long-lived ZF to the fluctuating ZF is markedly higher for the ITER MHD equilibrium as compared with circular configurations, thereby producing a more effective ITG turbulence suppression, in spite of a higher linear growth rate. As a result, the nonlinear critical temperature gradient, R/LTcrit,NL, is about twice the linear critical temperature gradient, R/LTcrit,lin. Moreover, the heat transport stiffness above the nonlinear threshold is considerably reduced as compared with circular cases. Plasma elongation is probably one of the essential causes of this behaviour: indeed, undamped ZF residual levels and geodesic acoustic mode damping are both increasing with elongation. Other possible causes of the difference, such as magnetic shear profile effects, are also investigated.
Global full-f gyrokinetic simulations of plasma turbulence
NASA Astrophysics Data System (ADS)
Grandgirard, V.; Sarazin, Y.; Angelino, P.; Bottino, A.; Crouseilles, N.; Darmet, G.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, Ph; Jolliet, S.; Latu, G.; Sonnendrücker, E.; Villard, L.
2007-12-01
Critical physical issues can be specifically tackled with the global full-f gyrokinetic code GYSELA. Three main results are presented. First, the self-consistent treatment of equilibrium and fluctuations highlights the competition between two compensation mechanisms for the curvature driven vertical charge separation, namely, parallel flow and polarization. The impact of the latter on the turbulent transport is discussed. In the non-linear regime, the benchmark with the Particle-In-Cell code ORB5 looks satisfactory. Second, the transport scaling with ρ* is found to depend both on ρ* itself and on the distance to the linear threshold. Finally, a statistical steady-state turbulent regime is achieved in a reduced version of GYSELA by prescribing a constant heat source.
A finite element Poisson solver for gyrokinetic particle simulations in a global field aligned mesh
Nishimura, Y. . E-mail: nishimuy@uci.edu; Lin, Z.; Lewandowski, J.L.V.; Ethier, S.
2006-05-20
A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations.
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Besse, N.; Bertrand, P.
2006-11-30
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
NASA Astrophysics Data System (ADS)
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Crouseilles, N.; Latu, G.; Sonnendrücker, E.; Besse, N.; Bertrand, P.
2006-11-01
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.
NASA Astrophysics Data System (ADS)
Spong, D. A.; Holod, I.; Todo, Y.; Osakabe, M.
2017-08-01
Energetic particles are inherent to toroidal fusion systems and can drive instabilities in the Alfvén frequency range, leading to decreased heating efficiency, high heat fluxes on plasma-facing components, and decreased ignition margin. The applicability of global gyrokinetic simulation methods to macroscopic instabilities has now been demonstrated and it is natural to extend these methods to 3D configurations such as stellarators, tokamaks with 3D coils and reversed field pinch helical states. This has been achieved by coupling the GTC global gyrokinetic PIC model to the VMEC equilibrium model, including 3D effects in the field solvers and particle push. This paper demonstrates the application of this new capability to the linearized analysis of Alfvénic instabilities in the LHD stellarator. For normal shear iota profiles, toroidal Alfvén instabilities in the n = 1 and 2 toroidal mode families are unstable with frequencies in the 75 to 110 kHz range. Also, an LHD case with non-monotonic shear is considered, indicating reductions in growth rate for the same energetic particle drive. Since 3D magnetic fields will be present to some extent in all fusion devices, the extension of gyrokinetic models to 3D configurations is an important step for the simulation of future fusion systems. ).
Spong, Donald A.; Holod, Ihor; Todo, Y.; ...
2017-06-23
Energetic particles are inherent to toroidal fusion systems and can drive instabilities in the Alfvén frequency range, leading to decreased heating efficiency, high heat fluxes on plasma-facing components, and decreased ignition margin. The applicability of global gyrokinetic simulation methods to macroscopic instabilities has now been demonstrated and it is natural to extend these methods to 3D configurations such as stellarators, tokamaks with 3D coils and reversed field pinch helical states. This has been achieved by coupling the GTC global gyrokinetic PIC model to the VMEC equilibrium model, including 3D effects in the field solvers and particle push. Here, this papermore » demonstrates the application of this new capability to the linearized analysis of Alfvénic instabilities in the LHD stellarator. For normal shear iota profiles, toroidal Alfvén instabilities in the n = 1 and 2 toroidal mode families are unstable with frequencies in the 75 to 110 kHz range. Also, an LHD case with non-monotonic shear is considered, indicating reductions in growth rate for the same energetic particle drive. Finally, since 3D magnetic fields will be present to some extent in all fusion devices, the extension of gyrokinetic models to 3D configurations is an important step for the simulation of future fusion systems.« less
Gyrokinetic and global fluid simulations of tokamak microturbulence and transport
Dimits, A.M.; Byers, J.A.; Williams, T.J.; Cohen, B.I.; Xu, W.Q.; Cohen, R.H.; Crotinger, J.A.; Shestakov, A.I.
1994-08-30
Results are presented from the first systematic nonlinear kinetic simulation study of the swings and parameter dependences of toroidal ion-temperature-gradient (ITG) turbulence and transport, and from the first such study that includes sheared toroidal flows. Key results include the observation of clear gyroBohm scaling of the turbulent transport and of a surprisingly weak dependence of the transport on toroidal flow shear. Based on the simulation results, a parameterization of the transport is given that includes the dependence on all of the relevant physical parameters. The transition from local to nonlocal transport as a function of the profile scale length has been investigated using two-dimensional global fluid simulations of dissipative drift-wave turbulence. Local gyroBohm scaling is observed, except at very short profile scale lengths.
Comparisons between global and local gyrokinetic simulations of an ASDEX Upgrade H-mode plasma
NASA Astrophysics Data System (ADS)
Navarro, Alejandro Bañón; Told, Daniel; Jenko, Frank; Görler, Tobias; Happel, Tim
2016-04-01
We investigate by means of local and global nonlinear gyrokinetic GENE simulations an ASDEX Upgrade H-mode plasma. We find that for the outer core positions (i.e., ρ tor ≈ 0.5 - 0.7 ), nonlocal effects are important. For nominal input parameters local simulations over-predict the experimental heat fluxes by a large factor, while a good agreement is found with global simulations. This was a priori not expected, since the values of 1 / ρ ⋆ were large enough that global and local simulations should have been in accordance. Nevertheless, due to the high sensitivity of the heat fluxes with respect to the input parameters, it is still possible to match the heat fluxes in local simulations with the experimental and global results by varying the ion temperature gradient within the experimental uncertainties. In addition to that, once an agreement in the transport quantities between local (flux-matched) and global simulations is achieved, an agreement for other quantities, such as density and temperature fluctuations, is also found. The case presented here clearly shows that even in the presence of global size-effects, the local simulation approach is still a valid and accurate approach.
Flux- and gradient-driven global gyrokinetic simulation of tokamak turbulencea)
NASA Astrophysics Data System (ADS)
Görler, Tobias; Lapillonne, Xavier; Brunner, Stephan; Dannert, Tilman; Jenko, Frank; Aghdam, Sohrab Khosh; Marcus, Patrick; McMillan, Ben F.; Merz, Florian; Sauter, Olivier; Told, Daniel; Villard, Laurent
2011-05-01
The Eulerian gyrokinetic turbulence code gene has recently been extended to a full torus code. Moreover, it now provides Krook-type sources for gradient-driven simulations where the profiles are maintained on average as well as localized heat sources for a flux-driven type of operation. Careful verification studies and benchmarks are performed successfully. This setup is applied to address three related transport issues concerning nonlocal effects. First, it is confirmed that in gradient-driven simulations, the local limit can be reproduced—provided that finite aspect ratio effects in the geometry are treated carefully. In this context, it also becomes clear that the profile widths (not the device width) may constitute a more appropriate measure for finite-size effects. Second, the nature and role of heat flux avalanches are discussed in the framework of both local and global, flux- and gradient-driven simulations. Third, simulations dedicated to discharges with electron internal barriers are addressed.
Flux- and gradient-driven global gyrokinetic simulation of tokamak turbulence
Goerler, Tobias; Jenko, Frank; Marcus, Patrick; Merz, Florian; Told, Daniel; Lapillonne, Xavier; Brunner, Stephan; Aghdam, Sohrab Khosh; McMillan, Ben F.; Sauter, Olivier; Villard, Laurent; Dannert, Tilman
2011-05-15
The Eulerian gyrokinetic turbulence code gene has recently been extended to a full torus code. Moreover, it now provides Krook-type sources for gradient-driven simulations where the profiles are maintained on average as well as localized heat sources for a flux-driven type of operation. Careful verification studies and benchmarks are performed successfully. This setup is applied to address three related transport issues concerning nonlocal effects. First, it is confirmed that in gradient-driven simulations, the local limit can be reproduced--provided that finite aspect ratio effects in the geometry are treated carefully. In this context, it also becomes clear that the profile widths (not the device width) may constitute a more appropriate measure for finite-size effects. Second, the nature and role of heat flux avalanches are discussed in the framework of both local and global, flux- and gradient-driven simulations. Third, simulations dedicated to discharges with electron internal barriers are addressed.
A 5D gyrokinetic full- f global semi-Lagrangian code for flux-driven ion turbulence simulations
NASA Astrophysics Data System (ADS)
Grandgirard, V.; Abiteboul, J.; Bigot, J.; Cartier-Michaud, T.; Crouseilles, N.; Dif-Pradalier, G.; Ehrlacher, Ch.; Esteve, D.; Garbet, X.; Ghendrih, Ph.; Latu, G.; Mehrenberger, M.; Norscini, C.; Passeron, Ch.; Rozar, F.; Sarazin, Y.; Sonnendrücker, E.; Strugarek, A.; Zarzoso, D.
2016-10-01
This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic GYSELA code is one of the few international 5D gyrokinetic codes able to perform global, full- f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the GYSELA code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.
Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments
Wang, W. X.; Lin, Z.; Tang, W. M.; Lee, W. W.; Ethier, S.; Lewandowski, J. L. V.; Rewoldt, G.; Hahm, T. S.; Manickam, J.
2006-09-15
A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Understanding TCV L-mode plasmas via global gyrokinetic GENE simulations
NASA Astrophysics Data System (ADS)
Merlo, Gabriele; Brunner, Stephan; Coda, Stefano; Goerler, Tobias; Huang, Zhouji; Jenko, Frank; Told, Daniel; Sauter, Olivier; Villard, Laurent
2016-10-01
It is known that global effects can have a significant influence on turbulent transport driven by microintabilities, especially for small size machines like the TCV tokamak. The global version of the gyrokinetic GENE code has been extensively used to model TCV plasmas for which finite ρ* effects are expected to be crucial in order to recover the experimentally observed behaviour. We will address in particular: (i) The effect of negative triangularity, which has been experimentally observed to lower up to a factor of two the heat flux through the lectron channel at all radial locations. Global effects and the inclusion of carbon impurities turn out to be the key elements required in order to match experiments and simulation results. (ii) The formation of either radially coherent or dispersive axisymmetric density fluctuations, experimentally interpreted as Geodesic Acoustic Modes. GENE simulations reproduce the observed behaviour and allow to conclude that the modification of safety factor alone cannot explain the transition between these two different fluctuation regimes.
Global gyrokinetic particle-in-cell simulations of internal kink instabilities
Mishchenko, Alexey; Zocco, Alessandro
2012-12-15
Internal kink instabilities have been studied in straight tokamak geometry employing an electromagnetic gyrokinetic particle-in-cell (PIC) code. The ideal-MHD internal kink mode and the collisionless m=1 tearing mode have been successfully simulated with the PIC code. Diamagnetic effects on the internal kink modes have also been investigated.
Global gyrokinetic simulations of the H-mode tokamak edge pedestal
Wan, Weigang; Parker, Scott E.; Chen, Yang; Groebner, Richard J.; Yan, Zheng; Pankin, Alexei Y.; Kruger, Scott E.
2013-05-15
Global gyrokinetic simulations of DIII-D H-mode edge pedestal show two types of instabilities may exist approaching the onset of edge localized modes: an intermediate-n, high frequency mode which we identify as the “kinetic peeling ballooning mode (KPBM),” and a high-n, low frequency mode. Our previous study [W. Wan et al., Phys. Rev. Lett. 109, 185004 (2012)] has shown that when the safety factor profile is flattened around the steep pressure gradient region, the high-n mode is clearly kinetic ballooning mode and becomes the dominant instability. Otherwise, the KPBM dominates. Here, the properties of the two instabilities are studied by varying the density and temperature profiles. It is found that the KPBM is destabilized by density and ion temperature gradient, and the high-n mode is mostly destabilized by electron temperature gradient. Nonlinear simulations with the KPBM saturate at high levels. The equilibrium radial electric field (E{sub r}) reduces the transport. The effect of the parallel equilibrium current is found to be weak.
Advanced methods in global gyrokinetic full f particle simulation of tokamak transport
Ogando, F.; Heikkinen, J. A.; Henriksson, S.; Janhunen, S. J.; Kiviniemi, T. P.; Leerink, S.
2006-11-30
A new full f nonlinear gyrokinetic simulation code, named ELMFIRE, has been developed for simulating transport phenomena in tokamak plasmas. The code is based on a gyrokinetic particle-in-cell algorithm, which can consider electrons and ions jointly or separately, as well as arbitrary impurities. The implicit treatment of the ion polarization drift and the use of full f methods allow for simulations of strongly perturbed plasmas including wide orbit effects, steep gradients and rapid dynamic changes. This article presents in more detail the algorithms incorporated into ELMFIRE, as well as benchmarking comparisons to both neoclassical theory and other codes.Code ELMFIRE calculates plasma dynamics by following the evolution of a number of sample particles. Because of using an stochastic algorithm its results are influenced by statistical noise. The effect of noise on relevant magnitudes is analyzed.Turbulence spectra of FT-2 plasma has been calculated with ELMFIRE, obtaining results consistent with experimental data.
Accuracy of momentum and gyrodensity transport in global gyrokinetic particle-in-cell simulations
McMillan, B. F.; Villard, L.
2014-05-15
Gyrokinetic Particle-In-Cell (PIC) simulations based on conservative Lagrangian formalisms admit transport equations for conserved quantities such as gyrodensity and toroidal momentum, and these can be derived for arbitrary wavelength, even though previous applications have used the long-wavelength approximation. In control-variate PIC simulations, a consequence of the different treatment of the background (f{sub 0}) and perturbed parts (δf), when a splitting f = f{sub 0} + δf is performed, is that analytical transport relations for the relevant fluxes and moments are only reproduced in the large marker number limit. The transport equations for f can be used to write the inconsistency in the perturbed quantities explicitly in terms of the sampling of the background distribution f{sub 0}. This immediately allows estimates of the error in consistency of momentum transport in control-variate PIC simulations. This inconsistency tends to accumulate secularly and is not directly affected by the sources and noise control in the system. Although physical tokamaks often rotate quite strongly, the standard gyrokinetic formalism assumes weak perpendicular flows, comparable to the drift speed. For systems with such weak flows, maintaining acceptably small relative errors requires that a number of markers scale with the fourth power of the linear system size to consistently resolve long-wavelength evolution. To avoid this unfavourable scaling, an algorithm for exact gyrodensity transport has been developed, and this is shown to allow accurate simulations with an order of magnitude fewer markers.
Proposal of a brand-new gyrokinetic algorithm for global MHD simulation
NASA Astrophysics Data System (ADS)
Naitou, Hiroshi; Kobayashi, Kenichi; Hashimoto, Hiroki; Andachi, Takehisa; Lee, Wei-Li; Tokuda, Shinji; Yagi, Masatoshi
2009-11-01
A new algorithm for the gyrokinetic PIC code is proposed. The basic equations are energy conserving and composed of (1) the gyrokinetic Vlasov (GKV) equation, (2) the Vortex equation, and (3) the generalized Ohm's law along the magnetic field. Equation (2) is used to advance electrostatic potential in time. Equation (3) is used to advance longitudinal component of vector potential in time as well as estimating longitudinal induced electric field to accelerate charged particles. The particle information is used to estimate pressure terms in equation (3). The idea was obtained in the process of reviewing the split-weight-scheme formalism. This algorithm was incorporated in the Gpic-MHD code. Preliminary results for the m=1/n=1 internal kink mode simulation in the cylindrical geometry indicate good energy conservation, quite low noise due to particle discreteness, and applicability to larger spatial scale and higher beta regimes. The advantage of new Gpic-MHD is that the lower order moments of the GKV equation are estimated by the moment equation while the particle information is used to evaluate the second order moment.
Predictions on heat transport and plasma rotation from global gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Sarazin, Y.; Grandgirard, V.; Abiteboul, J.; Allfrey, S.; Garbet, X.; Ghendrih, Ph.; Latu, G.; Strugarek, A.; Dif-Pradalier, G.; Diamond, P. H.; Ku, S.; Chang, C. S.; McMillan, B. F.; Tran, T. M.; Villard, L.; Jolliet, S.; Bottino, A.; Angelino, P.
2011-10-01
Flux-driven global gyrokinetic codes are now mature enough to make predictions in terms of turbulence and transport in tokamak plasmas. Some of the recent breakthroughs of three such codes, namely GYSELA, ORB5 and XGC1, are reported and compared wherever appropriate. In all three codes, turbulent transport appears to be mediated by avalanche-like events, for a broad range of ρ* = ρi/a values, ratio of the gyro-radius over the minor radius. Still, the radial correlation length scales with ρi, leading to the gyro-Bohm scaling of the effective transport coefficient below ρ* ≈ 1/300. The possible explanation could be due to the fact that avalanches remain meso-scale due to the interaction with zonal flows, whose characteristic radial wavelength appears to be almost independent of the system size. As a result of the radial corrugation of the turbulence driven zonal and mean flows, the shear of the radial electric field can be significantly underestimated if poloidal rotation is assumed to be governed by the neoclassical theory, especially at low collisionality. Indeed, the turbulence contribution to the poloidal rotation increases when collisionality decreases. Finally, the numerical verification of toroidal momentum balance shows that both neoclassical and turbulent contributions to the Reynolds' stress tensor play the dominant role. The phase space analysis further reveals that barely passing supra-thermal particles mostly contribute to the toroidal flow generation, consistently with quasi-linear predictions.
Bass, E. M.; Waltz, R. E.
2013-01-15
The unstable spectrum of Alfven eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfven eigenmode (RSAE) at toroidal mode number n=3 is mapped. The RSAE second harmonic and an unstable beta-induced Alfven eigenmode (BAE) are simultaneously tracked alongside the primary RSAE. An observed twist in the eigenmode pattern, caused mostly by shear in the driving EP profile, is shown through artificially varying the E Multiplication-Sign B rotational velocity shear to depend generally on shear in the local wave phase velocity. Coupling to the BAE and to the toroidal Alfven eigenmode limit the RSAE frequency sweeps at the lower and upper end, respectively. While the present fully gyrokinetic model (including thermal ions and electrons) constitutes the best treatment of compressibility physics available, the BAE frequency is overpredicted by about 20% against experiment here and is found to be sensitive to energetic beam ion pressure. The RSAE frequency is more accurately matched except when it is limited by the BAE. Simulations suggest that the experiment is very close to marginal AE stability at points of RSAE-BAE coupling. A recipe for comparing the radial profile of quasilinear transport flux from local modes to that from global modes paves the way for the development of a stiff (critical gradient) local AE transport model based on local mode stability thresholds.
Gyrokinetic simulations of ETG Turbulence*
NASA Astrophysics Data System (ADS)
Nevins, William
2005-10-01
Recent gyrokinetic simulations of electron temperature gradient (ETG) turbulence [1,2] produced different results despite similar plasma parameters. Ref.[1] differs from Ref.[2] in that [1] eliminates magnetically trapped particles ( r/R=0 ), while [2] retains magnetically trapped particles ( r/R 0.18 ). Differences between [1] and [2] have been attributed to insufficient phase-space resolution and novel physics associated with toroidicity and/or global simulations[2]. We have reproduced the results reported in [2] using a flux-tube, particle-in-cell (PIC) code, PG3EQ[3], thereby eliminating global effects as the cause of the discrepancy. We observe late-time decay of ETG turbulence and the steady-state heat transport in agreement with [2], and show this results from discrete particle noise. Discrete particle noise is a numerical artifact, so both the PG3EQ simulations reported here and those reported in Ref.[2] have little to say about steady-state ETG turbulence and the associated anomalous electron heat transport. Our attempts to benchmark PIC and continuum[4] codes at the plasma parameters used in Ref.[2] produced very large, intermittent transport. We will present an alternate benchmark point for ETG turbulence, where several codes reproduce the same transport levels. Parameter scans about this new benchmark point will be used to investigate the parameter dependence of ETG transport and to elucidate saturation mechanisms proposed in Refs.[1,2] and elsewhere[5-7].*In collaboration with A. Dimits (LLNL), J. Candy, C. Estrada-Mila (GA), W. Dorland (U of MD), F. Jenko, T. Dannert (Max-Planck Institut), and G. Hammett (PPPL). Work at LLNL performed for US DOE under Contract W7405-ENG-48.[1] F. Jenko and W. Dorland, PRL 89, 225001 (2002).[2] Z. Lin et al, 2004 Sherwood Mtg.; 2004 TTF Mtg.; Fusion Energy 2004 (IAEA, Vienna, 2005); Bull. Am. Phys. Soc. (November, 2004); 2005 TTF Mtg.; 2005 Sherwood Mtg.; Z. Lin, et al, Phys. Plasmas 12, 056125 (2005). [3] A.M. Dimits
NASA Astrophysics Data System (ADS)
Bass, E. M.; Waltz, R. E.
2012-10-01
In ITER, convection of fusion-produced alpha particles by energetic particle (EP)-driven Alfv'en eigenmodes (AEs) risks wall damage and loss of alpha heating needed for ignition. We examine beam-excited AEs and induced quasilinear transport in a DIII-D AE experiment using the gyrokinetic code GYRO [1]. Global, linear eigenvalue simulations show reverse-shear AEs (RSAEs), toroidal AEs, and beta-induced AEs interacting over one (equilibrium time scale) RSAE frequency sweep. Eigenfunction modifications over MHD, including a poloidal twist and broad AE footprint observed in electron cyclotron emission imaging [2], show the value of a kinetic approach. Under a simple quasilinear saturation assumption, a sequence of comparatively inexpensive local simulations quantitatively recreates some global features, notably the quasilinear transport footprint. Accordingly, we present here a stiff EP transport model where AEs limit the EP density gradient to the local stability threshold, and a TGLF-driven quasilinear model elsewhere. The model gives some``worst case'' predictions of the AE-limited alpha profile in ITER.[4pt] [1] J. Candy and R.E. Waltz, Phys. Rev. Lett. 91, 045001 (2003). [2] B.J. Tobias, et al., Phys. Rev. Lett. 106, 075003 (2011).
Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.
2009-07-15
In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino et al., Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino et al., Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker et al., Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Koenies et al., Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino et al., Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.
NASA Astrophysics Data System (ADS)
Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.
2009-07-01
In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino et al., Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino et al., Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker et al., Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Könies et al., Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino et al., Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.
Gyrokinetic simulation of current-driven instabilities
NASA Astrophysics Data System (ADS)
McClenaghan, Joseph
The gyrokinetic toroidal code(GTC) capability has been extended for simulating current-driven instabilities in magnetized plasmas such as kink and resistive tearing modes with kinetic effects. This new gyrokinetic capability enables first-principles, integrated simulations of macroscopic magnetohydrodynamic(MHD) modes, which limit the performance of burning plasmas and threaten the integrity of fusion devices. The excitation and evolution of macroscopic MHD modes often depend on the kinetic effects at microscopic scales and the nonlinear coupling of multiple physical processes. GTC simulation in the fluid limit of the internal kink modes in cylindrical geometry has been verified by benchmarking with an MHD eigenvalue code. The global simulation domain covers the magnetic axis which is necessary for simulating the macroscopic MHD modes. Gyrokinetic simulations of the internal kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface. This new GTC capability for current-driven instability has now been extended to simulate fishbone instabilities excited by energetic particles and resistive tearing modes. GTC has also been applied to study the internal kink modes in astrophysical jets that are formed around supermassive black holes. Linear simulations find that the internal kink modes in astrophysical jets are unstable with a broad eigenmode. Nonlinear saturation amplitude of these kink modes is observed to be small, suggesting that the jets can remain collimated even in the presence of the internal kink modes. Generation of a mean parallel electric field by the nonlinear dynamics of internal kink modes and the potential implication of this field on particle acceleration in jets has been examined.
Gyrokinetic Turbulence Simulations for Stellarators
NASA Astrophysics Data System (ADS)
Merz, F.; Xanthopoulos, P.; Gorler, T.; Jenko, F.; Mikkelsen, D.
2007-11-01
While there is an abundance of publications on plasma microturbulence in tokamaks, not much is presently known about its character in nonaxisymmetric devices. The present work constitutes the first attempt to investigate turbulent transport in modern stellarators, using the gyrokinetic turbulence code Gene and realistic magnetic equilibria. First, linear and nonlinear gyrokinetic simulations of ion-temperature-gradient (ITG) and trapped electron modes are presented for the optimized stellarator Wendelstein 7-X which is currently under construction at Greifswald, Germany. The newly developed code Tracer -- based on field line tracing -- is employed to extract the required geometric information from the MHD equilibria [Phys. Plasmas 13, 092301 (2006)]. Extensive linear studies reveal substantial differences with respect to axisymmetric geometry [Phys. Plasmas 14, 042501 (2007)]. Nonlinear ITG simulations are also presented [Phys. Rev. Lett., in print]. Several fundamental features are discussed, including the role of zonal flows for turbulence saturation, the resulting flux-gradient relationship and the co-existence of ITG modes with trapped ion modes in the saturated state. Similar studies will be presented for the stellarator experiment NCSX at PPPL with the aim to comprehend the effects of quasi-axisymmetric geometry on the properties - both linear and nonlinear - of various microinstabilities.
Electromagnetic Gyrokinetic Simulations
Wan, W
2003-11-19
A new electromagnetic kinetic electron {delta} particle simulation model has been demonstrated to work well at large values of plasma {beta} times the ion-to-electron mass ratio. The simulation is three-dimensional using toroidal flux-tube geometry and includes electron-ion collisions. The model shows accurate shear Alfven wave damping and microtearing physics. Zonal flows with kinetic electrons are found to be turbulent with the spectrum peaking at zero and having a width in the frequency range of the driving turbulence. This is in contrast with adiabatic electron cases where the zonal flows are near stationary, even though the linear behavior of the zonal flow is not significantly affected by kinetic electrons. zonal fields are found to be very weak, consistent with theoretical predictions for {beta} below the kinetic ballooning limit. Detailed spectral analysis of the turbulence data is presented in the various limits.
Intercode comparison of gyrokinetic global electromagnetic modes
Görler, T. Tronko, N.; Hornsby, W. A.; Bottino, A.; Sonnendrücker, E.; Kleiber, R.; Norscini, C.; Grandgirard, V.; Jenko, F.
2016-07-15
Aiming to fill a corresponding lack of sophisticated test cases for global electromagnetic gyrokinetic codes, a new hierarchical benchmark is proposed. Starting from established test sets with adiabatic electrons, fully gyrokinetic electrons, and electrostatic fluctuations are taken into account before finally studying the global electromagnetic micro-instabilities. Results from up to five codes involving representatives from different numerical approaches as particle-in-cell methods, Eulerian and Semi-Lagrangian are shown. By means of spectrally resolved growth rates and frequencies and mode structure comparisons, agreement can be confirmed on ion-gyro-radius scales, thus providing confidence in the correct implementation of the underlying equations.
Neoclassical equilibrium in gyrokinetic simulations
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.
2009-06-15
This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.
Neoclassical equilibrium in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.
2009-06-01
This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.
Testing gyrokinetic simulations of electron turbulence
NASA Astrophysics Data System (ADS)
Holland, C.; DeBoo, J. C.; Rhodes, T. L.; Schmitz, L.; Hillesheim, J. C.; Wang, G.; White, A. E.; Austin, M. E.; Doyle, E. J.; Peebles, W. A.; Petty, C. C.; Zeng, L.; Candy, J.
2012-06-01
An extensive set of tests comparing gyrokinetic predictions of temperature-gradient driven electron turbulence to power balance transport analyses and fluctuation measurements are presented. These tests use data from an L-mode validation study on the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614) in which the local value of a/L_{T_e } =-(a/T_e )(dT_e /dr) is varied by modulated electron cyclotron heating; the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) is used to make the gyrokinetic predictions. Using a variety of novel measures, both local and global nonlinear simulations are shown to predict key characteristics of the electron energy flux Qe and long-wavelength (low-k) Te fluctuations, but systematically underpredict (by roughly a factor of two) the ion energy flux Qi. A new synthetic diagnostic for comparison to intermediate wavelength Doppler backscattering measurements is presented, and used to compare simulation predictions against experiment. In contrast to the agreement observed in the low-k Te fluctuation comparisons, little agreement is found between the predicted and measured intermediate-k density fluctuation responses. The results presented in this paper significantly expand upon those previously reported in DeBoo et al (2010 Phys. Plasmas 17 056105), comparing transport and multiple turbulence predictions from numerically converged local and global simulations for all four experimental heating configurations (instead of only fluxes and low-k Te fluctuations for one condition) to measurements and power balance analyses.
Gyrokinetic particle simulation of beta-induced Alfven eigenmode
Zhang, H. S.; Lin, Z.; Holod, I.; Xiao, Y.; Wang, X.; Zhang, W. L.
2010-11-15
The beta-induced Alfven eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.
Dynamic procedure for filtered gyrokinetic simulations
Morel, P.; Banon Navarro, A.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2012-01-15
Large eddy simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the gene code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved direct numerical simulations. Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in ion temperature gradient driven turbulence. Moreover, the degree of anisotropy of the problem, which can vary with parameters, can be adapted dynamically by the method that shows gyrokinetic large eddy simulation to be a serious candidate to reduce numerical cost of gyrokinetic solvers.
Gyrokinetic simulation of microturbulence in EAST tokamak
NASA Astrophysics Data System (ADS)
Xiao, Yong; Zhang, Taige; Zhao, Chen
2014-10-01
A complete understanding of anomalous transport is critical for designing future magnetic fusion reactors. It is generally accepted that the micro-scale turbulence leads to anomalous transport. For low beta toroidal plasmas, the electrostatic modes may dominate and ion temperature gradient (ITG) mode and trapped electron mode (TEM) are two very important candidates accounting for ion and electron turbulent transport respectively. Recently the massively parallel gyrokinetic simulation has emerged as a major tool to investigate the nonlinear physics of the turbulent transport. The newly-developed capabilities enable the gyrokinetic code GTC to simulate the turbulent transport for real tokamak plasma shape and profiles. These capabilities include a new gyrokinetic Poisson solver and zonal flow solver suitable for general plasma shape and profiles, improvements on the conventional four-point gyroaverage and newly-developed nonuniform initial marker loading. The GTC code is now able to import experimental plasma profiles and equilibrium magnetic field that come from the EFIT or TRANSP equilibrium reconstruction. Linear and nonlinear gyrokinetic simulations are carried out with the new capabilities in GTC for the electron coherent mode (ECM) recently observed in the EAST tokamak (EAST shot # 38300). We found that in the pedestal region with strong electron temperature gradient, the unstable waves propagate in the electron diamagnetic direction, showing a trapped electron mode (TEM) feature. It is also found in the collisionless limit, the linear mode frequency is higher than that from the experiment.
NASA Astrophysics Data System (ADS)
Parker, Scott
2012-10-01
Global electromagnetic gyrokinetic simulations show the existence of near threshold conditions, for both a high-n Kinetic Ballooning Mode (KBM) and an intermediate-n kinetic version of Peeling-Ballooning Mode (PBM). The KBM and the PBM have been used to constrain the EPED model [1]. Global gyrokinetic simulations show that the H-mode pedestal, just prior to the onset of the Edge Localized Mode (ELM), is very near the KBM threshold. Two DIII-D experimental discharges are studied, one reporting KBM features in fluctuation measurements [2]. Simulations find that in addition to the high-n KBM, an intermediate-n electromagnetic mode is unstable. This kinetic version of the PBM has phase velocity in the electron diamagnetic direction, but otherwise has features similar to the MHD PBM. When the magnetic shear is reduced in a narrow region near the steep pressure gradient, the intermediate-n ``kinetic PBM'' is stabilized, while the high-n KBM becomes the most unstable mode. Global simulation results of the KBM compare favorably with flux tube simulations. The KBM transitions to an unstable electrostatic ion mode as the plasma beta is reduced. The intermediate-n ``kinetic peeling ballooning mode'' is sensitive to the q-profile and only seen in global electromagnetic simulations. Collisions increase the KBM critical beta and growth rate. These results indicate that an improved pedestal model should include, in detail, any corrections to the bootstrap current, and any other equilibrium effects that might reduce the local magnetic shear. It is known that the bootstrap current may flatten the q-profile in the steep gradient region [3]. Simulations are carried out using the global electromagnetic GEM code, including kinetic electrons, electron-ion collisions and the effects of realistic magnetic geometry. In addition to global linear analysis, nonlinear simulations will be reported showing that, while the equilibrium radial electric field has a weak effect on the linear growth
Gyrokinetic simulations of turbulent transport: size scaling and chaotic behaviour
NASA Astrophysics Data System (ADS)
Villard, L.; Bottino, A.; Brunner, S.; Casati, A.; Chowdhury, J.; Dannert, T.; Ganesh, R.; Garbet, X.; Görler, T.; Grandgirard, V.; Hatzky, R.; Idomura, Y.; Jenko, F.; Jolliet, S.; Khosh Aghdam, S.; Lapillonne, X.; Latu, G.; McMillan, B. F.; Merz, F.; Sarazin, Y.; Tran, T. M.; Vernay, T.
2010-12-01
Important steps towards the understanding of turbulent transport have been made with the development of the gyrokinetic framework for describing turbulence and with the emergence of numerical codes able to solve the set of gyrokinetic equations. This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. Solving 5D gyrokinetic equations for each species requires state-of-the-art high performance computing techniques involving massively parallel computers and parallel scalable algorithms. The various numerical schemes that have been explored until now, Lagrangian, Eulerian and semi-Lagrangian, each have their advantages and drawbacks. A past controversy regarding the finite size effect (finite ρ*) in ITG turbulence has now been resolved. It has triggered an intensive benchmarking effort and careful examination of the convergence properties of the different numerical approaches. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the ρ* → 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary: inconsistent approximations that are sometimes used can lead to important discrepancies. Turbulent processes are characterized by a chaotic behaviour, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation. Further developments concerning non-adiabatic electron dynamics around mode-rational surfaces and electromagnetic effects are discussed.
Benchmarking finite- β ITG gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Nevins, W. M.; Dimits, A. M.; Candy, J.; Holland, C.; Howard, N.
2016-10-01
We report the results of an electromagnetic gyrokinetic-simulation benchmarking study based on a well-diagnosed ion-temperature-gradient (ITG)-turbulence dominated experimental plasma. We compare the 4x3 matrix of transport/transfer quantities for each plasma species; namely the (a) particle flux, Γa, (b) momentum flux, Πa, (c) energy flux, Qa, and (d) anomalous heat exchange, Sa, with each transport coefficient broken down into: (1) electrostatic (δφ) (2) transverse electromagnetic (δA∥) , and (3) compressional electromagnetic, (δB∥) contributions. We compare realization-independent quantities (correlation functions, spectral densities, etc.), which characterize the fluctuating fields from various gyrokinetic simulation codes. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and by GA under Contract DE-FG03-95ER54309. This work was supported by the U.S. DOE, Office of Science, Fusion Energy Sciences.
Cummings, Julian C.
2013-05-15
This project was a collaboration between researchers at the California Institute of Technology and the University of California, Irvine to investigate the utility of a global field-aligned mesh and gyrokinetic field solver for simulations of the tokamak plasma edge region. Mesh generation software from UC Irvine was tested with specific tokamak edge magnetic geometry scenarios and the quality of the meshes and the solutions to the gyrokinetic Poisson equation were evaluated.
Continuum Edge Gyrokinetic Theory and Simulations
Xu, X Q; Xiong, Z; Dorr, M R; Hittinger, J A; Bodi, K; Candy, J; Cohen, B I; Cohen, R H; Colella, P; Kerbel, G D; Krasheninnikov, S; Nevins, W M; Qin, H; Rognlien, T D; Snyder, P B; Umansky, M V
2007-01-09
The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential, and mirror ratio; and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the banana regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL. (5) Our 5D gyrokinetic formulation yields a set of nonlinear electrostatic gyrokinetic equations that are for both neoclassical and turbulence simulations.
Comparisons of Kinetic Electron Models in Gyrokinetic Particle Simulations
NASA Astrophysics Data System (ADS)
Wang, W. X.; Lin, Z.; Lewandowski, J. L. V.; Lee, W. W.
2001-10-01
Comparisons of the hybrid [1] and split-weight [2,3] schemes for the electron dynamics in gyrokinetic particle simulations has been carried out. The emphasis here is to understand the regions of validity for these schemes as well as their numerical properties with regard to noise, time step and accuracy. The numerical issues for the implementation of these schemes in our 3D global gyrokinetic particle code (GTC) in general geometry [4] will also be discussed. Work supported by US DoE. [1] Z. Lin and L. Chen, Phys. Plasmas <8>, 1447 (2001). [2] I. Manuilskiy and W. W. Lee, Phys. Plasmas <7>, 1381 (2000). [3] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm and Z. Lin, Phys. Plasmas (to appear). [4] Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang and R. White, Science <281>, 1835 (1998).
Gyrokinetic Simulation of TAE in Fusion plasmas
NASA Astrophysics Data System (ADS)
Wang, Zhixuan
Linear gyrokinetic simulation of fusion plasmas finds a radial localization of the toroidal Alfvén eigenmodes (TAE) due to the non-perturbative energetic particles (EP) contribution. The EP-driven TAE has a radial mode width much smaller than that predicted by the magnetohydrodynamic (MHD) theory. The TAE radial position stays around the strongest EP pressure gradients when the EP profile evolves. The non-perturbative EP contribution is also the main cause for the breaking of the radial symmetry of the ballooning mode structure and for the dependence of the TAE frequency on the toroidal mode number. These phenomena are beyond the picture of the conventional MHD theory. Linear gyrokinetic simulation of the electron cyclotron heating (ECH) experiments on DIII-D successfully recover the TAE and RSAE. The EP profile, rather than the electron temperature, is found to be the key factor determining whether TAE or RSAE is the dominant mode in the system in our simulation. Investigation on the nonlinear gyrokinetic simulation model reveals a missing nonlinear term which has important contributions to the zonal magnetic fields. A new fluid-electron hybrid model is proposed to keep this nonlinear term in the lowest order fluid part. Nonlinear simulation of TAE using DIII-D parameters confirms the importance of this new term for the zonal magnetic fields. It is also found that zonal structures dominated by zonal electric fields are forced driven at about twice the linear growth rate of TAE in the linear phase. The zonal flows then limit the nonlinear saturation level by tearing the eigenmode structures apart. In the nonlinear phase of the simulation, the major frequency in the system chirps down by about 30% and stays there.
NASA Astrophysics Data System (ADS)
Bass, E. M.; Waltz, R. E.
2013-01-01
The unstable spectrum of Alfvén eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfvén eigenmode (RSAE) at toroidal mode number n =3 is mapped. The RSAE second harmonic and an unstable beta-induced Alfvén eigenmode (BAE) are simultaneously tracked alongside the primary RSAE. An observed twist in the eigenmode pattern, caused mostly by shear in the driving EP profile, is shown through artificially varying the E ×B rotational velocity shear to depend generally on shear in the local wave phase velocity. Coupling to the BAE and to the toroidal Alfvén eigenmode limit the RSAE frequency sweeps at the lower and upper end, respectively. While the present fully gyrokinetic model (including thermal ions and electrons) constitutes the best treatment of compressibility physics available, the BAE frequency is overpredicted by about 20% against experiment here and is found to be sensitive to energetic beam ion pressure. The RSAE frequency is more accurately matched except when it is limited by the BAE. Simulations suggest that the experiment is very close to marginal AE stability at points of RSAE-BAE coupling. A recipe for comparing the radial profile of quasilinear transport flux from local modes to that from global modes paves the way for the development of a stiff (critical gradient) local AE transport model based on local mode stability thresholds.
Gyrokinetic turbulence simulations at high plasma beta
Pueschel, M. J.; Kammerer, M.; Jenko, F.
2008-10-15
Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for {beta} values up to and beyond the kinetic ballooning threshold. The {beta} scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of {beta} values just below the respective ideal limit. The magnetic transport scales like {beta}{sup 2} and is well described by a Rechester-Rosenbluth-type ansatz.
Gyrokinetic simulations of ion and impurity transport
Estrada-Mila, C.; Candy, J.; Waltz, R.E.
2005-02-01
A systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas 4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple D-v (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 50-50 deuterium-tritium plasma, where a symmetry breaking is observed indicating the potential for fuel separation in a burning plasma. Quasilinear theory together with linear simulations shows that the symmetry breaking which enhances the tritium confinement arises largely from finite-Larmor-radius effects. To justify the numerical methods used in the paper, a variety of linear benchmarks and nonlinear grid refinement studies are detailed.
Gyrokinetic simulations of ion and impurity transport
NASA Astrophysics Data System (ADS)
Estrada-Mila, C.; Candy, J.; Waltz, R. E.
2005-02-01
A systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas 4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple D-v (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 50-50 deuterium-tritium plasma, where a symmetry breaking is observed indicating the potential for fuel separation in a burning plasma. Quasilinear theory together with linear simulations shows that the symmetry breaking which enhances the tritium confinement arises largely from finite-Larmor-radius effects. To justify the numerical methods used in the paper, a variety of linear benchmarks and nonlinear grid refinement studies are detailed.
Gyrokinetic simulation of internal kink modes
Naitou, Hiroshi; Tsuda, Kenji; Lee, W.W.; Sydora, R.D.
1995-05-01
Internal disruption in a tokamak has been simulated using a three-dimensional magneto-inductive gyrokinetic particle code. The code operates in both the standard gyrokinetic mode (total-f code) and the fully nonlinear characteristic mode ({delta}f code). The latter, a recent addition, is a quiet low noise algorithm. The computational model represents a straight tokamak with periodic boundary conditions in the toroidal direction. The plasma is initially uniformly distributed in a square cross section with perfectly conducting walls. The linear mode structure of an unstable m = 1 (poloidal) and n = 1 (toroidal) kinetic internal kink mode is clearly observed, especially in the {delta}f code. The width of the current layer around the x-point, where magnetic reconnection occurs, is found to be close to the collisionless electron skin depth. This is consistent with the theory in which electron inertia has a dominant role. The nonlinear behavior of the mode is found to be quite similar for both codes. Full reconnection in the Alfven time scale is observed along with the electrostatic potential structures created during the full reconnection phase. The E x B drift due to this electrostatic potential dominates the nonlinear phase of the development after the full reconnection.
Predictive Gyrokinetic Transport Simulations and Application of Synthetic Diagnostics
NASA Astrophysics Data System (ADS)
Candy, J.
2009-11-01
In this work we make use of the gyrokinetic transport solver TGYRO [1] to predict kinetic plasma profiles consistent with energy and particle fluxes in the DIII-D tokamak. TGYRO uses direct nonlinear and neoclassical fluxes calculated by the GYRO and NEO codes, respectively, to solve for global, self-consistent temperature and density profiles via Newton iteration. Previous work has shown that gyrokinetic simulation results for DIII-D discharge 128913 match experimental data rather well in the plasma core, but with a discrepancy in both fluxes and fluctuation levels emerging closer to the edge (r/a > 0.8). The present work will expand on previous results by generating model predictions across the entire plasma core, rather than at isolated test radii. We show that TGYRO predicts temperature and density profiles in good agreement with experimental observations which simultaneously yield near-exact (to within experimental uncertainties) agreement with power balance calculations of the particle and energy fluxes for r/a <=0.8. Moreover, we use recently developed synthetic diagnostic algorithms [2] to show that TGYRO also predicts density and electron temperature fluctuation levels in close agreement with experimental measurements across the simulated plasma volume. 8pt [1] J. Candy, C. Holland, R.E. Waltz, M.R. Fahey, and E. Belli, ``Tokamak profile prediction using direct gyrokinetic and neoclassical simulation," Phys. Plasmas 16, 060704 (2009). [2] C. Holland, A.E. White, G.R. McKee, M.W. Shafer, J. Candy, R.E. Waltz, L. Schmitz, and G.R. Tynan, ``Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence," Phys. Plasmas 16, 052301 (2009).
Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas
NASA Astrophysics Data System (ADS)
Jenko, F.; Dorland, W.
2001-12-01
One of the central physics issues currently targeted by nonlinear gyrokinetic simulations is the role of finite-β effects. The latter change the MHD equilibrium, introduce new dynamical space and time scales, alter and enlarge the zoo of electrostatic microinstabilities and saturation mechanisms, and lead to turbulent transport along fluctuating magnetic field lines. It is shown that the electromagnetic effects on primarily electrostatic microinstabilities are generally weakly or moderately stabilizing. However, the saturation of these modes and hence the determination of the transport level in the quasi-stationary turbulent state can be dominated by nonlinear electromagnetic effects and yield surprising results. Despite this, the induced transport is generally electrostatic in nature well below the ideal ballooning limit.
Gyrokinetic simulations of the tearing instability
Numata, Ryusuke; Dorland, William; Howes, Gregory G.; Loureiro, Nuno F.; Tatsuno, Tomoya
2011-11-15
Linear gyrokinetic simulations covering the collisional-collisionless transitional regime of the tearing instability are performed. It is shown that the growth rate scaling with collisionality agrees well with that predicted by a two-fluid theory for a low plasma beta case in which ion kinetic dynamics are negligible. Electron wave-particle interactions (Landau damping), finite Larmor radius, and other kinetic effects invalidate the fluid theory in the collisionless regime, in which a general non-polytropic equation of state for pressure (temperature) perturbations should be considered. We also vary the ratio of the background ion to electron temperatures and show that the scalings expected from existing calculations can be recovered, but only in the limit of very low beta.
Gyrokinetic particle simulation of beta-induced Alfvén eigenmode
NASA Astrophysics Data System (ADS)
Zhang, H. S.; Lin, Z.; Holod, I.; Wang, X.; Xiao, Y.; Zhang, W. L.
2010-11-01
The beta-induced Alfvén eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.
Gyrokinetic simulations of microturbulence in DIII-D tokamak pedestal
NASA Astrophysics Data System (ADS)
Holod, Ihor; Fulton, Daniel; Taimourzadeh, Sam; Lin, Zhihong; Nazikian, Raffi; Spong, Donald
2015-11-01
The characteristics of H-mode pedestal are generally believed to be constrained by current-driven peeling-ballooning modes and pressure-driven instabilities, such as kinetic ballooning mode (KBM). In this work we use global gyrokinetic code (GTC) to identify and study the edge pressure-driven instabilities in the H-mode pedestal using realistic geometry and plasma profiles of DIII-D shot 131997. In our simulations we observe the KBM mode marginally dominant in the steep gradient region (ψN = 0 . 98), in the range of kθ ~ 1 cm-1 which corresponds to the most unstable mode number in the nonlinearly saturated state. For shorter wavelengths the trapped electron mode becomes dominant since its linear growth rate increases with the mode number, while the KBM gets saturated. In the pedestal top region (ψN = 0 . 95) the ITG dominates. Resonant magnetic perturbations (RMP) are widely applied for ELM mitigation. During RMP suppression, the increase of edge turbulence is often observed. To understand this phenomena we use gyrokinetic simulations to address the direct effect of magnetic perturbations on the microturbulence. Simulations with 3D equilibrium reconstructed by VMEC code have been compared with toroidally averaged equilibrium, using identical pressure profiles. Work supported by DOE grant DE-SC0010416 and by General Atomics subcontract.
Gyrokinetic simulations of particle transport in pellet fuelled JET discharges
NASA Astrophysics Data System (ADS)
Tegnered, D.; Oberparleiter, M.; Nordman, H.; Strand, P.; Garzotti, L.; Lupelli, I.; Roach, C. M.; Romanelli, M.; Valovič, M.; Contributors, JET
2017-10-01
Pellet injection is a likely fuelling method of reactor grade plasmas. When the pellet ablates, it will transiently perturb the density and temperature profiles of the plasma. This will in turn change dimensionless parameters such as a/{L}n,a/{L}T and plasma β. The microstability properties of the plasma then changes which influences the transport of heat and particles. In this paper, gyrokinetic simulations of a JET L-mode pellet fuelled discharge are performed. The ion temperature gradient/trapped electron mode turbulence is compared at the time point when the effect from the pellet is the most pronounced with a hollow density profile and when the profiles have relaxed again. Linear and nonlinear simulations are performed using the gyrokinetic code GENE including electromagnetic effects and collisions in a realistic geometry in local mode. Furthermore, global nonlinear simulations are performed in order to assess any nonlocal effects. It is found that the positive density gradient has a stabilizing effect that is partly counteracted by the increased temperature gradient in the this region. The effective diffusion coefficients are reduced in the positive density region region compared to the intra pellet time point. No major effect on the turbulent transport due to nonlocal effects are observed.
Gyrokinetic particle simulation of neoclassical transport
Lin, Z.; Tang, W.M.; Lee, W.W.
1995-08-01
A time varying weighting ({delta}{ital f} ) scheme for gyrokinetic particle simulation is applied to a steady-state, multispecies simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated that like-particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion--electron plasma. An important physics feature of the present scheme is the introduction of toroidal flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient-driven electron particle flux and the bootstrap current while reducing temperature gradient-driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examined by taking into account finite banana width effects. In general, in the present work a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes is demonstrated. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Gyrokinetic Simulation of Residual Stress from Diamagnetic Velocity Shears
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
2010-11-01
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the parallel velocity (and parallel velocity itself) vanishes. Previously [1] we demonstrated with gyrokinetic (GYRO) simulations that TAM pinching from the diamagnetic level shear in the ExB velocity could provide the residual stress needed for spontaneous toroidal rotation. Here we show that the shear in the diamagnetic velocities themselves provide comparable residual stress (and level of stabilization). The sign of the residual stress, quantified by the ratio of TAM flow to ion power flow (M/P), depends on the signs of the various velocity shears as well as ion (ITG) versus electron (TEM) mode directed turbulence. The residual stress from these temperature and density gradient diamagnetic velocity shears is demonstrated in global gyrokinetic simulation of ``null'' rotation DIIID discharges by matching M/P profiles within experimental error. 8pt [1] R.E. Waltz, G.M. Staebler, J. Candy, and F.L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009).
NASA Astrophysics Data System (ADS)
Dominski, J.; McMillan, B. F.; Brunner, S.; Merlo, G.; Tran, T.-M.; Villard, L.
2017-02-01
The influence of the fine layers of the non-adiabatic passing electron response on electrostatic turbulent transport, previously studied systematically in flux tube geometry [Dominski et al., Phys. Plasmas 22, 062303 (2015)], is pursued in global geometry in conditions relevant for the TCV tokamak with a deuterium plasma (mi/me = 3672). The spectral organization of the passing electron turbulent flux and its dependence on the radial profile of the safety factor are revealed. A radially dependent toroidal spectral analysis of the turbulent fluxes led to the key result that the particle and heat diffusivities of passing-electrons are proportional to the local density of low-order mode rational surfaces. To permit this study of the short radial scales associated with the passing electron dynamics, a new field solver valid at an arbitrary wavelength is implemented in ORB5, for the gyrokinetic quasi-neutrality equation. A benchmark is conducted against the global version of the gyrokinetic code GENE, showing very good agreement.
Gyrokinetic particle simulation of a field reversed configuration
Fulton, D. P. Lau, C. K.; Holod, I.; Lin, Z.; Dettrick, S.
2016-01-15
Gyrokinetic particle simulation of the field-reversed configuration (FRC) has been developed using the gyrokinetic toroidal code (GTC). The magnetohydrodynamic equilibrium is mapped from cylindrical coordinates to Boozer coordinates for the FRC core and scrape-off layer (SOL), respectively. A field-aligned mesh is constructed for solving self-consistent electric fields using a semi-spectral solver in a partial torus FRC geometry. This new simulation capability has been successfully verified and driftwave instability in the FRC has been studied using the gyrokinetic simulation for the first time. Initial GTC simulations find that in the FRC core, the ion-scale driftwave is stabilized by the large ion gyroradius. In the SOL, the driftwave is unstable on both ion and electron scales.
Propagation of global shear Alfven waves in gyrokinetic tokamak plasmas
NASA Astrophysics Data System (ADS)
Nishimura, Y.; Lin, Z.; Holod, I.; Chen, L.; Decyk, V.; Klasky, S.; Ma, K.; Adams, M.; Ethier, S.; Hahm, T.; Lee, W.; Lewandowski, J.; Rewoldt, G.; Wang, W.
2006-04-01
Employing the electromagnetic gyrokinetic simulation models, Alfven wave dynamics in global tokamak geometry is studied. Based on a small parameter expansion by the square-root of the electron-ion mass ratio, the fluid-kinetic hybrid electron model solves the adiabatic response in the lowest order and solves the kinetic response in the higher orders. We verify the propagation of shear Alfven waves in the absence of drives or damping mechanisms by perturbing the magnetic field lines at t=0 in a global eigenmode structure. The Alfven wave experiences continuum damping. In the presence of energetic particles, excitations of toroidal Alfven eigenmode (TAE) is expected within the frequency gap. With the ηi gradient drive, at a critical β value, the kinetic ballooning mode (KBM) is excited below the ideal MHD limit. W.W.Lee et al., Phys. Plasmas 8, 4435 (2001). Z.Lin and L.Chen, Phys. Plasmas 8, 1447 (2001). J.A.Tataronis and W. Grossman, Z. Phys. 14, 203 (1973). C.Z.Cheng, L.Chen, and M.S.Chance, Ann.Phys. 161, 21 (1984). C.Z.Cheng, Nucl. Fusion 22, 773 (1982).
Ion transport barriers triggered by plasma polarization in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Strugarek, A.; Sarazin, Y.; Zarzoso, D.; Abiteboul, J.; Brun, A. S.; Cartier-Michaud, T.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, Ph; Grandgirard, V.; Latu, G.; Passeron, C.; Thomine, O.
2013-07-01
The creation of ion transport barriers by externally induced sheared E × B flows is investigated with the global, full-f and flux-driven gyrokinetic code GYSELA. A gyrokinetic source of vorticity is designed and proves to be efficient in polarizing the plasma. Induced sheared electric fields develop in the turbulent core and are accompanied by the creation of a transport barrier. The barrier and the sheared flow relax quasi-periodically because of zonal flow activity and a destabilizing temperature anisotropy induced by the vorticity source. A new cyclic mechanism leading to the relaxation of transport barriers in tokamaks is discovered.
Gyrokinetic theory and simulation of turbulent energy exchange
Waltz, R. E.; Staebler, G. M.
2008-01-15
A previous gyrokinetic theory of turbulent heating [F. L. Hinton and R. E. Waltz, Phys. Plasma 13, 102301 (2006)] is simplified and extended to show that the local radial average of terms in the gyrokinetic turbulent heating (which survive in the drift kinetic limit) are actually closer to a turbulent energy exchange between electrons and ions. The integrated flow for the local exchange is simulated with the GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] delta-f gyrokinetic code and found to be small in a well studied DIII-D [M. A. Mahdavi and J. L. Luxon, ''DIII-D Tokamak Special Issue'' Fusion Sci. Technol. 48, 2 (2005)] L-mode discharge.
Gyrokinetic Simulations of Microinstabilities in Stellarator Geometry
J.L.V. Lewandowski
2003-08-29
A computational study of microinstabilities in general geometry is presented. The ion gyrokinetic is solved as an initial value problem. The advantage of this approach is the accurate treatment of some important kinetic effects. The magnetohydrodynamic equilibrium is obtained from a three-dimensional local equilibrium model. The use of a local magnetohydrodynamic equilibrium model allows for a computationally-efficient systematic study of the impact of the magnetic structure on microinstabilities.
ADVANCES IN COMPREHENSIVE GYROKINETIC SIMULATIONS OF TRANSPORT IN TOKAMAKS
WALTZ RE; CANDY J; HINTON FL; ESTRADA-MILA C; KINSEY JE
2004-10-01
A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite {beta}, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}{sub *}) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or a globally with physical profile variation. Rohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, plasma pinches and impurity flow, and simulations at fixed flow rather than fixed gradient are illustrated and discussed.
John A. Krommes
2007-10-09
The present state of the theory of fluctuations in gyrokinetic GK plasmas and especially its application to sampling noise in GK particle-in-cell PIC simulations is reviewed. Topics addressed include the Δf method, the fluctuation-dissipation theorem for both classical and GK many-body plasmas, the Klimontovich formalism, sampling noise in PIC simulations, statistical closure for partial differential equations, the theoretical foundations of spectral balance in the presence of arbitrary noise sources, and the derivation of Kadomtsev-type equations from the general formalism.
ADVANCES IN COMPREHENSIVE GYROKINETIC SIMULATIONS OF TRANSPORT IN TOKAMAKS
WALTZ,R.E; CANDY,J; HINTON,F.L; ESTRADA-MILA,C; KINSEY,J.E
2004-10-01
A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite {beta}, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}{sub *}) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or globally with physical profile variation. Bohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, are illustrated.
Full f gyrokinetic method for particle simulation of tokamak transport
Heikkinen, J.A. Janhunen, S.J.; Kiviniemi, T.P.; Ogando, F.
2008-05-10
A gyrokinetic particle-in-cell approach with direct implicit construction of the coefficient matrix of the Poisson equation from ion polarization and electron parallel nonlinearity is described and applied in global electrostatic toroidal plasma transport simulations. The method is applicable for calculation of the evolution of particle distribution function f including as special cases strong plasma pressure profile evolution by transport and formation of neoclassical flows. This is made feasible by full f formulation and by recording the charge density changes due to the ion polarization drift and electron acceleration along the local magnetic field while particles are advanced. The code has been validated against the linear predictions of the unstable ion temperature gradient mode growth rates and frequencies. Convergence and saturation in both turbulent and neoclassical limit of the ion heat conductivity is obtained with numerical noise well suppressed by a sufficiently large number of simulation particles. A first global full f validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. At high Mach number (M{sub p}{approx}1) of the poloidal flow, the radial electric field is significantly enhanced over the standard neoclassical prediction. The neoclassical radial electric field together with the related GAM oscillations is found to regulate the turbulent heat and particle diffusion levels particularly strongly in a large aspect ratio tokamak at low plasma current.
McClenaghan, J.; Lin, Z.; Holod, I.; Deng, W.; Wang, Z.
2014-12-15
The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynamic eigenvalue code. Gyrokinetic simulations of the kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface.
Gyrokinetic simulation of driftwave instability in field-reversed configuration
Fulton, D. P.; Lau, C. K.; Holod, I.; Lin, Z.; Schmitz, L.; Tajima, T.; Binderbauer, M. W.
2016-05-15
Following the recent remarkable progress in magnetohydrodynamic (MHD) stability control in the C-2U advanced beam driven field-reversed configuration (FRC), turbulent transport has become one of the foremost obstacles on the path towards an FRC-based fusion reactor. Significant effort has been made to expand kinetic simulation capabilities in FRC magnetic geometry. The recently upgraded Gyrokinetic Toroidal Code (GTC) now accommodates realistic magnetic geometry from the C-2U experiment at Tri Alpha Energy, Inc. and is optimized to efficiently handle the FRC's magnetic field line orientation. Initial electrostatic GTC simulations find that ion-scale instabilities are linearly stable in the FRC core for realistic pressure gradient drives. Estimated instability thresholds from linear GTC simulations are qualitatively consistent with critical gradients determined from experimental Doppler backscattering fluctuation data, which also find ion scale modes to be depressed in the FRC core. Beyond GTC, A New Code (ANC) has been developed to accurately resolve the magnetic field separatrix and address the interaction between the core and scrape-off layer regions, which ultimately determines global plasma confinement in the FRC. The current status of ANC and future development targets are discussed.
On the influence of initial state on gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.; Angelino, P.
2008-04-01
The influence of the initial state on the turbulence and transport is addressed in collisionless, global, and full-f gyrokinetic simulations solving both the equilibrium and the fluctuations. For two strongly differing initial states, it is found that the steady turbulent regime exhibits nearly identical statistical properties. This result is in marked contrast with the claim of different final states. In fact, a long transient with very different properties finally evolves towards the same turbulent regime for long simulation times. When the initial state is a local Maxwellian, i.e., constant on flux surfaces, a large-scale sheared electric potential develops on short time scales to compensate for the vertical curvature and grad-B drifts. We predict analytically (i) the temporal dynamics at short times of this electric potential, (ii) its poloidal structure, and (iii) its saturation time. All agree well with numerical simulations using the GYSELA code. The impact on the transport is twofold, as compared to the canonical initial state, where f only depends on the motion invariants: (i) the turbulence is delayed due to a weaker effective growth rate, (ii) the same transport level is obtained at long times and the turbulence exhibits nearly identical statistical characteristics. In agreement, the electric potential of these two cases has the same magnitude despite very different transients.
Gyrokinetic Simulation of Low-n Tearing Modes
NASA Astrophysics Data System (ADS)
Chen, Yang
2015-11-01
Direct gyrokinetic simulation of the low-n tearing mode in a tokamak plasma has been a great computational challenge, for two reasons. First, low-n tearing modes, unlike the micro-tearing modes, have very small growth rates and very fine mode structure in the tearing layer, which requires a large number of radial grid cells and fine control of numerical dissipation. Second, kinetic electron effects are needed in the tearing layer. Here, we first present linear gyrokinetic simulation of the low-n tearing mode in cylindrical geometry. Ions are gyrokinetic and electrons are either drift kinetic or fluid. New field solvers have been developed in the gyrokinetic code GEM [Chen and Parker, J. Comput. Phys. 220, 839 (2007)] to simulate low-n modes. For the fluid electron model, an eigenmode analysis with finite Larmor radius effects has been developed to study the linear resistive tearing mode. Excellent agreement between eigenmode analysis and initial value gyrokinetic simulation is obtained. The mode growth rate is shown to scale with resistivity as η 1 / 3, the same as the semi-collisional regime in previous kinetic treatments. Simulation of the collisionless and semi-collisional tearing mode with drift kinetic electrons has been carried out with GEM's direct split-weight control-variate algorithm. It is found that a full torus simulation of the m=2, n=1 tearing mode in a present day large tokamak is still difficult with kinetic electrons, but a generalized matching technique can be used to ameliorate the problem. The radial dimension is divided into an external region and the tearing region, with the external region described by a reduced model that gives the boundary condition for the tearing region. The size of the tearing region is small compared with the minor radius, but not arbitrarily small as done in the standard asymptotic matching approach. Gyrokinetic simulation verifies the collisionless tearing mode growth rate with finite electron mass, the semi
Benchmarking gyrokinetic simulations in a toroidal flux-tube
NASA Astrophysics Data System (ADS)
Chen, Y.; Parker, S. E.; Wan, W.; Bravenec, R.
2013-09-01
A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementation shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v||-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.
Benchmarking gyrokinetic simulations in a toroidal flux-tube
Chen, Y.; Parker, S. E.; Wan, W.; Bravenec, R.
2013-09-15
A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementation shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v{sub ||}-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.
Gyrokinetic particle simulation of the beta-induced Alfven eigen mode
NASA Astrophysics Data System (ADS)
Zhang, Huasen; Lin, Zhihong; Holod, Ihor; Wang, Xin; Xiao, Yong; Zhang, Wenlu
2010-11-01
The beta-induced Alfven eigen mode (BAE) is studied using the global gyrokinetic particle code GTC. In our simulation, BAE is successfully excited by antenna and energetic particle density gradient. Through the antenna frequency scan, we can measure the BAE frequency and damping rate by numerical fitting the saturation amplitude. BAE excitation by energetic particles shows that the BAE propagates in the ion diamagnetic direction and the frequency has a little downshift, which is due to modification of the energetic particles. The frequency and growth rate in gyrokinetic simulation is a little different from drift kinetic simulation, which is expected due to the finite larmor radius effect. We also find that the BAE frequency is related to the wavelength and the plasma beta while the growth rate is sensitive to the energetic particle properties. Benchmarks between GTC and HMGC are also done through initial perturbation, antenna excitation and energetic particle excitation. The simulation results agree with each other very well.
Low dimensional gyrokinetic PIC simulation by δf method
NASA Astrophysics Data System (ADS)
Chen, C. M.; Nishimura, Yasutaro; Cheng, C. Z.
2015-11-01
A step by step development of our low dimensional gyrokinetic Particle-in-Cell (PIC) simulation is reported. One dimensional PIC simulation of Langmuir wave dynamics is benchmarked. We then take temporal plasma echo as a test problem to incorporate the δf method. Electrostatic driftwave simulation in one dimensional slab geometry is resumed in the presence of finite density gradients. By carefully diagnosing contour plots of the δf values in the phase space, we discuss the saturation mechanism of the driftwave instabilities. A v∥ formulation is employed in our new electromagnetic gyrokinetic method by solving Helmholtz equation for time derivative of the vector potential. Electron and ion momentum balance equations are employed in the time derivative of the Ampere's law. This work is supported by Ministry of Science and Technology of Taiwan, MOST 103-2112-M-006-007 and MOST 104-2112-M-006-019.
A fully nonlinear characteristic method for gyrokinetic simulation
Parker, S.E.; Lee, W.W.
1992-07-01
We present a new scheme which evolves the perturbed part of the distribution function along a set of characteristics that solves the fully nonlinear gyrokinetic equations. This nonlinear characteristic method for particle simulation is an extension of the partially linear weighting scheme, and may be considered an improvement of existing {delta} f methods. Some of the features of this new method are: the ability to keep all of the nonlinearities, particularly those associated with parallel acceleration; the loading of the physical equilibrium distribution function f{sub o} (e.g., a Maxwellian), with or without the multiple spatial scale approximation; the use of a single of trajectories for the particles; and also, the retention of the conservation properties of the original gyrokinetic system in the numerically converged limit. Therefore, one can take advantage of the low noise property of the weighting scheme together with the quiet start techniques to simulate weak instabilities, with a substantially reduced number of particles than required for a conventional simulation. The new method is used to study a one dimensional drift wave model which isolates the parallel velocity nonlinearity. A mode coupling calculation of the saturation mechanism is given, which is in good agreement with the simulation results and predicts a considerably lower saturation level then the estimate of Sagdeev and Galeev. Finally, we extend the nonlinear characteristic method to the electromagnetic gyrokinetic equations in general geometry.
Graphics Processing Unit Acceleration of Gyrokinetic Turbulence Simulations
NASA Astrophysics Data System (ADS)
Hause, Benjamin; Parker, Scott
2012-10-01
We find a substantial increase in on-node performance using Graphics Processing Unit (GPU) acceleration in gyrokinetic delta-f particle-in-cell simulation. Optimization is performed on a two-dimensional slab gyrokinetic particle simulation using the Portland Group Fortran compiler with the GPU accelerator compiler directives. We have implemented the GPU acceleration on a Core I7 gaming PC with a NVIDIA GTX 580 GPU. We find comparable, or better, acceleration relative to the NERSC DIRAC cluster with the NVIDIA Tesla C2050 computing processor. The Tesla C 2050 is about 2.6 times more expensive than the GTX 580 gaming GPU. Optimization strategies and comparisons between DIRAC and the gaming PC will be presented. We will also discuss progress on optimizing the comprehensive three dimensional general geometry GEM code.
Simulation of neoclassical transport with the continuum gyrokinetic code COGENT
Dorf, M. A.; Cohen, R. H.; Dorr, M.; Rognlien, T.; Hittinger, J.; Compton, J.; Colella, P.; Martin, D.; McCorquodale, P.
2013-01-25
The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.
Simulation of neoclassical transport with the continuum gyrokinetic code COGENT
Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...
2013-01-25
The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy.more » Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.« less
Split-Weight δ f Schemes for Gyrokinetic Particle Simulation
NASA Astrophysics Data System (ADS)
Lee, W. W.; Lewandowski, J. L. V.; Lin, Z.; Hahm, T. S.
2000-10-01
One of the most challenging problems in gyrokinetic particle simulation is the treatment of the electrons. A straightforward implementation of the electron dynamics has many pitfalls. The split weight scheme, (I. Manuilskiy and W. W. Lee, Phys. Plasmas 7), 1381 (2000) in which the perturbed distribution for the electrons, δ fe (≡ Fe - F_0e), is split into e (φ /T_e) F_0e and δ h_e, where Fe is the total distribution, F_0e is the equilibrium part, δ h is the non-adiabatic part, and φ is the electrostatic potential, can circumvent the parallel Courant condition of k_allel v_te Δ t < 1, and, thereby, increase the time steps. For finite-β plasmas, the schemes with φ replaced by ψ ≡ φ -(v_allel/c) A_allel or ψ ≡ φ -(ω/k_allel c) A_allel for the adiabatic response make it possible to produce shear-Alfven waves without the nonadiabatic response of the fast electrons. (W. W. Lee, J. L. V. Lewandowski and T. S. Hahm, in preparation.) The implementation the the schemes in the 3D global toroidal GTC code, (Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. White, Science), 281, 1835 (1998). and the associated numerical schemes for solving field equations involving time derivatives of the potentials and the use of the adiabatic field pusher to advance the electrons will be reported.
Gyrokinetic simulations predict anomalous poloidal rotation in tokamak plasmas
NASA Astrophysics Data System (ADS)
Dif-Pradalier, Guilhem; Grandgirard, Virginie; Sarazin, Yanick; Garbet, Xavier; Ghendrih, Phillippe; Angelino, Paolo
2008-11-01
First-principle based collisionless gyrokinetic theory consensually provides today's deepest insight on turbulence-related problems in plasma physics. Conversely, neoclassical theory describes the effects of binary Coulomb collisions in a toroidal and inhomogeneous magnetic geometry and its consequences on particle trapping. The interplay between turbulence and collisions is a subject of great current focus for first-principle modeling since recent evidences have started to emphasise its relevance for the onset and the control of enhanced confinement regimes in the next-generation devices like Iter. A finite differences Fokker-Planck ion-ion collision operator is implemented in the full-f and global GYSELA code and has been thoroughly benchmarked in neoclassical regimes. Two types of simulations are compared, either purely neoclassical or turbulent including neoclassical effects. In each case, three different values of collisionality in the banana regime are investigated. Preliminary results show an enhancement of about 30% of the poloidal rotation of the main ions (Z=1) in the turbulent regime as compared to its neoclassical value. In all cases the radial force balance equation is satisfied within a few percent. Most of this increase comes from the radial electric field.
Tokamak profile prediction using direct gyrokinetic and neoclassical simulation
Candy, J.; Waltz, R. E.; Belli, E.; Holland, C.; Fahey, M. R.
2009-06-15
Tokamak transport modeling scenarios, including ITER [ITER Physics Basis Editors, Nucl. Fusion 39, 2137 (1999)] performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes (local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles). Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] code, for turbulent transport, and the NEO[E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 (2008)] code, for kinetic neoclassical transport. Results for DIII-D L-mode discharge 128913 are given, with computational and experimental results consistent in the region 0{<=}r/a{<=}0.8.
Tokamak profile prediction using direct gyrokinetic and neoclassical simulation
Candy, Jeff; Holland, Chris; Waltz, R. E.; Fahey, Mark R; Belli, E
2009-01-01
okamak transport modeling scenarios, including ITER ITER Physics Basis Editors, Nucl. Fusion 39, 2137 1999 performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles . Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D J. L. Luxon, Nucl. Fusion 42, 614 2002 plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 2003 code, for turbulent transport, and the NEO E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 2008 code, for kinetic neoclassical transport. Results for DIII-D L-mode discharge 128913 are given, with computational and experimental results consistent in the region 0 <= r/a <= 0.8.
Gyrokinetic Particle Simulation of Microturbulence in Transport Time Scale
NASA Astrophysics Data System (ADS)
Lee, W. W.
2003-10-01
Recent investigations on Alfven waves in gyrokinetic plasmas and their relationship with those in the MHD theory have enabled us to extend the gyrokinetic particle simulation techniques into the kinetic-MHD regime when the finite-Larmor radius effects are important and the time step restrictions imposed by compressional Alfven waves are not desirable.[1,2] Some of the numerical schemes have already been devised based on their thermodynamic properties.[1,2] Here, we propose to use gyrokinetic particle simulation to study microturbulence in transport time scale. The procedures involve the use of finite-β microturbulence simulation as well as the use of transport coefficients in the steady state for predicting density,temperature and parallel current profile changes, along with the use of perpendicular current information for the establishment of equilibrium magnetic structure. Details will be given. [1] W. W. Lee and H. Qin, Phys. Plasmas, to appear (August 2003). [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Phys. Plasmas 8, 4435 (2001).
Multi-code benchmark of global gyrokinetic electromagnetic instabilities
NASA Astrophysics Data System (ADS)
Goerler, Tobias; Bottino, Alberto; Hornsby, William A.; Kleiber, Ralf; Tronko, Natalia; Grandgirard, Virginie; Norscini, Claudia; Sonnendruecker, Eric
2015-11-01
Considering the recent major extensions of global gyrokinetic codes towards a comprehensive and self-consistent treatment of electromagnetic (EM) effects, corresponding verification tests are obvious and necessary steps to be taken. While a number of (semi-)analytic test cases and benchmarks exist in the axisymmetric limit, microinstabilities and particularly EM turbulence are rarely addressed. In order to remedy this problem, a hierarchical linear gyrokinetic benchmark study is presented starting with electrostatic ion temperature gradient microinstabilities with adiabatic electron response and progressing finally to the characterization of fully EM instabilities as a function of β. The inter-code comparison involves contributions from Eulerian Vlasov, Lagrangian PIC, and Semi-Lagrange codes at least in one level of this verification exercise, thus confirming a high degree of reliability for the implementations that has rarely been achieved before in this context. Additionally, possible extensions of this benchmark into the physically more relevant nonlinear turbulence regime will be discussed, e.g., relaxation problems or gradient-driven setups. This work has been carried out within the framework of the EUROfusion Consortium.
Flux-driven gyrokinetic simulations of ion turbulent transport at low magnetic shear
NASA Astrophysics Data System (ADS)
Sarazin, Y.; Strugarek, A.; Dif-Pradalier, G.; Abiteboul, J.; Allfrey, S.; Garbet, X.; Ghendrih, Ph; Grandgirard, V.; Latu, G.
2010-11-01
Ion Temperature Gradient driven turbulence is investigated with the global full-f gyrokinetic code GYSELA for different magnetic equilibria. Reversed shear and monotonous q profile cases do not exhibit dramatic changes nor in the dynamics nor in the level of turbulence, leading to similar mean profiles. Especially, no transport barrier is observed in the vicinity of s = 0 in the general case, although the radial extent of the gap without resonant modes is larger than the typical turbulence correlation length. Conversely, a transport barrier is found to develop in the gap region if non resonant modes are artificially suppressed from the simulation. Such simulations tend to reconcile previously published contradictory results, while extending the analysis to more realistic flux-driven gyrokinetic regimes.
Global gyrokinetic models for energetic particle driven Alfvén instabilities in 3D equilibria
NASA Astrophysics Data System (ADS)
Spong, Don; Holod, Ihor
2015-11-01
The GTC global gyrokinetic PIC model has been adapted to 3D VMEC equilibria and provides a new method for the analysis of Alfvénic instabilities in stellarators, 3D tokamaks, and helical RFP states. The gyrokinetic orderings (k||/k⊥ << 1, ω/Ωci << 1, ρEP/L << 1) are applicable to a range of energetic particle driven instabilities that have been observed in 3D configurations. Applications of this model to stellarators have indicated that a variety of different Alfvén instabilities can be excited, depending on the toroidal mode number, fast ion average energy and fast ion density profile. Both an LHD discharge where bursting n = 1 Alfvén activity in the TAE gap was observed and a W7-X case have been examined. TAE,/EAE/GAE modes have been found in the simulations, depending on the mode family and fast ion profiles used. The dynamical evolution of the instabilities shows the field period coupling between n and n + Nfp expected for a stellarator. The development of gyrofluid reduced models that can capture relevant physics aspects of the gyrokinetic models will also be discussed. Research sponsored by the U.S. Department of Energy under Contract DE-AC05-00OR22725 with UT-Battelle, LLC and the GSEP SciDAC Center.
Plasma Simulation Using Gyrokinetic-Gyrofluid Hybrid Models
Scott Parker
2009-04-09
We are developing kinetic ion models for the simulation of extended MHD phenomena. The model they have developed uses full Lorentz force ions, and either drift-kinetic or gyro-kinetic electrons. Quasi-neutrality is assumed and the displacement current is neglected. They are also studying alpha particle driven Toroidal Alfven Eigenmodes (TAE) in the GEM gyrokinetic code [Chen 07]. The basic kinetic ion MHD model was recently reported in an invited talk given by Dan Barnes at the 2007 American Physical Society - Division of Plasma Physics (APS-DPP) and it has been published [Jones 04, Barnes 08]. The model uses an Ohm's law that includes the Hall term, pressure term and the electron inertia [Jones 04]. These results focused on the ion physics and assumed an isothermal electron closure. It is found in conventional gyrokinetic turbulence simulations that the timestep cannot be made much greater than the ion cyclotron period. However, the kinetic ion MHD model has the compressional mode, which further limits the timestep. They have developed an implicit scheme to avoid this timestep constraint. They have also added drift kinetic electrons. This model has been benchmarked linearly. Waves investigated where shear and compressional Alfven, whisterl, ion acoustic, and drift waves, including the kinetic damping rates. This work is ongoing and was first reported at the 2008 Sherwood Fusion Theory Conference [Chen 08] and they are working on a publication. They have also formulated an integrated gyrokinetic electron model, which is of interest for studying electron gradient instabilities and weak guide-field magnetic reconnection.
Phase space structures in gyrokinetic simulations of fusion plasma turbulence
NASA Astrophysics Data System (ADS)
Ghendrih, Philippe; Norscini, Claudia; Cartier-Michaud, Thomas; Dif-Pradalier, Guilhem; Abiteboul, Jérémie; Dong, Yue; Garbet, Xavier; Gürcan, Ozgür; Hennequin, Pascale; Grandgirard, Virginie; Latu, Guillaume; Morel, Pierre; Sarazin, Yanick; Storelli, Alexandre; Vermare, Laure
2014-10-01
Gyrokinetic simulations of fusion plasmas give extensive information in 5D on turbulence and transport. This paper highlights a few of these challenging physics in global, flux driven simulations using experimental inputs from Tore Supra shot TS45511. The electrostatic gyrokinetic code GYSELA is used for these simulations. The 3D structure of avalanches indicates that these structures propagate radially at localised toroidal angles and then expand along the field line at sound speed to form the filaments. Analysing the poloidal mode structure of the potential fluctuations (at a given toroidal location), one finds that the low modes m = 0 and m = 1 exhibit a global structure; the magnitude of the m = 0 mode is much larger than that of the m = 1 mode. The shear layers of the corrugation structures are thus found to be dominated by the m = 0 contribution, that are comparable to that of the zonal flows. This global mode seems to localise the m = 2 mode but has little effect on the localisation of the higher mode numbers. However when analysing the pulsation of the latter modes one finds that all modes exhibit a similar phase velocity, comparable to the local zonal flow velocity. The consequent dispersion like relation between the modes pulsation and the mode numbers provides a means to measure the zonal flow. Temperature fluctuations and the turbulent heat flux are localised between the corrugation structures. Temperature fluctuations are found to exhibit two scales, small fluctuations that are localised by the corrugation shear layers, and appear to bounce back and forth radially, and large fluctuations, also readily observed on the flux, which are associated to the disruption of the corrugations. The radial ballistic velocity of both avalanche events if of the order of 0.5ρ∗c0 where ρ∗ = ρ0/a, a being the tokamak minor radius and ρ0 being the characteristic Larmor radius, ρ0 = c0/Ω0. c0 is the reference ion thermal velocity and Ω0 = qiB0/mi the reference
Gyrokinetic Simulation of Energetic Particles Turbulence and Transport in Fusion Plasmas
NASA Astrophysics Data System (ADS)
Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Xiao, Yong; Bierwage, Andreas; Spong, Donald; Chu, Ming
2009-05-01
The confinement of the energetic particles (EP) is a critical issue in the International Thermonuclear Experimental Reactor (ITER), since that ignition relies on the self-heating by the fusion products. Shear Alfven wave excitations by EP in toroidal systems, for example Toroidal Alfven Eigenmode (TAE) and Energetic Particle Mode (EPM) have been investigated as primary candidate for fluctuation-induced transport of EP in fusion plasma. In this work, TAE excitations by energetic particles are investigated in large scale first-principle simulations of fusion plasmas using the global gyrokinetic toroidal code (GTC) [Lin, Science 1998]. Comprehensive linear benchmarking results are reported between GTC, GYRO, fluid code TAEFL, and Magnetohydrodynamic-gyrokinetic hybrid code HMGC.
Applications of large eddy simulation methods to gyrokinetic turbulence
Bañón Navarro, A. Happel, T.; Teaca, B. [Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB; Max-Planck für Sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau; Max-Planck Jenko, F. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching; Max-Planck Hammett, G. W. [Max-Planck Collaboration: ASDEX Upgrade Team
2014-03-15
The large eddy simulation (LES) approach—solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model—is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system.
Gyrokinetic simulation of isotope scaling in tokamak plasmas
Lee, W.W.; Santoro, R.A.
1995-07-01
A three-dimensional global gyrokinetic particle code in toroidal geometry has been used for investigating the transport properties of ion temperature gradient (ITG) drift instabilities in tokamak plasmas. Using the isotopes of hydrogen (H{sup +}), deuterium (D{sup +}) and tritium (T{sup +}), we have found that, under otherwise identical conditions, there exists a favorable isotope scaling for the ion thermal diffusivity, i.e., Xi decreases with mass. Such a scaling, which exists both at the saturation of the instability and also at the nonlinear steady state, can be understood from the resulting wavenumber and frequency spectra.
Optimized Loading for Particle-in-cell Gyrokinetic Simulations
J.L.V. Lewandowski
2004-05-13
The problem of particle loading in particle-in-cell gyrokinetic simulations is addressed using a quadratic optimization algorithm. Optimized loading in configuration space dramatically reduces the short wavelength modes in the electrostatic potential that are partly responsible for the non-conservation of total energy; further, the long wavelength modes are resolved with good accuracy. As a result, the conservation of energy for the optimized loading is much better that the conservation of energy for the random loading. The method is valid for any geometry and can be coupled to optimization algorithms in velocity space.
Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode
NASA Astrophysics Data System (ADS)
Cheng, Junyi; Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Li, Ding; Chen, Yang; Cao, Jintao
2016-05-01
The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.
Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode
Cheng, Junyi; Chen, Yang; Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Li, Ding; Cao, Jintao
2016-05-15
The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.
Effects of the magnetic equilibrium on gyrokinetic simulations of tokamak microinstabilities
Wan, Weigang; Chen, Yang; Parker, Scott E.; Groebner, Richard J.
2015-06-15
The general geometry of the experimental tokamak magnetic equilibrium is implemented in the global gyrokinetic simulation code GEM. Compared to the general geometry, the well used Miller parameterization of the magnetic equilibrium is a good approximation in the core region and up to the top of the pedestal. Linear simulations indicate that results with the two geometries agree for r/a ≤ 0.9. However, in the edge region, the instabilities are sensitive to the magnetic equilibrium in both the L-mode and the H-mode plasmas. A small variation of the plasma shaping parameters leads to large changes to the edge instability.
Direct identification of predator-prey dynamics in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Kobayashi, Sumire; Gürcan, Özgür D.; Diamond, Patrick H.
2015-09-01
The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.
Direct identification of predator-prey dynamics in gyrokinetic simulations
Kobayashi, Sumire Gürcan, Özgür D; Diamond, Patrick H.
2015-09-15
The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.
What happens to full-f gyrokinetic transport and turbulence in a toroidal wedge simulation?
Kim, Kyuho; Chang, C. S.; Seo, Janghoon; ...
2017-01-24
Here, in order to save the computing time or to fit the simulation size into a limited computing hardware in a gyrokinetic turbulence simulation of a tokamak plasma, a toroidal wedge simulation may be utilized in which only a partial toroidal section is modeled with a periodic boundary condition in the toroidal direction. The most severe restriction in the wedge simulation is expected to be in the longest wavelength turbulence, i.e., ion temperature gradient (ITG) driven turbulence. The global full-f gyrokinetic code XGC1 is used to compare the transport and turbulence properties from a toroidal wedge simulation against the fullmore » torus simulation in an ITG unstable plasma in a model toroidal geometry. It is found that (1) the convergence study in the wedge number needs to be conducted all the way down to the full torus in order to avoid a false convergence, (2) a reasonably accurate simulation can be performed if the correct wedge number N can be identified, (3) the validity of a wedge simulation may be checked by performing a wave-number spectral analysis of the turbulence amplitude |δΦ| and assuring that the variation of δΦ between the discrete kθ values is less than 25% compared to the peak |δΦ|, and (4) a frequency spectrum may not be used for the validity check of a wedge simulation.« less
What happens to full-f gyrokinetic transport and turbulence in a toroidal wedge simulation?
NASA Astrophysics Data System (ADS)
Kim, Kyuho; Chang, C. S.; Seo, Janghoon; Ku, S.; Choe, W.
2017-01-01
In order to save the computing time or to fit the simulation size into a limited computing hardware in a gyrokinetic turbulence simulation of a tokamak plasma, a toroidal wedge simulation may be utilized in which only a partial toroidal section is modeled with a periodic boundary condition in the toroidal direction. The most severe restriction in the wedge simulation is expected to be in the longest wavelength turbulence, i.e., ion temperature gradient (ITG) driven turbulence. The global full-f gyrokinetic code XGC1 is used to compare the transport and turbulence properties from a toroidal wedge simulation against the full torus simulation in an ITG unstable plasma in a model toroidal geometry. It is found that (1) the convergence study in the wedge number needs to be conducted all the way down to the full torus in order to avoid a false convergence, (2) a reasonably accurate simulation can be performed if the correct wedge number N can be identified, (3) the validity of a wedge simulation may be checked by performing a wave-number spectral analysis of the turbulence amplitude |δΦ| and assuring that the variation of δΦ between the discrete kθ values is less than 25% compared to the peak |δΦ| , and (4) a frequency spectrum may not be used for the validity check of a wedge simulation.
Graphics Processing Unit Acceleration of Gyrokinetic Turbulence Simulations
NASA Astrophysics Data System (ADS)
Hause, Benjamin; Parker, Scott; Chen, Yang
2013-10-01
We find a substantial increase in on-node performance using Graphics Processing Unit (GPU) acceleration in gyrokinetic delta-f particle-in-cell simulation. Optimization is performed on a two-dimensional slab gyrokinetic particle simulation using the Portland Group Fortran compiler with the OpenACC compiler directives and Fortran CUDA. Mixed implementation of both Open-ACC and CUDA is demonstrated. CUDA is required for optimizing the particle deposition algorithm. We have implemented the GPU acceleration on a third generation Core I7 gaming PC with two NVIDIA GTX 680 GPUs. We find comparable, or better, acceleration relative to the NERSC DIRAC cluster with the NVIDIA Tesla C2050 computing processor. The Tesla C 2050 is about 2.6 times more expensive than the GTX 580 gaming GPU. We also see enormous speedups (10 or more) on the Titan supercomputer at Oak Ridge with Kepler K20 GPUs. Results show speed-ups comparable or better than that of OpenMP models utilizing multiple cores. The use of hybrid OpenACC, CUDA Fortran, and MPI models across many nodes will also be discussed. Optimization strategies will be presented. We will discuss progress on optimizing the comprehensive three dimensional general geometry GEM code.
Gyrokinetic theory and simulation of angular momentum transport
Waltz, R. E.; Staebler, G. M.; Candy, J.; Hinton, F. L.
2007-12-15
A gyrokinetic theory of turbulent toroidal angular momentum transport as well as modifications to neoclassical poloidal rotation from turbulence is formulated starting from the fundamental six-dimensional kinetic equation. The gyro-Bohm scaled transport is evaluated from toroidal delta-f gyrokinetic simulations using the GYRO code [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. The simulations recover two pinch mechanisms in the radial transport of toroidal angular momentum: The slab geometry ExB shear pinch [Dominguez and Staebler, Phys. Fluids B 5, 387 (1993)] and the toroidal geometry 'Coriolis' pinch [Peeters, Angioni, and Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. The pinches allow the steady state null stress (or angular momentum transport flow) condition required to understand intrinsic (or spontaneous) toroidal rotation in heated tokamak without an internal source of torque [Staebler, Kinsey, and Waltz, Bull. Am. Phys. Soc. 46, 221 (2001)]. A predicted turbulent shift in the neoclassical poloidal rotation [Staebler, Phys. Plasmas 11, 1064 (2004)] appears to be small at the finite relative gyroradius (rho-star) of current experiments.
Implications of advanced collision operators for gyrokinetic simulation
NASA Astrophysics Data System (ADS)
Belli, E. A.; Candy, J.
2017-04-01
In this work, we explore both the potential improvements and pitfalls that arise when using advanced collision models in gyrokinetic simulations of plasma microinstabilities. Comparisons are made between the simple-but-standard electron Lorentz operator and specific variations of the advanced Sugama operator. The Sugama operator describes multi-species collisions including energy diffusion, momentum and energy conservation terms, and is valid for arbitrary wavelength. We report scans over collision frequency for both low and high {k}θ {ρ }s modes, with relevance for multiscale simulations that couple ion and electron scale physics. The influence of the ion–ion collision terms—not retained in the electron Lorentz model—on the damping of zonal flows is also explored. Collision frequency scans for linear and nonlinear simulations of ion-temperature-gradient instabilities including impurity ions are presented. Finally, implications for modeling turbulence in the highly collisional edge are discussed.
Gyrokinetic simulations of off-axis minimum-q profile corrugations
Waltz, R.E.; Austin, M.E.; Burrell, K.H.; Candy, J.
2006-05-15
Quasiequilibrium radial 'profile corrugations' in the electron temperature gradient are found at lowest-order singular surfaces in global gyrokinetic code simulations of both monotonic-q and off-axis minimum-q discharges. The profile corrugations in the temperature and density gradients are time-averaged components of zonal flows. The m/n=2/1 electron temperature gradient corrugation is measurably large and appears to trigger an internal transport barrier as the off-axis minimum-q=2 surfaces enter the plasma.
Gyrokinetic particle-in-cell simulations of Alfvén eigenmodes in presence of continuum effects
Mishchenko, Alexey Könies, Axel; Hatzky, Roman
2014-05-15
First-principle gyrokinetic particle-in-cell simulations of a global Toroidal Alfvén Eigenmode (TAE) are undertaken in the presence of a strong coupling with the continuum. Effects of the bulk plasma temperature on the interplay between the TAE and Kinetic Alfvén Waves (KAWs) are investigated. A global TAE-KAW structure is identified which appears to be more unstable with respect to the fast ions than a simple (fluid-like) TAE mode.
NASA Astrophysics Data System (ADS)
Howard, N. T.; Greenwald, M.; Mikkelsen, D. R.; Reinke, M. L.; White, A. E.; Ernst, D.; Podpaly, Y.; Candy, J.
2012-06-01
Nonlinear gyrokinetic simulations of impurity transport are compared to experimental impurity transport for the first time. The GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) was used to perform global, nonlinear gyrokinetic simulations of impurity transport for a standard Alcator C-Mod, L-mode discharge. The laser blow-off technique was combined with soft x-ray measurements of a single charge state of calcium to provide time-evolving profiles of this non-intrinsic, non-recycling impurity over a radial range of 0.0 ⩽ r/a ⩽ 0.6. Experimental transport coefficient profiles and their uncertainties were extracted from the measurements using the impurity transport code STRAHL and rigorous Monte Carlo error analysis. To best assess the agreement of gyrokinetic simulations with the experimental profiles, the sensitivity of the GYRO predicted impurity transport to a wide range of turbulence-relevant plasma parameters was investigated. A direct comparison of nonlinear gyrokinetic simulation and experiment is presented with an in depth discussion of error sources and a new data analysis methodology.
Gyrokinetic simulation and theory for kinetic ballooning mode
NASA Astrophysics Data System (ADS)
Li, Yue-Yan; Xiao, Yong
2016-10-01
The kinetic ballooning mode (KBM) plays an important role in H mode formation and edge-localized mode (ELM) physics and internal transport barrier. A thorough understanding of the linear KBM physics is crucial to understanding the nonlinear edge physics in tokamaks. The second stability regime in small shear and sufficiently large pressure gradient has been predicted by the ballooning MHD theory. In the present work, a kinetic ballooning mode is found for the second stability regime in s-alpha space. This KBM mode is characterized by a broad-spread eigenfunction in the ballooning space, and destabilized dramatically by the ion temperature gradient. Such KBM mode almost exists in the entire second stability regime. Also KBM has been found in the sufficiently small shear even with negative shear. The gyrokinetic code GTC is employed to study the KBM physics, and finds that the linear KBM growth rate and frequency are very sensitive to the equilibrium profile. The effect of parallel current and density has been investigated, and comparisons between gyrokinetic simulation and analytic theory are carried out. The results shows that parallel current response have a strong effect in stabilize KBM instability, which could have a large effect on nonlinear electromagnetic turbulent transport.
Toroidal universal drift instability: A global gyrokinetic study
Chowdhury, J.; Ganesh, R.; Brunner, S.; Vaclavik, J.; Villard, L.
2010-10-15
An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau resonance and transit resonance, which are considered to be important for the toroidal universal mode, are kept for both species. A systematic parametric study is carried out for the mode. The toroidal universal drift mode is observed to sustain finite temperature gradient and can thus coexist with the temperature gradient driven modes and may contribute to the observed particle transport along with other drift modes. Especially at intermediate scales between the ion temperature gradient driven mode and electron temperature gradient driven mode, this branch of the drift instability can also be a plausible candidate for the observed particle loss. The effect of magnetic fluctuations on the mode is also investigated. In contrast to the slab mode, the toroidal branch of the universal drift mode is found to be strongly stabilized by electromagnetic effects at finite plasma {beta}. Finally, the effect of trapped electrons on the universal mode is studied and compared with the other possible modes in the same parameter regime, namely, ion temperature gradient mode in the presence of trapped electrons and pure trapped electron modes.
Toroidal universal drift instability: A global gyrokinetic study
NASA Astrophysics Data System (ADS)
Chowdhury, J.; Ganesh, R.; Brunner, S.; Vaclavik, J.; Villard, L.
2010-10-01
An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau resonance and transit resonance, which are considered to be important for the toroidal universal mode, are kept for both species. A systematic parametric study is carried out for the mode. The toroidal universal drift mode is observed to sustain finite temperature gradient and can thus coexist with the temperature gradient driven modes and may contribute to the observed particle transport along with other drift modes. Especially at intermediate scales between the ion temperature gradient driven mode and electron temperature gradient driven mode, this branch of the drift instability can also be a plausible candidate for the observed particle loss. The effect of magnetic fluctuations on the mode is also investigated. In contrast to the slab mode, the toroidal branch of the universal drift mode is found to be strongly stabilized by electromagnetic effects at finite plasma β. Finally, the effect of trapped electrons on the universal mode is studied and compared with the other possible modes in the same parameter regime, namely, ion temperature gradient mode in the presence of trapped electrons and pure trapped electron modes.
Electron heat transport from stochastic fields in gyrokinetic simulations
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-15
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as {beta}{sub e} is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of {beta}{sub e}. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, d{sub m}[A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
Turbulence spectra and transport barriers in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Sarazin, Y.; Grandgirard, V.; Angelino, P.; Casati, A.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, Ph.; Gürcan, O.; Hennequin, P.; Sabot, R.
2008-11-01
The energy spectra of the Ion Temperature Gradient driven fluctuations are investigated with the global full-f gyrokinetic code GYSELA. For monotonous q profile, the poloidal spectrum can equally be fitted with two power laws or with a unique exponential. When prescribing an additional sheared radial electric field in view of triggering a transport barrier, the system is found to promptly polarize and screen this field, likely in a transient evolution towards a canonical equilibrium. For a reversed q profile, the negative shear region exhibits larger fluctuations, possibly due to the slab branch of ITG, characterized by a flatter spectrum. No clear transport barrier signature is observed in the vicinity of s = 0 when the radial extent of the gap without resonant modes is smaller than the turbulence correlation length.
Analysis and gyrokinetic simulation of MHD Alfven wave interactions
NASA Astrophysics Data System (ADS)
Nielson, Kevin Derek
The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the
Xiao, Yong; Holod, Ihor; Wang, Zhixuan; Lin, Zhihong; Zhang, Taige
2015-02-15
Developments in gyrokinetic particle simulation enable the gyrokinetic toroidal code (GTC) to simulate turbulent transport in tokamaks with realistic equilibrium profiles and plasma geometry, which is a critical step in the code–experiment validation process. These new developments include numerical equilibrium representation using B-splines, a new Poisson solver based on finite difference using field-aligned mesh and magnetic flux coordinates, a new zonal flow solver for general geometry, and improvements on the conventional four-point gyroaverage with nonuniform background marker loading. The gyrokinetic Poisson equation is solved in the perpendicular plane instead of the poloidal plane. Exploiting these new features, GTC is able to simulate a typical DIII-D discharge with experimental magnetic geometry and profiles. The simulated turbulent heat diffusivity and its radial profile show good agreement with other gyrokinetic codes. The newly developed nonuniform loading method provides a modified radial transport profile to that of the conventional uniform loading method.
Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode
Zhang, H. S.; Liu, Y. Q.; Lin, Z.; Zhang, W. L.
2016-04-15
The beta-induced Alfven-acoustic eigenmode (BAAE) in toroidal plasmas is verified and studied by global gyrokinetic particle simulations. When ion temperature is much lower than electron temperature, the existence of the weakly damped BAAE is verified in the simulations using initial perturbation, antenna excitation, and energetic particle excitation, respectively. When the ion temperature is comparable to the electron temperature, the unstable BAAE can be excited by realistic energetic particle density gradient, even though the stable BAAE (in the absence of energetic particles) is heavily damped by the thermal ions. In the simulations with reversed magnetic shear, BAAE frequency sweeping is observed and poloidal mode structure has a triangle shape with a poloidal direction similar to that observed in tokamak experiments. The triangle shape changes the poloidal direction, and no frequency sweeping is found in the simulations with normal magnetic shear.
Howard, N. T.; Greenwald, M.; White, A. E.; Reinke, M. L.; Ernst, D.; Podpaly, Y.; Mikkelsen, D. R.; Candy, J.
2012-05-15
Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.
Uncertainty estimation and a stopping rule in nonlinear gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Oberparleiter, Michael; Nordman, Hans; Verdoolaege, Geert; Jenko, Frank
2016-11-01
We present a method to estimate the mean and uncertainty of fluctuating quantities, such as spatially averaged density and temperature fluctuations or radial fluxes, from initial value simulations of the Eulerian gyrokinetic code GENE[1, 2]. Since the time series are autocorrelated in time, the data is grouped into batches based on the autocorrelation time and their means form the sample for further statistical treatment, such as calculating the standard error of the mean.Based on this uncertainty estimate we develop a stopping rule for a nonlinear simulation: First, regression tests ensure that it has reached a stationary (quasisteady) state and data before this point is discarded. Then the previously described estimate is calculated. If the estimated relative error is below a prescribed threshold, the simulation is stopped. This scheme is applied to several previously performed GENE simulations ranging from simple benchmarks to modelling of JET and ASDEX discharges. It can be demonstrated that a number of simulations could be around 30% shorter if a maximal statistical relative uncertainty of 5% is desired for all monitored quantities.
Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence
NASA Astrophysics Data System (ADS)
Wang, Eric
2010-11-01
One of the fundamental components of a steady state tokamak or stellerator fusion reactor is the structural integrity of nested magnetic surfaces. The consequences of losing this integrity can have very serious implications, ranging from sawtooth crashes to disruptions. In the present work, we use GYRO to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as β is varied from .1% to .7%, as first investigated in [J. Candy, Phys. Plasmas 12, 072307 (2005)]. By integrating the self-consistent magnetic field lines to produce Poincare surface of section plots, we demonstrate destruction of magnetic surfaces for all nonzero values of β. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. We can quantify the stochastic electron heat transport by using test particles to estimate the magnetic diffusion coefficient Dst [A.B. Rechester and M.N. Rosenbluth, PRL 40, 38 (1978)] for hundreds of time slices in each simulation and find the time-history of Dst to be highly correlated with the electron heat transport due to ``magnetic-flutter'' computed in the simulations. The mechanism that couples electromagnetic turbulence to the linearly damped high-n tearing modes that are responsible for reconnection will be discussed.
Shear-Alfv'en Waves in Gyrokinetic Particle Simulation
NASA Astrophysics Data System (ADS)
Dickerson, Thomas D.; Startsev, Edward A.; Lee, W. W.
2012-10-01
Numerical properties of shear-Alfv'en waves in slab geometry have been studied using a Particle-in-Cell code implementing the recently developed double split-weight scheme [1]. This scheme separates the non-adiabatic response of the particles from both their adiabatic responses and the field-line bending effects arising from the background density and temperature gradients of both the electrons and the ions. This scheme is an improvement over the original split-weight scheme [2] in the presence of the zeroth-order inhomogeneities. The present studies consist of testing numerical restrictions on temporal resolution in the simulation of these waves in one and two dimensions, and on spatial resolutions on the formation of shear Alfv'en eigenmodes in two dimensional sheared slab simulations. For example, it is found that the correct behavior of ion temperature gradient modes in terms of frequencies and growth rates can be maintained with time steps larger than the limit imposed by the shear-Alfven waves. Details will be reported.[4pt] [1] E. A. Startsev and W. W. Lee, ``Finite-Beta Simulation of Microinstabilities,'' manuscript in preparation (2012). [0pt] [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm and Z. Lin, ``Shear-Alf'en Waves in Gyrokinetic Plasmas,'' Phys. Plasmas 10, 4435 (2001).
Impact of a hollow density profile on turbulent particle fluxes: Gyrokinetic and fluid simulations
NASA Astrophysics Data System (ADS)
Tegnered, D.; Oberparleiter, M.; Strand, P.; Nordman, H.
2017-07-01
Hollow density profiles may occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the pellet fuelling scheme inefficient. In the present work, the particle transport driven by Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence in hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT, and magnetic shear are investigated. In addition, the effects of a fast species are studied and global ITG simulations in a simplified physics description are performed in order to investigate nonlocal effects. It is found that β in particular, has a stabilizing effect in the negative R/Ln region. Both nonlinear GENE and EDWM simulations show a decrease in inward flux for negative R/Ln and a change in the direction from inward to outward for positive R/Ln. Moreover, the addition of fast particles was shown to decrease the inward main ion particle flux in the positive gradient region further. This might have serious consequences for pellet fuelling of high β plasmas. Additionally, the heat flux in global ITG turbulence simulations indicates that nonlocal effects can play a different role from usual in connection with pellet fuelling.
Full-f gyrokinetic simulation over a confinement time
Idomura, Yasuhiro
2014-02-15
A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., “Consequences of profile shearing on toroidal momentum transport,” Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the radial electric field shear but also on the radial electric field itself. Based on the toroidal angular momentum conservation, it is found that in the steady null momentum transport state, the turbulent residual stress is cancelled by the neoclassical counterpart, which is greatly enhanced in the presence of turbulent fluctuations.
Non-Maxwellian background effects in gyrokinetic simulations with GENE
NASA Astrophysics Data System (ADS)
Di Siena, A.; Görier, T.; Doerk, H.; Citrin, J.; Johnson, T.; Schneider, M.; Poli, E.; Contributors, JET
2016-11-01
The interaction between fast particles and core turbulence has been established as a central issue for a tokamak reactor. Recent results predict significant enhancement of electromagnetic stabilisation of ITG turbulence in the presence of fast ions. However, most of these simulations were performed with the assumption of equivalent Maxwellian distributed particles, whereas to rigorously model fast ions, a non-Maxwellian background distribution function is needed. To this aim, the underlying equations in the gyrokinetic code GENE have been re-derived and implemented for a completely general background distribution function. After verification studies, a previous investigation on a particular JET plasma has been revised with linear simulations. The plasma is composed by Deuterium, electron, Carbon impurities, NBI fast Deuterium and ICRH 3He. Fast particle distributions have been modelled with a number of different analytic choices in order to study the impact of non-Maxwellian distributions on the plasma turbulence: slowing down and anisotropic Maxwellian. Linear growth rates are studied as a function of the wave number and compared with those obtained using an equivalent Maxwellian. Generally, the choice of the 3He distribution seems to have a stronger impact on the microinstabilities than that of the fast Deuterium.
The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations
Hornsby, W. A. Migliano, P.; Buchholz, R.; Kroenert, L.; Weikl, A.; Peeters, A. G.; Zarzoso, D.; Poli, E.; Casson, F. J.
2015-02-15
Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η{sup 1∕7} scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.
Gyrokinetic Simulation of Microturbulent Saturation at Finite β
NASA Astrophysics Data System (ADS)
Terry, P. W.; Pueschel, M. J.; Carmody, D.; Whelan, G. G.
2014-10-01
Saturation and zonal flow physics for microturbulence is investigated for tokamaks and the RFP using gyrokinetic computation to understand scalings with respect magnetic shear and β. Modeling an MST discharge shows that the critical instability gradient for TEM is higher than the tokamak threshold by the aspect ratio (R / a) . This factor is rooted in the shorter magnetic field scale length of the RFP. Nonlinear simulations show strong zonal flows and a large Dimits shift exceeding the tokamak shift by a factor of order (R / a) . The non zonal transition (NZT), a critical β for which zonal flows are disabled by flutter-induced charge loss is also considered. The critical β occurs when the radial displacement of a magnetic field line over a half connection length is equal to the radial correlation length. These quantities scale with the connection length and magnetic drift scale lengths entering the instability threshold and quasilinear diffusivities, making the RFP critical β for NZT higher than the tokamak value by (R / a) 1 . 5 times tokamak q. These results are consistent with magnetic shear and q dependence in the kinetic ballooning threshold, indicating that β effects will only arise at high β relative to typical RFP operation.
Gyrokinetic δ particle simulation of trapped electron mode driven turbulence
NASA Astrophysics Data System (ADS)
Lang, Jianying
2007-11-01
Turbulent transport driven by collisionless trapped electron modes (CTEM) is systematically studied using gyrokinetic delta-f particle-in-cell simulation. Scaling with local plasma parameters, including density gradient, electron temperature gradient, magnetic shear, temperature ratio and aspect ratio, is investigated. Simulation results are compared with previous simulations and theoretical predictions. Nonlinearly the transport level increases with increasing magnetic shear. We explain the nonlinear magnetic shear scaling by differences in the radial correlation lengths caused by toroidal coupling. The turbulence is more radially elongated at higher magnetic shear compared with low magnetic shear. We show that the suppression effect of zonal flow on CTEM transport depends on both the electron temperature gradient and the electron to ion temperature ratio. This helps explain the previous contradictory conclusions on the importance of zonal flows in different parameter regimes.ootnotetextT. Dannert, F. Jenko, Phys. Plasmas 12, 072309 (2005); D. Ernst, et al., Phys. Plasmas 11, 2637 (2004). Zonal flow suppression is consistent with the rate of EXB shearing from the ambient turbulence as well as the radial broadening of the spectra. Strong geodesic acoustic modes (GAMs) are generated along with zonal flows and the frequency of the GAMs agrees well with kinetic theory.ootnotetextT. Watari, et al., Phys. Plasmas 13, 062504 (2006). We further explore the nonlinear saturation mechanism when the zonal flows are not important. We find that when only a single toroidal mode (and its conjugate) is kept, reasonable nonlinear saturation is obtained. Investigating a range of n, modes with larger mode number n saturate at a higher level relative to lower n modes, indicating a turbulent inverse cascade process.
A minimal collision operator for implementing neoclassical transport in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Angelino, P.; Sarazin, Y.; Grandgirard, V.; Ghendrih, P.; Samain, A.
2008-11-01
This paper presents a class of collision operators, which reproduce neoclassical transport and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on a variational entropy method, which allows a fast calculation of the neoclassical diffusivity and poloidal velocity.
Gyrokinetic Simulation of Reverse Shear Alfven Eigenmodes in DIII-D Plasmas
NASA Astrophysics Data System (ADS)
Chen, Yang; Parker, Scott; Fu, Guo-Yong
2012-03-01
We present simulation results of the beam driven Reverse Shear Alfven Eigenmodes (RSAE) observed in DIII-D discharge 142111 using the Particle-in-Cell gyrokinetic code GEM [1]. Bulk ions and energetic particles are gyrokinetic, but electrons are described by a mass-less fluid model. Two schemes for obtaining the electric potential are implemented, one by solving the gyrokinetic Poisson equation for φ directly, the other by solving the gyrokinetic moment (GKM) equation for φ/t and then integrating in time. The GKM approach is found to be more robust for linear simulations (allowing larger time steps) but less robust for nonlinear simulations. Previous simulations reproduced the chirping in frequency as seen in the experiment. Recently it has been reported by other simulation codes (GTC, GYRO and TAEFL) that the shearing direction of the mode structure in the poloidal plane disagrees with observation. We found that the mode structure, including the shearing in the poloidal plane, is in general sensitive to the beam distribution. By changing the radial profile of the beam density while keeping the velocity dependence fixed, both shearing directions can be produced in the simulation. [4pt] [1] Y. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007)
Fahey, Mark R.; Candy, Jeff
2013-11-07
This project initiated the development of TGYRO ? a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale GYRO turbulence simulations into a framework for practical multi-scale simulation of conventional tokamaks as well as future reactors. Using a lightweight master transport code, multiple independent (each massively parallel) gyrokinetic simulations are coordinated. The capability to evolve profiles using the TGLF model was also added to TGYRO and represents a more typical use-case for TGYRO. The goal of the project was to develop a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale gyrokinetic turbulence simulations into a framework for practical multi-scale simulation of a burning plasma core ? the International Thermonuclear Experimental Reactor (ITER) in particular. This multi-scale simulation capability will be used to predict the performance (the fusion energy gain, Q) given the H-mode pedestal temperature and density. At present, projections of this type rely on transport models like GLF23, which are based on rather approximate fits to the results of linear and nonlinear simulations. Our goal is to make these performance projections with precise nonlinear gyrokinetic simulations. The method of approach is to use a lightweight master transport code to coordinate multiple independent (each massively parallel) gyrokinetic simulations using the GYRO code. This project targets the practical multi-scale simulation of a reactor core plasma in order to predict the core temperature and density profiles given the H-mode pedestal temperature and density. A master transport code will provide feedback to O(16) independent gyrokinetic simulations (each massively parallel). A successful feedback scheme offers a novel approach to predictive modeling of an important national and international problem. Success in this area of fusion simulations will allow US scientists to direct the research path of ITER over the next two
Center for Gyrokinetic Particle Simulations of Turbulent Transport. Final report
Parker, Scott; Chen, Yang
2011-05-02
This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of
Gyrokinetic simulations of neoclassical transport using a minimal collision operator
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.; Angelino, P.
2008-11-01
Conventional neoclassical predictions are successfully recovered within a gyrokinetic framework using a minimal Fokker-Planck collision operator. This operator is shown to accurately describe some essential features of neoclassical theory, namely the neoclassical transport, the poloidal rotation and the linear damping of axisymmetric flows while interestingly preserving a high numerical efficiency. Its form makes it especially adapted to Eulerian or Semi-Lagrangian schemes.
Alternate treatment of the polarization drift for gyrokinetic PIC simulations
NASA Astrophysics Data System (ADS)
Lodestro, L. L.; Dimits, A. M.; Nevins, W. M.
2003-10-01
Tokamak edge turbulence is characterized by a range of spatial scales up through k_⊥ρ_pol ˜ 1, and can involve fluctuation amplitudes of order unity. To apply gyrokinetic methods to the study of such turbulence, an extension of the usual formulation is therefore required. A promising route appears to have been developed in Ref. 1footnotetextA.M. Dimits, L.L. LoDestro, and D.H.E. Dubin, Phys. Fluids B 4, 277 (1992)., where it is shown that with the use of expansion parameter ɛ=tilde v/v_th i ˜ k_⊥ρ_ie(φ-A_\\|/c)/T≪1, the nonlinear gyrokinetic equations span the usual drift-kinetic and gyrokinetic regimes. However, there remain technical difficulties with the numerical implementation of the polarization drift in Poisson's equation when the fluctuations are large. In this paper we present our progress assessing the various methods that have been proposed for treating the polarization drift.
Leerink, S; Bulanin, V V; Gurchenko, A D; Gusakov, E Z; Heikkinen, J A; Janhunen, S J; Lashkul, S I; Altukhov, A B; Esipov, L A; Kantor, M Yu; Kiviniemi, T P; Korpilo, T; Kuprienko, D V; Petrov, A V
2012-10-19
Direct measurements of micro-, meso-, and macroscale transport phenomena in the FT-2 tokamak are shown to be quantitatively reproduced by global full f nonlinear gyrokinetic simulation predictions. A detailed agreement with mean equilibrium E×B flows, oscillating fine-scale zonal flows, and turbulence spectra observed by a set of sophisticated microwave backscattering techniques as well as a good fit of the thermal diffusivity data are demonstrated. A clear influence of the impurity ions on the fluctuating radial electric field is observed.
Verification of Gyrokinetic (delta)f Simulations of Electron Temperature Gradient Turbulence
Nevins, W M; Parker, S E; Chen, Y; Candy, J; Dimits, A; Dorland, W; Hammett, G W; Jenko, F
2007-05-07
The GEM gyrokinetic {delta}f simulation code [Chen, 2003] [Chen, 2007] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [Nevins, 2006]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.
Astrophysical Gyrokinetics: Basic Equations and Linear Theory
NASA Astrophysics Data System (ADS)
Howes, Gregory G.; Cowley, Steven C.; Dorland, William; Hammett, Gregory W.; Quataert, Eliot; Schekochihin, Alexander A.
2006-11-01
Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.
Block-structured grids in full velocity space for Eulerian gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Jarema, D.; Bungartz, H. J.; Görler, T.; Jenko, F.; Neckel, T.; Told, D.
2017-06-01
Global, i.e., full-torus, gyrokinetic simulations play an important role in exploring plasma microturbulence in magnetic fusion devices with strong radial variations. In the presence of steep temperature profiles, grid-based Eulerian approaches can become quite challenging as the correspondingly varying velocity space structures need to be accommodated and sufficiently resolved. A rigid velocity space grid then requires a very high number of discretization nodes resulting in enormous computational costs. To tackle this issue and reduce the computational demands, we introduce block-structured grids in the all velocity space dimensions. The construction of these grids is based on a general approach, making them suitable for various Eulerian implementations. In the current study, we explain the rationale behind the presented approach, detail the implementation, and provide simulation results obtained with the block-structured grids. The achieved reduction in the number of computational nodes depends on the temperature profile and simulation scenario provided. In the test cases at hand, about ten times fewer grid points are required for nonlinear simulations performed with block-structured grids in the plasma turbulence code GENE (http://genecode.org). With the speed-up found to scale almost exactly reciprocal to the number of grid points, the new implementation greatly reduces the computational costs and therefore opens new possibilities for applications of this software package.
NASA Astrophysics Data System (ADS)
Zhao, Deng; Waltz, R. E.
2015-10-01
This paper presents the numerical methods for the nonlinear simulations of cyclokinetic [Waltz and Zhao Deng (2013)] equations in Fourier harmonics of the gyro-phase. A parallel processed, implicit time advanced, Eulerian (or continuum) code (rCYCLO) is developed. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantees accurate conservation of the incremental entropy. By comparing the cyclokinetic simulations with the corresponding gyrokinetics, we quantitatively test the breakdown of gyrokinetics at high turbulence levels over a range of large relative ion cyclotron frequency (10 <Ω∗ < 100 where Ω∗ = 1 /ρ∗, and ρ∗ is the relative ion gyroradius). As an important code verification, the rCYCLO gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω∗ ⩾ 50) and low turbulence levels. In the case of linearly stable ion cyclotron modes, the cyclokinetic transport is lower (not higher) than the gyrokinetic transport at high turbulence levels and low-Ω∗ values.
Gyrokinetic Particle Simulation of Fast Electron Driven Beta-induced Alfven Eigenmodes
NASA Astrophysics Data System (ADS)
Zhang, Wenlu; Cheng, Junyi; Lin, Zhihong
2016-10-01
The fast electron driven beta induced Alfven eigenmode (e-BAE) has been routinely observed in HL-2A tokamak. We study e-BAE for the first time using global gyrokinetic GTC simulation, where the fast electrons are described by the drift kinetic model. Frequency chirping is observed in nonlinear simulations in the absence of sources and sinks, which provide a new nonlinear paradigm beyond the standard ``bump-on-tail'' model. For weakly driven case, nonlinear frequency is observed to be in phase with particle flux, and nonlinear mode structure is almost the same as linear stage. In the strongly driven case, BAAE is also unstable and co-exists with BAE after the BAE saturation. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of the coherent structures in the fast electron phase space, where the dynamics of the coherent structure is controlled by the formation and destruction of phrase space islands in the canonical variables. Zonal fields are found to affect wave-particle resonance in the nonlinear e-BAE simulations.
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma
Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.; ...
2017-05-29
Here, five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currentsmore » to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.« less
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma
NASA Astrophysics Data System (ADS)
Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.; Hakim, A.
2017-06-01
Five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.
NASA Astrophysics Data System (ADS)
Zhang, Chenxi; Zhang, Wenlu; Lin, Zhihong; Li, Ding
2013-05-01
This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitation and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.
Zhang, Chenxi; Li, Ding; Zhang, Wenlu; Lin, Zhihong
2013-05-15
This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitation and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.
Deng, Zhao; Waltz, R. E.
2015-05-15
This paper presents numerical simulations of the nonlinear cyclokinetic equations in the cyclotron harmonic representation [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Simulations are done with a local flux-tube geometry and with the parallel motion and variation suppressed using a newly developed rCYCLO code. Cyclokinetic simulations dynamically follow the high-frequency ion gyro-phase motion which is nonlinearly coupled into the low-frequency drift-waves possibly interrupting and suppressing gyro-averaging and increasing the transport over gyrokinetic levels. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the breakdown of gyrokinetics at high turbulence levels is quantitatively tested over a range of relative ion cyclotron frequency 10 < Ω*{sup }< 100 where Ω*{sup }= 1/ρ*, and ρ* is the relative ion gyroradius. The gyrokinetic linear mode rates closely match the cyclokinetic low-frequency rates for Ω*{sup }> 5. Gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω*{sup }≥ 50) and low turbulence level as required. Cyclokinetic transport is found to be lower than gyrokinetic transport at high turbulence levels and low-Ω* values with stable ion cyclotron (IC) modes. The gyrokinetic approximation is found to break down when the density perturbations exceed 20%. For cyclokinetic simulations with sufficiently unstable IC modes and sufficiently low Ω*{sup }∼ 10, the high-frequency component of cyclokinetic transport level can exceed the gyrokinetic transport level. However, the low-frequency component of the cyclokinetic transport and turbulence level does not exceed that of gyrokinetics. At higher and more physically relevant Ω*{sup }≥ 50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport and turbulence level is still smaller than that of
Simulating the effects of stellarator geometry on gyrokinetic drift-wave turbulence
NASA Astrophysics Data System (ADS)
Baumgaertel, Jessica Ann
Nuclear fusion is a clean, safe form of energy with abundant fuel. In magnetic fusion energy (MFE) experiments, the plasma fuel is confined by magnetic fields at very high temperatures and densities. One fusion reactor design is the non-axisymmetric, torus-shaped stellarator. Its fully-3D fields have advantages over the simpler, better-understood axisymmetric tokamak, including the ability to optimize magnetic configurations for desired properties, such as lower transport (longer confinement time). Turbulence in the plasma can break MFE confinement. While turbulent transport is known to cause a significant amount of heat loss in tokamaks, it is a new area of research in stellarators. Gyrokinetics is a good mathematical model of the drift-wave instabilities that cause turbulence. Multiple gyrokinetic turbulence codes that had great success comparing to tokamak experiments are being converted for use with stellarator geometry. This thesis describes such adaptations of the gyrokinetic turbulence code, GS2. Herein a new computational grid generator and upgrades to GS2 itself are described, tested, and benchmarked against three other gyrokinetic codes. Using GS2, detailed linear studies using the National Compact Stellarator Experiment (NCSX) geometry were conducted. The first compares stability in two equilibria with different β=(plasma pressure)/(magnetic pressure). Overall, the higher β case was more stable than the lower β case. As high β is important for MFE experiments, this is encouraging. The second compares NCSX linear stability to a tokamak case. NCSX was more stable with a 20% higher critical temperature gradient normalized by the minor radius, suggesting that the fusion power might be enhanced by ˜ 50%. In addition, the first nonlinear, non-axisymmetric GS2 simulations are presented. Finally, linear stability of two locations in a W7-AS plasma were compared. The experimentally-measured parameters used were from a W7-AS shot in which measured heat fluxes
Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
2011-04-15
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium ExB velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or ''profile shear'' in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) ExB and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a ''null'' toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the ExB shear and parallel velocity (Coriolis force) pinching components from the larger ''diffusive'' parallel velocity shear driven component and
NASA Astrophysics Data System (ADS)
Pochelon, Antoine
2010-11-01
Due to turbulence, core energy transport in tokamaks generally exceeds collisional transport by at least an order of magnitude. It is therefore crucial to understand the instabilities driving the turbulent state and to find ways to control them. Shaping the plasma is one of these fundamental tools. In low collisionality plasmas, such as in a reactor, changing triangularity from positive (delta=+0.4) to negative triangularity (delta=-0.4) is shown on TCV to reduce the energy transport by a factor two. This opens the possibility of having H-mode-like confinement time within an L-mode edge, or reduced ELMs. An optimum triangularity can be sought between steep edge barriers (delta>0), plagued by large ELMs, and improved core confinement (delta<0). Recent correlation ECE measurements show that the reduction of transport at negative delta is reflected in a reduction by a factor of two of both the amplitude of temperature fluctuations in the broadband frequency range 30-150 kHz, and the fluctuation correlation length, measured at mid-radius. In addition, the fluctuations amplitude is reduced with increasing collisionality, consistent with a reduction of the Trapped Electron Modes (TEM) drive. The effect of negative triangularity on turbulence and transport is compared to gyrokinetic code results: First, global linear simulations predict shorter radial TEM wavelength, consistent with the shorter radial turbulence correlation length observed. Second, at least close to the strongly shaped plasma boundary, local nonlinear simulations predict lower TEM induced transport with decreased triangularity. Calculations are now being extended to global nonlinear simulations.
Gyrokinetic simulations of collisionless reconnection in turbulent non-uniform plasmas
Kobayashi, Sumire; Rogers, Barrett N.; Numata, Ryusuke
2014-04-15
We present nonlinear gyrokinetic simulations of collisionless magnetic reconnection with non-uniformities in the plasma density, the electron temperature, and the ion temperature. The density gradient can stabilize reconnection due to diamagnetic effects but destabilize driftwave modes that produce turbulence. The electron temperature gradient triggers microtearing modes that drive rapid small-scale reconnection and strong electron heat transport. The ion temperature gradient destabilizes ion temperature gradient modes that, like the driftwaves, may enhance reconnection in some cases.
NASA Astrophysics Data System (ADS)
Zarzoso, D.; Migliano, P.; Grandgirard, V.; Latu, G.; Passeron, C.
2017-07-01
The modification of radial structure, frequency and intensity of turbulent transport in the presence of energetic-particle-driven geodesic acoustic modes (EGAMs) is analysed by means of full-f global gyro-kinetic simulations using Gysela code. It is observed that turbulence leads to a smoother evolution of the distribution function, less pronounced flattening of the distribution function in velocity space during the nonlinear saturation of EGAMs and reduced saturation level of electrostatic potential with respect to the case where turbulence is artificially suppressed. It is shown that EGAMs are excited and impact turbulent transport in the region where the EP is localised, fading away the staircase structure observed in the absence of energetic particles. For the first time, evidences of a three-wave coupling between turbulent modes and EGAMs in gyro-kinetic simulations are provided by means of bispectral analysis using wavelet transform in time. The coupling evolves from the standard self-regulation of turbulence by the zero-frequency zonal component to a steady-state regime where turbulence dynamics is dominated by the zonal component oscillating at the EGAM frequency.
Candy, J.; Waltz, R.E.
2006-03-15
Equations which describe the evolution of volume-averaged gyrokinetic entropy are derived and added to GYRO [J. Candy and R.E. Waltz, J. Comput. Phys. 186, 545 (2003)], a Eulerian gyrokinetic turbulence simulation code. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor energy flux is significantly changed by a 16-fold increase (from 32 to 512 grid points per cell) in the number of grid points in the two-dimensional velocity space. Third, the measured flux is invariant to an eightfold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that Eulerian gyrokinetic codes miss important velocity-space structure. The issues of density and energy conservation and their relation to negligible second-order effects such as the parallel nonlinearity are also discussed.
NASA Astrophysics Data System (ADS)
Deng, Zhao
2014-10-01
Gyrokinetic simulations of L-mode near edge tokamak plasmas with the GYRO code underpredict both the transport and the turbulence levels by 5 to 10 fold, which suggest either some important mechanism is missing from current gyrokinetic codes like GYRO or the gyrokinetic approximation itself is breaking down. It is known that GYRO drift-kinetic simulations with gyro-averaging suppressed recover most of the missing transport. With these motivations, we developed a flux tube nonlinear cyclokinetic code rCYCLO with the parallel motion and variation suppressed. rCYCLO dynamically follows the high frequency ion gyro-phase motion (with no averaging) which is nonlinearly coupled into the low frequency drift-waves thereby interrupting and possibly suppressing the gyro-averaging. By comparison with the corresponding gyrokinetic simulations, we can test the conditions for the breakdown of gyrokinetics. rCYCLO nonlinearly couples ∇B driven ion temperature gradient (ITG) modes and collisional fluid electron drift modes to ion cyclotron (IC) modes. As required, rCYCLO cyclokinetic transport recovers gyrokinetics at high relative ion cyclotron frequency (Ω*) and low turbulence levels. However, because the IC modes are stable and act as a turbulence sink, we have found that at high turbulence levels and low-Ω* cyclokinetic transport is lower (not higher) than gyrokinetic transport. Work is in progress with unstable IC modes to explore the possibility of driving cyclokinetic transport higher than gyrokinetic transport. Supported by the CSC, NSFC No. 1126114032, No. 10975012 ITER-CN No. 2013GB112006 and the US DOE under DE-FG02-95ER54309.
Barnes, M.; Dorland, W.; Tatsuno, T.; Abel, I. G.; Hammett, G. W.; Ricci, P.; Rogers, B. N.; Schekochihin, A. A.
2009-07-15
A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Comm. 88, 128 (1995)] is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.
NASA Astrophysics Data System (ADS)
Taimourzadeh, Sam; Holod, Ihor; Lin, Zhihong; Nazikian, Raffi
2015-11-01
It has been demonstrated that edge localized modes (ELMs) can be fully suppressed in DIII-D H-mode plasmas with the application of resonant magnetic perturbations (RMPs), and that there is a corresponding reduction of pedestal gradients, changes in rotation, and changes in the radial electric field (Er) profile. However, with the application of RMPs there is also an increase in short wavelength, electrostatic turbulence on top of the pedestal, as observed with BES, DBS, and other fluctuation diagnostics. The effects of Er shear on this turbulence, is investigated using gyrokinetic simulations via the gyrokinetic toroidal code (GTC) for in DIII-D shot 158103, at times 3750 ms (RMP on, ELM active) and 3050 ms (RMP on, ELM suppressed).
Nature of turbulent transport across sheared zonal flows: insights from gyro-kinetic simulations
Sanchez, Raul; Newman, David E; Leboeuf, Jean-Noel; Decyk, Viktor
2011-01-01
The traditional view regarding the reduction of turbulence-induced transport across a stable sheared flow invokes a reduction of the characteristic length scale in the direction perpendicular to the flow as a result of the shearing and stretching of eddies caused by the differential pull exerted in the direction of the flow. A reduced effective transport coefficient then suffices to capture the reduction, that can then be readily incorporated into a transport model. However, recent evidence from gyrokinetic simulations of the toroidal ion-temperature-gradient mode suggests that the dynamics of turbulent transport across sheared flows changes in a more fundamental manner, and that the use of reduced effective transport coefficients fails to capture the full dynamics that may exhibit both subdiffusion and non-Gaussian statistics. In this contribution, after briefly reviewing these results, we propose some candidates for the physical mechanisms responsible for endowing transport with such non-diffusive characteristics, backing these proposals with new numerical gyrokinetic data
Fluid electron, gyrokinetic ion simulations of linear internal kink and energetic particle modes
NASA Astrophysics Data System (ADS)
Cole, Michael; Mishchenko, Alexey; Könies, Axel; Kleiber, Ralf; Borchardt, Matthias
2014-07-01
The internal kink mode is an important plasma instability responsible for a broad class of undesirable phenomena in tokamaks, including the sawtooth cycle and fishbones. To predict and discover ways to mitigate this behaviour in current and future devices, numerical simulations are necessary. The internal kink mode can be modelled by reduced magnetohydrodynamics (MHD). Fishbone modes are an inherently kinetic and non-linear phenomenon based on the n = 1 Energetic Particle Mode (EPM), and have been studied using hybrid codes that combine a reduced MHD bulk plasma model with a kinetic treatment of fast ions. In this work, linear simulations are presented using a hybrid model which couples a fluid treatment of electrons with a gyrokinetic treatment of both bulk and fast ions. Studies of the internal kink mode in geometry relevant to large tokamak experiments are presented and the effect of gyrokinetic ions is considered. Interaction of the kink with gyrokinetic fast ions is also considered, including the destabilisation of the linear n = 1 EPM underlying the fishbone.
Fluid electron, gyrokinetic ion simulations of linear internal kink and energetic particle modes
Cole, Michael Mishchenko, Alexey; Könies, Axel; Kleiber, Ralf; Borchardt, Matthias
2014-07-15
The internal kink mode is an important plasma instability responsible for a broad class of undesirable phenomena in tokamaks, including the sawtooth cycle and fishbones. To predict and discover ways to mitigate this behaviour in current and future devices, numerical simulations are necessary. The internal kink mode can be modelled by reduced magnetohydrodynamics (MHD). Fishbone modes are an inherently kinetic and non-linear phenomenon based on the n = 1 Energetic Particle Mode (EPM), and have been studied using hybrid codes that combine a reduced MHD bulk plasma model with a kinetic treatment of fast ions. In this work, linear simulations are presented using a hybrid model which couples a fluid treatment of electrons with a gyrokinetic treatment of both bulk and fast ions. Studies of the internal kink mode in geometry relevant to large tokamak experiments are presented and the effect of gyrokinetic ions is considered. Interaction of the kink with gyrokinetic fast ions is also considered, including the destabilisation of the linear n = 1 EPM underlying the fishbone.
NASA Astrophysics Data System (ADS)
Tangri, Varun; Terry, P. W.; Waltz, R. E.
2011-05-01
A simple large-aspect-ratio (R0/r) circular equilibrium model is developed for low-beta reversed field pinch (RFP) geometry. The model is suitable for treating small scale instability and turbulent transport driven by ion temperature gradient (ITG) and related electron drift modes in gyrokinetic simulations. The equilibrium model is an RFP generalization of the common tokamak s-α model to small safety factor (q), where the poloidal field dominates the toroidal field. The model accommodates the RFP toroidal field reversal (where q vanishes) by generalizing the cylindrical force-free Bessel function model (BFM) [J. B. Taylor, Phys. Rev. Lett. 33, 1139 (1974)] to toroidal geometry. The global equilibrium can be described in terms of the RFP field reversal and pinch parameters [F ,Θ]. This new toroidal Bessel function model (TBFM) has been incorporated into the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J.Comput. Phys. 186, 545 (2003)] and used here to explore local electrostatic ITG adiabatic electron instability rates for typical low-q RFP parameters.
Tangri, Varun; Terry, P. W.; Waltz, R. E.
2011-05-15
A simple large-aspect-ratio (R{sub 0}/r) circular equilibrium model is developed for low-beta reversed field pinch (RFP) geometry. The model is suitable for treating small scale instability and turbulent transport driven by ion temperature gradient (ITG) and related electron drift modes in gyrokinetic simulations. The equilibrium model is an RFP generalization of the common tokamak s-{alpha} model to small safety factor (q), where the poloidal field dominates the toroidal field. The model accommodates the RFP toroidal field reversal (where q vanishes) by generalizing the cylindrical force-free Bessel function model (BFM) [J. B. Taylor, Phys. Rev. Lett. 33, 1139 (1974)] to toroidal geometry. The global equilibrium can be described in terms of the RFP field reversal and pinch parameters [F,{Theta}]. This new toroidal Bessel function model (TBFM) has been incorporated into the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J.Comput. Phys. 186, 545 (2003)] and used here to explore local electrostatic ITG adiabatic electron instability rates for typical low-q RFP parameters.
Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks
Swamy, Aditya K.; Ganesh, R.; Chowdhury, J.; Brunner, S.; Vaclavik, J.; Villard, L.
2014-08-15
Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient η{sub e}. Scans at different β values show an inverse relationship between the η{sub e} threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.
Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.
Xu, X Q
2008-07-01
We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.
Gyrokinetic simulation of edge blobs and divertor heat-load footprint
NASA Astrophysics Data System (ADS)
Chang, C. S.; Ku, S.; Hager, R.; Churchill, M.; D'Azevedo, E.; Worley, P.
2015-11-01
Gyrokinetic study of divertor heat-load width Lq has been performed using the edge gyrokinetic code XGC1. Both neoclassical and electrostatic turbulence physics are self-consistently included in the simulation with fully nonlinear Fokker-Planck collision operation and neutral recycling. Gyrokinetic ions and drift kinetic electrons constitute the plasma in realistic magnetic separatrix geometry. The electron density fluctuations from nonlinear turbulence form blobs, as similarly seen in the experiments. DIII-D and NSTX geometries have been used to represent today's conventional and tight aspect ratio tokamaks. XGC1 shows that the ion neoclassical orbit dynamics dominates over the blob physics in setting Lq in the sample DIII-D and NSTX plasmas, re-discovering the experimentally observed 1/Ip type scaling. Magnitude of Lq is in the right ballpark, too, in comparison with experimental data. However, in an ITER standard plasma, XGC1 shows that the negligible neoclassical orbit excursion effect makes the blob dynamics to dominate Lq. Differently from Lq 1mm (when mapped back to outboard midplane) as was predicted by simple-minded extrapolation from the present-day data, XGC1 shows that Lq in ITER is about 1 cm that is somewhat smaller than the average blob size. Supported by US DOE and the INCITE program.
SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas
Lin, Zhihong
2013-12-18
During the first year of the SciDAC gyrokinetic particle simulation (GPS) project, the GPS team (Zhihong Lin, Liu Chen, Yasutaro Nishimura, and Igor Holod) at the University of California, Irvine (UCI) studied the tokamak electron transport driven by electron temperature gradient (ETG) turbulence, and by trapped electron mode (TEM) turbulence and ion temperature gradient (ITG) turbulence with kinetic electron effects, extended our studies of ITG turbulence spreading to core-edge coupling. We have developed and optimized an elliptic solver using finite element method (FEM), which enables the implementation of advanced kinetic electron models (split-weight scheme and hybrid model) in the SciDAC GPS production code GTC. The GTC code has been ported and optimized on both scalar and vector parallel computer architectures, and is being transformed into objected-oriented style to facilitate collaborative code development. During this period, the UCI team members presented 11 invited talks at major national and international conferences, published 22 papers in peer-reviewed journals and 10 papers in conference proceedings. The UCI hosted the annual SciDAC Workshop on Plasma Turbulence sponsored by the GPS Center, 2005-2007. The workshop was attended by about fifties US and foreign researchers and financially sponsored several gradual students from MIT, Princeton University, Germany, Switzerland, and Finland. A new SciDAC postdoc, Igor Holod, has arrived at UCI to initiate global particle simulation of magnetohydrodynamics turbulence driven by energetic particle modes. The PI, Z. Lin, has been promoted to the Associate Professor with tenure at UCI.
Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows
Lin, Z.; Hahm, T.S.; Lee, W.W.; Tang, W.M.; White, R.B.
2000-02-15
A fully three-dimensional gyrokinetic particle code using magnetic coordinates for general geometry has been developed and applied to the investigation of zonal flows dynamics in toroidal ion-temperature-gradient turbulence. Full torus simulation results support the important conclusion that turbulence-driven zonal flows significantly reduce the turbulent transport. Linear collisionless simulations for damping of an initial poloidal flow perturbation exhibit an asymptotic residual flow. The collisional damping of this residual causes the dependence of ion thermal transport on the ion-ion collision frequency even in regimes where the instabilities are collisionless.
NASA Astrophysics Data System (ADS)
White, A. E.; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G.; Mikkelsen, D. R.; Edlund, E. M.; Kung, C.; Holland, C.; Candy, J.; Petty, C. C.; Reinke, M. L.; Theiler, C.
2015-05-01
For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.
White, A. E. Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G.; Mikkelsen, D. R.; Edlund, E. M.; Kung, C.; Holland, C.; Candy, J.; Petty, C. C.; Reinke, M. L.; and others
2015-05-15
For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.
NASA Astrophysics Data System (ADS)
Lee, W. W.; White, Roscoe
2016-10-01
A novel mechanism for producing the equilibrium potential well near the edge of a tokamak has been recently proposed. Briefly, because of the difference in gyroradii between electrons and ions, an equilibrium electrostatic potential is generated in the presence of spatial inhomogeneity of the background plasma, which, in turn, produces a well associated with the radial electric field, Er, as observed at the edge of many tokamak experiments. Specifically, this theoretically predicted Er field, which can be regarded as producing a long radial wave length zonal flow, agrees well with recent experimental measurements on JET, NSTX and C-Mod. A possible verification of this new mechanism using a proposed procedure involving global gyrokinetic particle simulation codes and equilibrium MHD codes will be discussed. The approach is iteratively to decouple the transport problem from the equilibrium problem, so that each may be treated accurately, and, then couple them through parameter exchanges. DoE-Grant DE-AC02-09CH11466.
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
2011-04-01
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium E ×B velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or "profile shear" in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) E ×B and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a "null" toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the E ×B shear and parallel velocity (Coriolis force) pinching components from the larger "diffusive" parallel velocity shear driven component and
Chang, C S; Ku, S; Tynan, G R; Hager, R; Churchill, R M; Cziegler, I; Greenwald, M; Hubbard, A E; Hughes, J W
2017-04-28
Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a realistic diverted tokamak edge geometry under strong forcing by a high rate of heat deposition. The results show that turbulent Reynolds-stress-driven sheared E×B flows act in concert with neoclassical orbit loss to quench turbulent transport and form a transport barrier just inside the last closed magnetic flux surface.
Verification of gyrokinetic {delta}f simulations of electron temperature gradient turbulence
Nevins, W. M.; Parker, S. E.; Chen, Y.; Candy, J.; Dimits, A.; Dorland, W.; Hammett, G. W.; Jenko, F.
2007-08-15
The GEM gyrokinetic {delta}f simulation code [Y. Chen and S. Parker, J. Comput. Phys. 189, 463 (2003); and ibid.220, 839 (2007)] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [W. M. Nevins, J. Candy, S. Cowley, T. Dannert, A. Dimits, W. Dorland, C. Estrada-Mila, G. W. Hammett, F. Jenko, M. J. Pueschel, and D. E. Shumaker, Phys. Plasmas 13, 122306 (2006)]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Waelbroeck, F. L.
2012-03-01
Static external resonant magnetic perturbations (RMPs) have been added to the δf gyrokinetic code GYRO. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr and the corresponding plasma torque (density) R[jrBθ/c], induced by islands that break the toroidal symmetry of a tokamak. This extends previous GYRO simulations for the transport of toroidal angular momentum (TAM) [1,2]. The focus is on full torus radial slice electrostatic simulations of induced q=m/n=6/3 islands with widths 5% of the minor radius. The island torque scales with the radial electric field Er the island width w, and the intensity I of the high-n micro-turbulence, as wErI^1/2. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that there is a small co-directed magnetic acceleration to the small diamagnetic co-rotation corresponding to the zero Er which can be called the residual stress [2] from an externally induced island. Finite-beta GYRO simulations of a core radial slice demonstrate island unlocking and the RMP screening. 6pt[1] R.E. Waltz, et al., Phys. Plasmas 14, 122507 (2007). [2] R.E. Waltz, et al., Phys. Plasmas 18, 042504 (2011).
Validation of nonlinear gyrokinetic simulations of L- and I-mode plasmas on Alcator C-Mod
NASA Astrophysics Data System (ADS)
Creely, A. J.; Howard, N. T.; Rodriguez-Fernandez, P.; Cao, N.; Hubbard, A. E.; Hughes, J. W.; Rice, J. E.; White, A. E.; Candy, J.; Staebler, G. M.; Conway, G. D.; Freethy, S. J.; Sung, C.
2017-05-01
New validation of global, nonlinear, ion-scale gyrokinetic simulations (GYRO) is carried out for L- and I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and temperature fluctuations. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale (cross-scale coupling) effects [Howard PoP 2016] may be less important in I-mode than in L-mode. New results presented here, however, show that global, nonlinear, ion-scale GYRO simulations are able to match the experimental ion heat flux, but underpredict electron heat flux (at most radii), electron temperature fluctuations, and perturbative thermal diffusivity in both L- and I-mode. Linear addition of electron heat flux from electron scale runs does not resolve this discrepancy. These results indicate that single-scale simulations do not sufficiently describe the I-mode core transport, and that multi-scale (coupled electron- and ion-scale) transport models are needed. A preliminary investigation with multi-scale TGLF, however, was unable to resolve the discrepancy between ion-scale GYRO and experimental electron heat fluxes and perturbative diffusivity, motivating further work with multi-scale GYRO simulations and a more comprehensive study with multi-scale TGLF.
Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas (GPS - TTBP) Final Report
Chame, Jacqueline
2011-05-27
The goal of this project is the development of the Gyrokinetic Toroidal Code (GTC) Framework and its applications to problems related to the physics of turbulence and turbulent transport in tokamaks,. The project involves physics studies, code development, noise effect mitigation, supporting computer science efforts, diagnostics and advanced visualizations, verification and validation. Its main scientific themes are mesoscale dynamics and non-locality effects on transport, the physics of secondary structures such as zonal flows, and strongly coherent wave-particle interaction phenomena at magnetic precession resonances. Special emphasis is placed on the implications of these themes for rho-star and current scalings and for the turbulent transport of momentum. GTC-TTBP also explores applications to electron thermal transport, particle transport; ITB formation and cross-cuts such as edge-core coupling, interaction of energetic particles with turbulence and neoclassical tearing mode trigger dynamics. Code development focuses on major initiatives in the development of full-f formulations and the capacity to simulate flux-driven transport. In addition to the full-f -formulation, the project includes the development of numerical collision models and methods for coarse graining in phase space. Verification is pursued by linear stability study comparisons with the FULL and HD7 codes and by benchmarking with the GKV, GYSELA and other gyrokinetic simulation codes. Validation of gyrokinetic models of ion and electron thermal transport is pursed by systematic stressing comparisons with fluctuation and transport data from the DIII-D and NSTX tokamaks. The physics and code development research programs are supported by complementary efforts in computer sciences, high performance computing, and data management.
Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics
Yu Lin; Xueyi Wang; Liu Chen; Zhihong Lin
2009-08-11
Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence test
NASA Astrophysics Data System (ADS)
Bañón Navarro, A.; Bardóczi, L.; Carter, T. A.; Jenko, F.; Rhodes, T. L.
2017-03-01
Neoclassical tearing modes have deleterious effects on plasma confinement and, if they grow large enough, they can lead to discharge termination. Therefore, they impose a major barrier in the development of operating scenarios of present-day tokamaks. Gyrokinetics offers a path toward studying multi-scale interactions with turbulence and the effect on plasma confinement. As a first step toward this goal, we have implemented static magnetic islands in nonlinear gyrokinetic simulations with the GENE code. We investigate the effect of the islands on profiles, flows, turbulence and transport and the scaling of these effects with respect to island size. We find a clear threshold island width, below which the islands have little or no effect while beyond this point the islands significantly perturb flows, increase turbulence and transport. Additionally, we study the effect of radially asymmetric islands on shear flows for the first time. We find that island induced shear flows can regulate turbulent fluctuation levels in the vicinity of the island separatrices. Throughout this work, we focus on experimentally relevant quantities, such as rms levels of density and electron temperature fluctuations, as well as amplitude and phasing of turbulence modulation. These simulations aim to provide guidelines for interpreting experimental results by comparing qualitative trends in the simulations with those obtained in tokamak experiments.
Gyrokinetic GDC turbulence simulations: confirming a new instability regime in LAPD plasmas
NASA Astrophysics Data System (ADS)
Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.
2016-10-01
Recent high-beta experiments at the LArge Plasma Device have found significant parallel magnetic fluctuations in the region of large pressure gradients. Linear gyrokinetic simulations show the dominant instability at these radii to be the gradient-driven drift coupling (GDC) mode, a non-textbook mode driven by pressure gradients and destabilized by the coupling of ExB and grad-B∥ drifts. Unlike in previous studies, the large parallel extent of the device allows for finite-kz versions of this instability in addition to kz = 0 . The locations of maximum linear growth match very well with experimentally observed peaks of B∥ fluctuations. Local nonlinear simulations reproduce many features of the observations fairly well, with the exception of Bperp fluctuations, for which experimental profiles suggest a source unrelated to pressure gradients. In toto, the results presented here show that turbulence and transport in these experiments are driven by the GDC instability, that important characteristics of the linear instability carry over to nonlinear simulations, and - in the context of validation - that the gyrokinetic framework performs surprisingly well far outside its typical area of application, increasing confidence in its predictive abilities. Supported by U.S. DOE.
Advances in stellarator gyrokinetics
NASA Astrophysics Data System (ADS)
Helander, P.; Bird, T.; Jenko, F.; Kleiber, R.; Plunk, G. G.; Proll, J. H. E.; Riemann, J.; Xanthopoulos, P.
2015-05-01
Recent progress in the gyrokinetic theory of stellarator microinstabilities and turbulence simulations is summarized. The simulations have been carried out using two different gyrokinetic codes, the global particle-in-cell code EUTERPE and the continuum code GENE, which operates in the geometry of a flux tube or a flux surface but is local in the radial direction. Ion-temperature-gradient (ITG) and trapped-electron modes are studied and compared with their counterparts in axisymmetric tokamak geometry. Several interesting differences emerge. Because of the more complicated structure of the magnetic field, the fluctuations are much less evenly distributed over each flux surface in stellarators than in tokamaks. Instead of covering the entire outboard side of the torus, ITG turbulence is localized to narrow bands along the magnetic field in regions of unfavourable curvature, and the resulting transport depends on the normalized gyroradius ρ* even in radially local simulations. Trapped-electron modes can be significantly more stable than in typical tokamaks, because of the spatial separation of regions with trapped particles from those with bad magnetic curvature. Preliminary non-linear simulations in flux-tube geometry suggest differences in the turbulence levels in Wendelstein 7-X and a typical tokamak.
Storelli, A. Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Singh, Rameswar; Morel, P.; Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Grandgirard, V.; Ghendrih, P.; Görler, T.
2015-06-15
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
NASA Astrophysics Data System (ADS)
Storelli, A.; Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Görler, T.; Singh, Rameswar; Morel, P.; Grandgirard, V.; Ghendrih, P.
2015-06-01
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
Gyrokinetic simulations of momentum transport and fluctuation spectra for ICRF-heated L-Mode plasmas
NASA Astrophysics Data System (ADS)
Sierchio, J. M.; White, A. E.; Howard, N. T.; Sung, C.; Ennever, P.; Porkolab, M.; Candy, J.
2014-10-01
We examine ICRF-heated L-mode plasmas in Alcator C-Mod, with differing momentum transport (hollow vs. peaked radial profiles of intrinsic toroidal rotation) but similar heat and particle transport. Nonlinear gyrokinetic simulations of heat and particle transport with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] have previously been compared with these experiments [White et al., Phys. Plasmas 20, 056106 (2013); Howard et al. PPCF submitted (2014)] as part of an effort to validate the gyrokinetic model for core turbulent transport in C-Mod plasmas. To further test the model for these plasmas, predicted core turbulence characteristics such as fluctuation spectra will be compared with experiment. Using synthetic diagnostics for the CECE, reflectometry, and PCI systems at C-Mod, synthetic spectra and, when applicable, fluctuation amplitudes, are generated. We compare these generated results with fluctuation measurements from the experiment. We also report the momentum transport results from simulations of these plasmas and compare them to experiment. Supported by USDoE award DE-FC02-99ER54512.
Relevance of the parallel nonlinearity in gyrokinetic simulations of tokamak plasmas
Candy, J.; Waltz, R. E.; Parker, S. E.; Chen, Y.
2006-07-15
The influence of the parallel nonlinearity on transport in gyrokinetic simulations is assessed for values of {rho}{sub *} which are typical of current experiments. Here, {rho}{sub *}={rho}{sub s}/a is the ratio of gyroradius, {rho}{sub s}, to plasma minor radius, a. The conclusion, derived from simulations with both GYRO [J. Candy and R. E. Waltz, J. Comput. Phys., 186, 585 (2003)] and GEM [Y. Chen and S. E. Parker J. Comput. Phys., 189, 463 (2003)] is that no measurable effect of the parallel nonlinearity is apparent for {rho}{sub *}<0.012. This result is consistent with scaling arguments, which suggest that the parallel nonlinearity should be O({rho}{sub *}) smaller than the ExB nonlinearity. Indeed, for the plasma parameters under consideration, the magnitude of the parallel nonlinearity is a factor of 8{rho}{sub *} smaller (for 0.000 75<{rho}{sub *}<0.012) than the other retained terms in the nonlinear gyrokinetic equation.
NASA Astrophysics Data System (ADS)
Chen, Yang; Fu, Guo-Yong; Parker, Scott
2016-10-01
We report simulation of simultaneous excitation of multiple Reverse Shear Alfven eigenmodes in DIII-D plasmas (discharge #142111), using the gyrokinetic ion/fluid electron hybrid model of GEM. Thermal ions and beam ions are gyrokinetic, electrons are fluid with finite-mass correction in the Ohm's law. The vorticity equation is solved instead of the quasi-neutrality condition. This improves numerical stability. We extend previous single-n nonlinear simulation to simultaneous excitation of toroidal modes with n = 0 and 2 < n < 15 . Both the zonal n = 0 mode and the n = 8 mode are observed to be force driven by the linearly dominant n = 4 mode coupled to itself, with a growth rate twice that of the n = 4 mode. The zonal mode (including the surface averaged ϕ and A∥) significantly reduces the initial saturation level of the n = 4 mode. Evolution of all the other modes are also dominated by nonlinear coupling to the n = 4 mode. The mechanism of zonal structure generation will be examined by comparing various terms in the vorticity equation, including the Reynolds stress, the magnetic stress and the beam ion nonlinear effect.
Unlike-particle collision operator for gyrokinetic particle simulations
Kolesnikov, R.A.; Wang, W.X.; Hinton, F.L.
2010-08-01
Plasmas in modern tokamak experiments contain a significant fraction of impurity ion species in addition to main deuterium background. A new unlike-particle collision operator for {delta}f particle simulation has been developed to self-consistently study the non-local effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for simulation of cross-collisions between different ion species includes test-particle and conserving field-particle operators. The field-particle operator is designed to enforce conservation of number, momentum and energy. It was shown that the new operator correctly simulates the thermal equilibration of different plasma components. It was verified that the ambipolar radial electric field reaches steady state when the total radial guiding center particle current vanishes.
Monte-Carlo finite elements gyrokinetic simulations of Alfven modes in tokamaks
NASA Astrophysics Data System (ADS)
Bottino, Alberto; Biancalani, Alessandro; Palermo, Francesco; Tronko, Natalia
2016-10-01
The global gyrokinetic code ORB5 can simultaneously include electromagnetic perturbations, general ideal MHD axisymmetric equilibria, zonal-flow preserving sources, collisions, and the ability to solve the full core plasma including the magnetic axis. In this work, a Monte Carlo Particle In Cell Finite Element model, starting from a gyrokinetic discrete Lagrangian, is derived and implemented into the ORB5 code. The variations of the Lagrangian are used to obtain the time continuous equations of motion for the particles and the Finite Element approximation of the field equations. The Noether theorem for the semi-discretised system, implies a certain number of conservation properties for the final set of equation. Linear and nonlinear results, concerning Alfvén instabilities, in the presence of an energetic particle population, and microinstabilities, such as electromagnetic ion temperature gradient (ITG) driven modes and kinetic ballooning modes (KBM), will be presented and discussed. Due to losses of energetic particles, Alfvén instabilities can not only affect plasma stability and damage the walls, but also strongly impact the heating efficiency of a fusion reactor and ultimately the possibility of reaching ignition.
Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence
Nevins, W M; Wang, E; Candy, J
2010-02-12
Analysis of the magnetic field structure from electromagnetic simulations of tokamak ion temperature gradient turbulence demonstrates that the magnetic field can be stochastic even at very low plasma pressure. The degree of magnetic stochasticity is quantified by evaluating the magnetic diffusion coefficient. We find that the magnetic stochasticity fails to produce a dramatic increase in the electron heat conductivity because the magnetic diffusion coefficient remains small.
Gyrokinetics Simulation of Energetic Particle Turbulence and Transport
Diamond, Patrick H.
2011-09-21
Progress in research during this year elucidated the physics of precession resonance and its interaction with radial scattering to form phase space density granulations. Momentum theorems for drift wave-zonal flow systems involving precession resonance were derived. These are directly generalizable to energetic particle modes. A novel nonlinear, subcritical growth mechanism was identified, which has now been verified by simulation. These results strengthen the foundation of our understanding of transport in burning plasmas
NASA Astrophysics Data System (ADS)
Oberparleiter, M.; Jenko, F.; Told, D.; Doerk, H.; Görler, T.
2016-04-01
Neoclassical and turbulent transport in tokamaks has been studied extensively over the past decades, but their possible interaction remains largely an open question. The two are only truly independent if the length scales governing each of them are sufficiently separate, i.e., if the ratio ρ* between ion gyroradius and the pressure gradient scale length is small. This is not the case in particularly interesting regions such as transport barriers. Global simulations of a collisional ion-temperature-gradient-driven microturbulence performed with the nonlinear global gyrokinetic code Gene are presented. In particular, comparisons are made between systems with and without neoclassical effects. In fixed-gradient simulations, the modified radial electric field is shown to alter the zonal flow pattern such that a significant increase in turbulent transport is observed for ρ*≳1 /300 . Furthermore, the dependency of the flux on the collisionality changes. In simulations with fixed power input, we find that the presence of neoclassical effects decreases the frequency and amplitude of intermittent turbulent transport bursts (avalanches) and thus plays an important role for the self-organisation behaviour.
NASA Astrophysics Data System (ADS)
White, A. E.; Howard, N. T.; Mikkelsen, D. R.; Greenwald, M.; Candy, J.; Waltz, R. E.
2011-11-01
This paper describes the use of nonlinear gyrokinetic simulations to assess the feasibility of a new correlation electron cyclotron emission (CECE) diagnostic that has been proposed for the Alcator C-Mod tokamak (Marmar et al 2009 Nucl. Fusion 49 104014). This work is based on a series of simulations performed with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545). The simulations are used to predict ranges of fluctuation level, peak poloidal wavenumber and radial correlation length of electron temperature fluctuations in the core of the plasma. The impact of antenna pattern and poloidal viewing location on measurable turbulence characteristics is addressed using synthetic diagnostics. An upper limit on the CECE sample volume size is determined. The modeling results show that a CECE diagnostic capable of measuring transport-relevant, long-wavelength (kθρs < 0.5) electron temperature fluctuations is feasible at Alcator C-Mod.
Gyrokinetic simulation of turbulence driven geodesic acoustic modes in edge plasmas of HL-2A tokamak
Liu Feng; Zhao, K. J.; Lin, Z.; Dong, J. Q.
2010-11-15
Strong correlation between high frequency microturbulence and low frequency geodesic acoustic mode (GAM) has been observed in the edge plasmas of the HL-2A tokamak, suggesting possible GAM generation via three wave coupling with turbulence, which is in turn modulated by the GAM. In this work, we use the gyrokinetic toroidal code to study the linear and nonlinear development of the drift instabilities, as well as the generation of the GAM (and low frequency zonal flows) and its interaction with the turbulence for realistic parameters in the edge plasmas of the HL-2A tokamak for the first time. The simulation results indicate that the unstable drift wave drives strong turbulence in the edge plasma of HL-2A. In addition, the generation of the GAM and its interaction with the turbulence are all observed in the nonlinear simulation. The simulation results are in reasonable agreement with the experimental observations.
Multi-scale gyrokinetic simulation of Alcator C-Mod tokamak discharges
NASA Astrophysics Data System (ADS)
Howard, N. T.; White, A. E.; Greenwald, M.; Holland, C.; Candy, J.
2014-03-01
Alcator C-Mod tokamak discharges have been studied with nonlinear gyrokinetic simulation simultaneously spanning both ion and electron spatiotemporal scales. These multi-scale simulations utilized the gyrokinetic model implemented by GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and the approximation of reduced electron mass (μ = (mD/me).5 = 20.0) to qualitatively study a pair of Alcator C-Mod discharges: a low-power discharge, previously demonstrated (using realistic mass, ion-scale simulation) to display an under-prediction of the electron heat flux and a high-power discharge displaying agreement with both ion and electron heat flux channels [N. T. Howard et al., Nucl. Fusion 53, 123011 (2013)]. These multi-scale simulations demonstrate the importance of electron-scale turbulence in the core of conventional tokamak discharges and suggest it is a viable candidate for explaining the observed under-prediction of electron heat flux. In this paper, we investigate the coupling of turbulence at the ion (kθρs˜O(1.0)) and electron (kθρe˜O(1.0)) scales for experimental plasma conditions both exhibiting strong (high-power) and marginally stable (low-power) low-k (kθρs < 1.0) turbulence. It is found that reduced mass simulation of the plasma exhibiting marginally stable low-k turbulence fails to provide even qualitative insight into the turbulence present in the realistic plasma conditions. In contrast, multi-scale simulation of the plasma condition exhibiting strong turbulence provides valuable insight into the coupling of the ion and electron scales.
Multi-scale gyrokinetic simulation of Alcator C-Mod tokamak discharges
Howard, N. T. White, A. E.; Greenwald, M.; Holland, C.; Candy, J.
2014-03-15
Alcator C-Mod tokamak discharges have been studied with nonlinear gyrokinetic simulation simultaneously spanning both ion and electron spatiotemporal scales. These multi-scale simulations utilized the gyrokinetic model implemented by GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and the approximation of reduced electron mass (μ = (m{sub D}/m{sub e}){sup .5} = 20.0) to qualitatively study a pair of Alcator C-Mod discharges: a low-power discharge, previously demonstrated (using realistic mass, ion-scale simulation) to display an under-prediction of the electron heat flux and a high-power discharge displaying agreement with both ion and electron heat flux channels [N. T. Howard et al., Nucl. Fusion 53, 123011 (2013)]. These multi-scale simulations demonstrate the importance of electron-scale turbulence in the core of conventional tokamak discharges and suggest it is a viable candidate for explaining the observed under-prediction of electron heat flux. In this paper, we investigate the coupling of turbulence at the ion (k{sub θ}ρ{sub s}∼O(1.0)) and electron (k{sub θ}ρ{sub e}∼O(1.0)) scales for experimental plasma conditions both exhibiting strong (high-power) and marginally stable (low-power) low-k (k{sub θ}ρ{sub s} < 1.0) turbulence. It is found that reduced mass simulation of the plasma exhibiting marginally stable low-k turbulence fails to provide even qualitative insight into the turbulence present in the realistic plasma conditions. In contrast, multi-scale simulation of the plasma condition exhibiting strong turbulence provides valuable insight into the coupling of the ion and electron scales.
GYROKINETIC PARTICLE SIMULATION OF TURBULENT TRANSPORT IN BURNING PLASMAS
Horton, Claude Wendell
2014-06-10
The SciDAC project at the IFS advanced the state of high performance computing for turbulent structures and turbulent transport. The team project with Prof Zhihong Lin [PI] at Univ California Irvine produced new understanding of the turbulent electron transport. The simulations were performed at the Texas Advanced Computer Center TACC and the NERSC facility by Wendell Horton, Lee Leonard and the IFS Graduate Students working in that group. The research included a Validation of the electron turbulent transport code using the data from a steady state university experiment at the University of Columbia in which detailed probe measurements of the turbulence in steady state were used for wide range of temperature gradients to compare with the simulation data. These results were published in a joint paper with Texas graduate student Dr. Xiangrong Fu using the work in his PhD dissertation. X.R. Fu, W. Horton, Y. Xiao, Z. Lin, A.K. Sen and V. Sokolov, “Validation of electron Temperature gradient turbulence in the Columbia Linear Machine, Phys. Plasmas 19, 032303 (2012).
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Simulation of Finite-Beta Effects in Gyrokinetic Plasmas
NASA Astrophysics Data System (ADS)
Startsev, Edward; Lee, Wei-Li
2006-10-01
A generalization of the original split-weight scheme for finite-beta plasmas [W. W. Lee, J. Lewandowski, Z. Lin and T. S. Hahm, Phys. Plasmas 8, 4435 (2001)] to multi-dimensional plasmas is developed. The scheme is based on the concept of perturbative particle simulation, where only the non-adiabatic response of the electrons, δh, is followed in time, where δh = F- (1+ψ) F0, F is the electron dunstibution function, F0 is the background electron distribution function, ψ=φ+ Ad x/c, and φ and A are the perturbed potentials. The procedure involves the Poisson solvers for φ, A, φ/ t, A/t, and 2̂A/ t^2, which, in turn, need up zeroth, first, second and third velocity-space moments for input. The use of the scheme for turbulence and MHD studies [Lee and Qin, Phys. Plasmas 10, 3196 (2003)] will be presented.
Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas
Ma, Kwan-Liu
2011-12-21
In this project, we have developed techniques for visualizing large-scale time-varying multivariate particle and field data produced by the GPS_TTBP team. Our basic approach to particle data visualization is to provide the user with an intuitive interactive interface for exploring the data. We have designed a multivariate filtering interface for scientists to effortlessly isolate those particles of interest for revealing structures in densely packed particles as well as the temporal behaviors of selected particles. With such a visualization system, scientists on the GPS-TTBP project can validate known relationships and temporal trends, and possibly gain new insights in their simulations. We have tested the system using over several millions of particles on a single PC. We will also need to address the scalability of the system to handle billions of particles using a cluster of PCs. To visualize the field data, we choose to use direct volume rendering. Because the data provided by PPPL is on a curvilinear mesh, several processing steps have to be taken. The mesh is curvilinear in nature, following the shape of a deformed torus. Additionally, in order to properly interpolate between the given slices we cannot use simple linear interpolation in Cartesian space but instead have to interpolate along the magnetic field lines given to us by the scientists. With these limitations, building a system that can provide an accurate visualization of the dataset is quite a challenge to overcome. In the end we use a combination of deformation methods such as deformation textures in order to fit a normal torus into their deformed torus, allowing us to store the data in toroidal coordinates in order to take advantage of modern GPUs to perform the interpolation along the field lines for us. The resulting new rendering capability produces visualizations at a quality and detail level previously not available to the scientists at the PPPL. In summary, in this project we have
Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas
Diamond, P.H.; Lin, Z.; Wang, W.; Horton, W.; Klasky, S.; Decyk, V.; Ma, K.-L.; Chames, J.; Adams, M.
2011-09-21
The three-year project GPS-TTBP resulted in over 152 publications and 135 presentations. This summary focuses on the scientific progress made by the project team. A major focus of the project was on the physics intrinsic rotation in tokamaks. Progress included the first ever flux driven study of net intrinsic spin-up, mediated by boundary effects (in collaboration with CPES), detailed studies of the microphysics origins of the Rice scaling, comparative studies of symmetry breaking mechanisms, a pioneering study of intrinsic torque driven by trapped electron modes, and studies of intrinsic rotation generation as a thermodynamic engine. Validation studies were performed with C-Mod, DIII-D and CSDX. This work resulted in very successful completion of the FY2010 Theory Milestone Activity for OFES, and several prominent papers of the 2008 and 2010 IAEA Conferences. A second major focus was on the relation between zonal flow formation and transport non-locality. This culminated in the discovery of the ExB staircase - a conceptually new phenomenon. This also makes useful interdisciplinary contact with the physics of the PV staircase, well-known in oceans and atmospheres. A third topic where progress was made was in the simulation and theory of turbulence spreading. This work, now well cited, is important for understanding the dynamics of non-locality in turbulent transport. Progress was made in studies of conjectured non-diffusive transport in trapped electron turbulence. Pioneering studies of ITB formation, coupling to intrinsic rotation and hysteresis were completed. These results may be especially significant for future ITER operation. All told, the physics per dollar performance of this project was quite good. The intense focus was beneficial and SciDAC resources were essential to its success.
Gyrokinetic simulations of solar wind turbulence from ion to electron scales.
Howes, G G; TenBarge, J M; Dorland, W; Quataert, E; Schekochihin, A A; Numata, R; Tatsuno, T
2011-07-15
A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.
Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence
Angioni, C.; Candy, J.; Waltz, R. E.; Fable, E.; Maslov, M.; Weisen, H.; Peeters, A. G.
2009-06-15
The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor.
NASA Astrophysics Data System (ADS)
Yi, Sumin; Jhang, Hogun; Kwon, J. M.
2016-10-01
We report the results of a gyrokinetic simulation study elucidating the characteristics of the current driven by electron temperature gradient (ETG) turbulence in toroidal geometry. We examined the amount of the ETG turbulence-driven current for different turbulence levels, which were obtained by varying the relative electron gyroradius ρ* = ρe/a. Simulations show that the amount of the ETG turbulence-driven current increases with ρ* due to the gyro-Bohm scaling of turbulence intensity. A perturbation of the equilibrium q-profile by the ETG turbulence-driven current becomes noticeable when ρ* > 1/4000. Even in a small ρ* case, the proportional relation between the ETG turbulence-driven current and turbulence intensity suggests that a considerable intrinsic current can be driven inside an edge pedestal where a steep gradient of the electron temperature profile can excite ETG turbulence in a narrow region.
Chang, C S; Ku, Seung-Hoe; Diamond, P. H.; Adams, Mark; Tchoua, Roselyne B; Chen, Yang; Cummings, J.; D'Azevedo, Ed F; Dif-Pradalier, Guilhem; Ethier, Stephane; Greengard, Leslie; Hahm, Taik Soo; Hinton, Fred; Keyes, David E; Klasky, Scott A; Lin, Z.; Lofstead, J.; Park, G.; Podhorszki, Norbert; Schwan, Karsten; Shoshani, A.; Silver, D.; Wolf, M.; Worley, Patrick H; Zorin, Denis
2009-01-01
Performance prediction for ITER is based upon the ubiquitous experimental observation that the plasma energy confinement in the device core is strongly coupled to the edge confinement for an unknown reason. The coupling time-scale is much shorter than the plasma transport time-scale. In order to understand this critical observation, a multi-scale turbulence-neoclassical simulation of integrated edge-core plasma in a realistic diverted geometry is a necessity, but has been a formidable task. Thanks to the recent development in high performance computing, we have succeeded in the integrated multiscale gyrokinetic simulation of the ion-temperature-gradient driven turbulence in realistic diverted tokamak geometry for the first time. It is found that modification of the self-organized criticality in the core plasma by nonlocal core-edge coupling of ITG turbulence can be responsible for the core-edge confinement coupling.
NASA Astrophysics Data System (ADS)
Chang, C. S.; Ku, S.; Diamond, P.; Adams, M.; Barreto, R.; Chen, Y.; Cummings, J.; D'Azevedo, E.; Dif-Pradalier, G.; Ethier, S.; Greengard, L.; Hahm, T. S.; Hinton, F.; Keyes, D.; Klasky, S.; Lin, Z.; Lofstead, J.; Park, G.; Parker, S.; Podhorszki, N.; Schwan, K.; Shoshani, A.; Silver, D.; Wolf, M.; Worley, P.; Weitzner, H.; Yoon, E.; Zorin, D.
2009-07-01
Performance prediction for ITER is based upon the ubiquitous experimental observation that the plasma energy confinement in the device core is strongly coupled to the edge confinement for an unknown reason. The coupling time-scale is much shorter than the plasma transport time-scale. In order to understand this critical observation, a multi-scale turbulence-neoclassical simulation of integrated edge-core plasma in a realistic diverted geometry is a necessity, but has been a formidable task. Thanks to the recent development in high performance computing, we have succeeded in the integrated multiscale gyrokinetic simulation of the ion-temperature-gradient driven turbulence in realistic diverted tokamak geometry for the first time. It is found that modification of the self-organized criticality in the core plasma by nonlocal core-edge coupling of ITG turbulence can be responsible for the core-edge confinement coupling.
Combining electromagnetic gyro-kinetic particle-in-cell simulations with collisions
NASA Astrophysics Data System (ADS)
Slaby, Christoph; Kleiber, Ralf; Könies, Axel
2017-09-01
It has been an open question whether for electromagnetic gyro-kinetic particle-in-cell (PIC) simulations pitch-angle collisions and the recently introduced pullback transformation scheme (Mishchenko et al., 2014; Kleiber et al., 2016) are consistent. This question is positively answered by comparing the PIC code EUTERPE with an approach based on an expansion of the perturbed distribution function in eigenfunctions of the pitch-angle collision operator (Legendre polynomials) to solve the electromagnetic drift-kinetic equation with collisions in slab geometry. It is shown how both approaches yield the same results for the frequency and damping rate of a kinetic Alfvén wave and how the perturbed distribution function is substantially changed by the presence of pitch-angle collisions.
NASA Astrophysics Data System (ADS)
Chang, C. S.; Ku, S.; Tynan, G. R.; Hager, R.; Churchill, R. M.; Cziegler, I.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.
2017-04-01
Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a realistic diverted tokamak edge geometry under strong forcing by a high rate of heat deposition. The results show that turbulent Reynolds-stress-driven sheared E ×B flows act in concert with neoclassical orbit loss to quench turbulent transport and form a transport barrier just inside the last closed magnetic flux surface.
Finite-β Split-weight Gyrokinetic Particle Simulation of Microinstabilities
NASA Astrophysics Data System (ADS)
Jenkins, Thomas G.; Lee, W. W.; Lewandowski, J. L. V.
2003-10-01
The finite-β split-weight gyrokinetic particle simulation scheme [1] has been implemented in two-dimensional slab geometry for the purpose of studying the effects of high temperature electrons on microinstabilities. Drift wave instabilities and ion temperature gradient modes are studied in both shearless slab and sheared slab geometries. The linear and nonlinear evolution of these modes, as well as the physics of microtearing, is compared with the results of Reynders [2] and Cummings [3]. [1] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Phys. Plasmas 8, 4435 (2001). [2] J. V. W. Reynders, Ph.D. thesis, Princeton University (1992). [3] J. C. Cummings, Ph.D. thesis, Princeton University (1995).
Chang, C. S.; Ku, S.; Tynan, G. R.; ...
2017-04-25
Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a realistic diverted tokamak edge geometry under strong forcing by a high rate of heat deposition. Here, the results show that turbulent Reynolds-stress-driven sheared E x B flows act in concert with neoclassical orbit loss to quench turbulent transport and formmore » a transport barrier just inside the last closed magnetic flux surface.« less
NASA Astrophysics Data System (ADS)
Dong, Ge; Bao, Jian; Bhattacharjee, Amitava; Brizard, Alain; Lin, Zhihong; Porazik, Peter
2017-08-01
The compressional component of magnetic perturbation δ B ∥ can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma β increases (β is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating δ B ∥ , and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when δ B ∥ is neglected for β e = 0.02 , and that δ B ∥ has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. The KBM growth rate decreases about 15% when equilibrium current is neglected.
Gyrokinetic simulation of I-mode C-Mod pedestal using GENE
NASA Astrophysics Data System (ADS)
Liu, Xing; David, H.; Kotschenreuther, M.; Mahajan, S.; Huges, J.; Hubbard, A.; Valanju, P.
2016-10-01
Naturally stable to ELMs, and with widths larger than EPED predictions, the I-modes are an excellent laboratory for investigating the role of drift microinstabilities in pedestal formation since I-mode pedestal are not ``limited'' by MHD instabilities-Peeling Ballooning or the Kinetic Ballooning. Because the Weakly Coherent Mode (WCM) is shown to be correlated, primarily, to particle transport, the pedestal heat transport, in some sense, must be controlled by drift-type modes. We present here a study based on gyrokinetic simulations (using GENE) to model heat transport in the I-mode pedestals in C-Mod. Nonlinear ETG simulations, found to be streamer-dominated, can match experimental heat flux with profile adjustment well within experimental error bars. The ETG simulations reveal very notable fine-scale structure (in the parallel direction) of the eigenfunctions in both linear and nonlinear simulations. Simulations, varying impurity level (Zeff) and temperature and density profiles (within experimental error bars), are used to probe the sensitivity of ETG heat transport to the most important input parameters. Efforts to identify an instability corresponding to the WCM will also be discussed. Work supported by USDOE Grant DE-FG02-04ER54742.
NASA Astrophysics Data System (ADS)
Sung, C.; White, A. E.; Mikkelsen, D. R.; Greenwald, M.; Holland, C.; Howard, N. T.; Churchill, R.; Theiler, C.
2016-04-01
Long wavelength turbulent electron temperature fluctuations (kyρs < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (kyρs ≲ 1.7) performed at r/a ˜ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the "Transport Shortfall" [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
Sung, C.; White, A. E.; Greenwald, M.; Howard, N. T.; Mikkelsen, D. R.; Churchill, R.; Holland, C.; Theiler, C.
2016-04-15
Long wavelength turbulent electron temperature fluctuations (k{sub y}ρ{sub s} < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (k{sub y}ρ{sub s} ≲ 1.7) performed at r/a ∼ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
White, A. E.; Schmitz, L.; Peebles, W. A.; Carter, T. A.; Doyle, E. J.; Rhodes, T. L.; Wang, G.; McKee, G. R.; Shafer, M. W.; Holland, C.; Tynan, G. R.; Austin, M. E.; Burrell, K. H.; Candy, J.; DeBoo, J. C.; Prater, R.; Staebler, G. M.; Waltz, R. E.; Makowski, M. A.
2008-05-15
For the first time, profiles (0.3<{rho}<0.9) of electron temperature and density fluctuations in a tokamak have been measured simultaneously and the results compared to nonlinear gyrokinetic simulations. Electron temperature and density fluctuations measured in neutral beam-heated, sawtooth-free low confinement mode (L-mode) plasmas in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] are found to be similar in frequency and normalized amplitude, with amplitude increasing with radius. The measured radial profile of two fluctuation fields allows for a new and rigorous comparison with gyrokinetic results. Nonlinear gyrokinetic flux-tube simulations predict that electron temperature and density fluctuations have similar normalized amplitudes in L-mode. At {rho}=0.5, simulation results match experimental heat diffusivities and density fluctuation amplitude, but overestimate electron temperature fluctuation amplitude and particle diffusivity. In contrast, simulations at {rho}=0.75 do not match either the experimentally derived transport properties or the measured fluctuation levels.
Continuum Gyrokinetic Simulations of Turbulence in Open-Field-Line Plasmas
NASA Astrophysics Data System (ADS)
Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.; Hakim, A.
2016-10-01
We have performed our first 3D2V gyrokinetic simulations of electrostatic plasma turbulence in open-field-line geometries using the full-F discontinuous-Galerkin code Gkeyll. These simulations include the basic elements of a scrape-off layer: localized sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath boundary conditions. The set of boundary conditions used in our model allows currents to flow through the walls and satisfies energy conservation. In addition to details of our numerical approach, we will present results from flux-tube simulations of devices containing straight-field lines (such as LAPD) and helical-field-lines (such as the TORPEX simple magnetized torus). Preliminary results show turbulent fluctuation levels similar to fluid simulations, which are comparable to the observed fluctuation level in LAPD but somewhat smaller than observed in TORPEX. This research was supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and U.S. DOE contract DE-AC02-09CH11466.
NASA Astrophysics Data System (ADS)
Toda, S.; Nakata, M.; Nunami, M.; Ishizawa, A.; Watanabe, T.-H.; Sugama, H.
2016-10-01
A reduced model of the turbulent ion heat diffusivity is proposed by the gyrokinetic simulation code (GKV-X) with the adiabatic electrons for the high-Ti Large Helical Device discharge. The plasma parameter region of the short poloidal wavelength is studied, where the ion temperature gradient mode becomes unstable. The ion heat diffusivity by the nonlinear simulation with the kinetic electrons is found to be several times larger than the simulation results using the adiabatic electrons in the radial region 0.46 <= r / a <= 0.80 . The electromagnetic contribution is about a several percent in the ion energy flux. The model of the turbulent diffusivity is derived as the function of the squared electrostatic potential fluctuation and the squared zonal flow potential. Next, the squared electrostatic potential fluctuation is approximated with the mixing length estimate. The squared zonal flow potential fluctuation is shown as the linear zonal flow response function. The reduced model of the turbulent diffusivity is derived as the function of the physical parameters by the linear GKV-X simulation with the kinetic electrons. This reduced model is applied to the transport code with the same procedure as.
Double-weight scheme for gyrokinetic simulation of electromagnetic instabilities in tokamaks
NASA Astrophysics Data System (ADS)
Startsev, Edward; Lee, Wei-Li; Wang, Weixing; Lu, Zhixin
2016-10-01
An application of recently developed perturbative particle simulation scheme for finite- β plasmas in the presence of background inhomogeneities is presented. The scheme uses two delta-f weights carried by each particle to represent particles density and pressure. Use of separate weight to represent particle pressure allows to alleviate cancelation problem in finite- β gyrokinetic simulations with fully kinetic electrons. Recently, we have successfully used the new double-weight scheme for simulation of linear tearing and drift-tearing modes, in both collisionless semi-collisional regimes in sheared slab and high-aspect ratio cylindrical cross-section tokamak geometries. Here, we present further development of this scheme which now includes effects of magnetic drifts for the simulation of linear semi-collisional micro-tearing (MTM) and kinetic ballooning (KBM) modes in realistic aspect ratio cylindrical cross-section tokamak using the modified turbulence code GTS. Work supported by U.S. DOE Contract DE-AC02-09-CH11466.
NASA Astrophysics Data System (ADS)
Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team
2016-10-01
The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.
NASA Astrophysics Data System (ADS)
Howard, N. T.; Holland, C.; White, A. E.; Greenwald, M.; Candy, J.; Creely, A. J.
2016-05-01
To better understand the role of cross-scale coupling in experimental conditions, a series of multi-scale gyrokinetic simulations were performed on Alcator C-Mod, L-mode plasmas. These simulations, performed using all experimental inputs and realistic ion to electron mass ratio ((mi/me)1/2 = 60.0), simultaneously capture turbulence at the ion ( kθρs˜O (1.0 ) ) and electron-scales ( kθρe˜O (1.0 ) ). Direct comparison with experimental heat fluxes and electron profile stiffness indicates that Electron Temperature Gradient (ETG) streamers and strong cross-scale turbulence coupling likely exist in both of the experimental conditions studied. The coupling between ion and electron-scales exists in the form of energy cascades, modification of zonal flow dynamics, and the effective shearing of ETG turbulence by long wavelength, Ion Temperature Gradient (ITG) turbulence. The tightly coupled nature of ITG and ETG turbulence in these realistic plasma conditions is shown to have significant implications for the interpretation of experimental transport and fluctuations. Initial attempts are made to develop a "rule of thumb" based on linear physics, to help predict when cross-scale coupling plays an important role and to inform future modeling of experimental discharges. The details of the simulations, comparisons with experimental measurements, and implications for both modeling and experimental interpretation are discussed.
Chen, Yang
2012-03-07
At Colorado University-Boulder the primary task is to extend our gyrokinetic Particle-in-Cell simulation of tokamak micro-turbulence and transport to the area of energetic particle physics. We have implemented a gyrokinetic ion/massless fluid electron hybrid model in the global {delta} f-PIC code GEM, and benchmarked the code with analytic results on the thermal ion radiative damping rate of Toroidal Alfven Eigenmodes (TAE) and with mode frequency and spatial structure from eigenmode analysis. We also performed nonlinear simulations of both a single-n mode (n is the toroidal mode number) and multiple-n modes, and in the case of single-n, benchmarked the code on the saturation amplitude vs. particle collision rate with analytical theory. Most simulations use the f method for both ions species, but we have explored the full-f method for energetic particles in cases where the burst amplitude of the excited instabilities is large as to cause significant re-distribution or loss of the energetic particles. We used the hybrid model to study the stability of high-n TAEs in ITER. Our simulations show that the most unstable modes in ITER lie in the rage of 10 < n < 20. Thermal ion pressure effect and alpha particles non-perturbative effect are important in determining the mode radial location and stability threshold. The thermal ion Landau damping rate and radiative damping rate from the simulations are compared with analytical estimates. The thermal ion Landau damping is the dominant damping mechanism. Plasma elongation has a strong stabilizing effect on the alpha driven TAEs. The central alpha particle pressure threshold for the most unstable n=15 mode is about {beta}{sub {alpha}}(0) = 0.7% for the fully shaped ITER equilibrium. We also carried nonlinear simulations of the most unstable n = 15 mode and found that the saturation amplitude for the nominal ITER discharge is too low to cause large redistribution or loss of alpha particles. To include kinetic electron effects
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Waelbroeck, F. L.
2012-03-01
Static external resonant magnetic field perturbations (RMPs) have been added to the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comp. Phys. 186, 545 (2003)]. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr, and the corresponding j→×B→ plasma torque (density) R[jrBp/c], induced by magnetic islands that break the toroidal symmetry of a tokamak. This extends the previous GYRO formulation for the transport of toroidal angular momentum (TAM) [R. E. Waltz, G. M. Staebler, J. Candy, and F. L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)]. The focus is on electrostatic full torus radial slice simulations of externally induced q =m/n=6/3 islands with widths 5% of the minor radius or about 20 ion gyroradii. Up to moderately strong E ×B rotation, the island torque scales with the radial electric field at the resonant surface Er, the island width w, and the intensity I of the high-n micro-turbulence, as Erw√I . The radial current inside the island is carried (entirely in the n =3 component) and almost entirely by the ion E ×B flux, since the electron E ×B and magnetic flutter particle fluxes are cancelled. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that while the expected magnetic braking of the toroidal plasma rotation occurs at strong co- and counter-current rotation, at null toroidal rotation, there is a small co-directed magnetic acceleration up to the small diamagnetic (ion pressure gradient driven) co-rotation corresponding to the zero Er and null torque. This could be called the residual stress from an externally induced island. At zero Er, the only effect is the expected partial flattening of the electron temperature gradient within the island. Finite-beta GYRO simulations demonstrate almost complete RMP field screening and n =3 mode unlocking at strong Er.
Hybrid simulations of the interaction of hot gyrokinetic particles with MHD waves
Belova, E.V.; Denton, R.E.; Hudson, M.K.; Chan, A.A.
1996-12-31
A self-consistent study of the interaction of energetic ions with low-frequency MHD waves is performed using hybrid MHD-gyrokinetic particle simulations. In particular, the excitation of magnetospheric hydromagnetic waves by magnetic drift-bounce resonance with energetic ring current ions is investigated. In the model, energetic ions are treated as gyrokinetic particles using fully electromagnetic gyro-center equations, while the cold background plasma is treated as a fluid. The particles are coupled to the fluid equations through their current which appear in the bulk plasma momentum equation: where {rho}{sub b}, V{sub b} and p{sub b} are bulk plasma density, velocity and pressure, n{sub h} and j{sub h} axe hot ion density and current density. Other equations for the bulk plasma axe that of the MHD equations including E = - V{sub b} x B/c. It is assumed that n{sub h} {much_lt} n{sub b}. Spatial gyroaveraging in the gyro-center equations of motion as well as transformation to physical space axe performed by using four or eight point gyroangle distribution, in order to include the finite Larmor radius effects. In test runs, good conservation of the total energy was obtained and the finite Larmor radius effects were well reproduced for k{sub {perpendicular}}{rho}{sub h} {approximately} 1. Since magnetic drift-bounce resonant instability is driven by radial pressure gradients and requires resonance between azimuthal ion drift motion and bounce motion along magnetic field line, 3-D simulations are necessary for its investigation. The use of a multiple spatial scale expansion method enables to separate the equilibrium spatial scale lengths from those of the perturbations. In this case the zero-order ion pressure and magnetic field gradients become input parameters for the 2-D simulation. The 2-D numerical model with fixed background inhomogeneity was developed and it is used to study the drift-bounce resonant instability in 2-D box geometry.
NASA Astrophysics Data System (ADS)
Xu, Yingfeng; Ye, Lei; Dai, Zongliang; Xiao, Xiaotao; Wang, Shaojie
2017-08-01
The electrostatic gyrokinetic nonlinear turbulence code NLT, which is based on a numerical Lie-transform perturbation method, is developed. For improving the computational efficiency and avoiding the numerical instabilities, field-aligned coordinates and a Fourier filter are adopted in the NLT code. Nonlinear tests of the ion temperature gradient driven turbulence with adiabatic electrons are performed for verifying the NLT code by comparing with other gyrokinetic codes. The time evolution of the ion heat diffusivity and the relation between the ion heat diffusivity and the ion temperature gradient are compared in the nonlinear tests. Good agreements are achieved from the nonlinear benchmarks between the NLT code and other codes. The mode structures of the perturbed electric potential representing different phases have been simulated.
Gyrokinetic Particle Simulation of Compressible Electromagnetic Turbulence in High-β Plasmas
Lin, Zhihong
2014-03-13
Supported by this award, the PI and his research group at the University of California, Irvine (UCI) have carried out computational and theoretical studies of instability, turbulence, and transport in laboratory and space plasmas. Several massively parallel, gyrokinetic particle simulation codes have been developed to study electromagnetic turbulence in space and laboratory plasmas. In space plasma projects, the simulation codes have been successfully applied to study the spectral cascade and plasma heating in kinetic Alfven wave turbulence, the linear and nonlinear properties of compressible modes including mirror instability and drift compressional mode, and the stability of the current sheet instabilities with finite guide field in the context of collisionless magnetic reconnection. The research results have been published in 25 journal papers and presented at many national and international conferences. Reprints of publications, source codes, and other research-related information are also available to general public on the PI’s webpage (http://phoenix.ps.uci.edu/zlin/). Two PhD theses in space plasma physics are highlighted in this report.
Bounce-Averaged Gyrokinetic Simulation of Current-Collection Feedback in a Laboratory Magnetosphere
NASA Astrophysics Data System (ADS)
Roberts, T. M.; Garnier, D.; Kesner, J.; Mauel, M. E.
2014-10-01
A self-consistent, nonlinear simulation of interchange dynamics including the bounce-averaged gyro-kinetics of trapped electrons was previously used to understand frequency sweeping and the turbulent cascades observed in dipole-confined plasmas. Through adjustment of the particle and heat sources this code reproduces dynamics that resemble the turbulence measured experimentally, both in spectral power-law trends and in the onset of a steepened density profile. Time stepping is performed in an explicit leap-frog manner and a flux-corrected transport algorithm is implemented. In this presentation, we discuss the physics and numerical methods of the simulations as well as plans for including the effects of a biasing electrode which can collect or inject electrons. By varying this source/sink of electrons at the electrode location based on the potential fluctuations occurring elsewhere, we study the effects of current-collection feedback to compare to recent experiments observed to regulate interchange turbulence. Supported by NSF-DOE Partnership for Plasma Science and DOE Grant DE-FG02-00ER54585 and NSF Award PHY-1201896.
Pedestal and edge electrostatic turbulence characteristics from an XGC1 gyrokinetic simulation
NASA Astrophysics Data System (ADS)
Churchill, R. M.; Chang, C. S.; Ku, S.; Dominski, J.
2017-10-01
Understanding the multi-scale neoclassical and turbulence physics in the edge region (pedestal + scrape-off layer (SOL)) is required in order to reliably predict performance in future fusion devices. We explore turbulent characteristics in the edge region from a multi-scale neoclassical and turbulent XGC1 gyrokinetic simulation in a DIII-D like tokamak geometry, here excluding neutrals and collisions. For an H-mode type plasma with steep pedestal, it is found that the electron density fluctuations increase towards the separatrix, and stay high well into the SOL, reaching a maximum value of δ {n}e/{\\bar{n}}e˜ 0.18. Blobs are observed, born around the magnetic separatrix surface and propagate radially outward with velocities generally less than 1 km s-1. Strong poloidal motion of the blobs is also present, near 20 km s-1, consistent with E × B rotation. The electron density fluctuations show a negative skewness in the closed field-line pedestal region, consistent with the presence of ‘holes’, followed by a transition to strong positive skewness across the separatrix and into the SOL. These simulations indicate that not only neoclassical phenomena, but also turbulence, including the blob-generation mechanism, can remain important in the steep H-mode pedestal and SOL. Qualitative comparisons will be made to experimental observations.
Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasma
Viktor K. Decyk
2008-04-24
The UCLA work on this grant was to design and help implement an object-oriented version of the GTC code, which is written in Fortran90. The GTC code is the main global gyrokinetic code used in this project, and over the years multiple, incompatible versions have evolved. The reason for this effort is to allow multiple authors to work together on GTC and to simplify future enhancements to GTC. The effort was designed to proceed incrementally. Initially, an upper layer of classes (derived types and methods) was implemented which called the original GTC code 'under the hood.' The derived types pointed to data in the original GTC code, and the methods called the original GTC subroutines. The original GTC code was modified only very slightly. This allowed one to define (and refine) a set of classes which described the important features of the GTC code in a new, more abstract way, with a minimum of implementation. Furthermore, classes could be added one at a time, and at the end of the each day, the code continued to work correctly. This work was done in close collaboration with Y. Nishimura from UC Irvine and Stefan Ethier from PPPL. Ten classes were ultimately defined and implemented: gyrokinetic and drift kinetic particles, scalar and vector fields, a mesh, jacobian, FLR, equilibrium, interpolation, and particles species descriptors. In the second state of this development, some of the scaffolding was removed. The constructors in the class objects now allocated the data and the array data in the original GTC code was removed. This isolated the components and now allowed multiple instantiations of the objects to be created, in particular, multiple ion species. Again, the work was done incrementally, one class at a time, so that the code was always working properly. This work was done in close collaboration with Y. Nishimura and W. Zhang from UC Irvine and Stefan Ethier from PPPL. The third stage of this work was to integrate the capabilities of the various versions of
Comparative study between ion-scale turbulence measurements and gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Lee, W.; Ko, S. H.; Choi, M. J.; Ko, W. H.; Lee, K. D.; Leem, J.; Yun, G. S.; Park, H. K.; Wang, W. X.; Budny, R. V.; Park, Y. S.; Luhmann, N. C., Jr.; Kim, K. W.; Kstar Team
2016-10-01
Ion gyroscale density fluctuations were measured with a microwave imaging reflectometer (MIR) in neutral beam injected L-mode plasmas on KSTAR. The spatial and temporal characteristic scales of the measured fluctuations were studied by comparing with the local equilibrium parameters relevant to the ion-scale turbulence. Linear and nonlinear gyrokinetic simulations predicted unstable modes with poloidal wavenumbers of 3 cm-1 (or kθρs 0.4) and the wavenumbers were also identified from the measured fluctuations. The poloidal wavenumber can be derived from the measured mode frequency and poloidal velocity. The dominant mode frequency and poloidal velocity were obtained from cross correlations among 16 poloidal channels. Both the mode frequency and poloidal velocity mostly are primarily due to the E x B flow velocity in fast rotating plasmas with neutral beam injection. Work supported by NRF Korea under Grant Number NRF-2014M1A7A1A03029865 and Korean Ministry of Science, ICT, and Future Planning under the KSTAR project contract.
Three-dimensional gyrokinetic simulation of the relaxation of a magnetized temperature filament
Sydora, R. D.; Morales, G. J.; Maggs, J. E.; Van Compernolle, B.
2015-10-15
An electromagnetic, 3D gyrokinetic particle code is used to study the relaxation of a magnetized electron temperature filament embedded in a large, uniform plasma of lower temperature. The study provides insight into the role played by unstable drift-Alfvén waves observed in a basic electron heat transport experiment [D. C. Pace et al., Phys. Plasmas 15, 122304 (2008)] in which anomalous cross-field transport has been documented. The simulation exhibits the early growth of temperature-gradient-driven, drift-Alfvén fluctuations that closely match the eigenmodes predicted by linear theory. At the onset of saturation, the unstable fluctuations display a spiral spatial pattern, similar to that observed in the laboratory, which causes the rearrangement of the temperature profile. After saturation of the linear instability, the system exhibits a markedly different behavior depending on the inclusion in the computation of modes without variation along the magnetic field, i.e., k{sub z} = 0. In their absence, the initial filament evolves into a broadened temperature profile, self-consistent with undamped, finite amplitude drift-Alfvén waves. But the inclusion of k{sub z} = 0 modes causes the destruction of the filament and damping of the drift-Alfvén modes leading to a final state consisting of undamped convective cells and multiple, smaller-scale filaments.
The direct method for gyrokinetic simulation with kinetic electrons and magnetic perturbations
NASA Astrophysics Data System (ADS)
Chen, Yang; Parker, Scott
2016-10-01
Over the past fifteen years we have developed two Particle-in-Cell (PIC) algorithms for gyrokinetic simulation of tokamak plasmas with kinetic electrons and magnetic perturbations. The first, called the Direct Method, uses an adjustable split-weight scheme and a control-variate method to properly handle the ``cancellation problem''. The second algorithm is the Closure Scheme, which solves the vorticity equation and the generalized Ohm's law, closing with an electron pressure calculated from delta-f PIC electrons. The extention of the Direct Method to handle low-n (long wavelength) fluctuations will be discussed. We will explain the algorithm, describe the low-n geometrical implementation, and present numerical observations in applying the Direct Method to various waves, including shear Alfven waves, ITGs and the n = 1 tearing mode. These observations suggest that, whereas the cancellation problem appears to be unavoidable and can be solved by the controlled variate method, the split-weight scheme is primarily a technique for numerical stability, and can probably be replaced by other techniques (such as the mixed-variable approach.
NASA Astrophysics Data System (ADS)
Martin, Mike; Landreman, Matt; Mandell, Noah; Dorland, William
2016-10-01
GryfX is a delta-f code that evolves the gyrofluid set of equations using sophisticated nonlinear closures, with the option to evolve zonal flows (ky =0) kinetically. Since fluid models require less memory to store than a kinetic model, GryfX is ideally suited and thus written to run on a Graphics Processing Unit (GPU), yielding about a 1,200 times performance advantage over GS2. Here we present the first stellarator simulations using GryfX. Results compare linear growth rates of the Ion Temperature Gradient (ITG) mode between GryfX and the gyrokinetic code, GS2, using stellarator geometries from the National Compact Stellarator Experiment (NCSX) and Wendelstein 7-X (W7X). Strong agreement of <10% for maximum growth rates is observed between GS2 and GryfX for temperature gradients away from marginal stability for both NCSX and W7X geometries. Nonlinear stellarator results using GS2/GryfX are also presented.
Multi-machine analysis of turbulent transport in helical systems via gyrokinetic simulation
NASA Astrophysics Data System (ADS)
Ishizawa, A.; Kishimoto, Y.; Watanabe, T.-H.; Sugama, H.; Tanaka, K.; Satake, S.; Kobayashi, S.; Nagasaki, K.; Nakamura, Y.
2017-06-01
We have investigated drift-wave instability and nonlinear turbulent transport in two configurations with different magnetic field structures by means of electromagnetic gyrokinetic simulations. Here, one is the neoclassically optimized Large Helical Device (LHD) plasma and the other is the Heliotron J (HJ) plasma. First, we show that the validation against the turbulent transport in the LHD plasma is successful, and that the neoclassically optimized configuration has smaller turbulent transport. Second, the neoclassical optimization through an enhanced toroidal mirror ratio, which is a capability of non-axisymmetric plasma, is found to improve the turbulent transport in the HJ plasma, which is qualitatively consistent with the observation in the HJ. Hence, the neoclassical optimization reduces the turbulent transport in both the LHD and HJ plasmas. Third, as a trial in evaluating the performance of a helical system designed with different concepts for stability, we compared turbulent transport in these plasmas and found that both the mixing-length-estimated diffusion and nonlinear turbulent transport of the HJ plasma are smaller than those of the LHD plasma in gyro-Bohm units. The significant difference is stronger zonal flows in the HJ plasma than in the LHD plasma.
Collisional Ion and Electron Scale Gyrokinetic Simulations in the Tokamak Pedestal
NASA Astrophysics Data System (ADS)
Belli, E. A.; Candy, J.; Snyder, P. B.
2016-10-01
A new gyrokinetic solver, CGYRO, has been developed for precise studies of high collisionality regimes, such as the H-mode pedestal and L-mode edge. Building on GYRO and NEO, CGYRO uses the same velocity-space coordinates as NEO to optimize the accuracy of the collision dynamics and allow for advanced operators beyond the standard Lorentz pitch-angle scattering model. These advanced operators include energy diffusion and finite-FLR collisional effects. The code is optimized for multiscale (coupled electron and ion turbulence scales) simulations, employing a new spatial discretization and array distribution scheme that targets scalability on next-generation (exascale) HPC systems. In this work, CGYRO is used to study the complex spectrum of modes in the pedestal region. The onset of the linear KBM with full collisional effects is assessed to develop an improved KBM/RBM model for EPED. The analysis is extended to high k to explore the role of electron-scale (ETG-range) physics. Comparisons with new analytic collisional theories are made. Inclusion of sonic toroidal rotation (including full centrifugal effects) for studies including heavy wall impurities is also reported. Work supported in part by the US DOE under DE-FC02-06ER54873 and DE-FC02-08ER54963.
NASA Astrophysics Data System (ADS)
Strugarek, A.; Sarazin, Y.; Zarzoso, D.; Abiteboul, J.; Brun, A. S.; Cartier-Michaud, T.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, Ph.; Grandgirard, V.; Latu, G.; Passeron, C.; Thomine, O.
2013-10-01
The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability— driven by the temperature anisotropy (T∥≠T⊥). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.
Strugarek, A; Sarazin, Y; Zarzoso, D; Abiteboul, J; Brun, A S; Cartier-Michaud, T; Dif-Pradalier, G; Garbet, X; Ghendrih, Ph; Grandgirard, V; Latu, G; Passeron, C; Thomine, O
2013-10-04
The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability--driven by the temperature anisotropy (T(∥)≠T(⊥)). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.
NASA Astrophysics Data System (ADS)
Gao, Xiaotian; Liu, Kaijun; Wang, Xueyi; Min, Kyungguk; Lin, Yu; Wang, Xiaogang
2017-06-01
Two-dimensional simulations using a gyrokinetic electron and fully kinetic ion (GeFi) scheme are preformed to study the excitation of fast magnetosonic waves in the terrestrial magnetosphere, which arise from the ion Bernstein instability driven by proton velocity distributions with a positive slope with respect to the perpendicular velocity. Since both ion and electron kinetics are relevant, particle-in-cell (PIC) simulations have often been employed to study the wave excitation. However, the full particle-in-cell scheme is computationally expensive for simulating waves in the ion scale because the electron scale must be fully resolved. Therefore, such simulations are limited to reduced proton-to-electron mass ratio ( m p / m e) and light-to-Alfvén speed ratio ( c / v A). The present study exploits the GeFi scheme that can break through these limitations to some extent, so larger m p / m e and c / v A can be used. In the simulations presented, the ion Bernstein instability is driven by a proton velocity distribution composed of 10% energetic protons with a shell distribution and 90% relatively cool, background protons with a Maxwellian distribution. The capability of the GeFi code in simulating the ion Bernstein instability is first demonstrated by comparing a GeFi simulation using reduced mass ratio ( m p / m e = 100) and speed ratio ( c / v A = 15) to a corresponding PIC simulation as well as linear dispersion analysis. A realistic speed ratio ( c / v A = 400) and a larger mass ratio ( m p / m e = 400) are then adopted in the GeFi code to explore how the results vary. It is shown that, as the increased m p / m e and c / v A lead to a larger lower hybrid frequency, ion Bernstein waves are excited at more ion cyclotron harmonics, consistent with the general prediction of linear dispersion theory. On the other hand, the GeFi simulations also revealed some interesting features after the instability saturation, which are likely related to nonlinear wave
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.
2016-04-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S.; Hager, R.; Chang, C.S.; Kwon, J.M.; Parker, S.E.
2016-06-15
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
Bass, E. M.; Waltz, R. E.
2010-11-15
Energetic particle (EP) transport from local high-n toroidal Alfven eigenmodes (TAEs) and energetic particle modes (EPMs) is simulated with a gyrokinetic code. Linear and nonlinear simulations have identified a parameter range where the longwave TAE and EPM are unstable alongside the well-known ion-temperature-gradient (ITG) and trapped-electron-mode (TEM) instabilities. A new eigenvalue solver in GYRO facilitates this mode identification. States of nonlinearly saturated local TAE/EPM turbulent intensity are identified, showing a 'soft' transport threshold for enhanced energetic particle transport against the TAE/EPM drive from the EP pressure gradient. The very long-wavelength (mesoscale) TAE/EPM transport is saturated partially by nonlinear interaction with microturbulent ITG/TEM-driven zonal flows. Fixed-gradient-length, nonlinearly saturated states are accessible over a relatively narrow range of EP pressure gradient. Within this range, and in the local limit employed, TAE/EPM-driven transport more closely resembles drift-wave microturbulent transport than 'stiff' ideal MHD transport with a clamped critical total pressure gradient. At a higher, critical EP pressure gradient, fixed-gradient nonlinear saturation fails: EP transport increases without limit and background transport decreases. Presumably saturation is then obtained by relaxation of the EP pressure gradient to near this critical EP pressure gradient. If the background plasma gradients driving the ITG/TEM turbulence and zonal flows are weakened, the critical gradient collapses to the TAE/EPM linear stability threshold. Even at the critical EP pressure gradient there is no evidence that TAE/EPM instability significantly increases transport in the background plasma channels.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S.; Hager, R.; Chang, C. S.; ...
2016-04-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
Mikkelsen, D. R. Bitter, M.; Delgado-Aparicio, L.; Hill, K. W.; Greenwald, M.; Howard, N. T.; Hughes, J. W.; Rice, J. E.; Reinke, M. L.; Podpaly, Y.; Ma, Y.; Candy, J.; Waltz, R. E.
2015-06-15
Peaked density profiles in low-collisionality AUG and JET H-mode plasmas are probably caused by a turbulently driven particle pinch, and Alcator C-Mod experiments confirmed that collisionality is a critical parameter. Density peaking in reactors could produce a number of important effects, some beneficial, such as enhanced fusion power and transport of fuel ions from the edge to the core, while others are undesirable, such as lower beta limits, reduced radiation from the plasma edge, and consequently higher divertor heat loads. Fundamental understanding of the pinch will enable planning to optimize these impacts. We show that density peaking is predicted by nonlinear gyrokinetic turbulence simulations based on measured profile data from low collisionality H-mode plasma in Alcator C-Mod. Multiple ion species are included to determine whether hydrogenic density peaking has an isotope dependence or is influenced by typical levels of low-Z impurities, and whether impurity density peaking depends on the species. We find that the deuterium density profile is slightly more peaked than that of hydrogen, and that experimentally relevant levels of boron have no appreciable effect on hydrogenic density peaking. The ratio of density at r/a = 0.44 to that at r/a = 0.74 is 1.2 for the majority D and minority H ions (and for electrons), and increases with impurity Z: 1.1 for helium, 1.15 for boron, 1.3 for neon, 1.4 for argon, and 1.5 for molybdenum. The ion temperature profile is varied to match better the predicted heat flux with the experimental transport analysis, but the resulting factor of two change in heat transport has only a weak effect on the predicted density peaking.
Modern gyrokinetic particle-in-cell simulation of fusion plasmas on top supercomputers
Wang, Bei; Ethier, Stephane; Tang, William; ...
2017-06-29
The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the petascale and beyond. Motivated by the goal of developing a modern code capable of dealing with the physics challenge of increasing problem size with sufficient resolution, new thread-level optimizations have been introduced as well as a key additional domain decomposition. GTC-P's multiple levels of parallelism, including inter-node 2D domain decomposition and particle decomposition, as well as intra-node shared memory partition and vectorization have enabled pushing the scalability ofmore » the PIC method to extreme computational scales. In this paper, we describe the methods developed to build a highly parallelized PIC code across a broad range of supercomputer designs. This particularly includes implementations on heterogeneous systems using NVIDIA GPU accelerators and Intel Xeon Phi (MIC) co-processors and performance comparisons with state-of-the-art homogeneous HPC systems such as Blue Gene/Q. New discovery science capabilities in the magnetic fusion energy application domain are enabled, including investigations of Ion-Temperature-Gradient (ITG) driven turbulence simulations with unprecedented spatial resolution and long temporal duration. Performance studies with realistic fusion experimental parameters are carried out on multiple supercomputing systems spanning a wide range of cache capacities, cache-sharing configurations, memory bandwidth, interconnects and network topologies. These performance comparisons using a realistic discovery-science-capable domain application code provide valuable insights on optimization techniques across one of the broadest sets of current high-end computing platforms worldwide.« less
Liu, Dongjian; Bao, Jian; Han, Tao; Wang, Jiaqi; Lin, Zhihong
2016-02-15
A finite-mass electron fluid model for low frequency electromagnetic fluctuations, particularly the collisionless tearing mode, has been implemented in the gyrokinetic toroidal code. Using this fluid model, linear properties of the collisionless tearing mode have been verified. Simulations verify that the linear growth rate of the single collisionless tearing mode is proportional to D{sub e}{sup 2}, where D{sub e} is the electron skin depth. On the other hand, the growth rate of a double tearing mode is proportional to D{sub e} in the parameter regime of fusion plasmas.
Bernstein, I.B.; Catto, P.J.
1984-05-01
A nonlinear gyrokinetic formalism is developed which permits mean velocities comparable to thermal speeds in arbitrary magnetic field geometry. The theory is fully electromagnetic and does not employ an eikonal ansatz. The freedom in the theory is exploited to display simply the connection with ideal magnetohydrodynamics.
NASA Astrophysics Data System (ADS)
Brunner, S.; Fivaz, M.; Tran, T. M.; Vaclavik, J.
1998-11-01
A solution to the full two-dimensional eigenvalue problem of electrostatic microinstabilities in a tokamak plasma is presented in the framework of gyrokinetic theory. The approach is the generalization of methods previously developed for a cylindrical system [S. Brunner and J. Vaclavik, Phys. Plasmas 5, 365 (1998)]. By solving the spectral problem in a special Fourier space adapted to the curved geometry, orbit width as well as Larmor radius can be kept to all orders. For a first numerical implementation, a large aspect ratio plasma with circular concentric magnetic surfaces is considered. A root finding algorithm for identifying the eigenfrequencies, based on a higher order Nyquist method, enables straightforward implementation on a parallel computer. Illustrative results for ion temperature gradient-related instabilities are presented. These include scaling studies of the radial width, and toroidicity and magnetic shear scans, as well as the effects of nonadiabatic trapped electron dynamics.
Defining an equilibrium state in global full-f gyrokinetic models
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.
2008-02-01
This paper tackles the delicate choice of the initial distribution function in full-f gyrokinetic codes such as G YSELA 5D, aiming at predicting the turbulent transport level in low collisional tokamak plasmas. It is found, both analytically and numerically, that a Maxwellian distribution function with constant profiles on magnetic flux surfaces leads to the fast generation of a large scale electric field. Such a field opposes the up-down charge separation governed by the inhomogeneity of the equilibrium magnetic field. If large enough, the shearing rate induced by the resulting poloidal E×B velocity could efficiently reduce the plasma micro-instabilities which account for the development of the turbulence. Starting in the ab initio code G YSELA 5 D from an equilibrium distribution function depending on motion invariants only is shown to cure such a problem. In this case, charge separation is counter-balanced by parallel flow, and the standard fluid force balance is recovered.
NASA Astrophysics Data System (ADS)
Ernst, Darin
2008-11-01
#1#23pt1.5pt 1.5pt#1###2˜ > > Trapped electron mode (TEM) turbulence exhibits rich zonal flow dynamics, which depends strongly on plasma parameters. The role zonal flows in TEM turbulence is explored through a series of linear and nonlinear gyrokinetic simulations using both PIC (the GEM code) and continuum (the GS2 code) methods. A new nonlinear upshift [1,2] in the TEM critical density gradient (associated with zonal flow dominated states near threshold) increases strongly with collisionality, for density gradient driven cases. In contrast, zonal flows have little effect on TEM turbulence with strong electron temperature gradients and Te= 3Ti [3]. This apparent contradiction has been resolved in parameteric studies showing that zonal flows are weaker as the electron temperature gradient and Te/Ti increase [4]. The parametric variation of zonal flows is consistent with linear stability properties and nonlinear instability theory. A new stability diagram based on 2,000 GS2 simulations clarifies the roles of resonant and non-resonant TEM, ``ubiquitous,'' and electron temperature gradient (ETG) driven modes. Larger electron temperature gradients couple TEM and ETG modes, resulting in short wavelengths kαρs>1. Accordingly, a sudden onset of nonlinear fine scale structure is seen for ηe≡dTe/dne> 1. For short wavelengths, the ions are more adiabatic, the zonal flow potential <φ>˜
Hilscher, P. P.; Imadera, K.; Li, J. Q.; Kishimoto, Y.
2013-08-15
We revisit the characteristics of stable, damped modes originating from the Landau damping by employing a discretized gyrokinetic Vlasov simulation and also eigenvalue analysis in an unsheared slab geometry. By comparing results between gyrokinetic simulation and an eigenvalue analysis, we found that there exists a critical collisionality β{sub c}{sup *} at which the Case-van Kampen (CvK) modes are damped down to the analytically estimated Landau damping rate and an eigenmode consistent with Landau's theory emerges. Consequently, the recurrence phenomenon disappears so that the Landau damping can be properly reproduced. The critical collisionality β{sub c}{sup *} depends on the resolution in velocity space; i.e., a higher (lower) resolution requires a lower (higher) collisionality, while tends to zero (β{sub c}{sup *}→0) as Δv→0. It is found through a reduced model that even in the collisionless case with marginally stable CvK modes, the linear mode coupling between unstable and stable/damped components through a tertiary mode and the resultant energy transfer can be properly calculated such that the stable/damped mode persists as an eigenstate.
Monte Carlo particle-in-cell methods for the simulation of the Vlasov-Maxwell gyrokinetic equations
NASA Astrophysics Data System (ADS)
Bottino, A.; Sonnendrücker, E.
2015-10-01
> The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov-Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations.
NASA Astrophysics Data System (ADS)
Manas, P.; Hornsby, W. A.; Angioni, C.; Camenen, Y.; Peeters, A. G.
2017-03-01
The impact of the neoclassical background on turbulent impurity transport is investigated by means of gyrokinetic simulations supported by fluid equations. The latter are derived, using a Laguerre polynomials expansion of the first order neoclassical distribution function, and analytical expressions of the turbulent momentum flux and impurity transport coefficients are assessed. Comparisons of gyrokinetic simulations including this neoclassical background (coupling between the codes GKW and NEO) and the fluid model are used to identify the main mechanisms behind the modification of the turbulent transport channels and benchmark the numerical implementation. These mechanisms include a modification of the parallel dynamics of the main ions and direct contributions stemming from the asymmetry in the parallel velocity space of the neoclassical distribution function. The latter which is found dominant for turbulent impurity transport, increases with increasing collisionality, R/{L}{Ti}, R/{L}n, impurity mass, safety factor and aspect ratio. These contributions to momentum and impurity fluxes are also found to depend on the directions of the toroidal magnetic field and plasma current.
Center for Gyrokinetic Particle Simulations of Turbulent Transport in Burning Plasmas
Scott, Parker
2011-05-02
This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of
3D hybrid simulations with gyrokinetic particle ions and fluid electrons
Belova, E.V.; Park, W.; Fu, G.Y.; Strauss, H.R.; Sugiyama, L.E.
1998-12-31
The previous hybrid MHD/particle model (MH3D-K code) represented energetic ions as gyrokinetic (or drift-kinetic) particles coupled to MHD equations using the pressure or current coupling scheme. A small energetic to bulk ion density ratio was assumed, n{sub h}/n{sub b} {much_lt} 1, allowing the neglect of the energetic ion perpendicular inertia in the momentum equation and the use of MHD Ohm`s law E = {minus}v{sub b} {times} B. A generalization of this model in which all ions are treated as gyrokinetic/drift-kinetic particles and fluid description is used for the electron dynamics is considered in this paper.
Multi-Channel Validation of Nonlinear Gyrokinetic Simulations in Alcator C-Mod I-mode Plasmas
NASA Astrophysics Data System (ADS)
Creely, A. J.
2016-10-01
New multi-channel validation of nonlinear gyrokinetic simulations (GYRO) is carried out for I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and density and temperature fluctuations. I-mode plasmas are characterized by high energy confinement, similar to H-mode, but with L-mode-like particle confinement, making them favorable for reactors due to natural absence of ELMs, but without impurity accumulation [Whyte NF 2010]. At C-Mod, I-mode plasmas have been obtained across a wide range of plasma currents (Ip = 0.55-1.2MA) and magnetic fields (Bt = 2.8-8.0T). I-mode is also actively studied at ASDEX Upgrade, DIII-D and other tokamaks [Hubbard NF 2016]. Open questions remain regarding core transport in I-mode compared to L and H-mode, making validation studies in I-mode of great interest. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale, cross-scale coupling effects [Howard PoP 2016] may be less important in I-mode than in L-mode. Adding the constraint of experimental perturbative heat diffusivity, however, revealed that ITG/TEM scale simulations do not adequately capture the high profile stiffness in I-mode [Creely NF 2016]. These results motivated more comprehensive comparisons of gyrokinetic simulations with I-mode plasmas. This talk expands upon past I-mode GYRO validation work to simultaneously constrain nonlinear gyrokinetic simulations with experimental electron and ion heat fluxes, electron temperature fluctuations measured with Correlation ECE, density fluctuations measured with Phase Contrast Imaging and reflectometry, and the temperature profile stiffness measured using partial sawtooth heat pulses. This work is supported by the US DOE under Grants DE-SC0006419 and DEFC02-99ER54512-CMOD.
NASA Astrophysics Data System (ADS)
Field, A. R.; Dunai, D.; Ghim, Y.-c.; Hill, P.; McMillan, B.; Roach, C. M.; Saarelma, S.; Schekochihin, A. A.; Zoletnik, S.; the MAST Team
2014-02-01
Observations of ion-scale (kyρi ⩽ 1) density turbulence of relative amplitude ≳0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial × 4 poloidal channel) imaging beam emission spectroscopy diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport barrier in the ion channel, the observed turbulence characteristics are compared with synthetic density turbulence data generated from global, non-linear, gyro-kinetic simulations using the particle-in-cell code NEMORB. This validation exercise highlights the need to include increasingly sophisticated physics, e.g., kinetic treatment of trapped electrons, equilibrium flow shear and collisions, to reproduce most of the characteristics of the observed turbulence. Even so, significant discrepancies remain: an underprediction by the simulations of the turbulence amplitude and heat flux at plasma periphery and the finding that the correlation times of the numerically simulated turbulence are typically two orders of magnitude longer than those measured in MAST. Comparison of these correlation times with various linear timescales suggests that, while the measured turbulence is strong and may be ‘critically balanced’, the simulated turbulence is weak.
NASA Astrophysics Data System (ADS)
Coulette, D.; Besse, N.
2017-04-01
In this paper, we present two codes for the linear stability analysis of the ion temperature gradient instability in toroidal geometry using a gyrokinetic multi-waterbag model for ion dynamics. The first one solves the linearized ion dynamics as an initial value problem, while the second relies on an asymptotic expansion in the so-called ballooning representation allowing us to build a tractable eigenvalue problem. Results from the two codes are presented and compared for equilibria based on modified Cyclone parameters. A good agreement between both codes is found for a class of equilibria with a narrow extent in perpendicular velocity and for which trapped particle orbits are ignored. The local spectrum computed by the eigenvalue is shown to agree remarkably well with previous Cyclone results when trapped particle orbits are included. Lastly we discuss how the equilibrium building procedure for this type of waterbag model requires particular care when dealing with closed equilibrium contours related to the presence of trapped particle orbits.
NASA Astrophysics Data System (ADS)
Kleiber, R.; Hatzky, R.; Könies, A.; Mishchenko, A.; Sonnendrücker, E.
2016-03-01
A new algorithm for electromagnetic gyrokinetic simulations, the so called "pullback transformation scheme" proposed by Mishchenko et al. [Phys. Plasmas 21, 092110 (2014)] is motivated as an explicit time integrator reset after each full timestep and investigated in detail. Using a numerical dispersion relation valid in slab geometry, it is shown that the linear properties of the scheme are comparable to those of an implicit v∥ -scheme. A nonlinear extension of the mixed variable formulation, derived consistently from a field Lagrangian, is proposed. The scheme shows excellent numerical properties with a low statistical noise level and a large time step especially for MHD modes. The example of a nonlinear slab tearing mode simulation is used to illustrate the properties of different formulations of the physical model equations.
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-15
We present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory.
NASA Astrophysics Data System (ADS)
White, Anne
2014-10-01
Understanding transport in high performance ELM-suppressed tokamak plasmas is of great interest for ITER and other future experiments. `I-mode' regime on Alcator C-Mod, also known as `improved L-mode' on ASDEX Upgrade, has several favorable characteristics: pedestals in electron and ion temperature, with ITER98y2 H-factors similar to and exceeding H-mode [Hubbard et al., Phys. Plasmas 18, 056115 (2011)], but without a density pedestal and without impurity accumulation and without ELMs. Most research on I-mode focuses on changes in edge and pedestal turbulence/transport and stability. In this work, transport in I-mode is probed by measuring changes in core turbulence across L-I transitions at Alcator C-Mod and comparing with nonlinear gyrokinetic simulations. Long wavelength (kθρs < 0.5) density fluctuation levels decrease from L-mode levels by up to 30% in I-mode, and long wavelength (kθρs < 0.3) electron temperature fluctuation levels decrease by up to 70%, reaching the instrumental sensitivity limit. Gyrokinetic simulation results suggest that ExB shear in the core of these intrinsically rotating plasmas can reduce the fluctuation amplitude in I-mode. As the pedestal temperature increases across slow L-I transitions, core density fluctuations (0.40 < ρ <0.95) are reduced prior to the onset of the edge-localized (0.99 < ρ < 1.0) weakly coherent mode (WCM) and prior to the reduction of low-frequency turbulence in the edge/pedestal region (0.99 < ρ < 1.0), which suggests that effects of profile stiffness across the radius can also lead to reduced core turbulence. By comparing experimental measurements from Alcator C-Mod to nonlinear gyrokinetic simulations and to different models of profile stiffness, this talk will explore the impact of core turbulence and transport on overall I-mode confinement and on the separation of particle and heat transport in I-mode. This work was supported by U.S. Department of Energy Contract DE-FC02-99ER54512-CMOD.
NASA Astrophysics Data System (ADS)
Cheng, Junyi; Chen, Yang; Zhang, Wenlu; Lin, Zhihong; Chen, Wei; Yu, Limin; Ding, Xuantong
2015-11-01
A verification and validation study is carried out for a sequence of fast electron driven beta-induced Alfven eigenmodes in HL-2A tokamak plasma. The fast electron driven beta induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electrons are described by the drift kinetic model. The phase space structure shows that only the processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels such as transit, drift-bounce, and processional resonance. For weakly nonlinear driven case, frequency is observed to be in phase with the particle energy flux, and mode structure is almost the same as linear stage . While in the strongly driven nonlinear case, BAAE is excited after the BAE mode saturated. The simulation of e-BAE with the HL-2A tokamak parameters is taken. Three modes n/m = 1/2 , 2/5 ,1/3 in HL-2A can be excited in our simulations.
NASA Astrophysics Data System (ADS)
Ku, S.; Chang, C.-S.; Adams, M.; Cummings, J.; Hinton, F.; Keyes, D.; Klasky, S.; Lee, W.; Lin, Z.; Parker, S.; CPES Team
2006-09-01
A gyrokinetic neoclassical solution for a diverted tokamak edge plasma has been obtained for the first time using the massively parallel Jaguar XT3 computer at Oak Ridge National Laboratory. The solutions show similar characteristics to the experimental observations: electric potential is positive in the scrape-off layer and negative in the H-mode layer, and the parallel rotation is positive in the scrape-off layer and at the inside boundary of the H-mode layer. However, the solution also makes a new physical discovery that there is a strong ExB convective flow in the scrape-off plasma. A general introduction to the edge simulation problem is also presented.
Adams, Mark; Chang, C. S.; Cummings, J.; Hinton, F.; Keyes, David E; Klasky, Scott A; Ku, S.; Lee, W. W.; Lin, Z.; Parker, Scott; CPES Team, the
2006-01-01
A gyrokinetic neoclassical solution for a diverted tokamak edge plasma has been obtained for the first time using the massively parallel Jaguar XT3 computer at Oak Ridge National Laboratory. The solutions show similar characteristics to the experimental observations: electric potential is positive in the scrape-off layer and negative in the H-mode layer, and the parallel rotation is positive in the scrape-off layer and at the inside boundary of the H-mode layer. However, the solution also makes a new physical discovery that there is a strong ExB convective flow in the scrape-off plasma. A general introduction to the edge simulation problem is also presented.
White, A E; Schmitz, L; Peebles, W A; Carter, T A; Rhodes, T L; Doyle, E J; Gourdain, P A; Hillesheim, J C; Wang, G; Holland, C; Tynan, G R; Austin, M E; McKee, G R; Shafer, M W; Burrell, K H; Candy, J; DeBoo, J C; Prater, R; Staebler, G M; Waltz, R E; Makowski, M A
2008-10-01
A correlation electron cyclotron emission (CECE) diagnostic has been used to measure local, turbulent fluctuations of the electron temperature in the core of DIII-D plasmas. This paper describes the hardware and testing of the CECE diagnostic and highlights the importance of measurements of multifield fluctuation profiles for the testing and validation of nonlinear gyrokinetic codes. The process of testing and validating such codes is critical for extrapolation to next-step fusion devices. For the first time, the radial profiles of electron temperature and density fluctuations are compared to nonlinear gyrokinetic simulations. The CECE diagnostic at DIII-D uses correlation radiometry to measure the rms amplitude and spectrum of the electron temperature fluctuations. Gaussian optics are used to produce a poloidal spot size with w(o) approximately 1.75 cm in the plasma. The intermediate frequency filters and the natural linewidth of the EC emission determine the radial resolution of the CECE diagnostic, which can be less than 1 cm. Wavenumbers resolved by the CECE diagnostic are k(theta) < or = 1.8 cm(-1) and k(r) < or = 4 cm(-1), relevant for studies of long-wavelength turbulence associated with the trapped electron mode and the ion temperature gradient mode. In neutral beam heated L-mode plasmas, core electron temperature fluctuations in the region 0.5 < r/a < 0.9, increase with radius from approximately 0.5% to approximately 2%, similar to density fluctuations that are measured simultaneously with beam emission spectroscopy. After incorporating "synthetic diagnostics" to effectively filter the code output, the simulations reproduce the characteristics of the turbulence and transport at one radial location r/a = 0.5, but not at a second location, r/a = 0.75. These results illustrate that measurements of the profiles of multiple fluctuating fields can provide a significant constraint on the turbulence models employed by the code.
White, A. E.; Schmitz, L.; Peebles, W. A.; Carter, T. A.; Rhodes, T. L.; Doyle, E. J.; Gourdain, P. A.; Hillesheim, J. C.; Wang, G.; Holland, C.; Tynan, G. R.; Austin, M. E.; McKee, G. R.; Shafer, M. W.; Burrell, K. H.; Candy, J.; DeBoo, J. C.; Prater, R.; Staebler, G. M.; Waltz, R. E.
2008-10-15
A correlation electron cyclotron emission (CECE) diagnostic has been used to measure local, turbulent fluctuations of the electron temperature in the core of DIII-D plasmas. This paper describes the hardware and testing of the CECE diagnostic and highlights the importance of measurements of multifield fluctuation profiles for the testing and validation of nonlinear gyrokinetic codes. The process of testing and validating such codes is critical for extrapolation to next-step fusion devices. For the first time, the radial profiles of electron temperature and density fluctuations are compared to nonlinear gyrokinetic simulations. The CECE diagnostic at DIII-D uses correlation radiometry to measure the rms amplitude and spectrum of the electron temperature fluctuations. Gaussian optics are used to produce a poloidal spot size with w{sub o}{approx}1.75 cm in the plasma. The intermediate frequency filters and the natural linewidth of the EC emission determine the radial resolution of the CECE diagnostic, which can be less than 1 cm. Wavenumbers resolved by the CECE diagnostic are k{sub {theta}}{<=}1.8 cm{sup -1} and k{sub r}{<=}4 cm{sup -1}, relevant for studies of long-wavelength turbulence associated with the trapped electron mode and the ion temperature gradient mode. In neutral beam heated L-mode plasmas, core electron temperature fluctuations in the region 0.5
NASA Astrophysics Data System (ADS)
Parra, Felix I.; Catto, Peter J.
2009-06-01
We compare two different derivations of the gyrokinetic equation: the Hamiltonian approach in Dubin D H E et al (1983 Phys. Fluids 26 3524) and the recursive methodology in Parra F I and Catto P J (2008 Plasma Phys. Control. Fusion 50 065014). We prove that both approaches yield the same result at least to second order in a Larmor radius over macroscopic length expansion. There are subtle differences in the definitions of some of the functions that need to be taken into account to prove the equivalence.
NASA Astrophysics Data System (ADS)
Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu
2016-07-01
The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me . In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me . The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where k →.B → =0 , consistent with previous analytical and simulation studies. Here, B → is the equilibrium magnetic field and k → is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at k →.B → ≠0 . In addition, the simulation results indicate that varying mi/me , the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.
Wang, Zhenyu; Lin, Yu; Wang, Xueyi; ...
2016-07-07
The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location wheremore » $$\\vec{k}$$• $$\\vec{B}$$ =0, consistent with previous analytical and simulation studies. Here, $$\\vec{B}$$ is the equilibrium magnetic field and $$\\vec{k}$$ is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at $$\\vec{k}$$ •$$\\vec{B}$$ ≠0. Additionally, the simulation results indicate that varying mi/me, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.« less
Gyrokinetic Simulations of RMP Effects on DIII-D Edge Turbulence
NASA Astrophysics Data System (ADS)
Taimourzadeh, Sam; Holod, Ihor; Lin, Zhihong; Nazikian, Raffi; Wingen, Andreas
2016-10-01
It has been demonstrated that edge localized modes (ELMs) can be fully suppressed in DIII-D H-mode plasmas with the application of resonant magnetic perturbations (RMPs), and that there is a corresponding reduction of pedestal gradients, changes in rotation, and changes in the radial electric field (Er) profile. However, with the application of RMPs there is also an increase in long wavelength, electrostatic turbulence on top of the pedestal, as observed with BES, DBS, and other fluctuation diagnostics. Using the Gyrokinetic Toroidal Code (GTC), DIII-D shots 158103, at times 3750 ms (ELMing w/ RMP) and 3050 ms (ELM suppressed w/ RMP), and shot 158104.1350 (ELMing) are investigated, and a link between increased pedestal top turbulence, during the ELM suppressed phase, and a shift in the Er profile is demonstrated.
Comparison of Implicit Multiscale Full Kinetics to Gyrokinetics
NASA Astrophysics Data System (ADS)
Parker, Scott; Sturdevant, Benjamin; Chen, Yang
2016-10-01
Recent progress has been made developing full kinetic Lorentz force ion dynamics using implicit multiscale techniques. It is now possible to capture low-frequency physics along with finite Larmor radius (FLR) effects with a fully kinetic multiscale delta-f particle simulation. The utility of such a model is to be able to verify gyrokinetics in situations where the smallness of the ordering parameters are under question. Additionally, such a model can help identify what higher order terms in gyrokinetics might be important. Orbit averaging and sub-cycling are utilized with an implicit particle time advance based on variational principles. This produces stable and accurate ion trajectories on long time scales. Excellent agreement with the gyrokinetic dispersion relation is obtained including full FLR effects. Ion Bernstein waves are easily suppressed with the implicit time advance. We have developed a global toroidal electrostatic adiabatic electron Lorentz ion code. We will report our linear results benchmarking Lorentz ions with gyrokinetics for the Cyclone base case. We will also present our progress on ion including drift-kinetic electrons and electromagnetic perturbations.
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-30
Here, we present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory. (C) 2015 AIP Publishing LLC.
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-30
Here, we present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory. (C) 2015 AIP Publishing LLC.
Gyrokinetic treatment of GAE modes in cylindrical geometry
Eremin, D.
2006-11-30
Global Alfven eigenmodes (GAEs) are investigated in cylindrical geometry both analytically and numerically. These modes are of particular importance in low-shear magnetic configurations, such as modern stellarators. Analytical treatment starts from the linearised equations of gyrokinetics and yields a generalized dispersion relation for GAE with FLR and kinetic effects taken into account, which is demonstrated to reduce to the well-known MHD counterpart in the appropriate limit. An eigenvalue code is developed to solve the dispersion relation, which is used to investigate the kinetic analogs of GAE modes in various regimes with different beta. On the other hand, GAE modes are simulated with global linear particle-in-cell (PIC) electromagnetic gyrokinetic code following self-consistent time evolution of electromagnetic fields and plasma. GAE modes are observed and their damping rate agrees with predictions made by the eigenvalue code.
Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu
2016-07-07
The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio m_{i}/m_{e}. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic m_{i}/m_{e}. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where $\\vec{k}$• $\\vec{B}$ =0, consistent with previous analytical and simulation studies. Here, $\\vec{B}$ is the equilibrium magnetic field and $\\vec{k}$ is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at $\\vec{k}$ •$\\vec{B}$ ≠0. Additionally, the simulation results indicate that varying m_{i}/m_{e}, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.
Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu
2016-07-07
The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio m_{i}/m_{e}. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic m_{i}/m_{e}. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where $\\vec{k}$• $\\vec{B}$ =0, consistent with previous analytical and simulation studies. Here, $\\vec{B}$ is the equilibrium magnetic field and $\\vec{k}$ is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at $\\vec{k}$ •$\\vec{B}$ ≠0. Additionally, the simulation results indicate that varying m_{i}/m_{e}, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.
NASA Astrophysics Data System (ADS)
Toda, S.; Nunami, M.; Ishizawa, A.; Watanabe, T.-H.; Sugama, H.
2014-11-01
How to apply a reduced model for the turbulent ion heat diffusivity [Nunami M et al. 2013 Phys. Plasmas, 20 092307] derived from a gyrokinetic code to a transport simulation is proposed. The reduced model is given by the function of the linear growth rate of the ion temperature gradient (ITG) mode and the decay time of zonal flows. The ion temperature gradient scale length is chosen for the additional modeling to include the linear growth rate of the ITG mode from a gyrokinetic code. The formula for the zonal flow decay time is derived at the given magnetic field configuration. The calculation of an extremely low computational cost in this article reproduces the results of the reduced model for the turbulent ion heat diffusivity within allowable errors.
Spong, D. A.; Bass, E. M.; Deng, W.; Heidbrink, W. W.; Lin, Z.; Tobias, B.; Van Zeeland, M. A.; Austin, M. E.; Domier, C. W.; Luhmann, N. C. Jr.
2012-08-15
A verification and validation study is carried out for a sequence of reversed shear Alfven instability time slices. The mode frequency increases in time as the minimum (q{sub min}) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (no. 142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL are compared. The experimental mode structure of the instability was measured using time-resolved two-dimensional electron cyclotron emission imaging. The three models reproduce the frequency upsweep event within {+-}10% of each other, and the average of the code predictions is within {+-}8% of the measurements; growth rates are predicted that are consistent with the observed spectral line widths. The mode structures qualitatively agree with respect to radial location and width, dominant poloidal mode number, ballooning structure, and the up-down asymmetry, with some remaining differences in the details. Such similarities and differences between the predictions of the different models and the experimental results are a valuable part of the verification/validation process and help to guide future development of the modeling efforts.
Particle-in-cell δf gyrokinetic simulations of the microtearing mode
Chowdhury, J.; Chen, Yang; Wan, Weigang; Parker, Scott E.; Guttenfelder, W.; Canik, J. M.
2016-01-15
The linear stability properties of the microtearing mode are investigated in the edge and core regimes of the National Spherical Torus Experiment (NSTX) using the particle-in-cell method based gyrokinetic code GEM. The dependence of the mode on various equilibrium quantities in both regions is compared. While the microtearing mode in the core depends upon the electron-ion collisions, in the edge region, it is found to be weakly dependent on the collisions and exists even when the collision frequency is zero. The electrostatic potential is non-negligible in each of the cases. It plays opposite roles in the core and edge of NSTX. While the microtearing mode is partially stabilized by the electrostatic potential in the core, it has substantial destabilizing effect in the edge. In addition to the spherical tokamak, we also study the microtearing mode for parameters relevant to the core of a standard tokamak. The fundamental characteristics of the mode remain the same; however, the electrostatic potential in this case is destabilizing as opposed to the core of NSTX. The velocity dependence of the collision frequency, which is crucial for the mode to grow in slab calculations, is not required to destabilize the mode in toroidal devices.
NASA Astrophysics Data System (ADS)
Gao, X.; Liu, K.; Wang, X.; Min, K.; Lin, Y.
2016-12-01
Two-dimensional simulations using a gyro-kinetic electron and fully-kinetic ion (GeFi) scheme are preformed to study the excitation of fast magnetosonic waves in the magnetosphere, which arise from the ion Bernstein instability driven by ring-like proton velocity distributions (with a positive slope with respect to the perpendicular velocity). Since both ion and electron kinetics are relevant, particle-in-cell (PIC) simulations have often been employed to study the wave excitation. However, such simulations are limited to reduced ion-to-electron mass ratio (mi/me) and light-to-Alfvén speed ratio (c/VA) due to the computationally expensive nature of PIC codes. The present study exploits a GeFi scheme that can break through these limitations and use larger/more realistic mi/me and c/VA. The capability of the GeFi code in simulating the ion Bernstein instability is first demonstrated by comparing a GeFi simulation using reduced mass ratio (mi/me=100) and speed ratio (c/VA=15) to a corresponding PIC simulation. A realistic speed ratio (c/VA=400) and a larger mass ratio (mi/me=400) are then adopted in the GeFi code to explore how the results vary. It is shown that the increased mi/me and c/VA lead to a larger lower hybrid frequency and allow waves to arise at more ion cyclotron harmonics, consistent with the general prediction of linear dispersion theory.
Byers, J.A.; Williams, T.J.; Cohen, B.I.; Dimits, A.M.
1994-04-27
One of the programs of the Magnetic fusion Energy (MFE) Theory and computations Program is studying the anomalous transport of thermal energy across the field lines in the core of a tokamak. We use the method of gyrokinetic particle-in-cell simulation in this study. For this LDRD project we employed massively parallel processing, new algorithms, and new algorithms, and new formal techniques to improve this research. Specifically, we sought to take steps toward: researching experimentally-relevant parameters in our simulations, learning parallel computing to have as a resource for our group, and achieving a 100 {times} speedup over our starting-point Cray2 simulation code`s performance.
Alfvén Waves in Gyrokinetic Plasmas
NASA Astrophysics Data System (ADS)
Lee, W. W.; Qin, H.; Lewandowski, J. L. V.
2002-11-01
The ordering that ρi << L_eq enables us to use the gyrokinetic description for a magnetically-confined plasma,^1-3 by seperating the fast gyromotion of the particle from its slow gyrocenter motion and the associated polarization effects. In this paper, we present a brief comparison of the properties of the Alfvén waves based on the conventional MHD descriptions with those under the gyrokinetic approximation, and show that the unique treatment of the polarization effects in the gyrokinetic formalism makes it possible to eliminate the compressional Alfvén waves without resorting to geometric simplification for the reduced gyrokinetic-MHD equations. Thus, one may use the existing gyrokinetic particle simulation techniques^1,4-5 together with the elliptic multigrid solver^6 on the modern day massively parallel computers to study the effects of neoclassical and microturbulence transport on the global (MHD) problems based on the realistic MHD equilibria. This work is supported by the US DoE SciDAC project. ^1W. W. Lee, Phys. Fluids 26, 556 ('83); J. Comp. Phys. 72, 243 ('87). 2T. S. Hahm, W. W. Lee and A. Brizard, Phys. Fluids 31, 1940 ('88). ^3H. Qin, W. M. Tang and W. W. Lee, Phys. Plasmas 7, 4433 ('00). 4I. Manuilskiy and W. W. Lee, Phys. Plasmas 7, 1381 ('00). ^5W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Phys. Plasmas 8, 4435 ('01). \\$^6J. L. V. Lewandowski, manuscript in preparation.
Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulations
White, A. E.; Howard, N. T.; Greenwald, M.; Reinke, M. L.; Sung, C.; Baek, S.; Barnes, M.; Dominguez, A.; Ernst, D.; Gao, C.; Hubbard, A. E.; Hughes, J. W.; Lin, Y.; Parra, F.; Porkolab, M.; Rice, J. E.; Walk, J.; Wukitch, S. J.; Team, Alcator C-Mod; Candy, J.; and others
2013-05-15
Multi-channel transport experiments have been conducted in auxiliary heated (Ion Cyclotron Range of Frequencies) L-mode plasmas at Alcator C-Mod [Marmar and Alcator C-Mod Group, Fusion Sci. Technol. 51(3), 3261 (2007)]. These plasmas provide good diagnostic coverage for measurements of kinetic profiles, impurity transport, and turbulence (electron temperature and density fluctuations). In the experiments, a steady sawtoothing L-mode plasma with 1.2 MW of on-axis RF heating is established and density is scanned by 20%. Measured rotation profiles change from peaked to hollow in shape as density is increased, but electron density and impurity profiles remain peaked. Ion or electron heat fluxes from the two plasmas are the same. The experimental results are compared directly to nonlinear gyrokinetic theory using synthetic diagnostics and the code GYRO [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. We find good agreement with experimental ion heat flux, impurity particle transport, and trends in the fluctuation level ratio (T(tilde sign){sub e}/T{sub e})/(ñ{sub e}/n{sub e}), but underprediction of electron heat flux. We find that changes in momentum transport (rotation profiles changing from peaked to hollow) do not correlate with changes in particle transport, and also do not correlate with changes in linear mode dominance, e.g., Ion Temperature Gradient versus Trapped Electron Mode. The new C-Mod results suggest that the drives for momentum transport differ from drives for heat and particle transport. The experimental results are inconsistent with present quasilinear models, and the strong sensitivity of core rotation to density remains unexplained.
NASA Astrophysics Data System (ADS)
Churchill, Randy; Chang, Cs; Ku, Seung-Hoe; Hager, Robert
2016-10-01
Turbulence in the edge (pedestal + SOL) is difficult to probe both experimentally and computationally, yet it may play a large role in the feasibility of a tokamak fusion reactor. XGC1 is a full-f gyrokinetic code aimed at including all of the important physics necessary to faithfully simulate transport in the edge region. Here we present statistical analyses of turbulent fluctuations of XGC1 outputs, including density, potential, and temperature. The skewness and kurtosis are investigated as indicators of the underlying distribution, and are shown to follow closely the skewness/kurtosis relation for gamma distributions. Spatial cross-correlation and cross-phase analysis will be presented to identify poloidal wavenumber regions of strongest particle and energy transport, helping to identify dominant turbulence modes in the pedestal and SOL. These comparisons will be made using both flux-surface averaged (important for total transport) and low-field side localized data (what experiments usually measure). Distributions of size and speed of edge turbulent eddies and blobs, and the connected physics associated with their radial transport will be explored. We acknowledge computing resources on Titan at OLCF through the 2015 INCITE and the 2016 ALCC Awards.
Muñoz, P. A. Kilian, P.; Büchner, J.; Told, D.; Jenko, F.
2015-08-15
In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (b{sub g}). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (β{sub i} = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (b{sub g} ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (b{sub g} ≳ 5). Kinetic PIC simulations using guide fields b{sub g} ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (β{sub i} = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (b{sub g} ≲ 3)
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Hinton, F. L.; Waltz, R. E.
2006-10-15
Expressions for particle and energy fluxes and heating rates due to turbulence are derived. These fluxes and heating rates are identified from moments of an extended drift-kinetic equation for the equilibrium distribution function. These include neoclassical as well as turbulent diffusion and heating. Phase-space conservation is demonstrated, allowing the drift-kinetic equation to be expressed in conservative form. This facilitates taking moments with few approximations, mainly those consistent with drift kinetics for the equilibrium distribution function and the relative smallness of the fluctuations. The turbulent heating is uniquely defined by choosing the standard gyrokinetic definition for the energy flux. With this definition, most of the heating can be expressed in the form of ohmic heating from turbulent parallel and perpendicular current density perturbations. The latter current is identified with grad-B and curvature drifts, plus terms involving magnetic perturbations (which are smaller for low beta). A small contribution to the heating comes from the divergence of an energy flux that is dependent on the finite gyroradius of the ions. The fluxes and heating rates are expressed in a form that can be easily evaluated from gyrokinetic turbulence simulations.
White, A. E.; Peebles, W. A.; Rhodes, T. L.; Schmitz, L.; Carter, T. A.; Hillesheim, J. C.; Doyle, E. J.; Zeng, L.; Holland, C. H.; Wang, G.; McKee, G. R.; Staebler, G. M.; Waltz, R. E.; DeBoo, J. C.; Petty, C. C.; Burrell, K. H.
2010-05-15
This paper presents new measurements of the cross-phase angle, alpha{sub n{sub eT{sub e}}}, between long-wavelength (k{sub t}hetarho{sub s}<0.5) density, n-tilde{sub e}, and electron temperature, T-tilde{sub e}, fluctuations in the core of DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak plasmas. The coherency and cross-phase angle between n-tilde{sub e} and T-tilde{sub e} are measured using coupled reflectometer and correlation electron cyclotron emission diagnostics that view the same plasma volume. In addition to the experimental results, two sets of local, nonlinear gyrokinetic turbulence simulations that are performed with the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are described. One set, called the pre-experiment simulations, was performed prior to the experiment in order to predict a change in alpha{sub n{sub eT{sub e}}} given experimentally realizable increases in the electron temperature, T{sub e}. In the experiment the cross-phase angle was measured at three radial locations (rho=0.55, 0.65, and 0.75) in both a 'Base' case and a 'High T{sub e}' case. The measured cross-phase angle is in good qualitative agreement with the pre-experiment simulations, which predicted that n-tilde{sub e} and T-tilde{sub e} would be out of phase. The pre-experiment simulations also predicted a decrease in cross-phase angle as T{sub e} is increased. Experimentally, this trend is observed at the inner two radial locations only. The second set of simulations, the postexperiment simulations, is carried out using local parameters taken from measured experimental profiles as input to GYRO. These postexperiment simulation results are in good quantitative agreement with the measured cross-phase angle, despite disagreements with transport fluxes. Directions for future modeling and experimental work are discussed.
Global particle-in-cell simulations of microturbulence with kinetic electrons
Lewandowski, J. L. V.; Rewoldt, G.; Ethier, S.; Lee, W. W.; Lin, Z.
2006-07-15
The effects of nonadiabatic electrons on ion temperature gradient drift instabilities have been studied in global toroidal geometry using the gyrokinetic particle simulation approach. Compared to the nonlinear global simulations based on only the adiabatic response of the electrons, we have found that the cross-field ion heat transport is two to three times larger in the presence of trapped electrons as compared to the purely adiabatic electron case, and that the zonal component of the electrostatic potential has a shorter wavelength. The numerical methods for calculating both the adiabatic and the nonadiabatic responses for the electrons are presented.
Micah Beck
2008-09-14
This project focused on the use of Logistical Networking technology to address the challenges involved in rapid sharing of data from the the Center's gyrokinetic particle simulations, which can be on the order of terabytes per time step, among researchers at a number of geographically distributed locations. There is a great need to manage data on this scale in a flexible manner, with simulation code, file system, database and visualization functions requiring access. The project used distributed data management infrastructure based on Logistical Networking technology to address these issues in a way that maximized interoperability and achieved the levels of performance the required by the Center's application community. The work focused on the development and deployment of software tools and infrastructure for the storage and distribution of terascale datasets generated by simulations running at the National Center for Computational Science at Oak Ridge National Laboratory.
2D properties of core turbulence on DIII-D and comparison to gyrokinetic simulations
Shafer, Morgan W; Fonck, R. J.; McKee, G. R.; Holland, Chris; White, A. E.; Schlossberg, D J
2012-01-01
Quantitative 2D characteristics of localized density fluctuations are presented over the range of 0.3 < r/a < 0.9 in L-mode plasmas on DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. Broadband density fluctuations increase in amplitude from (n) over tilde/n < 0.5% in the deep core to (n) over tilde/n similar to 2.5% near the outer region. The observed Doppler-shift due to the E x B velocity matches well with the measured turbulence group and phase velocities (in toroidally rotating neutral beam heated plasmas). Turbulence decorrelation rates are found to be similar to 200 kHz at the edge and to decrease toward the core (0.45 < r/a < 0.9) where they approach the E x B shearing rate (similar to 50 kHz). Radial and poloidal correlation lengths are found to scale with the ion gyroradius and exhibit an asymmetric poloidally elongated eddy structure. The ensemble-averaged turbulent eddy structure changes its tilt with respect to the radial-poloidal coordinates in the core, consistent with an E x B shear mechanism. The 2D spatial correlation and wavenumber spectra [S(k(r); k(theta))] are presented and compared to nonlinear flux-tube GYRO simulations at two radii, r/a = 0.5 and r/a = 0.75, showing reasonable overall agreement, but the GYRO spectrum exhibits a peak at finite kr for r/a = 0.75 that is not observed experimentally; E x B shear may cause this discrepancy. (C) 2012 American Institute of Physics.
Petascale Parallelization of the Gyrokinetic Toroidal Code
Ethier, Stephane; Adams, Mark; Carter, Jonathan; Oliker, Leonid
2010-05-01
The Gyrokinetic Toroidal Code (GTC) is a global, three-dimensional particle-in-cell application developed to study microturbulence in tokamak fusion devices. The global capability of GTC is unique, allowing researchers to systematically analyze important dynamics such as turbulence spreading. In this work we examine a new radial domain decomposition approach to allow scalability onto the latest generation of petascale systems. Extensive performance evaluation is conducted on three high performance computing systems: the IBM BG/P, the Cray XT4, and an Intel Xeon Cluster. Overall results show that the radial decomposition approach dramatically increases scalability, while reducing the memory footprint - allowing for fusion device simulations at an unprecedented scale. After a decade where high-end computing (HEC) was dominated by the rapid pace of improvements to processor frequencies, the performance of next-generation supercomputers is increasingly differentiated by varying interconnect designs and levels of integration. Understanding the tradeoffs of these system designs is a key step towards making effective petascale computing a reality. In this work, we examine a new parallelization scheme for the Gyrokinetic Toroidal Code (GTC) [?] micro-turbulence fusion application. Extensive scalability results and analysis are presented on three HEC systems: the IBM BlueGene/P (BG/P) at Argonne National Laboratory, the Cray XT4 at Lawrence Berkeley National Laboratory, and an Intel Xeon cluster at Lawrence Livermore National Laboratory. Overall results indicate that the new radial decomposition approach successfully attains unprecedented scalability to 131,072 BG/P cores by overcoming the memory limitations of the previous approach. The new version is well suited to utilize emerging petascale resources to access new regimes of physical phenomena.
Free Energy Cascade in Gyrokinetic Turbulence
Banon Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-02-04
In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.
Nonlinear gyrokinetic equations for tokamak microturbulence
Hahm, T.S.
1988-05-01
A nonlinear electrostatic gyrokinetic Vlasov equation, as well as Poisson equation, has been derived in a form suitable for particle simulation studies of tokamak microturbulence and associated anomalous transport. This work differs from the existing nonlinear gyrokinetic theories in toroidal geometry, since the present equations conserve energy while retaining the crucial linear and nonlinear polarization physics. In the derivation, the action-variational Lie perturbation method is utilized in order to preserve the Hamiltonian structure of the original Vlasov-Poisson system. Emphasis is placed on the dominant physics of the collective fluctuations in toroidal geometry, rather than on details of particle orbits. 13 refs.
Shear-Alfven waves in gyrokinetic plasmas
Lee, W. W.; Lewandowski, J. L. V.; Hahm, T. S.; Lin, Z.
2001-10-01
It is found that the thermal fluctuation level of the shear-Alfven waves in a gyrokinetic plasma is dependent on plasma {beta}((equivalent to)c{sub s}{sup 2}/v{sub A}{sup 2}), where c{sub s} is the ion acoustic speed and v{sub A} is the Alfven velocity. This unique thermodynamic property based on the fluctuation--dissipation theorem is verified in this paper using a new gyrokinetic particle simulation scheme, which splits the particle distribution function into the equilibrium part as well as the adiabatic and nonadiabatic parts. The numerical implication of this property is discussed.
Gyrokinetic studies of stellarator turbulent transport via Gene
NASA Astrophysics Data System (ADS)
Mynick, H. E.; Xanthopoulos, P.; Boozer, A. H.
2009-05-01
We study the turbulence and turbulent transport in stellarators (and tokamaks), via analysis of simulation results from the 3D gyrokinetic code Gene with particular emphasis on the configuration-dependence of turbulence characteristics. Present day stellarator designs seek to optimize stellarator neoclassical transport. With the advent of simulation codes like Gene, one can now seek to characterize and then optimize designs for TOTAL transport. The comparison between different configurations in stellarator parameter space is of 2 types, global and local. Global comparisons look at changes in plasma performance (eg, levels of turbulent fluxes and zonal flows, dependence of these on plasma gradients) between very different designs (eg, a QA versus a QI/QO design). Local comparisons look at the changes in performance between slight variants of the same design. Both aid in gaining insight into which geometric features (curvature, local and global shear, etc) are important in determining the turbulent characteristics. P. Xanthopoulos, F. Jenko, Phys.Plasmas 13, 092301 (2006).
Coury, M.; Guttenfelder, W.; Mikkelsen, D. R.; ...
2016-06-30
Linear (local) gyrokinetic predictions of edge microinstabilities in highly shaped, lithiated and non-lithiated NSTX discharges are reported using the gyrokinetic code GS2. Microtearing modes dominate the non-lithiated pedestal top. The stabilization of these modes at the lithiated pedestal top enables the electron temperature pedestal to extend further inwards, as observed experimentally. Kinetic ballooning modes are found to be unstable mainly at the mid-pedestal of both types of discharges, with un- stable trapped electron modes nearer the separatrix region. At electron wavelengths, ETG modes are found to be unstable from mid-pedestal outwards for ηe, exp ~2.2 with higher growth rates formore » the lithiated discharge. Near the separatrix, the critical temperature gradient for driving ETG modes is reduced in the presence of lithium, re ecting the reduction of the lithiated density gradients observed experimentally. A preliminary linear study in the edge of non-lithiated discharges shows that the equilibrium shaping alters the electrostatic modes stability, found more unstable at high plasma shaping.« less
Coury, M.; Guttenfelder, W.; Mikkelsen, D. R.; Canik, J. M.; Canal, G. P.; Diallo, A.; Kaye, S.; Kramer, G. J.; Maingi, R.
2016-06-30
Linear (local) gyrokinetic predictions of edge microinstabilities in highly shaped, lithiated and non-lithiated NSTX discharges are reported using the gyrokinetic code GS2. Microtearing modes dominate the non-lithiated pedestal top. The stabilization of these modes at the lithiated pedestal top enables the electron temperature pedestal to extend further inwards, as observed experimentally. Kinetic ballooning modes are found to be unstable mainly at the mid-pedestal of both types of discharges, with un- stable trapped electron modes nearer the separatrix region. At electron wavelengths, ETG modes are found to be unstable from mid-pedestal outwards for η_{e, exp} ~2.2 with higher growth rates for the lithiated discharge. Near the separatrix, the critical temperature gradient for driving ETG modes is reduced in the presence of lithium, re ecting the reduction of the lithiated density gradients observed experimentally. A preliminary linear study in the edge of non-lithiated discharges shows that the equilibrium shaping alters the electrostatic modes stability, found more unstable at high plasma shaping.
Coury, M.; Guttenfelder, W.; Mikkelsen, D. R.; Canik, J. M.; Canal, G. P.; Diallo, A.; Kaye, S.; Kramer, G. J.; Maingi, R.
2016-06-30
Linear (local) gyrokinetic predictions of edge microinstabilities in highly shaped, lithiated and non-lithiated NSTX discharges are reported using the gyrokinetic code GS2. Microtearing modes dominate the non-lithiated pedestal top. The stabilization of these modes at the lithiated pedestal top enables the electron temperature pedestal to extend further inwards, as observed experimentally. Kinetic ballooning modes are found to be unstable mainly at the mid-pedestal of both types of discharges, with un- stable trapped electron modes nearer the separatrix region. At electron wavelengths, ETG modes are found to be unstable from mid-pedestal outwards for η_{e, exp} ~2.2 with higher growth rates for the lithiated discharge. Near the separatrix, the critical temperature gradient for driving ETG modes is reduced in the presence of lithium, re ecting the reduction of the lithiated density gradients observed experimentally. A preliminary linear study in the edge of non-lithiated discharges shows that the equilibrium shaping alters the electrostatic modes stability, found more unstable at high plasma shaping.
Continuum Gyrokinetic Edge New Technology
Dorr, M. R.; Hittinger, J. A.; Dorf, M.; Cohen, R.; Ghosh, D.; Lee, W.; Reynolds, C.
2016-05-02
COGENT is a simulation code that models the plasma evolution in the edge region of a tokamak fusion reactor, from the open field line scrape-off layer, across the separatrix, and into the core. The model is based on the 4D gyrokinetic closure of the kinetic equations for a plasma coupled to an electrostatic potential field. The background magnetic field is prescribed either analytically or generated from experimental data, and the grid is aligned with magnetic flux surfaces. Multiple collision operator options are provided, from Krook to fully nonlinear Fokker-Planck.
Beyond scale separation in gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Garbet, X.; Sarazin, Y.; Grandgirard, V.; Dif-Pradalier, G.; Darmet, G.; Ghendrih, Ph.; Angelino, P.; Bertrand, P.; Besse, N.; Gravier, E.; Morel, P.; Sonnendrücker, E.; Crouseilles, N.; Dischler, J.-M.; Latu, G.; Violard, E.; Brunetti, M.; Brunner, S.; Lapillonne, X.; Tran, T.-M.; Villard, L.; Boulet, M.
2007-09-01
This paper presents the results obtained with a set of gyrokinetic codes based on a semi-Lagrangian scheme. Several physics issues are addressed, namely, the comparison between fluid and kinetic descriptions, the intermittent behaviour of flux driven turbulence and the role of large scale flows in toroidal ITG turbulence. The question of the initialization of full-F simulations is also discussed.
Global particle-in-cell simulations of plasma pressure effects on Alfvenic modes
Mishchenko, Alexey; Koenies, Axel; Hatzky, Roman
2011-01-15
Global linear gyrokinetic particle-in-cell simulations of electromagnetic modes in realistic tokamak geometry are reported. The effect of plasma pressure on Alfvenic modes is studied. It is shown that the fast-particle pressure can considerably affect the shear Alfven wave continuum structure and hence the toroidicity-induced gap in the continuum. It is also found that the energetic ions can substantially reduce the growth rate of the ballooning modes (and perhaps completely stabilize them in a certain parameter range). Ballooning modes are found to be the dominant instabilities if the bulk-plasma pressure gradient is large enough.
NASA Astrophysics Data System (ADS)
Hakim, Ammar; Hammett, Greg; Shi, Eric
2016-10-01
We have developed a hybrid discontinuous/continuous Galerkin scheme for gyrokinetic equations. Our scheme solves the equations in the Poisson bracket formulation and, with a careful choice of basis functions, conserves energy exactly. We use a sparse grid representation to reduce cost. We have developed a novel form of sheath boundary conditions, going beyond logical-sheath BCs, that allows current flow into the boundaries, yet retains overall charge continuity as well as conserves energy. First applications to a simplified model of the NSTX-like scrape-off-layer (SOL) are presented. We treat the SOL in simplified geometry, retaining magnetic curvature effects, and study the turbulent spreading of particle and heat flux. Extensions to include magnetic fluctuations and collisions are discussed. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.
Second order gyrokinetic theory for particle-in-cell codes
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-15
The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell–Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell–Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell–Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.
Second order gyrokinetic theory for particle-in-cell codes
NASA Astrophysics Data System (ADS)
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-01
The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell-Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell-Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.
Simulating Global Climate Summits
ERIC Educational Resources Information Center
Vesperman, Dean P.; Haste, Turtle; Alrivy, Stéphane
2014-01-01
One of the most persistent and controversial issues facing the global community is climate change. With the creation of the UN Framework Convention on Climate Change (UNFCCC) in 1992 and the Kyoto Protocol (1997), the global community established some common ground on how to address this issue. However, the last several climate summits have failed…
Simulating Global Climate Summits
ERIC Educational Resources Information Center
Vesperman, Dean P.; Haste, Turtle; Alrivy, Stéphane
2014-01-01
One of the most persistent and controversial issues facing the global community is climate change. With the creation of the UN Framework Convention on Climate Change (UNFCCC) in 1992 and the Kyoto Protocol (1997), the global community established some common ground on how to address this issue. However, the last several climate summits have failed…
Carlos Serrano, Lawrence Doolittle
2015-10-29
GFS is a simulation engine that is used for the characterization of Accelerator performance parameters based on the machine layout, configuration and noise sources. It combines extensively tested Feedback models with a longitudinal phase space tracking simulator along with the interaction between the two via beam-based feedback using a computationally efficient simulation engine. The models include beam instrumentation, considerations on loop delays for in both the R and beam-based feedback loops, as well as the ability to inject noise (both correlated and uncorrelated) at different points of the machine including a full characterization of the electron gun performance parameters.
Carlos Serrano, Lawrence Doolittle
2015-10-29
GFS is a simulation engine that is used for the characterization of Accelerator performance parameters based on the machine layout, configuration and noise sources. It combines extensively tested Feedback models with a longitudinal phase space tracking simulator along with the interaction between the two via beam-based feedback using a computationally efficient simulation engine. The models include beam instrumentation, considerations on loop delays for in both the R and beam-based feedback loops, as well as the ability to inject noise (both correlated and uncorrelated) at different points of the machine including a full characterization of the electron gun performance parameters.
Self-consistent modeling of multiscale gyrokinetics and transport
NASA Astrophysics Data System (ADS)
Parker, Jeffrey; Lodestro, Lynda; Told, Daniel; Jenko, Frank
2016-10-01
In the core of tokamak plasmas, a separation of timescales between turbulence and transport makes direct simulation of both processes computationally expensive. A workable, practical method to exploit the separation of timescales will be a key component in enabling the self-consistent solution of macroscopic profiles of density and temperature. We report on progress to implement the LoDestro scheme coupled with the gyrokinetic code GENE to perform for the first time coupled turbulence and transport simulations using a global gyrokinetic code. One of the advantages of the LoDestro scheme, which is essentially a method of solving an implicitly advanced nonlinear transport problem, is that it does not use Newton iteration and hence avoids difficulties that arise from calculating Jacobians or Jacobian-vector products in the presence of noisy fluxes. Instead, the implicit timestep equation is solved with an iteration scheme by representing the turbulent flux as the sum of diffusive and convective pieces, after which Picard iteration is used to converge to the self-consistent solution. Preliminary results will be presented. Prepared by LLNL under Contract DE-AC52-07NA27344.
Gyrokinetic Models for Edge Plasmas*
NASA Astrophysics Data System (ADS)
Dimits, Andris
2010-11-01
The use of gyrokinetic equations for the simulation of magnetic fusion edge and scrapeoff-layer plasmas requires that the equations be valid for large relative perturbation amplitudes and, possibly, large flows. The Hamiltonian gyrokinetic theory has therefore been extended to two new orderings [1,2] that are more general than the standard ones in that they allow for potential perturbations or ExB flows of order the thermal levels. These theories both generalize and show that additional terms should have been present some related prior work. Here, full (low-β) electromagnetic toroidal equation sets are presented, and he energy conservation relations are derived using Noether's theorem in a Lagrangian variational approach. Useful subsidiary and reduced orderings are also considered that result in considerable simplification, and methods for the numerical implementation of the new terms in the equations will also be discussed. *This work was performed for US DOE by LLNL under Contract DE-AC52-07NA27344 and is part of the ESL. [4pt] [1] A.M. Dimits et al., Phys. Fluids B4, 274 (1992). [0pt] [2] A.M. Dimits, Phys. Plasmas 17, 055901 (2010).
NASA Astrophysics Data System (ADS)
Spong, D. A.; Bass, E. M.; Deng, W.; Heidbrink, W. W.; Lin, Z.; Tobias, B.; Van Zeeland, M. A.; Austin, M. E.; Domier, C. W.; Luhmann, N. C.
2012-08-01
A verification and validation study is carried out for a sequence of reversed shear Alfvén instability time slices. The mode frequency increases in time as the minimum (qmin) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (#142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL are compared. The experimental mode structure of the instability was measured using time-resolved two-dimensional electron cyclotron emission imaging. The three models reproduce the frequency upsweep event within ±10% of each other, and the average of the code predictions is within ±8% of the measurements; growth rates are predicted that are consistent with the observed spectral line widths. The mode structures qualitatively agree with respect to radial location and width, dominant poloidal mode number, ballooning structure, and the up-down asymmetry, with some remaining differences in the details. Such similarities and differences between the predictions of the different models and the experimental results are a valuable part of the verification/validation process and help to guide future development of the modeling efforts.
Global Simulation of Aviation Operations
NASA Technical Reports Server (NTRS)
Sridhar, Banavar; Sheth, Kapil; Ng, Hok Kwan; Morando, Alex; Li, Jinhua
2016-01-01
The simulation and analysis of global air traffic is limited due to a lack of simulation tools and the difficulty in accessing data sources. This paper provides a global simulation of aviation operations combining flight plans and real air traffic data with historical commercial city-pair aircraft type and schedule data and global atmospheric data. The resulting capability extends the simulation and optimization functions of NASA's Future Air Traffic Management Concept Evaluation Tool (FACET) to global scale. This new capability is used to present results on the evolution of global air traffic patterns from a concentration of traffic inside US, Europe and across the Atlantic Ocean to a more diverse traffic pattern across the globe with accelerated growth in Asia, Australia, Africa and South America. The simulation analyzes seasonal variation in the long-haul wind-optimal traffic patterns in six major regions of the world and provides potential time-savings of wind-optimal routes compared with either great circle routes or current flight-plans if available.
Linear global gyrokinetic simulations of toroidal Alfven eigenmodes in KSTAR plasmas
NASA Astrophysics Data System (ADS)
Shahzad, M.; Rizvi, H.; Ryu, C. M.
2016-12-01
Excitation of toroidal Alfven eigenmodes (TAEs) in KSTAR tokamak plasmas has been studied by using the GENE code. Verification and benchmark analysis are performed for Alfven eigenmodes (AEs) excited by the energetic particles (EPs) in comparison with the AEs from the GYGLES code, and excellent agreements are found. In addition, the threshold value of the EP density gradient to destabilize the TAE has been investigated. For the plasma equilibrium of KSTAR discharge (10574), TAEs of n = 2 are found to be excited by coupling of adjoining poloidal harmonics (5, 6), (6, 7), and (7, 8). The dependence of the growth rate and frequency of the TAE on the EP density gradient is examined. It is found that the threshold value of EP density gradient increases with the higher poloidal mode coupling, of which location moves outward in the radial direction. The growth rates of TAEs with higher poloidal mode numbers are smaller than those with lower poloidal mode numbers, indicating that perpendicular wavenumbers play an important role. The efficiency of the EP drive for the TAE decreases for a higher poloidal mode coupling. At a higher EP density gradient, TAEs with higher poloidal harmonics are less unstable due to the decrease in the radial extents of the modes.
Simulating PACE Global Ocean Radiances
NASA Technical Reports Server (NTRS)
Gregg, Watson W.; Rousseaux, Cecile S.
2017-01-01
The NASA PACE mission is a hyper-spectral radiometer planned for launch in the next decade. It is intended to provide new information on ocean biogeochemical constituents by parsing the details of high resolution spectral absorption and scattering. It is the first of its kind for global applications and as such, poses challenges for design and operation. To support pre-launch mission development and assess on-orbit capabilities, the NASA Global Modeling and Assimilation Office has developed a dynamic simulation of global water-leaving radiances, using an ocean model containing multiple ocean phytoplankton groups, particulate detritus, particulate inorganic carbon (PIC), and chromophoric dissolved organic carbon (CDOC) along with optical absorption and scattering processes at 1 nm spectral resolution. The purpose here is to assess the skill of the dynamic model and derived global radiances. Global bias, uncertainty, and correlation are derived using available modern satellite radiances at moderate spectral resolution. Total chlorophyll, PIC, and the absorption coefficient of CDOC (aCDOC), are simultaneously assimilated to improve the fidelity of the optical constituent fields. A 5-year simulation showed statistically significant (P < 0.05) comparisons of chlorophyll (r = 0.869), PIC (r = 0.868), and a CDOC (r =0.890) with satellite data. Additionally, diatoms (r = 0.890), cyanobacteria (r = 0.732), and coccolithophores (r = 0.716) were significantly correlated with in situ data. Global assimilated distributions of optical constituents were coupled with a radiative transfer model (Ocean-Atmosphere Spectral Irradiance Model, OASIM) to estimate normalized water-leaving radiances at 1 nm for the spectral range 250-800 nm. These unassimilated radiances were within 0.074 mW/sq cm/micron/sr of MODIS-Aqua radiances at 412, 443, 488, 531, 547, and 667 nm. This difference represented a bias of 10.4% (model low). A mean correlation of 0.706 (P < 0.05) was found with global
NASA Astrophysics Data System (ADS)
Kim, Kyuho; Kwon, Jae-Min; Chang, C. S.; Seo, Janghoon; Ku, S.; Choe, W.
2017-06-01
Flux-driven full-f gyrokinetic simulations are performed to study carbon impurity effects on the ion temperature gradient (ITG) turbulence and ion thermal transport in a toroidal geometry. Employing the full-f gyrokinetic code XGC1, both main ions and impurities are evolved self-consistently including turbulence and neoclassical physics. It is found that the carbon impurity profile self-organizes to form an inwardly peaked density profile, which weakens the ITG instabilities and reduces the overall fluctuations and ion thermal transport. A stronger reduction appears in the low frequency components of the fluctuations. The global structure of E × B flow also changes, resulting in the reduction of global avalanche like transport events in the impure plasma. Detailed properties of impurity transport are also studied, and it is revealed that both the inward neoclassical pinch and the outward turbulent transport are equally important in the formation of the steady state impurity profile.
Global Health Simulation During Residency
Rosenman, Jane R.; Fischer, Philip R.; Arteaga, Grace M.; Hulyalkar, Manasi; Butteris, Sabrina M.; Pitt, Michael B.
2016-01-01
Resident participation in international health electives (IHEs) has been shown to be beneficial, yet not all residents have the opportunity to participate. We sought to determine whether participating in simulated global health cases, via the standardized Simulation Use for Global Away Rotations (SUGAR) curriculum, was useful for all pediatric residents, not merely those planning to go on an IHE. Pediatric residents in our program took part in 2 SUGAR cases and provided feedback via an online survey. Thirty-six of 40 residents participated (90%); 72% responded to the survey. Three of 10 residents not previously planning to work in resource-limited settings indicated participation in SUGAR made them more likely to do so. Nearly all residents (88%) felt SUGAR should be part of the residency curriculum. All felt better prepared for working cross-culturally. While designed to prepare trainees for work in resource-limited settings, SUGAR may be beneficial for all residents. PMID:27583300
Gyrokinetic characterization of the isotope effect in turbulent transport at the FT-2 tokamak
NASA Astrophysics Data System (ADS)
Niskala, P.; Gurchenko, A. D.; Gusakov, E. Z.; Altukhov, A. B.; Esipov, L. A.; Kantor, M. Yu; Kiviniemi, T. P.; Kouprienko, D.; Korpilo, T.; Lashkul, S. I.; Leerink, S.; Perevalov, A. A.; Rochford, R.
2017-04-01
Isotope effect allows fusion devices to perform better when heavier hydrogen isotopes are used as fuel, but the reason for this improvement is not yet understood. We present the first direct evidence of the isotope effect on particle confinement in the FT-2 tokamak and investigate it via gyrokinetic simulations. Experimental measurements for comparable hydrogen and deuterium discharges show that the particle confinement time increases by 40% for the heavier isotope species. The isotope effect on particle flux is reproduced in global and local gyrokinetic simulations. Global ELMFIRE simulations demonstrate a systemic reduction in particle fluxes across the radial range, showing a ratio of fluxes {{{Γ }}}{{H}}/{{{Γ }}}{{D}}=1.3 at the edge and {{{Γ }}}{{H}}/{{{Γ }}}{{D}}=1.4 at r/a=0.6. Local GENE simulations agree qualitatively with the result. Besides the fluctuation level, smaller scales and a favorable shift in the cross-phase between the turbulent fluctuations are found to contribute to the isotope effect in the simulations.
Dif-Pradalier, G; Grandgirard, V; Sarazin, Y; Garbet, X; Ghendrih, Ph
2009-08-07
The impact of ion-ion collisions on confinement is investigated with the full-f and global gyrokinetic Gysela code through a series of nonlinear turbulence simulations for tokamak parameters. A twofold scan in the turbulence drive and in collisionality is performed, highlighting (i) a heat transport expressed in terms of critical quantities-threshold and exponent, (ii) a first evidence of turbulent generation of poloidal momentum, and (iii) the dominance of mean flow shear, mediated through the turbulent corrugation of the mean profiles, with regard to the oft-invoked zonal flow shear.
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.
2009-08-01
The impact of ion-ion collisions on confinement is investigated with the full-f and global gyrokinetic Gysela code through a series of nonlinear turbulence simulations for tokamak parameters. A twofold scan in the turbulence drive and in collisionality is performed, highlighting (i) a heat transport expressed in terms of critical quantities—threshold and exponent, (ii) a first evidence of turbulent generation of poloidal momentum, and (iii) the dominance of mean flow shear, mediated through the turbulent corrugation of the mean profiles, with regard to the oft-invoked zonal flow shear.
Global Simulations of Magnetotail Reconnection
NASA Technical Reports Server (NTRS)
Kuznetsova, M. M.; Hesse, M.; Rastatter, L.; Toth, G.; Gombosi, T.
2007-01-01
There is a growing number of observational evidences of dynamic quasi-periodical magnetosphere response to continuously southward interplan etary magnetic field (IMF). However, traditional global MHD simulatio ns with magnetic reconnection supported by numerical dissipation and ad hoc anomalous resistivity driven by steady southward IMF often prod uce only quasi-steady configurations with almost stationary near-eart h neutral line. This discrepancy can be explained by the assumption that global MHD simulations significantly underestimate the reconnectio n rate in the magnetotail during substorm expansion phase. Indeed, co mparative studies of magnetic reconnection in small scale geometries demonstrated that traditional resistive MHD did not produce the fast r econnection rates observed in kinetic simulations. The major approxim ation of the traditional MHD approach is an isotropic fluid assumption) with zero off-diagonal pressure tensor components. The approximatio n, however, becomes invalid in the diffusion region around the reconn ection site where ions become unmagnetized and experience nongyrotropic behaviour. Deviation from gyrotropy in particle distribution functi on caused by kinetic effects manifests itself in nongyrotropic pressu re tensor with nonzero off-diagonal components. We use the global MHD code BATS-R-US and replace ad hoc parameters such as "critical curren t density" and "anomalous resistivity" with a physically motivated di ssipation model. The key element of the approach is to identify diffusion regions where the isotropic fluid MHD approximation is not applic able. We developed an algorithm that searches for locations of magnet otail reconnection sites. The algorithm takes advantage of block-based domain-decomposition technique employed by the BATS-R-US. Boundaries of the diffusion region around each reconnection site are estimated from the gyrotropic orbit threshold condition, where the ion gyroradius is equal to the distance to the
Global Simulations of Magnetotail Reconnection
NASA Technical Reports Server (NTRS)
Kuznetsova, M. M.; Hesse, M.; Rastatter, L.; Toth, G.; Gombosi, T.
2007-01-01
There is a growing number of observational evidences of dynamic quasi-periodical magnetosphere response to continuously southward interplan etary magnetic field (IMF). However, traditional global MHD simulatio ns with magnetic reconnection supported by numerical dissipation and ad hoc anomalous resistivity driven by steady southward IMF often prod uce only quasi-steady configurations with almost stationary near-eart h neutral line. This discrepancy can be explained by the assumption that global MHD simulations significantly underestimate the reconnectio n rate in the magnetotail during substorm expansion phase. Indeed, co mparative studies of magnetic reconnection in small scale geometries demonstrated that traditional resistive MHD did not produce the fast r econnection rates observed in kinetic simulations. The major approxim ation of the traditional MHD approach is an isotropic fluid assumption) with zero off-diagonal pressure tensor components. The approximatio n, however, becomes invalid in the diffusion region around the reconn ection site where ions become unmagnetized and experience nongyrotropic behaviour. Deviation from gyrotropy in particle distribution functi on caused by kinetic effects manifests itself in nongyrotropic pressu re tensor with nonzero off-diagonal components. We use the global MHD code BATS-R-US and replace ad hoc parameters such as "critical curren t density" and "anomalous resistivity" with a physically motivated di ssipation model. The key element of the approach is to identify diffusion regions where the isotropic fluid MHD approximation is not applic able. We developed an algorithm that searches for locations of magnet otail reconnection sites. The algorithm takes advantage of block-based domain-decomposition technique employed by the BATS-R-US. Boundaries of the diffusion region around each reconnection site are estimated from the gyrotropic orbit threshold condition, where the ion gyroradius is equal to the distance to the
Gyrokinetic Studies of Magnetic Reconnection
NASA Astrophysics Data System (ADS)
Pueschel, Moritz J.; Jenko, Frank; Told, Daniel; Buechner, Joerg
2011-10-01
Collisionless magnetic reconnection constitutes an effective mechanism for particle acceleration in astrophysical plasmas, in particular the solar corona. In addition, it is also of relevance to fusion experiments. Gyrokinetic simulations with the GENE code are performed to explore the temporal evolution of current sheets in two-dimensional slab geometry with a strong guide field. After successful code-code benchmarking, Extensive parameter studies are performed, covering a wide range of physical scenarios. In particular, differing findings regarding the influence of the ion temperature are explained. In its nonlinear phase, the characteristics of the reconnection process depend on whether the system is driven or decaying. Decaying turbulence sees an inverse cascade, and all energy is ultimately transferred to the largest radial scale. If driven by a Krook-type term, the system develops into a turbulent, quasi-stationary state. An important quantity to investigate in nonlinear simulations is the parallel electric field which is able to accelerate particles along the background magnetic field. The spatial structure of this field is studied for the different nonlinear cases, and its amplitude reported as a function of the drive frequency.
NASA Astrophysics Data System (ADS)
White, A. E.
2012-10-01
New experiments at Alcator C-Mod are challenging and expanding our understanding of electron, impurity particle, and momentum transport. Understanding these coupled transport channels is important, since alpha particles will slow down mostly on electrons in ITER intrinsically rotating, alpha-heated plasmas. Core density fluctuations are reduced in high performance (H98˜1) I-mode plasmas by up to 30% compared to L-mode. At the L-I transition, the core turbulence changes lead the edge turbulence changes. This is in contrast to observations at L-H transitions, where the edge turbulence changes lead the core turbulence changes. It is also found that L-mode and I-mode plasmas are both ITG dominant, with lower linear ITG growth rates in I-mode. TRANSP analysis indicates that core electron heat transport is reduced in I-mode compared to L-mode, with little change in ion heat transport. This indicates that significant electron heat transport is driven by ITG turbulence in L-mode. However, impurity particle transport is similar in L-mode and I-mode, suggesting that tracking changes in ITG drive alone does not describe as well the transport in this channel. Additionally, in L-mode plasmas, small < 20% changes in line averaged density lead to dramatic differences in the on-axis rotation, due to a hollowing of the radial profile at marginally lower density. This change in the shape of the rotation profile in L-mode plasmas does not appear to occur at the ITG/TEM boundary, contrary to similar phenomena seen in Ohmic plasmas. For the first time, local, long-wavelength density and electron temperature fluctuations in the core plasma (0.4 < r/a < 0.9) at C-Mod have been measured with reflectometry and correlation ECE. These new fluctuation measurements at C-Mod will allow for better testing and validation of transport models. Gyrokinetic simulations are in progress to interpret the new multichannel and multifield turbulence/transport results from C-Mod.
Gyrofluid-Gyrokinetic Hybrid Turbulence Model
NASA Astrophysics Data System (ADS)
Dorland, William; Mandell, Noah
2015-11-01
Gyrofluid models of tokamak turbulence are efficient compared to gyrokinetic models, in three senses. First, it is typically easier to develop one's intuition from fluid equations than kinetic equations. Second, because gyrofluid equations are only three-dimensional (instead of 5D or 6D), simulations with gyrofluid models require less memory than kinetic simulations and can therefore more easily fit on highly-optimized computing hardware, such as graphics processors. The third advantage is a result of the first two: one can develop and test ideas quickly with gyrofluid models. The disadvantage of gyrofluid models is their potential lack of physics fidelity. In this poster, we present our attempt to take full advantage of gyrofluid models, without sacrificing physics fidelity. Our approach is encapsulated in the Gryf-X code, which is an implementation of hybrid gyrofluid/gyrokinetic equations. The key improvements that we have brought to bear are: an improved understanding of the cascade of free energy simultaneously in k⊥ and v⊥ an improved model of zonal flow physics; and an implementation of the equations on modern heterogeneous computing platforms, both as a standalone simulation tool and as a component of TRINITY (a transport modeling code for tokamaks).
NASA Astrophysics Data System (ADS)
Howard, N. T.; Greenwald, M.; Mikkelsen, D. R.; White, A. E.; Reinke, M. L.; Ernst, D.; Podpaly, Y.; Candy, J.
2012-05-01
Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.
A basic plasma test for gyrokinetics: GDC turbulence in LAPD
NASA Astrophysics Data System (ADS)
Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.
2017-02-01
Providing an important step towards validating gyrokinetics under comparatively little-explored conditions, simulations of pressure-gradient-driven plasma turbulence in the Large Plasma Device (LAPD) are compared with experimental observations. The corresponding signatures confirm the existence of a novel regime of turbulence, based on the recently-discovered gradient-driven drift coupling (GDC) instability, which is thus confirmed as a candidate mechanism for turbulence in basic, space and astrophysical plasmas. Despite the limitations of flux-tube gyrokinetics for this scenario, when accounting for box size scaling by applying a scalar factor η =6, agreement between simulations and experiment improves to within a factor of two for key observables: compressional magnetic, density, and temperature fluctuations, both in amplitude and structure. Thus, a first, strong indication is presented that the GDC instability seen in gyrokinetics appears to operate in the experiment and that the essential instability physics is present in the numerical model. Overall, the gyrokinetic framework and its numerical implementation in the Gene code therefore perform well for LAPD plasmas very different from their brethren in fusion experiments.
Wang, W X; Hahm, T S; Ethier, S; Rewoldt, G; Lee, W W; Tang, W M; Kaye, S M; Diamond, P H
2009-01-23
A significant inward flux of toroidal momentum is found in global gyrokinetic simulations of ion temperature gradient turbulence, leading to core plasma rotation spin-up. The underlying mechanism is identified to be the generation of residual stress due to the k parallel symmetry breaking induced by global quasistationary zonal flow shear. Simulations also show a significant off-diagonal element associated with the ion temperature gradient in the neoclassical momentum flux, while the overall neoclassical flux is small. In addition, the residual turbulence found in the presence of strong E x B flow shear may account for neoclassical-level ion heat and anomalous momentum transport widely observed in experiments.
Leerink, S.; Heikkinen, J. A.; Janhunen, S. J.; Kiviniemi, T. P.; Nora, M.; Ogando, F.
2008-09-15
The ELMFIRE gyrokinetic simulation code has been used to perform full f simulations of the FT-2 tokamak. The dynamics of the radial electric field and the creation of poloidal velocity in the presence of turbulence are presented.
The theory of gyrokinetic turbulence: A multiple-scales approach
NASA Astrophysics Data System (ADS)
Plunk, Gabriel Galad
gradient (ETG)) which rules out the possibility that ultra-fine streamers could produce significant transport, (3) a demonstration that the variation in the phasing of the primary mode (which depend on the values, of the equilibrium scale lengths of the system) effects the strength of the secondary instability, distinguishing the gyrokinetic model from a previous gyrofluid model, (4) parameter scans for the mean-scale gradient lengths which suggest a possible role of secondary instabilities in the Dimits shift and the formation of electron internal transport barriers (ITB) in tokamaks, (5) a formulation of the theory for fully gyrokinetic ions and electrons in order to explore the transition between ETG and ITG scales and (6) demonstrate the existence of a mechanism for the saturation of long-wavelength ETG modes in this ETG-ITG transition range (modes which have been demonstrated in simulations not to saturate when employing the ETG Boltzmann-ion gyrokinetic system). The final project is an application of the methods from inertial range understanding of fluid turbulence, to describe the stationary state of fully developed two-dimensional gyrokinetic turbulence. This work explores the relatively new idea of a phase-space cascade, whereby fine scales are nonlinearly generated in both position space and velocity space, and ultimately smoothed by collisional entropy production. This process constitutes the thermodynamic balance which occurs in the true steady state of a turbulent plasma, including those found in fusion devices. The results of this work include (1) exact third order relations (in analogy to Kolmogorov's four-fifths law), (2) phenomenological scaling theories for the forward and inverse cascades, (3) a detailed description of the relationship of the two-dimensional gyrokinetic cascade to the Charney-Hasegawa-Mima and two-dimensional Navier-Stokes cascades, (4) a Hankel transform formalism for treating velocity scales in the distribution function and (4) power
Nonlinear theory of drift-cyclotron kinetics and the possible breakdown of gyro-kinetics
Waltz, R. E.; Deng Zhao
2013-01-15
A nonlinear theory of drift-cyclotron kinetics (termed cyclo-kinetics here) is formulated to test the breakdown of the gyro-kinetic approximations. Six dimensional cyclo-kinetics can be regarded as an extension of five dimensional gyro-kinetics to include high-frequency cyclotron waves, which can interrupt the low-frequency gyro-averaging in the (sixth velocity grid) gyro-phase angle. Nonlinear cyclo-kinetics has no limit on the amplitude of the perturbations. Formally, there is no gyro-averaging when all cyclotron (gyro-phase angle) harmonics of the perturbed distribution function (delta-f) are retained. Retaining only the (low frequency) zeroth cyclotron harmonic in cyclo-kinetics recovers both linear and nonlinear gyro-kinetics. Simple recipes are given for converting continuum nonlinear delta-f gyro-kinetic transport simulation codes to cyclo-kinetics codes by retaining (at least some) higher cyclotron harmonics.
Global simulation of field-reversed configuration using fully kinetic ion and drift kinetic electron
NASA Astrophysics Data System (ADS)
Lau, Calvin; Fulton, Daniel; Kuley, Animesh; Bao, Jian; Lin, Zhihong; Binderbauer, Michael; Tajima, Toshiki; Schmitz, Lothar; the TAE Team Team
2016-10-01
In the last several years, the C-2/C-2U advanced beam-driven field-reversed configuration (FRC) experiments at Tri Alpha Energy have progressed to consistent, reproducible plasma lifetimes of 10+ ms, i.e. FRCs have reached transport limited regimes. In FRC geometry, the thermal ion gyroradius is on the order of the size of the plasma near the magnetic null-point. Fast ion orbits intersect both the FRC core and the scrape-off layer (SOL) regions. Previous local simulations of electrostatic drift-wave instabilities using the Gyrokinetic Toroidal Code (GTC) find the core to be robustly stable with driftwave instability only in the SOL at frequencies approaching the ion cyclotron frequency. Therefore, FRC transport studies require fully kinetic ion simulations with cross-separatrix coupling between the core and SOL. Here we report progress of such global simulations using fully kinetic ions and drift kinetic electrons, including the implementation of the Boris push scheme for cyclotron motion and cylindrical coordinates for the separatrix. Supported by the Norman Rostoker Fellowship.
Global particle-in-cell simulations of microturbulence with kinetic electrons
NASA Astrophysics Data System (ADS)
Lewandowski, Jerome
2005-10-01
A systematic approach (called the splitting scheme [1]) to accurately model electron kinetic effects in gyrokinetic PIC simulation is presented. The 1D application of the scheme shows that the linear properties of the simulated plasma are more accurate [1]than the conventional perturbative delta-f scheme and that the nonlinear properties are considerably improved [2] It will be shown that an accurate loading of the initial distribution function based on a neural network algorithm [3] and a noise-free collisional operator [4]for PIC codes allow for even longer simulations with good momentum and energy conservation properties. The toroidal version of the scheme, which relies on a global finite-element elliptic solver [5] is used in the GTC code [6]; preliminary results on trapped- electron mode modified ITG turbulence will be reported.[1]J.L.V. Lewandowski, Phys. Plasmas 8, 3204 (2003)[2]J.L.V. Lewandowski, PPCF, 45, L49 (2003)[3]J.L.V. Lewandowski, Phys. Lett. A, 291 (2003)[4] J.L.V. Lewandowski, Phys. Plasmas 12, 2322 (2005)[5] Y. Nishimura et al, submitted to JCP (2004) [6] Z. Lin et al, Phys. Plasmas 6, 1857 (2000) [supported by Scidac Center for GPS project
Confronting Global Issues: A Multipurpose IR Simulation
ERIC Educational Resources Information Center
Shellman, Stephen M.; Turan, Kursad
2006-01-01
This article describes an international relations simulation that focuses on threats of transnational insurgent organizations, the future of the Iraqi regime, and the effect of globalization on foreign policies. It contains both the Simulation Director's Guide and the Participant's Guide. The guides explain the steps taken to run the simulation…
Confronting Global Issues: A Multipurpose IR Simulation
ERIC Educational Resources Information Center
Shellman, Stephen M.; Turan, Kursad
2006-01-01
This article describes an international relations simulation that focuses on threats of transnational insurgent organizations, the future of the Iraqi regime, and the effect of globalization on foreign policies. It contains both the Simulation Director's Guide and the Participant's Guide. The guides explain the steps taken to run the simulation…
Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes
NASA Astrophysics Data System (ADS)
Tronko, N.; Bottino, A.; Chandre, C.; Sonnendruecker, E.
2017-06-01
The reduced particle model is the central element for the systematic derivation of the gyrokinetic Vlasov-Maxwell equations from first principles. Coupled to the fields inside the gyrokinetic field-particle Lagrangian, the reduced particle model defines polarization and magnetization effects appearing in the gyrokinetic Maxwell equations. It is also used for the reconstruction of the gyrokinetic Vlasov equation from the particle characteristics. Various representations of reduced particle models are available according to the choice of the gyrokinetic phase space coordinates. In this paper, the Hamiltonian representation of the reduced particle dynamics at an order suitable for the implementation in particle-in-cell simulations is explicitly derived from the general reduction procedure. The second-order (with respect to the fluctuating electromagnetic fields), full finite Larmor radius (FLR) Hamiltonian gyrokinetic particle model as well as the second-order model suitable specifically for the long-wavelength approximation (i.e., containing up to the second-order FLR corrections), are derived and compared to the model recently implemented in the particle-in-cell code ORB5. We show that the same long-wavelength approximate equations can also be derived by taking the proper limit of the full FLR model.
SciDAC Center for Plasma Edge Simulation
Lin, Zhihong
2013-12-17
This project with a total funding of $592,998 for six years has partially supported four postdoctoral researchers at the University of California, Irvine (UCI). The UCI team has formulated electrostatic and electromagnetic global gyrokinetic particle simulation models with kinetic electrons, implemented these models in the edge code XGC1, performed benchmark between GTC and XGC1, developed computational tools for gyrokinetic particle simulation in tokamak edge geometry, and initiated preparatory study of edge turbulence using GTC code. The research results has been published in 12 papers and presented at many international and national conferences.
Global Positioning System Simulator Field Operational Procedures
NASA Technical Reports Server (NTRS)
Kizhner, Semion; Quinn, David A.; Day, John H. (Technical Monitor)
2002-01-01
Global Positioning System (GPS) simulation is an important activity in the development or qualification of GPS signal receivers for space flight. Because a GPS simulator is a critical resource it is highly desirable to develop a set of field operational procedures to supplement the basic procedures provided by most simulator vendors. Validated field procedures allow better utilization of the GPS simulator in the development of new test scenarios and simulation operations. These procedures expedite simulation scenario development while resulting in scenarios that are more representative of the true design, as well as enabling construction of more complex simulations than previously possible, for example, spacecraft maneuvers. One difficulty in the development of a simulation scenario is specifying various modes of test vehicle motion and associated maneuvers requiring that a user specify some (but not all) of a few closely related simulation parameters. Currently this can only be done by trial and error. A stand-alone procedure that implements the simulator maneuver motion equations and solves for the motion profile transient times, jerk and acceleration would be of considerable value. Another procedure would permit the specification of some configuration parameters that would determine the simulated GPS signal composition. The resulting signal navigation message, for example, would force the receiver under test to use only the intended C-code component of the simulated GPS signal. A representative class of GPS simulation-related field operational procedures is described in this paper. These procedures were developed and used in support of GPS integration and testing for many successful spacecraft missions such as SAC-A, EO-1, AMSAT, VCL, SeaStar, sounding rockets, and by using the industry standard Spirent Global Simulation Systems Incorporated (GSSI) STR series simulators.
Discoveries from the exploration of gyrokinetic momentum transporta)
NASA Astrophysics Data System (ADS)
Staebler, G. M.; Waltz, R. E.; Kinsey, J. E.
2011-05-01
The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.
Discoveries from the exploration of gyrokinetic momentum transport
Staebler, G.M.; Waltz, R. E.; Kinsey, J. E.
2011-05-15
The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.
Transport, noise, and conservation properties in gyrokinetic plasmas
NASA Astrophysics Data System (ADS)
Jenkins, Thomas
2005-10-01
The relationship between various transport properties (such as particle and heat flux, entropy production, heating, and collisional dissipation) [1] is examined in electrostatic gyrokinetic simulations of ITG modes in simple geometry. The effect of the parallel velocity nonlinearity on the achievement of steady-state solutions and the transport properties of these solutions is examined; the effects of nonadiabatic electrons are also considered. We also examine the effectiveness of the electromagnetic split-weight scheme [2] in reducing the noise and improving the conservation properties (energy, momentum, particle number, etc.) of gyrokinetic plasmas. [1] W. W. Lee and W. M. Tang, Phys. Fluids 31, 612 (1988). [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z.Lin, Phys. Plasmas 8, 4435 (2001).
Nonlinear gyrokinetic theory for finite-BETA plasmas
Hahm, T.S.; Lee, W.W.; Brizard, A.
1988-02-01
A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.
Global magnetohydrodynamic simulations of the magnetosphere
NASA Astrophysics Data System (ADS)
Walker, Raymond J.; Ogino, Tatsuki
1989-04-01
The use of a global MHD simulation to study the magnetospheric configuration is demonstrated by reviewing some of the results obtained with the model of Ogino (1986). The steady-state configuration of the magnetosphere in the absence of an IMF is considered, and it is demonstrated that this configuration is changed when a northward or southward IMF is introduced. It is noted that the magnetosphere is very dynamic, and that, since global MHD simulations are intrinsically time-dependent, they offer the possibility of modeling the time sequence of events in the magnetosphere. Results are presented from a calculation in which a magnetospheric substrom is modeled.
Global magnetohydrodynamic simulations of the magnetosphere
NASA Technical Reports Server (NTRS)
Walker, Raymond J.; Ogino, Tatsuki
1989-01-01
The use of a global MHD simulation to study the magnetospheric configuration is demonstrated by reviewing some of the results obtained with the model of Ogino (1986). The steady-state configuration of the magnetosphere in the absence of an IMF is considered, and it is demonstrated that this configuration is changed when a northward or southward IMF is introduced. It is noted that the magnetosphere is very dynamic, and that, since global MHD simulations are intrinsically time-dependent, they offer the possibility of modeling the time sequence of events in the magnetosphere. Results are presented from a calculation in which a magnetospheric substrom is modeled.
Testing Gyrokinetics on C-Mod and NSTX
M.H. Redi; W. Dorland; C.L. Fiore; D. Stutman; J.A. Baumgaertel; B. Davis; S.M. Kaye; D.C. McCune; J. Menard; G. Rewoldt
2005-06-20
Quantitative benchmarks of computational physics codes against experiment are essential for the credible application of such codes. Fluctuation measurements can provide necessary critical tests of nonlinear gyrokinetic simulations, but such require extraordinary computational resources. Linear micro-stability calculations with the GS2 [1] gyrokinetic code have been carried out for tokamak and ST experiments which exhibit internal transport barriers (ITB) and good plasma confinement. Qualitative correlation is found for improved confinement before and during ITB plasmas on Alcator C-Mod [2] and NSTX [3], with weaker long wavelength micro-instabilities in the plasma core regions. Mixing length transport models are discussed. The NSTX L-mode is found to be near marginal stability for kinetic ballooning modes. Fully electromagnetic, linear, gyrokinetic calculations of the Alcator C-Mod ITB during off-axis rf heating, following four plasma species and including the complete electron response show ITG/TEM microturbulence is suppressed in the plasma core and in the barrier region before barrier formation, without recourse to the usual requirements of velocity shear or reversed magnetic shear [4-5]. No strongly growing long or short wavelength drift modes are found in the plasma core but strong ITG/TEM and ETG drift wave turbulence is found outside the barrier region. Linear microstability analysis is qualitatively consistent with the experimental transport analysis, showing low transport inside and high transport outside the ITB region before barrier formation, without consideration of ExB shear stabilization.
Differential formulation of the gyrokinetic Landau operator
NASA Astrophysics Data System (ADS)
Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David
2017-02-01
Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth-MacDonald-Judd potential functions must be kept gyroangle dependent.
Differential formulation of the gyrokinetic Landau operator
Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David
2017-01-05
Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.
'Disaster day': global health simulation teaching.
Mohamed-Ahmed, Rayan; Daniels, Alex; Goodall, Jack; O'Kelly, Emily; Fisher, James
2016-02-01
As society diversifies and globalisation quickens, the importance of teaching global health to medical undergraduates increases. For undergraduates, the majority of exposure to 'hands-on' teaching on global health occurs during optional elective periods. This article describes an innovative student-led initiative, 'Disaster Day', which used simulation to teach global health to undergraduates. The teaching day began with an introduction outlining the work of Médecins Sans Frontières and the basic principles of resuscitation. Students then undertook four interactive simulation scenarios: Infectious Diseases in a Refugee Camp, Natural Disaster and Crush Injury, Obstetric Emergency in a Low-Income Country, and Warzone Gunshot Wound. Sessions were facilitated by experienced doctors and fourth-year students who had been trained in the delivery of the scenarios. Students completed pre- and post-session evaluation forms that included the self-rating of confidence in eight learning domains (using a five-point Likert scale). Twenty-seven students voluntarily attended the session, and all provided written feedback. Analysis of the pre- and post-session evaluations demonstrated statistically significant improvements in confidence across all but one domains (Wilcoxon signed rank test). Free-text feedback was overwhelmingly positive, with students appreciating the practical aspect of the scenarios. For undergraduates, the majority of exposure to 'hands-on' teaching on global health occurs during optional elective periods Simulation-based teaching can provide students with 'hands-on' exposure to global health in a controlled, reproducible fashion and appears to help develop their confidence in a variety of learning domains. The more widespread use of such teaching methods is encouraged: helping tomorrow's doctors develop insight into global health challenges may produce more rounded clinicians capable of caring for more culturally diverse populations. © 2015 John Wiley & Sons
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-15
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cell equations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheath boundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. This test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokinetic equations and some of the numerical challenges in developing an edge gyrokinetic code.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
NASA Astrophysics Data System (ADS)
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-01
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cell equations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheath boundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. This test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokinetic equations and some of the numerical challenges in developing an edge gyrokinetic code.
A Short Introduction to General Gyrokinetic Theory
H. Qin
2005-02-14
Interesting plasmas in the laboratory and space are magnetized. General gyrokinetic theory is about a symmetry, gyro-symmetry, in the Vlasov-Maxwell system for magnetized plasmas. The most general gyrokinetic theory can be geometrically formulated. First, the coordinate-free, geometric Vlasov-Maxwell equations are developed in the 7-D phase space, which is defined as a fiber bundle over the space-time. The Poincar{copyright}-Cartan-Einstein 1-form pullbacked onto the 7-D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinite small generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincar{copyright}-Cartan-Einstein 1-form, which also generates the most relaxed condition under which the gyro-symmetry still exists. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Since the general gyrokinetic system-developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and Liouville volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfven wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered. Three examples of applications of the general gyrokinetic theory developed in the areas of plasma equilibrium and plasma waves are
ERIC Educational Resources Information Center
Lawless, Kimberly A.; Brown, Scott W.
2015-01-01
GlobalEd 2 (GE2) is a set of technology-mediated, problem-based learning (PBL) simulations for middle-grade students, that capitalises on the multidisciplinary nature of the social sciences as an expanded curricular space for students to learn and apply scientific literacies and concepts, while simultaneously also enriching their understanding of…
ERIC Educational Resources Information Center
Lawless, Kimberly A.; Brown, Scott W.
2015-01-01
GlobalEd 2 (GE2) is a set of technology-mediated, problem-based learning (PBL) simulations for middle-grade students, that capitalises on the multidisciplinary nature of the social sciences as an expanded curricular space for students to learn and apply scientific literacies and concepts, while simultaneously also enriching their understanding of…
Global kinetic ballooning mode simulations in BOUT++
NASA Astrophysics Data System (ADS)
Ma, C. H.; Xu, X. Q.
2017-01-01
We report on simulation results of a 3+1 gyro-Landau-fluid (GLF) model in BOUT++ framework, which contributes to increasing the physics understanding of the edge turbulence. We find that there is no second stability region of kinetic ballooning modes (KBM) in the concentric circular geometry. The first unstable β of KBM decreases below the ideal ballooning mode threshold with increasing {ηi} . In order to study the KBM in the real tokamak equilibrium, we find that the approximation of shifted circular geometry (β \\ll {{\\varepsilon}2} ) is not valid for a high β global equilibrium near the second stability region of KBM. Thus we generate a series of real equilibria from a global equilibrium solver CORSICA, including both Shafranov shift and elongation effects, but not including bootstrap current. In these real equilibria, the second stability region of KBM are observed in our global linear simulations. The most unstable mode for different β are the same while the mode number spectrum near the second stability region is wider than the case near the first stability region. The nonlinear simulations show that the energy loss of an ELM keeps increasing with β, because the linear drive of the turbulence remains strong for the case near the second stability region during profile evolution.
Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence
NASA Astrophysics Data System (ADS)
Belli, Emily Ann
Advanced numerical algorithms for gyrokinetic simulations are explored for more effective studies of plasma turbulent transport. The gyrokinetic equations describe the dynamics of particles in 5-dimensional phase space, averaging over the fast gyromotion, and provide a foundation for studying plasma microturbulence in fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/continuum gyrokinetic solvers are compared. An iterative implicit scheme based on numerical approximations of the plasma response is developed. This method reduces the long time needed to set-up implicit arrays, yet still has larger time step advantages similar to a fully implicit method. Various model preconditioners and iteration schemes, including Krylov-based solvers, are explored. An Alternating Direction Implicit algorithm is also studied and is surprisingly found to yield a severe stability restriction on the time step. Overall, an iterative Krylov algorithm might be the best approach for extensions of core tokamak gyrokinetic simulations to edge kinetic formulations and may be particularly useful for studies of large-scale ExB shear effects. The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic equilibria based on interpolations of representative JET-like shapes. High shaping is found to be a stabilizing influence on both the linear ITG instability and nonlinear ITG turbulence. A scaling of the heat flux with elongation of chi ˜ kappa-1.5 or kappa-2 (depending on the triangularity) is observed, which is consistent with previous gyrofluid simulations. Thus, the GS2 turbulence simulations are explaining a significant fraction, but not all, of the empirical elongation scaling. The remainder of the scaling may come from (1) the edge boundary conditions for core turbulence, and (2) the larger Dimits nonlinear critical temperature gradient shift due to the
Hatch, David R.; Del-Castillo-Negrete, Diego B; Terry, P.W.
2012-01-01
Higher order singular value decomposition (HOSVD) is explored as a tool for analyzing and compressing gyrokinetic data. An efficient numerical implementation of an HOSVD algorithm is described. HOSVD is used to analyze the full six-dimensional (three spatial, two velocity space, and time dimensions) gyrocenter distribution function from gyrokinetic simulations of ion temperature gradient, electron temperature gradient, and trapped electron mode driven turbulence. The HOSVD eigenvalues for the velocity space coordinates decay very rapidly, indicating that only a few structures in velocity space can capture the most important dynamics. In almost all of the cases studied, HOSVD extracts parallel velocity space structures which are very similar to orthogonal polynomials. HOSVD is also used to compress gyrokinetic datasets, an application in which it is shown to significantly outperform the more commonly used singular value decomposition. It is shown that the effectiveness of the HOSVD compression improves as the dimensionality of the dataset increases. (C) 2012 Elsevier Inc. All rights reserved.
Low frequency fully kinetic simulation of the toroidal ion temperature gradient instability
NASA Astrophysics Data System (ADS)
Sturdevant, B. J.; Chen, Y.; Parker, S. E.
2017-08-01
A fully kinetic ion model is useful for the verification of gyrokinetic turbulence simulations in certain regimes, where the gyrokinetic model may break down due to the lack of small ordering parameters. However, for a fully kinetic model to be of value, it must first be able to accurately simulate low frequency drift-type instabilities typically well within the domain of gyrokinetics. Here, a fully kinetic ion model is formulated with weak gradient drive terms and applied to the toroidal ion-temperature-gradient (ITG) instability for the first time. Implementation in toroidal geometry is discussed, where orthogonal coordinates are used for particle dynamics, but field-line-following coordinates are used for the field equation allowing for high resolution of the field-aligned mode structure. Variational methods are formulated for integrating the equation of motion allowing for accuracy at a modest time-step size. Linear results are reported for both the slab and toroidal ITG instabilities. Good agreement with full Vlasov and gyrokinetic theory is demonstrated in slab geometry. Good agreement with global gyrokinetic simulation is also shown in toroidal geometry.
Global magnetohydrodynamic simulations of the magnetosphere
Walker, R.J.; Ogino, T.
1989-04-01
Global magnetohydrodynamic (MHD) simulations of the interaction between the solar wind and a planetary magnetosphere enable us to calculate self-consistently the time-dependent three-dimensional configuration of the magnetosphere. To demonstrate the application of a global MHD model to the magnetosphere, the authors have calculated the dependence of the magnetospheric configuration and polar-cap structure on the north-south component of the interplanetary magnetic field (IMF). First, they modeled the magnetosphere in the absence of an IMF and found a slowly evolving system in which steady convection leads to slow reconnection in the plasma sheet. When a uniform northward IMF was initially imposed throughout the system the plasma sheet thickened in a small region near the noon-midnight meridian and extended into the tail lobes. When viewed from the polar cap, this appears as a narrow finger of closed field lines extending into the polar cap. The plasma sheet thickening is caused by reconnection on the nightside magnetopause. This plasma sheet extension becomes less pronounced when the northward IMF enters the simulation box with the solar wind. For both cases the convection near midnight is toward the sun, and region-1-type field-aligned currents appear on both sides of the plasma sheet extension. For northward IMF the resulting magnetospheric configuration approached a quasi-steady state in which stable magnetospheric convection was maintained. The simulation results indicate that the presence of a northward B in the plasma sheet stabilizes the tail.
Global Simulations of the Jovian Magnetosphere
NASA Astrophysics Data System (ADS)
Chané, E.; Saur, J.; Poedts, S.
2012-12-01
We present global numerical simulations of the interactions between the solar wind and Jupiter's magnetosphere. In our model, an inner boundary region representing the effects of Jupiter's ionosphere (ion-neutral collisions) and the mass-loading associated with the Io torus are explicitly included. To test the quality of our model, the results of four simulations performed on a relatively coarse mesh, using different mass-loading rates and different ionospheric conductances are compared with analytical models, in situ measurements and remote-sensing observations. Our azimuthal velocity profiles and the position of the corotation break-down are in good quantitative agreement with Hill [1979, 2001], with profiles calculated with the model of Saur et al. [2004], and with Voyager observations [McNutt et al., 1981]. In addition, one simulation is performed on a high resolution mesh. The position of the corotation break-down in the equatorial plane maps, as expected, to the main auroral oval in the ionosphere with a clearly visible corotation enforcing current system. The dawn dusk asymmetry (Khurana, 2004) is also visible in the simulations, with a thicker current sheet on the dusk side and with faster azimuthal plasma flows on the dawn side. Finally, our simulations reproduce the discontinuity in Jupiter's main auroral oval in the prenoon sector observed by Radioti et al. (2008).
Validation of the gyrokinetic model in ITG and TEM dominated L-mode plasmas
NASA Astrophysics Data System (ADS)
Howard, N. T.; White, A. E.; Reinke, M. L.; Greenwald, M.; Holland, C.; Candy, J.; Walk, J. R.
2013-12-01
A rigorous validation of the gyrokinetic model was performed in both ion temperature gradient (ITG) and trapped electron mode (TEM) dominated Alcator C-Mod plasmas at (normalized midplane minor radius) r/a = 0.5 and 0.8. Analysis focuses on two L-mode discharges operated with 1.2 and 3.5 MW of ion cyclotron resonance heating. In depth investigation into the experimental uncertainties and simulation sensitivities in these discharges allows for a stringent test of the gyrokinetic model implemented by the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) in both the centre of the stiff gradient region (r/a = 0.5) and the middle of the region often associated with the transport ‘shortfall’(r/a = 0.8). To identify the nature of the plasma turbulence and to ensure a robust evaluation of the model's ability to reproduce experiment, the sensitivity of the simulation results to experimental uncertainty in turbulence drive and suppression terms were determined at both radial locations. When significant TEM activity is present, nonlinear gyrokinetic simulations are found to reproduce both electron and ion experimental heat fluxes within their diagnosed uncertainties. In contrast, in the absence of TEM, electron heat fluxes are robustly under predicted by low-k, gyrokinetic simulation.
Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER
Chang, Choong Seock; Ku, Seung -Hoe; Loarte, Alberto; ...
2017-07-11
Here, the XGC1 edge gyrokinetic code is used to study the width of the heat-flux to divertor plates in attached plasma condition. The flux-driven simulation is performed until an approximate power balance is achieved between the heat-flux across the steep pedestal pressure gradient and the heat-flux on the divertor plates.
Search for the Missing L-mode Edge Transport and Possible Breakdown of Gyrokinetics
NASA Astrophysics Data System (ADS)
Waltz, R. E.
2012-10-01
While GYRO simulations of typical core (0 < r/a < 0.7) DIII-D L-modes seems to be in good agreement with experiment, simulated low-k (kθρs< 1) transport and turbulence intensity is more than 5-fold lower than experimentally inferred levels in the near edge L-mode (r/a=0.7-0.95) DIII-D shot 128913 [1]. Global edge slice GYRO simulations of this and the well-studied discharge 101391 [2] are presented here to document the shortfall. TGLF transport code simulations over a large L-mode database indicate this short fall is not atypical so that L-mode edges transit to H-like pedestal profiles contrary to experiment. High edge e-i collisionality stabilizes the TEM modes so that diffusivities (χ) decrease like T^7/2/n to the cold edge. The very high magnetic shear and density gradients stabilize the ITG despite the very high temperature gradient drive and high q. High-k ETG can make-up for the shortfall in the electron but increases ion transport very little. Near L-edge transport is highly local. Focusing on local simulations at r/a=0.9, the ion channel short fall can exceed 10-fold. An artificial 10-fold increase in collisionality is needed to reach the expected resistive g-mode scaling with χ increasing like nT-1/2. Identical GYRO drift kinetic ion simulations (suppressing the gyroaverage) are close to experiment levels suggesting a possible breakdown of low-frequency gyrokinetics. Formulation of a nonlinear theory of 6D drift-cyclotron kinetics following the fast time scale of the gyrophase to test the breakdown of 5D gyrokinetics with reduced model simulations is presented. 6pt [1] C. Holland, A.E. White, et al., Phys. Plasmas 16, 052301 (2009). [2] R.E. Waltz, J. Candy, C.C. Petty, Phys. Plasmas 13, 072304 (2006).
A study of self organized criticality in ion temperature gradient mode driven gyrokinetic turbulence
Mavridis, M.; Isliker, H.; Vlahos, L.; Görler, T.; Jenko, F.; Told, D.
2014-10-15
An investigation on the characteristics of self organized criticality (Soc) in ITG mode driven turbulence is made, with the use of various statistical tools (histograms, power spectra, Hurst exponents estimated with the rescaled range analysis, and the structure function method). For this purpose, local non-linear gyrokinetic simulations of the cyclone base case scenario are performed with the GENE software package. Although most authors concentrate on global simulations, which seem to be a better choice for such an investigation, we use local simulations in an attempt to study the locally underlying mechanisms of Soc. We also study the structural properties of radially extended structures, with several tools (fractal dimension estimate, cluster analysis, and two dimensional autocorrelation function), in order to explore whether they can be characterized as avalanches. We find that, for large enough driving temperature gradients, the local simulations exhibit most of the features of Soc, with the exception of the probability distribution of observables, which show a tail, yet they are not of power-law form. The radial structures have the same radial extent at all temperature gradients examined; radial motion (transport) though appears only at large temperature gradients, in which case the radial structures can be interpreted as avalanches.
Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks
NASA Astrophysics Data System (ADS)
Qin, Hong
A general gyrokinetic formalism and appropriate computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both magnetohydrodynamic (MHD) instabilities and electromagnetic drift waves. The gyrokinetic system of equation is derived by phase- space Lagrangian Lie perturbation methods which enable applications to modes with arbitrary wavelength. An important component missing from previous electromagnetic gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed in the present analysis. This is accomplished by introducing a new ``distribution function'' and an associated governing gyrokinetic equation. Consequently, the compressional Alfvén waves and cyclotron waves can be systematically treated. The new insights into the gyrokinetic perpendicular dynamics uncovered here clarify the understanding of the gyrokinetic approach-the real spirit of the gyrokinetic reduction is to decouple the gyromotion from the guiding center orbital motion, instead of averaging it out. The gyrokinetic perpendicular dynamics is in fact essential to the recovery of the MHD model from a fully kinetic derivation. In particular, it serves to generalize, in gyrokinetic framework, Spitzer's solution of the fluid/particle paradox to a broader regime of applicability. The gyrokinetic system is also shown to be reducible to a simpler form to deal with shear Alfvén waves. This consists of an appropriate form of the gyrokinetic equation governing the distribution function, the gyrokinetic Poisson equation, and a newly derived gyrokinetic moment equation. If all of the kinetic effects are neglected, the gyrokinetic moment equation is shown to recover the ideal MHD equation for shear Alfvén modes. In addition, a gyrokinetic Ohm's law, including both the perpendicular and the parallel components, is
Global Cloud Liquid Water Path Simulations(.
NASA Astrophysics Data System (ADS)
Lemus, Lilia; Rikus, Lawrie; Martin, C.; Platt, R.
1997-01-01
A new parameterization of cloud liquid water and ice content has been included in the Bureau of Meteorology Global Assimilation and Prediction System. The cloud liquid water content is derived from the mean cloud temperatures in the model using an empirical relationship based on observations. The results from perpetual January and July simulations are presented and show that the total cloud water path steadily decreases toward high latitudes, with two relative maxima at midlatitudes and a peak at low latitudes. To validate the scheme, the simulated fields need to be processed to produce liquid water paths that can be directly compared with the corresponding field derived from Special Sensor Microwave/Imager (SSM/I) data. This requires the identification of cloud ice water content within the parameterization and a prescription to account for the treatment of strongly precipitating subgrid-scale cloud. The resultant cloud liquid water paths agree qualitatively with the SSM/I data but show some systematic errors that are attributed to corresponding errors in the model's simulation of cloud amounts. Given that a more quantitative validation requires substantial improvement in the model's diagnostic cloud scheme, the comparison with the SSM/I data indicates that the cloud water path, derived from the cloud liquid water content parameterization introduced in this paper, is consistent with the observations and can be usefully incorporated in the prediction system.
Electromagnetic nonlinear gyrokinetics with polarization drift
NASA Astrophysics Data System (ADS)
Duthoit, F.-X.; Hahm, T. S.; Wang, Lu
2014-08-01
A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.
Electromagnetic nonlinear gyrokinetics with polarization drift
Duthoit, F.-X.; Hahm, T. S.; Wang, Lu
2014-08-15
A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.
Adaptive wavelet simulation of global ocean dynamics
NASA Astrophysics Data System (ADS)
Kevlahan, N. K.-R.; Dubos, T.; Aechtner, M.
2015-07-01
In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.
Global Diffusion Tractography by Simulated Annealing.
Robini, Marc C; Ozon, Matthew; Frindel, Carole; Yang, Feng; Zhu, Yuemin
2017-03-01
Our goal is to develop a robust global tractography method for cardiac diffusion imaging. A graph is stretched over the whole myocardium to represent the fiber structure, and the solutions are minima of a graph energy measuring the fidelity to the data along with the fiber density and curvature. The optimization is performed by a variant of simulated annealing that offers increased design freedom without sacrificing theoretical convergence guarantees. Numerical experiments on synthetic and real data demonstrate the capability of our tractography algorithm to deal with low angular resolution, highly noisy data. In particular, our algorithm outperforms the Bayesian model-based algorithm of Reisert et al. (NeuroImage, vol. 54, no. 2, 2011) and the graph-based algorithm of Frindel et al. (Magn. Reson. Med., vol. 64, no. 4, 2010) at the noise levels typical of in vivo imaging. The proposed algorithm avoids the drawbacks of local techniques and is very robust to noise, which makes it a promising tool for in vivo diffusion imaging of moving organs. Our approach is global in terms of both the fiber structure representation and the minimization problem. It also allows us to adjust the trajectory density by simply changing the vertex-lattice spacing in the graph model, a desirable feature for multiresolution tractography analysis.
Gyrokinetic studies of core turbulence features in ASDEX Upgrade H-mode plasmas
Navarro, A. Bañón Told, D.; Happel, T.; Görler, T.; Abiteboul, J.; Bustos, A.; Doerk, H.; Jenko, F.
2015-04-15
Gyrokinetic validation studies are crucial for developing confidence in the model incorporated in numerical simulations and thus improving their predictive capabilities. As one step in this direction, we simulate an ASDEX Upgrade discharge with the GENE code, and analyze various fluctuating quantities and compare them to experimental measurements. The approach taken is the following. First, linear simulations are performed in order to determine the turbulence regime. Second, the heat fluxes in nonlinear simulations are matched to experimental fluxes by varying the logarithmic ion temperature gradient within the expected experimental error bars. Finally, the dependence of various quantities with respect to the ion temperature gradient is analyzed in detail. It is found that density and temperature fluctuations can vary significantly with small changes in this parameter, thus making comparisons with experiments very sensitive to uncertainties in the experimental profiles. However, cross-phases are more robust, indicating that they are better observables for comparisons between gyrokinetic simulations and experimental measurements.
Toroidal Alfvén eigenmodes with nonlinear gyrokinetic and fluid hybrid models
NASA Astrophysics Data System (ADS)
Cole, M. D. J.; Biancalani, A.; Bottino, A.; Kleiber, R.; Könies, A.; Mishchenko, A.
2017-02-01
Alfvén eigenmodes may be important in driving fast particle transport in magnetic confinement fusion devices, with potentially deleterious results. To explain and predict this behaviour, numerical simulations are necessary. In order to predict transport, modes must be simulated through to their nonlinear saturated state. In this work, the first simulations of non-linear wave-particle interaction between an energetic particle population and a Toroidal Alfvén Eigenmode are performed in which fluctuations responding self-consistently to modification of the fast particle profile are calculated with gyrokinetic treatment of all plasma species. Results from two such gyrokinetic codes are compared with new results from non-perturbative and perturbative fluid-gyrokinetic hybrid codes. There is a power-law relationship between the saturated magnetic perturbation amplitude, δB/B0, and the linear mode growth rate, γL. All models show a transition from a higher to a lower exponent regime with increasing γL. Measured values of the higher exponent from different codes fall in a range between 1.45 and 1.79, while the lower exponent falls in a range between 0.47 and 0.79. There is a consistent difference of 1.0 between the higher and lower exponents independent of the model. The absolute level of saturated δB/B0 is determined by the damping rate. In the fluid-gyrokinetic hybrid codes, an ad-hoc damping is applied, while in the gyrokinetic case the measured damping is consistent with the estimated rate of physical electron Landau damping.
Lapillonne, X.; Brunner, S.; Dannert, T.; Jolliet, S.; Marinoni, A.; Villard, L.; Goerler, T.; Jenko, F.; Merz, F.
2009-03-15
In the context of gyrokinetic flux-tube simulations of microturbulence in magnetized toroidal plasmas, different treatments of the magnetic equilibrium are examined. Considering the Cyclone DIII-D base case parameter set [Dimits et al., Phys. Plasmas 7, 969 (2000)], significant differences in the linear growth rates, the linear and nonlinear critical temperature gradients, and the nonlinear ion heat diffusivities are observed between results obtained using either an s-{alpha} or a magnetohydrodynamic (MHD) equilibrium. Similar disagreements have been reported previously [Redd et al., Phys. Plasmas 6, 1162 (1999)]. In this paper it is shown that these differences result primarily from the approximation made in the standard implementation of the s-{alpha} model, in which the straight field line angle is identified to the poloidal angle, leading to inconsistencies of order {epsilon} ({epsilon}=a/R is the inverse aspect ratio, a the minor radius and R the major radius). An equilibrium model with concentric, circular flux surfaces and a correct treatment of the straight field line angle gives results very close to those using a finite {epsilon}, low {beta} MHD equilibrium. Such detailed investigation of the equilibrium implementation is of particular interest when comparing flux tube and global codes. It is indeed shown here that previously reported agreements between local and global simulations in fact result from the order {epsilon} inconsistencies in the s-{alpha} model, coincidentally compensating finite {rho}{sup *} effects in the global calculations, where {rho}{sup *}={rho}{sub s}/a with {rho}{sub s} the ion sound Larmor radius. True convergence between local and global simulations is finally obtained by correct treatment of the geometry in both cases, and considering the appropriate {rho}{sup *}{yields}0 limit in the latter case.
MERLIN Performance Simulation of Global CH4
NASA Astrophysics Data System (ADS)
Ehret, G.; Flamant, P.; Kiemle, C.; Quatrevalet, M.; Amediek, A.
2011-12-01
optically thin layers which also impact on the measurement performance are derived from CALIOP measurements for selected scenes. Global error maps for all four seasons are generated in order to demonstrate the CH4 flux error reduction potential by use of hypothetical MERLIN observations in observation simulation system experiments (OSSEs).
Gyrokinetic linear stability analysis of NSTX L-mode plasmas
NASA Astrophysics Data System (ADS)
Han, Ke; Ren, Yang
2016-10-01
NSTX offered unique opportunities in studying transport and turbulence with low aspect ratio, strong plasma shaping and strong E ×B shear. NSTX L-mode plasmas have some favorable properties to facilitate the study of the relation between microturbulence and thermal transport: easier to obtain stationary profiles; easier to maintain MHD quiescence; no complications from edge transport barrier. Studies of NSTX RF/NBI-heated L-mode plasmas have provided new insight into the role of ion and electron-scale turbulence in driving anomalous transport. Here we present linear stability analysis of some NSTX L-mode plasmas with GS2 gyrokinetic code. GS2 is an initial value gyrokinetic code which, in its linear mode, finds the fastest growing mode for a given pair of poloidal and radial wavenumbers. The linear simulations used local Miller equilibria and plasma parameters derived from measured experimental profiles with electromagnetic effects, electron and ion collisions and carbon impurity. The work is supported by DOE, China Scholarship Council, the Natural Science Foundation of China (61402138) and the Natural Science Foundation of Heilongjiang Province (E201452).
Gyrokinetic modelling of stationary electron and impurity profiles in tokamaks
Skyman, A. Tegnered, D. Nordman, H. Strand, P.
2014-09-15
Particle transport due to Ion Temperature Gradient (ITG)/Trapped Electron Mode (TEM) turbulence is investigated using the gyrokinetic code GENE. Both a reduced quasilinear treatment and nonlinear simulations are performed for typical tokamak parameters corresponding to ITG dominated turbulence. The gyrokinetic results are compared and contrasted with results from a computationally efficient fluid model. A selfconsistent treatment is used, where the stationary local profiles are calculated corresponding to zero particle flux simultaneously for electrons and trace impurities. The scaling of the stationary profiles with magnetic shear, safety factor, electron-to-ion temperature ratio, collisionality, toroidal sheared rotation, plasma β, triangularity, and elongation is investigated. In addition, the effect of different main ion mass on the zero flux condition is discussed. The electron density gradient can significantly affect the stationary impurity profile scaling. It is therefore expected that a selfconsistent treatment will yield results more comparable to experimental results for parameter scans where the stationary background density profile is sensitive. This is shown to be the case in scans over magnetic shear, collisionality, elongation, and temperature ratio, for which the simultaneous zero flux electron and impurity profiles are calculated. A slight asymmetry between hydrogen, deuterium, and tritium with respect to profile peaking is obtained, in particular, for scans in collisionality and temperature ratio.
Towards nonhydrostatic simulation of moist global flows
NASA Astrophysics Data System (ADS)
Kurowski, Marcin J.; Grabowski, Wojciech W.; Smolarkiewicz, Piotr K.
2015-04-01
High-resolution simulation of moist global flows for numerical weather prediction and climate research requires convection-permitting nonhydrostatic flow solvers valid across the entire range of spatial scales, from small-scale dynamics to planetary-scale flows. Fluid flow solvers based on compressible dynamics meet such a requirement, but they need special treatments of acoustic modes to make them computationally efficient. Soundproof (e.g., anelastic) solvers filter out acoustic modes, but their application to the large-scale dynamics has been questioned in the past. In addition, mesoscale and large-scale hydrostatic pressure perturbations are typically excluded from moist thermodynamics in standard anelastic models. This presentation will review these issues and report application of the explicit/implicit compressible and anelastic versions of the finite-difference non-oscillatory forward-in-time EULAG model to the idealized baroclinic instability problem and to the Held-Suarez climate benchmark. All model versions share a common numerical framework and allow confident assessment of the impacts of governing equations mathematical formulations on model solutions. The implicit compressible version allows time steps as large as the anelastic version, typically two orders of magnitude larger than required by the explicit compressible version. We will show an excellent agreement between solutions obtained with the explicit and implicit compressible versions. Systematic differences between compressible and anelastic solutions are present in the baroclinic test case. In contrast, the climate benchmark shows that the compressible and anelastic model versions simulate similar zonally averaged fields, and that the meridional transports of entropy, momentum and moisture agree well between the two model versions.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the
Gyrokinetic Calculations of Microinstabilities and Transport During RF H-Modes on Alcator C-Mod
M.H. Redi; C. Fiore; P. Bonoli; C. Bourdelle; R. Budny; W.D. Dorland; D. Ernst; G. Hammett; D. Mikkelsen; J. Rice; S. Wukitch
2002-06-18
Physics understanding for the experimental improvement of particle and energy confinement is being advanced through massively parallel calculations of microturbulence for simulated plasma conditions. The ultimate goal, an experimentally validated, global, non-local, fully nonlinear calculation of plasma microturbulence is still not within reach, but extraordinary progress has been achieved in understanding microturbulence, driving forces and the plasma response in recent years. In this paper we discuss gyrokinetic simulations of plasma turbulence being carried out to examine a reproducible, H-mode, RF heated experiment on the Alcator CMOD tokamak3, which exhibits an internal transport barrier (ITB). This off axis RF case represents the early phase of a very interesting dual frequency RF experiment, which shows density control with central RF heating later in the discharge. The ITB exhibits steep, spontaneous density peaking: a reduction in particle transport occurring without a central particle source. Since the central temperature is maintained while the central density is increasing, this also suggests a thermal transport barrier exists. TRANSP analysis shows that ceff drops inside the ITB. Sawtooth heat pulse analysis also shows a localized thermal transport barrier. For this ICRF EDA H-mode, the minority resonance is at r/a * 0.5 on the high field side. There is a normal shear profile, with q monotonic.
The nonlinear gyro-kinetic flux tube code GKW
NASA Astrophysics Data System (ADS)
Peeters, A. G.; Camenen, Y.; Casson, F. J.; Hornsby, W. A.; Snodin, A. P.; Strintzi, D.; Szepesi, G.
2009-12-01
A new nonlinear gyro-kinetic flux tube code (GKW) for the simulation of micro instabilities and turbulence in magnetic confinement plasmas is presented in this paper. The code incorporates all physics effects that can be expected from a state of the art gyro-kinetic simulation code in the local limit: kinetic electrons, electromagnetic effects, collisions, full general geometry with a coupling to a MHD equilibrium code, and E×B shearing. In addition the physics of plasma rotation has been implemented through a formulation of the gyro-kinetic equation in the co-moving system. The gyro-kinetic model is five-dimensional and requires a massive parallel approach. GKW has been parallelised using MPI and scales well up to 8192+ cores. The paper presents the set of equations solved, the numerical methods, the code structure, and the essential benchmarks. Program summaryProgram title: GKW Catalogue identifier: AEES_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEES_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 29 998 No. of bytes in distributed program, including test data, etc.: 206 943 Distribution format: tar.gz Programming language: Fortran 95 Computer: Not computer specific Operating system: Any for which a Fortran 95 compiler is available Has the code been vectorised or parallelised?: Yes. The program can efficiently utilise 8192+ processors, depending on problem and available computer. 128 processors is reasonable for a typical nonlinear kinetic run on the latest x86-64 machines. RAM:˜128 MB-1 GB for a linear run; 25 GB for typical nonlinear kinetic run (30 million grid points) Classification: 19.8, 19.9, 19.11 External routines: None required, although the functionality of the program is somewhat limited without a MPI implementation (preferably MPI-2) and the FFTW3 library. Nature of problem: Five
Electron heat transport from stochastic fields in gyrokinetic simulationsa)
NASA Astrophysics Data System (ADS)
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-01
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as βe is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of βe. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, dm [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
Comparison of two-fluid and gyrokinetic models for kinetic Alfvén waves in solar and space plasmas
Yang, L.; Wu, D. J.; Wang, S. J.; Lee, L. C.
2014-09-01
An analytical comparative study of a two-fluid and a gyrokinetic model of kinetic Alfvén waves (KAWs) is presented for various solar and space plasma environments. Based on the linear KAW dispersion relation for gyrokinetics (Howes et al. 2006), the wave group velocity and electromagnetic polarizations are obtained analytically. Then the gyrokinetic wave properties are compared with those of the two-fluid model. The results show that both models agree well with each other not only in the long wavelength regime (>> the ion gyroradius ρ {sub i}) for all cases considered, but also in wavelengths ∼ρ {sub i} and <<ρ {sub i} (still much larger than the electron gyroscale) for a moderate or low (≲ 1) and a high (>>1) ion/electron temperature ratio T {sub 0i}/T {sub 0e}, respectively. However, the fluid model calculations deviate strongly from the gyrokinetic model at scales <ρ {sub i} for a relatively low T {sub 0i}/T {sub 0e} due to the electron gyroradius effect. Meanwhile, the plasma β {sub i} can make the gyrokinetic dispersion relation of KAWs become complex and sometimes have an oscillation-like structure. With the inherent simplicity of the fluid theory, these results may improve our understanding of the applicability of the two-fluid model, and may have important implications for computer simulation studies of KAWs in the solar and space plasma surroundings.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-03
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. We focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cellequations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheathboundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. Finally, this test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-03
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. We focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cellequations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheathboundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. Finally, this test problem also helps illustratemore » some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.« less
Gyrokinetic theory of the screw pinch
NASA Astrophysics Data System (ADS)
Stéfant, Robert J.
1989-06-01
The gyrokinetic differential equation for waves propagating in a hot collisionless current-carrying plasma is derived in cylindrical geometry. It is shown that the averaging of the wave electric field over the ion Larmor circle leads to a transcendental differential equation (d.e.) of infinite order in the radial derivative. This reduces to a d.e. of sixth order when the scale length of the plasma inhomogeneity Ln is greater than the ion gyroradius ρi by a factor (M/m)1/2, where M and m are, respectively, the ion and electron mass. This sixth-order d.e. describes the properties of the two (compressional and torsional) Alfvén modes and the ion acoustic mode. When Ln <(M/m)1/2ρi, the plasma can only support modes of the magnetokinetic (short wavelength) type. In the absence of a finite Larmor radius (FLR) effect, shear, and equilibrium current, we find that the correct equation to start with is the Hain and Lust [Z. Naturforsch. A 13, 936 (1958)] d.e. of second order that is singular at the Alfvén resonance layer (ARL). The ARL behaves in that case like a Budden absorption layer that traps the global Alfvén eigenmodes (GAEM) inside the plasma cavity where they are damped by transit time magnetic pumping (TTMP). The logarithmic singularity does not disappear with the introduction of the FLR effect in the Hain and Lust d.e., but only with the TTMP damping term. There is no mode conversion between the fast magnetosonic mode and the shear or magnetokinetic mode at the ARL or anywhere in the plasma. In the presence of shear and equilibrium current, the correct equation to use is a d.e. of fourth (or greater) order whose solutions descibe the shear Alfvén mode in the long wavelength limit or the magnetokinetic mode at shorter wavelengths. In the true magnetohydrodynamic (MHD) limit, both modes become degenerate. It is shown that the slow Alfvén eigenmodes are (almost) completely decoupled from the fast magnetosonic wave and therefore the growth rates show no
Gyrokinetic modeling of impurity peaking in JET H-mode plasmas
NASA Astrophysics Data System (ADS)
Manas, P.; Camenen, Y.; Benkadda, S.; Weisen, H.; Angioni, C.; Casson, F. J.; Giroud, C.; Gelfusa, M.; Maslov, M.
2017-06-01
Quantitative comparisons are presented between gyrokinetic simulations and experimental values of the carbon impurity peaking factor in a database of JET H-modes during the carbon wall era. These plasmas feature strong NBI heating and hence high values of toroidal rotation and corresponding gradient. Furthermore, the carbon profiles present particularly interesting shapes for fusion devices, i.e., hollow in the core and peaked near the edge. Dependencies of the experimental carbon peaking factor ( R / L nC ) on plasma parameters are investigated via multilinear regressions. A marked correlation between R / L nC and the normalised toroidal rotation gradient is observed in the core, which suggests an important role of the rotation in establishing hollow carbon profiles. The carbon peaking factor is then computed with the gyrokinetic code GKW, using a quasi-linear approach, supported by a few non-linear simulations. The comparison of the quasi-linear predictions to the experimental values at mid-radius reveals two main regimes. At low normalised collisionality, ν * , and T e / T i < 1 , the gyrokinetic simulations quantitatively recover experimental carbon density profiles, provided that rotodiffusion is taken into account. In contrast, at higher ν * and T e / T i > 1 , the very hollow experimental carbon density profiles are never predicted by the simulations and the carbon density peaking is systematically over estimated. This points to a possible missing ingredient in this regime.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J. W.
2015-09-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a stochastic Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Free energy balance in gyrokinetic turbulence
Banon Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-09-15
Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.
Free energy balance in gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Bañón Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Görler, T.; Jenko, F.
2011-09-01
Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.
Neoclassical physics in full distribution function gyrokinetics
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Diamond, P. H.; Grandgirard, V.; Sarazin, Y.; Abiteboul, J.; Garbet, X.; Ghendrih, Ph.; Latu, G.; Strugarek, A.; Ku, S.; Chang, C. S.
2011-06-01
Treatment of binary Coulomb collisions when the full gyrokinetic distribution function is evolved is discussed here. A spectrum of different collision operators is presented, differing through both the physics that can be addressed and the numerics they are based on. Eulerian-like (semi-Lagrangian) and particle in cell (PIC) (Monte-Carlo) schemes are successfully cross-compared, and a detailed confrontation to neoclassical theory is shown.
Gyrokinetic modeling: A multi-water-bag approach
Morel, P.; Gravier, E.; Besse, N.; Klein, R.; Ghizzo, A.; Bertrand, P.; Garbet, X.; Ghendrih, P.; Grandgirard, V.; Sarazin, Y.
2007-11-15
Predicting turbulent transport in nearly collisionless fusion plasmas requires one to solve kinetic (or, more precisely, gyrokinetic) equations. In spite of considerable progress, several pending issues remain; although more accurate, the kinetic calculation of turbulent transport is much more demanding in computer resources than fluid simulations. An alternative approach is based on a water-bag representation of the distribution function that is not an approximation but rather a special class of initial conditions, allowing one to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations while keeping its kinetic character. The main result for the water-bag model is a lower cost in the parallel velocity direction since no differential operator associated with some approximate numerical scheme has to be carried out on this variable v{sub parallel}. Indeed, a small bag number is sufficient to correctly describe the ion temperature gradient instability.
Gyrokinetic turbulence under near-separatrix or nonaxisymmetric conditionsa)
NASA Astrophysics Data System (ADS)
Jenko, F.; Told, D.; Xanthopoulos, P.; Merz, F.; Horton, L. D.
2009-05-01
Linear and nonlinear gyrokinetic simulations with the GENE code [F. Jenko et al., Phys. Plasmas 7, 1904 (2000)] for tokamak edge plasmas as well as for stellarator core plasmas are presented, shedding light on the behavior of plasma microturbulence under near-separatrix or nonaxisymmetric conditions. To this aim, the required geometric coefficients are inferred directly from the magnetohydrodynamic equilibria of three different devices via the newly developed GIST code. It is found that the residual electron heat transport level in the H-mode edge can be explained in terms of high-wave-number fluctuations driven by electron temperature gradient modes. Moreover, the study of adiabatic ion temperature gradient turbulence in optimized stellarators points to the possibility of a systematic geometric optimization with respect to anomalous transport in nonaxisymmetric devices.
Gyrokinetic statistical absolute equilibrium and turbulence
NASA Astrophysics Data System (ADS)
Zhu, Jian-Zhou; Hammett, Gregory W.
2010-12-01
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.
Generalized Covariant Gyrokinetic Dynamics of Magnetoplasmas
Cremaschini, C.; Tessarotto, M.; Nicolini, P.; Beklemishev, A.
2008-12-31
A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurring typically in the vicinity of massive stellar objects (black holes, neutron stars, active galactic nuclei, etc.), is the accurate description of single-particle covariant dynamics, based on gyrokinetic theory (Beklemishev et al., 1999-2005). Provided radiation-reaction effects are negligible, this is usually based on the assumption that both the space-time metric and the EM fields (in particular the magnetic field) are suitably prescribed and are considered independent of single-particle dynamics, while allowing for the possible presence of gravitational/EM perturbations driven by plasma collective interactions which may naturally arise in such systems. The purpose of this work is the formulation of a generalized gyrokinetic theory based on the synchronous variational principle recently pointed out (Tessarotto et al., 2007) which permits to satisfy exactly the physical realizability condition for the four-velocity. The theory here developed includes the treatment of nonlinear perturbations (gravitational and/or EM) characterized locally, i.e., in the rest frame of a test particle, by short wavelength and high frequency. Basic feature of the approach is to ensure the validity of the theory both for large and vanishing parallel electric field. It is shown that the correct treatment of EM perturbations occurring in the presence of an intense background magnetic field generally implies the appearance of appropriate four-velocity corrections, which are essential for the description of single-particle gyrokinetic dynamics.
Gyrokinetic Statistical Absolute Equilibrium and Turbulence
Jian-Zhou Zhu and Gregory W. Hammett
2011-01-10
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.
A flux-matched gyrokinetic analysis of DIII-D L-mode turbulence
NASA Astrophysics Data System (ADS)
Görler, T.; White, A. E.; Told, D.; Jenko, F.; Holland, C.; Rhodes, T. L.
2014-12-01
Previous nonlinear gyrokinetic simulations of specific DIII-D L-mode cases have been found to significantly underpredict the ion heat transport and associated density and temperature fluctuation levels by up to almost one of order of magnitude in the outer-core domain, i.e., roughly in the last third of the minor radius. Since then, this so-called shortfall issue has been subject to various speculations on possible reasons and furthermore motivation for a number of dedicated comparisons for L-mode plasmas in comparable machines. However, only a rather limited number of simulations and gyrokinetic codes has been applied to the original scenario, thus calling for further dedicated investigations in order to broaden the scientific basis. The present work contributes along these lines by employing another well-established gyrokinetic code in a numerically and physically comprehensive manner. Contrary to the previous studies, only a mild underprediction is observed at the outer radial positions which can furthermore be overcome by varying the ion temperature gradient within the error bars associated with the experimental measurement. The significance and reliability of these simulations are demonstrated by benchmarks, numerical convergence tests, and furthermore by extensive validation studies. The latter involve cross-phase and cross-power spectra analyses of various fluctuating quantities and confirm a high degree of realism. The code discrepancies come as a surprise since the involved software packages had been benchmarked repeatedly and very successfully in the past. Further collaborative effort in identifying the underlying difference is hence required.
Hybrid Gyrofluid/Gyrokinetic Modeling of Tokamak Turbulence with GryfX
NASA Astrophysics Data System (ADS)
Mandell, Noah; Dorland, Bill; Highcock, Edmund; Hammett, Greg
2016-10-01
Gyrofluid models are more efficient than gyrokinetic models, but have a disadvantage in their potential lack of physics fidelity. Here we present three major improvements to the physics fidelity and speed of gyrofluid models, which we encapsulate in the GryfX gyrofluid turbulence code. First, we implement a new nonlinear closure to model the cascade of free energy simultaneously in k⊥ and v⊥ via nonlinear phase-mixing (NLPM). Second, we use a hybrid algorithm that improves zonal flow physics by simulating zonal flow modes with a fully gyrokinetic model. These two improvements bring heat flux predictions from nonlinear GryfX simulations into agreement with the gyrokinetic code GS2. Third, we implement the equations on modern heterogeneous computing platforms, both as a standalone simulation tool that exploits the power of GPUs and as a component of TRINITY (a transport modeling code for tokamaks). GryfX has a roughly 1,200 times performance advantage over GS2 due to the combination of GPU acceleration and the reduction of hundreds of velocity space grid points to six gyrofluid moments. This makes GryfX ideal for large parameter scans, and enables the use of the TRINITY-GryfX system for efficient multi-scale analysis of tokamak turbulence on transport time scales. Present address: Chalmers University, Gothenburg, Sweden.
A flux-matched gyrokinetic analysis of DIII-D L-mode turbulence
Görler, T. Told, D.; White, A. E.; Jenko, F.; Holland, C.; Rhodes, T. L.
2014-12-15
Previous nonlinear gyrokinetic simulations of specific DIII-D L-mode cases have been found to significantly underpredict the ion heat transport and associated density and temperature fluctuation levels by up to almost one of order of magnitude in the outer-core domain, i.e., roughly in the last third of the minor radius. Since then, this so-called shortfall issue has been subject to various speculations on possible reasons and furthermore motivation for a number of dedicated comparisons for L-mode plasmas in comparable machines. However, only a rather limited number of simulations and gyrokinetic codes has been applied to the original scenario, thus calling for further dedicated investigations in order to broaden the scientific basis. The present work contributes along these lines by employing another well-established gyrokinetic code in a numerically and physically comprehensive manner. Contrary to the previous studies, only a mild underprediction is observed at the outer radial positions which can furthermore be overcome by varying the ion temperature gradient within the error bars associated with the experimental measurement. The significance and reliability of these simulations are demonstrated by benchmarks, numerical convergence tests, and furthermore by extensive validation studies. The latter involve cross-phase and cross-power spectra analyses of various fluctuating quantities and confirm a high degree of realism. The code discrepancies come as a surprise since the involved software packages had been benchmarked repeatedly and very successfully in the past. Further collaborative effort in identifying the underlying difference is hence required.
The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence
Staebler, Gary M.; Candy, John; Howard, Nathan T.; ...
2016-06-29
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the thresholdmore » for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. Finally, the zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ionscale gyrokinetic simulations.« less
The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence
Staebler, Gary M.; Candy, John; Howard, Nathan T.; Holland, Christopher
2016-06-29
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. Finally, the zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ionscale gyrokinetic simulations.
The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence
Staebler, G. M.; Candy, J.; Howard, N. T.; Holland, C.
2016-06-15
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.
Status of Continuum Edge Gyrokinetic Code Physics Development
Xu, X Q; Xiong, Z; Dorr, M R; Hittinger, J A; Kerbel, G D; Nevins, W M; Cohen, B I; Cohen, R H
2005-05-31
We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D ({psi}, {theta}, {epsilon}, {mu}) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in ({nu}{sub {parallel}},{nu}{sub {perpendicular}}) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt|{sub coll} to/from ({epsilon}, {mu}) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassical theory for core plasma parameters; and we study the transition from collisional to collisionless end-loss. In the real X-point geometry, we find that the particles are trapped near outside midplane and in the X-point regions due to the magnetic configurations. The sizes of banana orbits are comparable to the pedestal width and/or the SOL width for energetic trapped particles. The effect of the real X-point geometry and edge plasma conditions on standard neoclassical theory will be evaluated, including a comparison of our 4D code with other kinetic
Non-physical momentum sources in slab geometry gyrokinetics
NASA Astrophysics Data System (ADS)
Parra, Felix I.; Catto, Peter J.
2010-08-01
We investigate momentum transport in the Hamiltonian electrostatic gyrokinetic formulation of Dubin et al (1983 Phys. Fluids 26 3524). We prove that the long wavelength electric field obtained from the gyrokinetic quasineutrality introduces a non-physical momentum source in the low flow ordering.
Global Responses to Potential Climate Change: A Simulation.
ERIC Educational Resources Information Center
Williams, Mary Louise; Mowry, George
This interdisciplinary five-day unit provides students with an understanding of the issues in the debate on global climate change. Introductory lessons enhance understanding of the "greenhouse gases" and their sources with possible global effects of climate change. Students then roleplay negotiators from 10 nations in a simulation of the…
Global Responses to Potential Climate Change: A Simulation.
ERIC Educational Resources Information Center
Williams, Mary Louise; Mowry, George
This interdisciplinary five-day unit provides students with an understanding of the issues in the debate on global climate change. Introductory lessons enhance understanding of the "greenhouse gases" and their sources with possible global effects of climate change. Students then roleplay negotiators from 10 nations in a simulation of the…
Gyrokinetic study of electromagnetic effects on toroidal momentum transport in tokamak plasmas
Hein, T.; Angioni, C.; Fable, E.; Candy, J.; Peeters, A. G.
2011-07-15
The effect of a finite {beta}{sub e} = 8{pi}n{sub e}T{sub e}/B{sup 2} on the turbulent transport of toroidal momentum in tokamak plasmas is discussed. From an analytical gyrokinetic model as well as local linear gyrokinetic simulations, it is shown that the modification of the parallel mode structure due to the nonadiabatic response of passing electrons, which changes the parallel wave vector k{sub ||} with increasing {beta}{sub e}, leads to a decrease in size of both the diagonal momentum transport as well as the Coriolis pinch under ion temperature gradient turbulence conditions, while for trapped electron modes, practically no modification is found. The decrease is particularly strong close to the onset of the kinetic ballooning modes. There, the Coriolis pinch even reverses its direction.
Zacharias, O.; Kleiber, R.; Borchardt, M.; Comisso, L.; Grasso, D.; Hatzky, R.
2014-06-15
The first detailed comparison between gyrokinetic and gyrofluid simulations of collisionless magnetic reconnection has been carried out. Both the linear and nonlinear evolution of the collisionless tearing mode have been analyzed. In the linear regime, we have found a good agreement between the two approaches over the whole spectrum of linearly unstable wave numbers, both in the drift kinetic limit and for finite ion temperature. Nonlinearly, focusing on the small-Δ′ regime, with Δ′ indicating the standard tearing stability parameter, we have compared relevant observables such as the evolution and saturation of the island width, as well as the island oscillation frequency in the saturated phase. The results are basically the same, with small discrepancies only in the value of the saturated island width for moderately high values of Δ′. Therefore, in the regimes investigated here, the gyrofluid approach can describe the collisionless reconnection process as well as the more complete gyrokinetic model.
Gyrokinetic theory of turbulent acceleration of parallel rotation in tokamak plasmas.
Wang, Lu; Diamond, P H
2013-06-28
A mechanism for turbulent acceleration of parallel rotation is discovered using gyrokinetic theory. This new turbulent acceleration term cannot be written as a divergence of parallel Reynolds stress. Therefore, turbulent acceleration acts as a local source or sink of parallel rotation. The physics of turbulent acceleration is intrinsically different from the Reynolds stress. For symmetry breaking by positive intensity gradient, a positive turbulent acceleration, i.e., cocurrent rotation, is predicted. The turbulent acceleration is independent of mean rotation and mean rotation gradient, and so constitutes a new candidate for the origin of spontaneous rotation. A quasilinear estimate for ion temperature gradient turbulence shows that the turbulent acceleration of parallel rotation is explicitly linked to the ion temperature gradient scale length and temperature ratio Ti0/Te0. Methods for testing the effects of turbulent parallel acceleration by gyrokinetic simulation and experiment are proposed.
Three dimensional global hybrid particle code simulations
NASA Astrophysics Data System (ADS)
Brecht, S. H.
This talk will address the development and use of the hybrid particle code approach to space simulations. For the most part there have been two types of codes used to address issues concerning plasma physics, MHD codes and kinetic particle codes. The MHD codes approach the problem of plasma dynamics from the point of view of a fluid, usually a single fluid. The kinetic codes address the problem of plasma dynamics by addressing the motion of individual particles (ions and electrons). The latter of the two codes is the most accurate numerical simulation approach available for the simulation of plasma dynamics. However, it has some limitation. The primary ones are that the spatial scale must include the Debye length in a plasma and the time step must resolve electron cyclotron or higher frequencies. The MHD approach basically solves the fluid equations with the addition of the magnetic field in the equations. The code has the advantage of being able to use large cells and large time steps. However, it does this at a significant cost in physics. It is still the tool of choice for many space simulations because some of the problems do meet the assumptions made in producing the equations and because the MHD code is just easier to use. In last 20 years or so another tool has been developed. It sets between the fully kinetic codes and the MHD codes. The ions are still treated as individual particles, but the electrons are treated as a fluid. This assumption coupled with the assumption of quasineutrality allows the hybrid particle code to address relatively large scale systems (Mars for example) while retaining some of the kinetic behavior of the plasma. This paper will review the history of the hybrid codes. It will review the equations solved and contrast these equations to the MHD equations. Particular attention will be paid to the assumptions made to produce either of these types of code. This is very important when considering the simulation of a planet such as Mars or
Intervention: Simulating the War on Global Terrorism
ERIC Educational Resources Information Center
Steinbrink, John E.; Helmer, Joel W.
2004-01-01
Students analyze a contemporary geopolitical event from a comprehensive geographic perspective using role play simulation, discussion, and decision-making. The three-day activity provides teachers with a realistic, ready-made classroom lesson that combines powerful conceptual learning with drama and surprise. The task of the teacher is to…
Intervention: Simulating the War on Global Terrorism
ERIC Educational Resources Information Center
Steinbrink, John E.; Helmer, Joel W.
2004-01-01
Students analyze a contemporary geopolitical event from a comprehensive geographic perspective using role play simulation, discussion, and decision-making. The three-day activity provides teachers with a realistic, ready-made classroom lesson that combines powerful conceptual learning with drama and surprise. The task of the teacher is to…
Cooperative global security programs modeling & simulation.
Briand, Daniel
2010-05-01
The national laboratories global security programs implement sustainable technical solutions for cooperative nonproliferation, arms control, and physical security systems worldwide. To help in the development and execution of these programs, a wide range of analytical tools are used to model, for example, synthetic tactical environments for assessing infrastructure protection initiatives and tactics, systematic approaches for prioritizing nuclear and biological threat reduction opportunities worldwide, and nuclear fuel cycle enrichment and spent fuel management for nuclear power countries. This presentation will describe how these models are used in analyses to support the Obama Administration's agenda and bilateral/multinational treaties, and ultimately, to reduce weapons of mass destruction and terrorism threats through international technical cooperation.
A very general electromagnetic gyrokinetic formalism
NASA Astrophysics Data System (ADS)
McMillan, B. F.; Sharma, A.
2016-09-01
We derive a gyrokinetic formalism which is very generally valid: the ordering allows both large inhomogeneities in plasma flow and magnetic field at long wavelength, such as typical drift-kinetic theories, as well as fluctuations at the gyro-scale. The underlying approach is to order the vorticity to be small, and to assert that the timescales in the local plasma frame are long compared to the gyrofrequency. Unlike most other derivations, we do not treat the long and short wavelength components of the fluctuating fields separately; the single-field description defines the particle motion and their interaction with the electromagnetic field at small-scale, the system-scale, and intermediate length scales in a unified fashion. As in earlier literature, the work consists of identifying a coordinate system where the gyroangle-dependent terms are small, and using a near-unity transform to systematically find a set of coordinates where the gyroangle dependence vanishes. We derive a gyrokinetic Lagrangian which is valid where the vorticity | ∇ × ( E × B / B ) | is small compared to the gyrofrequency Ω, and the magnetic field scale length is long compared to the gyroradius; we also require that time variation be slow in an appropriately chosen reference frame. This appears to be a minimum set of constraints on a gyrokinetic theory and is substantially more general than earlier approaches. It is the general-geometry electromagnetic extension of Dimits, Phys. Plasmas 17, 055901 (2010) (which is an electrostatic formalism with a homogeneous background magnetic field). This approach also does not require a separate treatment of fluctuating and background components of the magnetic field, unlike much of the previous literature. As a consequence, the "cross terms" due to a combination of long- and short-wavelength variation, which were ignored in the earlier work (but derived in a more restrictive ordering in Parra and Calvo, Plasma Phys. Controlled Fusion 53, 045001 (2011
Teaching Global Awareness with Simulations and Games. Grades 6-12. Global Awareness Series.
ERIC Educational Resources Information Center
Lamy, Steven L.; And Others
This teaching guide contains 15 simulation/games for students in grades 6-12 on the topic of global awareness. The overall objective is to help students understand various global concepts and social studies content. Specifically, it gives students the chance to experience and understand international/intercultural situations which involve people…
Beyond linear gyrocenter polarization in gyrokinetic theory
Brizard, Alain J.
2013-09-15
The concept of polarization in gyrokinetic theory is clarified and generalized to include contributions from the guiding-center (zeroth-order) polarization as well as the nonlinear (second-order) gyrocenter polarization. The guiding-center polarization, which appears as the antecedent (zeroth-order) of the standard linear (first-order) gyrocenter polarization, is obtained from a modified guiding-center transformation. The nonlinear gyrocenter polarization is derived either variationally from the third-order gyrocenter Hamiltonian or directly by gyrocenter push-forward method.
Gyrokinetic Study of L-H Transition with Profile Evolution
NASA Astrophysics Data System (ADS)
Xie, Hua-Sheng; GTC Team
2015-11-01
Recent simulations based on gyrokinetic toroidal code (GTC) and theory based on model eigen equation (H. S. Xie and Y. Xiao, arXiv:1503.04440) have found that the eigenstates of mirco-instabilities (trapped electron mode TEM or ion temperature gradient mode ITG) under strong and weak gradients are not the same. Under weak gradient, the most unstable mode is on the ground state, with conventional ballooning mode structure. When the gradient exceed a critical value, the most unstable mode jump to non-ground state. The mode structures of non-ground state are rich and unconventional, and thus can reduced the transport level, which can provide a explanation to the H-mode in the mirco-scale aspect. Nonlinear simulations (H. S. Xie, Y. Xiao and Z. Lin, 9th West Lake International Symposium on Plasma Simulation, May. 18-21, 2015, Hangzhou, China) verified this and have also found a turning point of the gradient. The turbulent transport coefficient would decrease with the gradient increasing when the gradient exceed a critical value. This provide a new route for the L to H transition without invoking shear flow or zonal flow. In the above works, the profiles are fixed. In this work, we will give some preliminary results on self-consistent simulations of L-H transition including the evolution of the radial plasma profiles. Collaboration with GTC team.
Linear gyrokinetic theory for kinetic magnetohydrodynamic eigenmodes in tokamak plasmas
NASA Astrophysics Data System (ADS)
Qin, H.; Tang, W. M.; Rewoldt, G.
1999-06-01
A two-dimensional (2D) numerical solution method is developed for the recently derived linear gyrokinetic system which describes arbitrary wavelength electromagnetic perturbations in tokamak plasmas. The system consists of the gyrokinetic equation, the gyrokinetic Poisson equation, and the gyrokinetic moment equation. Since familiar magnetohydrodynamic (MHD) results can be recovered entirely from this gyrokinetic model, and all interesting kinetic effects are intrinsically included, this gyrokinetic system offers an approach for kinetic MHD phenomena which is more rigorous, self-consistent, and comprehensive than the previous hybrid models. Meanwhile, drift type microinstabilities can be also investigated systematically in this theoretical framework. The linear gyrokinetic equation is solved for the distribution function in terms of the perturbed fields by integrating along unperturbed particle orbits. The solution is substituted back into the gyrokinetic moment equation and the gyrokinetic Poisson equation. When the boundary conditions are incorporated, an eigenvalue problem is formed. The resulting numerical code, KIN-2DEM, is applied to kinetic ballooning modes, internal kink modes, and toroidal Alfvén eigenmodes (TAEs). The numerical results are benchmarked against the well-established FULL code [G. Rewoldt, W. M. Tang, and M. S. Chance, Phys. Fluids 25, 480 (1982)], the PEST code [J. Manickam, Nucl. Fusion 24, 595 (1984)], and the NOVA-K code [C. Z. Cheng, Phys. Rep. 211, No. 1 (1992)]. More importantly, kinetic effects on MHD modes can be investigated nonperturbatively. In particular, the kinetic effects of the background plasma on internal kink modes and the hot particle destabilization of TAEs are studied numerically.
Meshless thin-shell simulation based on global conformal parameterization.
Guo, Xiaohu; Li, Xin; Bao, Yunfan; Gu, Xianfeng; Qin, Hong
2006-01-01
This paper presents a new approach to the physically-based thin-shell simulation of point-sampled geometry via explicit, global conformal point-surface parameterization and meshless dynamics. The point-based global parameterization is founded upon the rigorous mathematics of Riemann surface theory and Hodge theory. The parameterization is globally conformal everywhere except for a minimum number of zero points. Within our parameterization framework, any well-sampled point surface is functionally equivalent to a manifold, enabling popular and powerful surface-based modeling and physically-based simulation tools to be readily adapted for point geometry processing and animation. In addition, we propose a meshless surface computational paradigm in which the partial differential equations (for dynamic physical simulation) can be applied and solved directly over point samples via Moving Least Squares (MLS) shape functions defined on the global parametric domain without explicit connectivity information. The global conformal parameterization provides a common domain to facilitate accurate meshless simulation and efficient discontinuity modeling for complex branching cracks. Through our experiments on thin-shell elastic deformation and fracture simulation, we demonstrate that our integrative method is very natural, and that it has great potential to further broaden the application scope of point-sampled geometry in graphics and relevant fields.
Enabling Global Kinetic Simulations of the Magnetosphere via Petascale Computing
NASA Astrophysics Data System (ADS)
Karimabadi, H.; Vu, H. X.; Omelchenko, Y. A.; Tatineni, M.; Majumdar, A.; Catalyurek, U. V.; Saule, E.
2009-11-01
The ultimate goal in magnetospheric physics is to understand how the solar wind transfers its mass, momentum and energy to the magnetosphere. This problem has turned out to be much more complex intellectually than originally thought. MHD simulations have proven useful in predicting eminent features of substorms and other global events. Given the complexity of solar wind-magnetosphere interactions, hybrid (electron fluid, kinetic ion) simulations have recently been emerging in the studies of the global dynamics of the magnetosphere with the goal of accurately predicting the energetic particle transport and structure of plasma boundaries. We take advantage of our recent innovations in hybrid simulations and the power of massively parallel computers to make breakthrough 3D global kinetic simulations of the magnetosphere. The preliminary results reveal many major differences with global MHD simulations. For example, the hybrid simulations predict the formation of the quadruple structure associated with reconnection events, ion/ion kink instability in the tail, turbulence in the magnetosheath, and formation of the ion foreshock region.
Global MHD simulations of plasmaspheric plumes
NASA Astrophysics Data System (ADS)
Lyon, J.; Ouellette, J.; Merkin, V. G.
2015-12-01
The plasmasphere represents a separate population from the rest of themagnetosphere, generally high density but cold. When the solar windturns strongly southward this plasma is convected toward the daysidemagnetopause and affects the interaction of the solar wind with themagnetosphere. We have used multi-fluid simulations using the LFMglobal MHD code to model this interaction. The plasmasphere isinitialized as a cold (~1eV) hydrogen plasma in a quiet northward IMFstate with a density distribution appropriate for K_p = 1. Thecorotation potential from the ionosphere spins up the plasmasphereinto rough corotation. After a initialization period of hours, asouthward IMF is introduced and the enhanced convection initiates asurge of plasmaspheric density to the dayside. We discuss two aspectsof this interaction, the effects on dayside reconnection and on theKelvin-Helmholtz instability (KHI). We find that the mass loading ofmagnetospheric flux tubes slows local reconnection rates, though notas much as predicted by Borovsky et al. [2013]. We findthat the total reconnection rate is reduced, although not as much aswould be predicted by just the sub-solar reconnection rate. The KHIis somewhat reduced by the plasmaspheric loading of density in the lowlatitude boundary layer. It has been suggested that the presence ofthe plasmasphere may lead to enhanced ULF wave power in the interiorof the magnetosphere from the KHI waves. We find only a minimal effect during northward IMF. For southward IMF, the situation is complicated by the interaction of KHI with non-steady reconnection.
The next-generation ESL continuum gyrokinetic edge code
NASA Astrophysics Data System (ADS)
Cohen, R.; Dorr, M.; Hittinger, J.; Rognlien, T.; Collela, P.; Martin, D.
2009-05-01
The Edge Simulation Laboratory (ESL) project is developing continuum-based approaches to kinetic simulation of edge plasmas. A new code is being developed, based on a conservative formulation and fourth-order discretization of full-f gyrokinetic equations in parallel-velocity, magnetic-moment coordinates. The code exploits mapped multiblock grids to deal with the geometric complexities of the edge region, and utilizes a new flux limiter [P. Colella and M.D. Sekora, JCP 227, 7069 (2008)] to suppress unphysical oscillations about discontinuities while maintaining high-order accuracy elsewhere. The code is just becoming operational; we will report initial tests for neoclassical orbit calculations in closed-flux surface and limiter (closed plus open flux surfaces) geometry. It is anticipated that the algorithmic refinements in the new code will address the slow numerical instability that was observed in some long simulations with the existing TEMPEST code. We will also discuss the status and plans for physics enhancements to the new code.
A gyrokinetic perspective on the JET-ILW pedestal
NASA Astrophysics Data System (ADS)
Hatch, D. R.; Kotschenreuther, M.; Mahajan, S.; Valanju, P.; Liu, X.
2017-03-01
JET has been unable to recover historical confinement levels when operating with an ITER-like wall (ILW) due largely to the inaccessibility of high pedestal temperatures. Finding a path to overcome this challenge is of utmost importance for both a prospective JET DT campaign and for future ITER operation. Gyrokinetic simulations (using the Gene code) quantitatively capture experimental transport levels for a representative experimental discharge and qualitatively recover the major experimental trends. Microtearing turbulence is a major transport mechanisms for the low-temperature pedestals characteristic of unseeded JET-ILW discharges. At higher temperatures and/or lower {ρ\\ast} , we identify electrostatic ITG transport of a type that is strongly shear-suppressed on smaller machines. Consistent with observations, this transport mechanism is strongly reduced by the presence of a low-Z impurity (e.g. carbon or nitrogen at the level of {{Z}\\text{eff}}∼ 2 ), recovering the accessibility of high pedestal temperatures. Notably, simulations based on dimensionless {ρ\\ast} scans recover historical scaling behavior except in the unique JET-ILW parameter regime where ITG turbulence becomes important. Our simulations also elucidate the observed degradation of confinement caused by gas puffing, emphasizing the important role of the density pedestal structure. This study maps out important regions of parameter space, providing insights that may point to optimal physical regimes that can enable the recovery of high pedestal temperatures on JET.
Computer simulations of the motion and decay of global strings
Hagmann, C.; Sikivie, P.
1990-01-01
Computer simulations have been carried out of the motion and decay of global strings, including spectrum analysis of the energy stored in the scalar field which describes the global string and the radiated Nambu-Goldstone bosons. We simulated relaxing pieces of bent string and collapsing loops. We find, for the string sizes investigated, that the spectrum of field energy hardens rather than softens while the string decays into Nambu-Goldstone radiation. We argue on theoretical grounds that is indeed the most plausible general behaviour. 19 refs., 12 figs.
Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations
Brizard, Alain J.; Tronko, Natalia
2011-08-15
The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas 7, 4816 (2000)]. From the gyrokinetic Noether canonical-momentum equation derived by the Noether method, the gyrokinetic parallel momentum equation and other gyrokinetic Vlasov-moment equations are obtained. In addition, an exact gyrokinetic toroidal angular-momentum conservation law is derived in axisymmetric tokamak geometry, where the transport of parallel-toroidal momentum is related to the radial gyrocenter polarization, which includes contributions from the guiding-center and gyrocenter transformations.
Venus - Computer Simulated Global View of Northern Hemisphere
1996-03-14
The northern hemisphere is displayed in this global view of the surface of Venus. NASA Magellan synthetic aperture radar mosaics from the first cycle of Magellan mapping were mapped onto a computer-simulated globe to create this image. http://photojournal.jpl.nasa.gov/catalog/PIA00252
Global simulations of the three-dimensional magnetosphere
NASA Technical Reports Server (NTRS)
Leboeuf, J. N.; Tajima, T.; Kennel, C. F.; Dawson, J. M.
1981-01-01
Global three-dimensional computer simulations of the magnetosphere using a particle MHD code, reproduce the steady-state Dungey magnetospheric topology in three dimensions. The formation of a compression zone downstream of the tail neutral line that is probably bounded by wake shocks is observed. This compression zone changes its cross-section with distance downstream.
Electromagnetic gyrokinetic turbulence in finite-beta helical plasmas
Ishizawa, A.; Watanabe, T.-H.; Sugama, H.; Nakajima, N.; Maeyama, S.
2014-05-15
A saturation mechanism for microturbulence in a regime of weak zonal flow generation is investigated by means of electromagnetic gyrokinetic simulations. The study identifies a new saturation process of the kinetic ballooning mode (KBM) turbulence originating from the spatial structure of the KBM instabilities in a finite-beta Large Helical Device (LHD) plasma. Specifically, the most unstable KBM in LHD has an inclined mode structure with respect to the mid-plane of a torus, i.e., it has a finite radial wave-number in flux tube coordinates, in contrast to KBMs in tokamaks as well as ion-temperature gradient modes in tokamaks and helical systems. The simulations reveal that the growth of KBMs in LHD is saturated by nonlinear interactions of oppositely inclined convection cells through mutual shearing as well as by the zonal flow. The saturation mechanism is quantitatively investigated by analysis of the nonlinear entropy transfer that shows not only the mutual shearing but also a self-interaction with an elongated mode structure along the magnetic field line.
GBS: Global 3D simulation of tokamak edge region
NASA Astrophysics Data System (ADS)
Zhu, Ben; Fisher, Dustin; Rogers, Barrett; Ricci, Paolo
2012-10-01
A 3D two-fluid global code, namely Global Braginskii Solver (GBS), is being developed to explore the physics of turbulent transport, confinement, self-consistent profile formation, pedestal scaling and related phenomena in the edge region of tokamaks. Aimed at solving drift-reduced Braginskii equations [1] in complex magnetic geometry, the GBS is used for turbulence simulation in SOL region. In the recent upgrade, the simulation domain is expanded into close flux region with twist-shift boundary conditions. Hence, the new GBS code is able to explore global transport physics in an annular full-torus domain from the top of the pedestal into the far SOL. We are in the process of identifying and analyzing the linear and nonlinear instabilities in the system using the new GBS code. Preliminary results will be presented and compared with other codes if possible.[4pt] [1] A. Zeiler, J. F. Drake and B. Rogers, Phys. Plasmas 4, 2134 (1997)
NASA Astrophysics Data System (ADS)
von Storch, H.; Zorita, E.; Gonzalez-Rouco, F.
2009-04-01
Estimations of future global sea-level rise brought about by increasing concentrations of atmospheric greenhouse gases of anthropogenic origin are based on simulations with coarse-resolution global climate models, which imposes some limitations on the skill of future projections because some of the processes that modulate the heat and fresh water flux into may not be adequately represented. To fill this gap, and until more complex climate models are available, some ad-hoc methods have been proposed that link the rise in global average temperature with the global mean sea-level rise. The statistical methods can be calibrated with observations and applied to the future global temperature rise simulated by climate models. This methods can be tested in the virtual reality simulated by global atmosphere.ocean models. Thereby, deficiencies can be identified and improvement suggested. The output of 1000-year long climate model simulation with the coupled atmosphere-ocean model ECHO-G over the past millennium has been used to determine the skill of different predictors to describe the variations of the rate of sea-level change in the simulation. These predictor variables comprise the global mean near-surface temperature, its rate of change with time and the heat-flux into the ocean. It is found that, in the framework of this climate simulation, global mean temperature is not a good predictor for the rate-of-change of sea-level. The correlation between both variables is not stable along the simulations and even its sign changes. A better predictor is the rate-of-change of temperature. Its correlation with the rate-of-change of sea-level is much more stable, it is always positive along the simulation, and there exists a lead-lag relationship between both that can be understood in simple physical terms. The best predictor among those tested is the heat-flux into the ocean. Its correlation is higher and there exists no time lag to the rate-of-change of sea-level, as expected
Beyond linear polarization in gyrokinetic theory
NASA Astrophysics Data System (ADS)
Brizard, Alain
2012-10-01
The concept of linear gyrocenter polarization in gyrokinetic theory is generalized to include contributions from guiding-center polarization as well as nonlinear (quadratic) gyrocenter polarization. The former polarization is obtained from Hamiltonian guiding-center theory in which higher-order corrections due to magnetic-field nonuniformity are retained [1]. The latter polarization can be derived either variationally from the cubic gyrocenter Hamiltonian [2] or directly by push-forward construction [3]. [4pt] [1] A.J. Brizard and N. Tronko, submitted for publication (2012).[0pt] [2] A. Mishchenko and A.J. Brizard, Phys. Plasmas 18, 022305 (2011).[0pt] [3] A.J. Brizard, Comm. Nonlin. Sci. Num. Sim. 13, 24 (2008).
Large scale dynamics in flux driven gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Sarazin, Y.; Grandgirard, V.; Abiteboul, J.; Allfrey, S.; Garbet, X.; Ghendrih, Ph.; Latu, G.; Strugarek, A.; Dif-Pradalier, G.
2010-05-01
The turbulent transport governed by the toroidal ion temperature gradient driven instability is analysed with the full-f global gyrokinetic code GYSELA (Grandgirard et al 2007 Plasma Phys. Control. Fusion 49 B173) when the system is driven by a prescribed heat source. Weak, yet finite, collisionality governs a neoclassical ion heat flux that can compete with the turbulent driven transport. In turn, the ratio of turbulent to neoclassical transport increases with the source magnitude, resulting in the degradation of confinement with additional power. The turbulent flux exhibits avalanche-like events, characterized by intermittent outbursts which propagate ballistically roughly at the diamagnetic velocity. Locally, the temperature gradient can drop well below the linear stability threshold. Large outbursts are found to correlate with streamer-like structures of the convection cells albeit their Fourier spectrum departs significantly from that of the most unstable linear modes. Last, the poloidal rotation of turbulent eddies is essentially governed by the radial electric field at moderate density gradient.
Simulation of the global contrail radiative forcing: A sensitivity analysis
NASA Astrophysics Data System (ADS)
Yi, Bingqi; Yang, Ping; Liou, Kuo-Nan; Minnis, Patrick; Penner, Joyce E.
2012-12-01
The contrail radiative forcing induced by human aviation activity is one of the most uncertain contributions to climate forcing. An accurate estimation of global contrail radiative forcing is imperative, and the modeling approach is an effective and prominent method to investigate the sensitivity of contrail forcing to various potential factors. We use a simple offline model framework that is particularly useful for sensitivity studies. The most-up-to-date Community Atmospheric Model version 5 (CAM5) is employed to simulate the atmosphere and cloud conditions during the year 2006. With updated natural cirrus and additional contrail optical property parameterizations, the RRTMG Model (RRTM-GCM application) is used to simulate the global contrail radiative forcing. Global contrail coverage and optical depth derived from the literature for the year 2002 is used. The 2006 global annual averaged contrail net (shortwave + longwave) radiative forcing is estimated to be 11.3 mW m-2. Regional contrail radiative forcing over dense air traffic areas can be more than ten times stronger than the global average. A series of sensitivity tests are implemented and show that contrail particle effective size, contrail layer height, the model cloud overlap assumption, and contrail optical properties are among the most important factors. The difference between the contrail forcing under all and clear skies is also shown.
T.S. Hahm; Z. Lin; P.H. Diamond; G. Rewoldt; W.X. Wang; S. Ethier; O. Gurcan; W.W. Lee; W.M. Tang
2004-12-21
An integrated program of gyrokinetic particle simulation and theory has been developed to investigate several outstanding issues in both turbulence and neoclassical physics. Gyrokinetic particle simulations of toroidal ion temperature gradient (ITG) turbulence spreading using the GTC code and its related dynamical model have been extended to the case with radially increasing ion temperature gradient, to study the inward spreading of edge turbulence toward the core. Due to turbulence spreading from the edge, the turbulence intensity in the core region is significantly enhanced over the value obtained from simulations of the core region only. Even when the core gradient is within the Dimits shift regime (i.e., self-generated zonal flows reduce the transport to a negligible value), a significant level of turbulence and transport is observed in the core due to spreading from the edge. The scaling of the turbulent front propagation speed is closer to the prediction from our nonlinear diffusion model than one based on linear toroidal coupling. A calculation of ion poloidal rotation in the presence of sharp density and toroidal angular rotation frequency gradients from the GTC-Neo particle simulation code shows that the results are significantly different from the conventional neoclassical theory predictions. An energy conserving set of a fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to edge turbulence, is being derived via the phase-space action variational Lie perturbation method. Our generalized ordering takes the ion poloidal gyroradius to be on the order of the radial electric field gradient length.
Evaluation of global and regional climate simulations over Africa
NASA Astrophysics Data System (ADS)
Nikulin, Grigory; Jones, Colin; Kjellström, Erik; Gbobaniyi, Emiola
2013-04-01
Two ensembles of climate simulations, one global and one regional, are evaluated and inter-compared over the Africa-CORDEX domain. The global ensemble includes eight coupled atmosphere ocean general circulation models (AOGCMs) from the CMIP5 project with horizontal resolution varying from about 1° to 3°, namely CanESM2, CNRM-CM5, HadGEM2-ES, NorESM1-M, EC-EARTH, MIROC5, GFDL-ESM2M and MPI-ESM-LR. In the regional ensemble all 8 AOGCMs are downscaled over the Africa-CORDEX domain at the Rossby Centre (SMHI) by a regional climate model - RCA4 at 0.44° resolution. The main focus is on ability of both global and regional ensembles to simulate precipitation in different climate zones of Africa. Precipitation climatology is characterized by seasonal means, inter-annual variability and by various characteristics of the rainy season: onset, cessation, mean intensity and intra-seasonal variability. To see potential benefits of higher resolution in the regional downscaling all precipitation statistics are inter-compared between the individual AOGCM-RCA4(AOGCM) pairs and between the two multi-model ensemble averages. A special attention in the study is on how the AOGCMs simulate teleconnection patterns of large-scale internal variability and how these teleconnection pattern are reproduced in the downscaled regional simulations.
Simulation of Aerosols and Chemistry with a Unified Global Model
NASA Technical Reports Server (NTRS)
Chin, Mian
2004-01-01
This project is to continue the development of the global simulation capabilities of tropospheric and stratospheric chemistry and aerosols in a unified global model. This is a part of our overall investigation of aerosol-chemistry-climate interaction. In the past year, we have enabled the tropospheric chemistry simulations based on the GEOS-CHEM model, and added stratospheric chemical reactions into the GEOS-CHEM such that a globally unified troposphere-stratosphere chemistry and transport can be simulated consistently without any simplifications. The tropospheric chemical mechanism in the GEOS-CHEM includes 80 species and 150 reactions. 24 tracers are transported, including O3, NOx, total nitrogen (NOy), H2O2, CO, and several types of hydrocarbon. The chemical solver used in the GEOS-CHEM model is a highly accurate sparse-matrix vectorized Gear solver (SMVGEAR). The stratospheric chemical mechanism includes an additional approximately 100 reactions and photolysis processes. Because of the large number of total chemical reactions and photolysis processes and very different photochemical regimes involved in the unified simulation, the model demands significant computer resources that are currently not practical. Therefore, several improvements will be taken, such as massive parallelization, code optimization, or selecting a faster solver. We have also continued aerosol simulation (including sulfate, dust, black carbon, organic carbon, and sea-salt) in the global model to cover most of year 2002. These results have been made available to many groups worldwide and accessible from the website http://code916.gsfc.nasa.gov/People/Chin/aot.html.
Simulation of Aerosols and Chemistry with a Unified Global Model
NASA Technical Reports Server (NTRS)
Chin, Mian
2004-01-01
This project is to continue the development of the global simulation capabilities of tropospheric and stratospheric chemistry and aerosols in a unified global model. This is a part of our overall investigation of aerosol-chemistry-climate interaction. In the past year, we have enabled the tropospheric chemistry simulations based on the GEOS-CHEM model, and added stratospheric chemical reactions into the GEOS-CHEM such that a globally unified troposphere-stratosphere chemistry and transport can be simulated consistently without any simplifications. The tropospheric chemical mechanism in the GEOS-CHEM includes 80 species and 150 reactions. 24 tracers are transported, including O3, NOx, total nitrogen (NOy), H2O2, CO, and several types of hydrocarbon. The chemical solver used in the GEOS-CHEM model is a highly accurate sparse-matrix vectorized Gear solver (SMVGEAR). The stratospheric chemical mechanism includes an additional approximately 100 reactions and photolysis processes. Because of the large number of total chemical reactions and photolysis processes and very different photochemical regimes involved in the unified simulation, the model demands significant computer resources that are currently not practical. Therefore, several improvements will be taken, such as massive parallelization, code optimization, or selecting a faster solver. We have also continued aerosol simulation (including sulfate, dust, black carbon, organic carbon, and sea-salt) in the global model to cover most of year 2002. These results have been made available to many groups worldwide and accessible from the website http://code916.gsfc.nasa.gov/People/Chin/aot.html.
NASA Astrophysics Data System (ADS)
Wang, Weixing
2008-11-01
Global gyrokinetic simulations using the GTS code [1] have found that a large inward flux of toroidal momentum is driven robustly in the post saturation phase of ion temperature gradient (ITG) turbulence. As a consequence, core plasma rotation spins up resulting in δu a few percent of vth in the case with no momentum source at the edge. The underlying physics for the inward flux is identified to be the generation of residual stress due to the k symmetry breaking [2] induced by self-generated zonal flow shear which is quasi-stationary in global simulations. The elatively low level momentum flux in the long- time steady state appears to be approximately diffusive, with effective χφ/χi on the order of unity, in broad agreement with experimental observations and theory predictions for ITG turbulence [3]. Neoclassical simulations using the GTC- NEO code [4] also show that the ion temperature gradient can drive a significant inward nondiffusive momentum flux. However, the overall neoclassical contribution to the momentum transport is negligibly small compared to experimental levels for NSTX and DIII-D plasmas. It is also found that finite residual turbulence can survive strong mean ExB shear flow induced damping. This residual turbulence in the presence of strong ExB shear may drive an insignificant ion heat flux reasonably close to the neoclassical value, and a finite momentum flux significantly higher than the neoclassical level. Moreover, the equilibrium ExB flow shear is found to reduce the turbulence driven transport for energy more efficiently than for momentum. These findings may offer an explanation for rather peculiar observations of near neoclassical ion heat and anomalous momentum transport in experiments, which has been often observed in various machines, but with little theoretical understanding. [1] W.X. Wang et al., Phys. Plasmas 14, 072306 (2007). [2] O.D. Gurcan et al., Phys. Plasmas 14, 042306 (2007). [3] N. Mattor and P.H. Diamond, Phys. Fluids 31
Benchmark Studies of the Gyro-Landau-Fluid code and Gyro-kinetic Codes on Kinetic Ballooning Modes
NASA Astrophysics Data System (ADS)
Tang, Tengfei; Xu, Xueqiao; Ma, Chenhao; Holland, Chris; Candy, Jeff
2015-11-01
A Gyro-Landau-Fluid (GLF) 3 +1 model has been implemented in BOUT + + framework recently, which contains full Finite-Larmor-Radius (FLR) effects, Landau damping and toroidal resonance. A linear global beta scan has been done using the cbm18 series equilibriums, showing that the unstable modes are kinetic ballooning modes (KBMs). In this work, we use the GYRO code, which is a gyrokinetic continuum code widely used for simulation of the plasma microturbulence, to benchmark with GLF 3 +1 code on KBMs. As the modes locate in peak pressure gradient region, a linear local beta scan using the same set of equilibriums has been done at this position for comparison. With the drift kinetic electron module in the GYRO code by including small electron-ion collision to damp electron modes, GYRO generated mode structures and parity suggest that they are kinetic ballooning modes, and the growth rate is comparable to the GLF results. However, a radial scan of the pedestal for a particular cbm18 equilibrium shows that the growth rate of the most unstable mode shifts outward to the bottom of pedestal and the real frequency of what was originally the KBMs steadily approaches and crosses over to the electron diamagnetic drift direction. Prepared by LLNL under Contract DE-AC52-07NA27344.
J. Squire, H. Qin and W.M. Tang
2012-09-25
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with the Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. __________________________________________________
Sanchez, R.; Newman, D. E.; Leboeuf, J.-N.; Decyk, V. K.; Carreras, B. A.
2008-11-14
It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.
Global simulation of interactions between groundwater and terrestrial ecosystems
NASA Astrophysics Data System (ADS)
Braakhekke, M. C.; Rebel, K.; Dekker, S. C.; Smith, B.; Van Beek, L. P.; Sutanudjaja, E.; van Kampenhout, L.; Wassen, M. J.
2016-12-01
In many places in the world ecosystems are influenced by the presence of a shallow groundwater table. In these regions upward water flux due to capillary rise increases soil moisture availability in the root zone, which has strong positive effect on evapotranspiration. Additionally it has important consequences for vegetation dynamics and fluxes of carbon and nitrogen. Under water limited conditions shallow groundwater stimulates vegetation productivity, and soil organic matter decomposition while under saturated conditions groundwater may have a negative effect on these processes due to lack of oxygen. Furthermore, since plant species differ with respect to their root distribution, preference for moisture conditions, and resistance to oxygen stress, shallow groundwater also influences vegetation type. Finally, processes such as denitrification and methane production occur under strictly anaerobic conditions and are thus strongly influenced by moisture availability. Most global hydrological models and several land surface models simulate groundwater table dynamics and their effects on land surface processes. However, these models typically have relatively simplistic representation of vegetation and do not consider changes in vegetation type and structure and are therefore less suitable to represent effects of groundwater on biogeochemical fluxes. Dynamic global vegetation models (DGVMs), describe land surface from an ecological perspective, combining detailed description of vegetation dynamics and structure and biogeochemical processes. These models are thus more appropriate to simulate the ecological and biogeochemical effects of groundwater interactions. However, currently virtually all DGVMs ignore these effects, assuming that water tables are too deep to affect soil moisture in the root zone. We have implemented a tight coupling between the dynamic global ecosystem model LPJ-GUESS and the global hydrological model PCR-GLOBWB. Using this coupled model we aim to
Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Hatch, D. R.; Jenko, F.; Bratanov, V.; Navarro, A. Bañón; Navarro
2014-08-01
A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phase-space scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code - the DNA code - that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is a critical balance - an equilibration of the parallel streaming time and the nonlinear correlation time - that extends to high Hermite number n. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using the Gene code are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.
NASA Astrophysics Data System (ADS)
Besse, Nicolas; Coulette, David
2016-08-01
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic
Besse, Nicolas
2016-08-15
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original
Global simulations of plasma turbulence in laboratory plasmas
NASA Astrophysics Data System (ADS)
Ricci, P.; Fasoli, A.; Furno, I.; Jolliet, S.; Loizu, J.; Mosetto, A.; Rogers, B. N.; Theiler, C.
2012-04-01
The Global Braginskii Solver (GBS) code has been developed in the last few years to simulate plasma turbulence in laboratory plasmas [1]. By solving the drift-reduced Braginkii equation in magnetic configurations of increasing complexity, from linear devices to the Simple Magnetized Toroidal (SMT) configuration, GBS performs non-linear self-consistent global three-dimensional simulations of the plasma dynamics, as the result of the interplay among the plasma source, the turbulent transport, and the plasma losses at the vessel. This gradual approach has allowed gaining a deep understanding of the turbulence dynamics, by identifying the instabilities responsible for driving plasma turbulence and to estimate the turbulence saturation amplitude. In particular, simulation results have pointed out the need of global simulations to correctly represent the dynamics of laboratory plasmas, as well as the importance of not separating fluctuations and equilibrium quantities. A code validation development project has been conducted side by side with the GBS development [2]. Such validation project has lead to the establishment of a rigorous methodology to carry out experiment-simulation comparison, and has allowed quantifying precisely the level of agreement between the GBS results and the experimental data from the TORPEX experiment at CRPP. [1] P. Ricci, B.N. Rogers, S. Brunner, Phys. Rev. Lett. 100, 225002 (2008); P. Ricci and B. N. Rogers, Phys. Rev. Lett. 104, 145001 (2010); B. N. Rogers and P. Ricci, Phys. Rev. Lett. 104, 225002 (2010); B. Li et al., Phys. Rev. E 83, 056406 (2011). [2] P. Ricci et al, Phys. Plasmas 16, 055703 (2009); P. Ricci et al., Phys. Plasmas 18, 032109 (2011).
ERIC Educational Resources Information Center
Henry, Jean-Baptiste
1994-01-01
A simulation exercise consisting of 12 stages corresponding to the life-stages of an enterprise is used as a language-learning technique for business French. The exercise develops both language and networking skills while presenting a creative challenge to students. (MSE)
Verification of Gyrokinetic codes: theoretical background and applications
NASA Astrophysics Data System (ADS)
Tronko, Natalia
2016-10-01
In fusion plasmas the strong magnetic field allows the fast gyro motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) codes play a major role in the understanding of the development and the saturation of turbulence and in the prediction of the consequent transport. We present a new and generic theoretical framework and specific numerical applications to test the validity and the domain of applicability of existing GK codes. For a sound verification process, the underlying theoretical GK model and the numerical scheme must be considered at the same time, which makes this approach pioneering. At the analytical level, the main novelty consists in using advanced mathematical tools such as variational formulation of dynamics for systematization of basic GK code's equations to access the limits of their applicability. The indirect verification of numerical scheme is proposed via the Benchmark process. In this work, specific examples of code verification are presented for two GK codes: the multi-species electromagnetic ORB5 (PIC), and the radially global version of GENE (Eulerian). The proposed methodology can be applied to any existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell equations using the generic variational formulation. Then, we derive and include the models implemented in ORB5 and GENE inside this hierarchy. At the computational level, detailed verification of global electromagnetic test cases based on the CYCLONE are considered, including a parametric β-scan covering the transition between the ITG to KBM and the spectral properties at the nominal β value.
Diagnosing global ocean content changes in historically forced CMIP simulations
NASA Astrophysics Data System (ADS)
Gleckler, P. J.; Durack, P. J.; Stouffer, R. J.; Johnson, G. C.; Forest, C. E.
2016-02-01
Formal detection and attribution studies have used observations and climate models to identify an anthropogenic warming signature in the upper (0700 m) ocean. Recently, as a result of the so-called surface warming hiatus, there has been considerable interest in global ocean heat content (OHC) changes in the deeper ocean, including natural and anthropogenically forced changes evidenced in observational, modelling, and data re-analysis studies. We rely on OHC change estimates from a diverse collection of measurement systems including data from the 19th Century Challenger expedition, a multi-decadal record of ship-based in-situ mostly upper ocean measurements, the more recent near-global Argo floats profiling to intermediate (2000 m) depths, and full-depth repeated transoceanic sections. By diagnosing simulated global OHC changes in historically-forced climate models in three depth layers, we show that the current generation of climate models is broadly consistent with multi-decadal estimates of upper, intermediate (700-2000 m) and deep (2000 m bottom) global OHC changes as well as with Argo-based estimates over the most recent period. Our results suggest that approximately half of the 1860 present human-caused increases in global ocean heat content may have occurred since 1998.
Global plasma simulations using dynamically generated chemical models
Munro, James J.; Tennyson, Jonathan
2008-07-15
Extensive molecular data are a key requirement in understanding modern technical plasmas. A method for coupling molecular data with chemical models in a global plasma simulation to enable rapid testing and evaluation of new plasmas is presented. A global plasma model (GLOBALKIN) is extended using an expert system (Quantemol-P) to enable ad hoc simulations using new plasma recipes. A set of atomic and molecular species to be considered in the plasma simulation is specified by the user. The expert system generates a complete set of reaction pathways for both the gas and surface reactions in a plasma. This set is pruned by discarding unphysical reactions and reaction data not appropriate to technical plasmas (such as autodetachment). The species, gas phase reactions, surface reactions, and plasma properties can be adjusted to control the simulation. The reaction list is populated through a database of molecular parameters and cross sections; missing data can be calculated through molecular cross sections using a further expert system (Quantemol-N) which applies the R-matrix method to electron-molecule collisions. For cases where the R-matrix method is not appropriate, other methods are used to maximize the range of cross-section data available. The Quantemol-P expert system allows rapid creation of new plasma recipes and investigation of their effects allowing a greater level of flexibility than previously achievable.
A model of the saturation of coupled electron and ion scale gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Staebler, G. M.; Howard, N. T.; Candy, J.; Holland, C.
2017-06-01
A new paradigm of zonal flow mixing as the mechanism by which zonal E × B fluctuations impact the saturation of gyrokinetic turbulence has recently been deduced from the nonlinear 2D spectrum of electric potential fluctuations in gyrokinetic simulations. These state of the art simulations span the physical scales of both ion and electron turbulence. It was found that the zonal flow mixing rate, rather than zonal flow shearing rate, competes with linear growth at both electron and ion scales. A model for saturation of the turbulence by the zonal flow mixing was developed and applied to the quasilinear trapped gyro-Landau fluid transport model (TGLF). The first validation tests of the new saturation model are reported in this paper with data from L-mode and high-β p regime discharges from the DIII-D tokamak. The shortfall in the predicted L-mode edge electron energy transport is improved with the new saturation model for these discharges but additional multiscale simulations are required in order to verify the safety factor and collisionality dependencies found in the modeling.
W.M. Tang
2005-01-03
The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics--the research arena from which this formalism was originally developed. It was presented as a component of the ''Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations'' held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources.
A model of the saturation of coupled electron and ion scale gyrokinetic turbulence
Staebler, Gary M.; Howard, Nathan T.; Candy, Jeffrey M.; ...
2017-05-09
A new paradigm of zonal flow mixing as the mechanism by which zonal E × B fluctuations impact the saturation of gyrokinetic turbulence has recently been deduced from the nonlinear 2D spectrum of electric potential fluctuations in gyrokinetic simulations. These state of the art simulations span the physical scales of both ion and electron turbulence. It was found that the zonal flow mixing rate, rather than zonal flow shearing rate, competes with linear growth at both electron and ion scales. A model for saturation of the turbulence by the zonal flow mixing was developed and applied to the quasilinear trappedmore » gyro-Landau fluid transport model (TGLF). The first validation tests of the new saturation model are reported in this paper with data from L-mode and high-βp regime discharges from the DIII-D tokamak. Lastly, the shortfall in the predicted L-mode edge electron energy transport is improved with the new saturation model for these discharges but additional multiscale simulations are required in order to verify the safety factor and collisionality dependencies found in the modeling.« less
Fluid and gyrokinetic modelling of particle transport in plasmas with hollow density profiles
NASA Astrophysics Data System (ADS)
Tegnered, D.; Oberparleiter, M.; Nordman, H.; Strand, P.
2016-11-01
Hollow density profiles occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the fuelling scheme inefficient. In the present work, the particle transport driven by ITG/TE mode turbulence in regions of hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description, and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT , and magnetic shear are investigated. It is found that β in particular has a stabilizing effect in the negative R/Ln region, both nonlinear GENE and EDWM show a decrease in inward flux for negative R/Ln and a change of direction from inward to outward for positive R/Ln . This might have serious consequences for pellet fuelling of high β plasmas.
The effect of global visual flow on simulator sickness
NASA Technical Reports Server (NTRS)
Sharkey, Thomas J.; Mccauley, Michael E.
1991-01-01
Simulator-induced sickness is investigated in experiments performed at the NASA Ames Army Crew Station Research Facility using the fixed-base helmet-mounted-display flight simulator described by Lypaczewski et al. (1986). The focus of the tests was on the possible roles of (1) global visual flow, as defined by Warren et al. (1982), and (2) maneuvering intensity (in the conflict hypothesis of Reason and Brand, 1975). The results, based on subjective evaluations, physiological measurements, and physical tests on 19 Army helicopter pilots performing a 40-min river-valley following task, are presented in extensive tables and graphs and discussed. The data are found to be in agreement with (1) and inconsistent with (2), indicating more sickness at lower altitude instead of with increased maneuvering. Shorter simulator sessions and postponement of low-altitude work until later in the training period are recommended.
Global MHD Simulation of Mesoscale Structures at the Magnetospheric Boundary
NASA Technical Reports Server (NTRS)
Berchem, Jean
1998-01-01
The research carried out for this protocol was focused on the study of mesoscales structures at the magnetospheric boundary. We investigated three areas: (1) the structure of the magnetospheric boundary for steady solar wind conditions; (2) the dynamics of the dayside magnetospheric boundary and (3) the dynamics of the distant tail magnetospheric boundary. Our approach was to use high resolution three-dimensional global magnetohydrodynamic (MHD) simulations of the interaction of the solar wind with the Earth's magnetosphere. We first considered simple variations of the interplanetary conditions to obtain generic cases that helped us in establishing the basic cause and effect relationships for steady solar wind conditions. Subsequently, we used actual solar wind plasma and magnetic field parameters measured by an upstream spacecraft as input to the simulations and compared the simulation results with sequences of events observed by another or several other spacecraft located downstream the bow shock. In particular we compared results with observations made when spacecraft crossed the magnetospheric boundary.
Impact of derived global weather data on simulated crop yields.
van Wart, Justin; Grassini, Patricio; Cassman, Kenneth G
2013-12-01
Crop simulation models can be used to estimate impact of current and future climates on crop yields and food security, but require long-term historical daily weather data to obtain robust simulations. In many regions where crops are grown, daily weather data are not available. Alternatively, gridded weather databases (GWD) with complete terrestrial coverage are available, typically derived from: (i) global circulation computer models; (ii) interpolated weather station data; or (iii) remotely sensed surface data from satellites. The present study's objective is to evaluate capacity of GWDs to simulate crop yield potential (Yp) or water-limited yield potential (Yw), which can serve as benchmarks to assess impact of climate change scenarios on crop productivity and land use change. Three GWDs (CRU, NCEP/DOE, and NASA POWER data) were evaluated for their ability to simulate Yp and Yw of rice in China, USA maize, and wheat in Germany. Simulations of Yp and Yw based on recorded daily data from well-maintained weather stations were taken as the control weather data (CWD). Agreement between simulations of Yp or Yw based on CWD and those based on GWD was poor with the latter having strong bias and large root mean square errors (RMSEs) that were 26-72% of absolute mean yield across locations and years. In contrast, simulated Yp or Yw using observed daily weather data from stations in the NOAA database combined with solar radiation from the NASA-POWER database were in much better agreement with Yp and Yw simulated with CWD (i.e. little bias and an RMSE of 12-19% of the absolute mean). We conclude that results from studies that rely on GWD to simulate agricultural productivity in current and future climates are highly uncertain. An alternative approach would impose a climate scenario on location-specific observed daily weather databases combined with an appropriate upscaling method. © 2013 John Wiley & Sons Ltd.
Impact of derived global weather data on simulated crop yields
van Wart, Justin; Grassini, Patricio; Cassman, Kenneth G
2013-01-01
Crop simulation models can be used to estimate impact of current and future climates on crop yields and food security, but require long-term historical daily weather data to obtain robust simulations. In many regions where crops are grown, daily weather data are not available. Alternatively, gridded weather databases (GWD) with complete terrestrial coverage are available, typically derived from: (i) global circulation computer models; (ii) interpolated weather station data; or (iii) remotely sensed surface data from satellites. The present study's objective is to evaluate capacity of GWDs to simulate crop yield potential (Yp) or water-limited yield potential (Yw), which can serve as benchmarks to assess impact of climate change scenarios on crop productivity and land use change. Three GWDs (CRU, NCEP/DOE, and NASA POWER data) were evaluated for their ability to simulate Yp and Yw of rice in China, USA maize, and wheat in Germany. Simulations of Yp and Yw based on recorded daily data from well-maintained weather stations were taken as the control weather data (CWD). Agreement between simulations of Yp or Yw based on CWD and those based on GWD was poor with the latter having strong bias and large root mean square errors (RMSEs) that were 26–72% of absolute mean yield across locations and years. In contrast, simulated Yp or Yw using observed daily weather data from stations in the NOAA database combined with solar radiation from the NASA-POWER database were in much better agreement with Yp and Yw simulated with CWD (i.e. little bias and an RMSE of 12–19% of the absolute mean). We conclude that results from studies that rely on GWD to simulate agricultural productivity in current and future climates are highly uncertain. An alternative approach would impose a climate scenario on location-specific observed daily weather databases combined with an appropriate upscaling method. PMID:23801639
NASA Astrophysics Data System (ADS)
Brizard, Alain J.
2017-08-01
The nonlinear (full-f) electromagnetic gyrokinetic Vlasov-Maxwell equations are derived in the parallel-symplectic representation from an Eulerian gyrokinetic variational principle. The gyrokinetic Vlasov-Maxwell equations are shown to possess an exact energy conservation law, which is derived by the Noether method from the gyrokinetic variational principle. Here, the gyrocenter Poisson bracket and the gyrocenter Jacobian contain contributions from the perturbed magnetic field. In the full-f formulation of the gyrokinetic Vlasov-Maxwell theory presented here, the gyrocenter parallel-Ampère equation contains a second-order contribution to the gyrocenter current density that is derived from the second-order gyrocenter ponderomotive Hamiltonian.
Higher-order energy-conserving gyrokinetic theory
Mishchenko, Alexey; Brizard, Alain J.
2011-02-15
A higher-order self-consistent energy-conserving gyrokinetic system of equations is derived. It is shown that additional terms appear in the quasineutrality condition. These terms are nonlinear in the electric field. The derivation includes higher-order terms in the gyrokinetic Hamiltonian (needed for the energy conservation) and employs a variational principle that automatically provides all the conservation laws through the Noether theorem. The equations derived here can be applied in certain transition layers such as the stellarator transport barriers caused by the transition between the electron and ion root regimes. The theory may also be of interest for the edge plasma, where the nonlinear terms in the quasineutrality equation could be relevant. The equations derived are simple enough and can readily be used in gyrokinetic codes.
Effects of collisions on conservation laws in gyrokinetic field theory
NASA Astrophysics Data System (ADS)
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2014-10-01
In gyrokinetic field theory, the gyrokinetic Vlasov equation, Poisson's equation, and Ampere's law are all obtained from the Lagrangian formulation, and conservation laws of energy and momentum for collisionless magnetized plasmas are derived by applying the Noether's theorem. In this work, effects of collisions on conservation laws are investigated by using the gyrokinetic Boltzmann equation which includes Landau's collision operator represented in the gyrocenter coordinates. Particle, energy, and momentum transport equations including collisional transport fluxes are systematically derived by modifying Noether's theorem. Then, the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include both collisional and turbulent transport fluxes which agree with those derived from the conventional recursive formulation with the WKB representation.
Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective
Lee, W. W.
2016-07-15
The effort to obtain a set of MagnetoHydroDynamic (MHD) equations for a magnetized collisionless plasma was started nearly 60 years ago by Chew et al. [Proc. R. Soc. London, Ser. A 236(1204), 112–118 (1956)]. Many attempts have been made ever since. Here, we will show the derivation of a set of these equations from the gyrokinetic perspective, which we call it gyrokinetic MHD, and it is different from the conventional ideal MHD. However, this new set of equations still has conservation properties and, in the absence of fluctuations, recovers the usual MHD equilibrium. Furthermore, the resulting equations allow for the plasma pressure balance to be further modified by finite-Larmor-radius effects in regions with steep pressure gradients. The present work is an outgrowth of the paper on “Alfven Waves in Gyrokinetic Plasmas” by Lee and Qin [Phys. Plasmas 10, 3196 (2003)].
Non-steady Reconnection in Global Simulations of Magnetosphere Dynamics
NASA Technical Reports Server (NTRS)
Kuznetsova, M. M.; Hesse, M.; Sibeck, D.; Rastaetter, L.; Toth, G.; Ridley, A.
2008-01-01
To analyze the non-steady magnetic reconnection during quasi-steady solar wind driving we employed high resolution global MHD model BATSRUS with non-MHD corrections in diffusion regions around the reconnection sites. To clarify the role of small-scale non-MHD effects on the global magnetospheric dynamic we performed simulations with different models of dissipation. We found that magnetopause surface is not in steady state even during extended periods of steady solar wind conditions. The so-called tilted reconnection lines become unstable due to formation of pressure bubbles, strong core field flux tubes, vortices, and traveling magnetic field cavities. Non-steady dayside reconnection results in formation of flux tubes with bended axis magnetically connecting magnetic field cavities generated at flanks and strong core segments formed near the subsolar region. We found that the rate of magnetic flux loading to the tail lobes is not very sensitive to the dissipation mechanism and details of the dayside reconnection. On the other hand the magnetotail reconnection rate, the speed of the reconnection site retreat and the global magnetotail dynamics strongly depend on the model of dissipation. THEMIS and Cluster observations are consistent with signatures predicted by simulations.
Application of Global Paleovegetation Data for Benchmarking Paleoclimate Simulations
NASA Astrophysics Data System (ADS)
Izumi, K.; Bartlein, P. J.
2011-12-01
Climate models provide an opportunity for testing hypotheses concerning the causes of past climatic variations, providing the consistent explanations of past climate changes, and simulating potential future climate changes. We compare paleovegetation syntheses from the Last Glacial Maximum (LGM) and Mid Holocene (MH) with simulations performed as part of the Paleoclimate Modelling Intercomparison Project (PMIP) 2 and 3 projects, with the aim of evaluating the ability of the simulations to reproduce the key regional and global patterns of climate recorded by the data. We apply two approaches using vegetation models in a data-model comparison framework: a forward-modeling approach that simulates vegetation using climate-model output, and an inverse-modeling approach that uses the vegetation data to infer the past values of the specific climate that controlled vegetation distributions. In the forward-modeling approach, we use the BIOME 4 equilibrium-biogeochemistry model and palaeovegetation data (e.g. BIOME 6000), which includes new regional pollen data sets from Australia, Southeast Asia, South America, and the Indian subcontinent, in order to evaluate the response of PMIP2 AOGCMs simulations of the LGM and MH. For the inverse approach, we use BIOME4 to iteratively estimate the potential paleoclimate consistent with based on the BIOME6000 data using a Monte Carlo Markov Chain algorithm. BIOME 4 employs mechanistic descriptions of the relationship of vegetation on climate and also allows the direct effects of carbon dioxide concentration to be considered. In addition to standard (i.e. map-comparison) approaches for comparing the simulated/observed vegetation and climate, we show some diagnostics based the mapping of observed and simulated biomes in climatic spaces. These diagnoses can provide information about the specific climatological explanations for the mismatches between the simulations and observations.
Radiation magnetohydrodynamics in global simulations of protoplanetary discs
NASA Astrophysics Data System (ADS)
Flock, M.; Fromang, S.; González, M.; Commerçon, B.
2013-12-01
Aims: Our aim is to study the thermal and dynamical evolution of protoplanetary discs in global simulations, including the physics of radiation transfer and magneto-hydrodynamic turbulence caused by the magneto-rotational instability. Methods: We have developed a radiative transfer method based on the flux-limited diffusion approximation that includes frequency dependent irradiation by the central star. This hybrid scheme is implemented in the PLUTO code. The focus of our implementation is on the performance of the radiative transfer method. Using an optimized Jacobi preconditioned BiCGSTAB solver, the radiative module is three times faster than the magneto-hydrodynamic step for the disc set-up we consider. We obtain weak scaling efficiencies of 70% up to 1024 cores. Results: We present the first global 3D radiation magneto-hydrodynamic simulations of a stratified protoplanetary disc. The disc model parameters were chosen to approximate those of the system AS 209 in the star-forming region Ophiuchus. Starting the simulation from a disc in radiative and hydrostatic equilibrium, the magneto-rotational instability quickly causes magneto-hydrodynamic turbulence and heating in the disc. We find that the turbulent properties are similar to that of recent locally isothermal global simulations of protoplanetary discs. For example, the rate of angular momentum transport α is a few times 10-3. For the disc parameters we use, turbulent dissipation heats the disc midplane and raises the temperature by about 15% compared to passive disc models. The vertical temperature profile shows no temperature peak at the midplane as in classical viscous disc models. A roughly flat vertical temperature profile establishes in the optically thick region of the disc close to the midplane. We reproduce the vertical temperature profile with viscous disc models for which the stress tensor vertical profile is flat in the bulk of the disc and vanishes in the disc corona. Conclusions: The present
Gyrokinetic predictions of multiscale transport in a DIII-D ITER baseline discharge
NASA Astrophysics Data System (ADS)
Holland, C.; Howard, N. T.; Grierson, B. A.
2017-06-01
New multiscale gyrokinetic simulations predict that electron energy transport in a DIII-D ITER baseline discharge with dominant electron heating and low input torque is multiscale in nature, with roughly equal amounts of the electron energy flux Q e coming from long wavelength ion-scale (k y ρ s < 1) and short wavelength electron-scale (k y ρ s > 1) fluctuations when the gyrokinetic results match independent power balance calculations. Corresponding conventional ion-scale simulations are able to match the power balance ion energy flux Q i, but systematically underpredict Q e when doing so. Significant nonlinear cross-scale couplings are observed in the multiscale simulations, but the exact simulation predictions are found to be extremely sensitive to variations of model input parameters within experimental uncertainties. Most notably, depending upon the exact value of the equilibrium E × B shearing rate γ E×B used, either enhancement or suppression of the long-wavelength turbulence and transport levels in the multiscale simulations is observed relative to what is predicted by ion-scale simulations. While the enhancement of the long wavelength fluctuations by inclusion of the short wavelength turbulence was previously observed in similar multiscale simulations of an Alcator C-Mod L-mode discharge, these new results show for the first time a complete suppression of long-wavelength turbulence in a multiscale simulation, for parameters at which conventional ion-scale simulation predicts small but finite levels of low-k turbulence and transport consistent with the power balance Q i. Although computational resource limitations prevent a fully rigorous validation assessment of these new results, they provide significant new evidence that electron energy transport in burning plasmas is likely to have a strong multiscale character, with significant nonlinear cross-scale couplings that must be fully understood to predict the performance of
Gyrokinetic predictions of multiscale transport in a DIII-D ITER baseline discharge
Holland, C.; Howard, N. T.; Grierson, B. A.
2017-05-08
New multiscale gyrokinetic simulations predict that electron energy transport in a DIII-D ITER baseline discharge with dominant electron heating and low input torque is multiscale in nature, with roughly equal amounts of the electron energy flux Qe coming from long wavelength ion-scale (kyρs < 1) and short wavelength electron-scale (kyρs > 1) fluctuations when the gyrokinetic results match independent power balance calculations. Corresponding conventional ion-scale simulations are able to match the power balance ion energy flux Qi, but systematically underpredict Qe when doing so. We observe significant nonlinear cross-scale couplings in the multiscale simulations, but the exact simulation predictions aremore » found to be extremely sensitive to variations of model input parameters within experimental uncertainties. Most notably, depending upon the exact value of the equilibrium E x B shearing rate γ E x B used, either enhancement or suppression of the long-wavelength turbulence and transport levels in the multiscale simulations is observed relative to what is predicted by ion-scale simulations. And while the enhancement of the long wavelength fluctuations by inclusion of the short wavelength turbulence was previously observed in similar multiscale simulations of an Alcator C-Mod L-mode discharge, these new results show for the first time a complete suppression of long-wavelength turbulence in a multiscale simulation, for parameters at which conventional ion-scale simulation predicts small but finite levels of low-k turbulence and transport consistent with the power balance Qi. Though computational resource limitations prevent a fully rigorous validation assessment of these new results, they provide significant new evidence that electron energy transport in burning plasmas is likely to have a strong multiscale character, with significant nonlinear cross-scale couplings that must be fully understood to predict the performance of those plasmas with confidence.« less
Effect of heterogeneousatmospheric CO2 on simulated global carbon budget
Zhang, Zhen; Jiang, Hong; Liu, Jinxun; Ju, Weimin; Zhang, Xiuying
2013-01-01
The effects of rising atmospheric carbon dioxide (CO2) on terrestrial carbon (C) sequestration have been a key focus in global change studies. As anthropological CO2 emissions substantially increase, the spatial variability of atmospheric CO2 should be considered to reduce the potential bias on C source and sink estimations. In this study, the global spatial–temporal patterns of near surface CO2 concentrations for the period 2003-2009 were established using the SCIAMACHY satellite observations and the GLOBALVIEW-CO2 field observations. With this CO2 data and the Integrated Biosphere Simulator (IBIS), our estimation of the global mean annual NPP and NEP was 0.5% and 7% respectively which differs from the traditional C sequestration assessments. The Amazon, Southeast Asia, and Tropical Africa showed higher C sequestration than the traditional assessment, and the rest of the areas around the world showed slightly lower C sequestration than the traditional assessment. We find that the variability of NEP is less intense under heterogeneous CO2 pattern on a global scale. Further studies of the cause of CO2 variation and the interactions between natural and anthropogenic processes of C sequestration are needed.
Global simulation of chemistry and radiative forcing of mineral aerosols
Zhang, Yang; Easter, R.C.; Ghan, S.J.; Leung, L.R.
1996-12-31
Mineral aerosols are increasingly gaining attention because of their roles in atmospheric chemistry and climate system. A global three-dimensional aerosol/chemistry model (GChM) coupled with a general circulation model (GCM) is used to simulate the sources/sinks, chemistry and radiative forcing of mineral aerosols. Regional and seasonal variations in distribution of mineral aerosols are predicted based on vegetation types, threshold wind velocities and soil moisture data. The role of mineral aerosols as a reactive surface available for heterogeneous uptake of gas-phase species in the global atmosphere is investigated along with their impact on the tropospheric sulfur cycle and the photochemical oxidant cycle. In particular, the heterogeneous surface reactions of SO{sub 2}, H{sub 2}SO{sub 4}, NO{sub 3}, N{sub 2}O{sub 5}, HNO{sub 3}, O{sub 3}, OH, HO{sub 2}, H{sub 2}O{sub 2} and CH{sub 3}O{sub 2} on mineral aerosols are simulated. The direct radiative forcing by mineral aerosols and the indirect forcing through influencing droplet number concentration are further estimated. The model simulation results are analyzed and compared against the available observational data.
Global Magnetospheric Simulations: coupling with ionospheric and solar wind models
NASA Astrophysics Data System (ADS)
Lapenta, Giovanni; Olshevskyi, Vyacheslav; Amaya, Jorge; Deca, Jan; Markidis, Stefano; Vapirev, Alexander
2013-04-01
We present results on the global fully kinetic model of the magnetosphere of the Earth. The simulations are based on the iPic3D code [1] that treats kinetically all plasma species solving implicitly the equations of motion for electrons and ions, coupled with the Maxwell equations. We present results of our simulations and discuss the coupling at the inner boundary near the Earth with models of the ionosphere and at the outer boundary with models of the arriving solar wind. The results are part of the activities of the Swiff FP7 project: www.swiff.eu [1] Stefano Markidis, Giovanni Lapenta, Rizwan-uddin, Multi-scale simulations of plasma with iPIC3D, Mathematics and Computers in Simulation, Volume 80, Issue 7, March 2010, Pages 1509-1519, ISSN 0378-4754, 10.1016/j.matcom.2009.08.038 [2] Giovanni Lapenta, Particle simulations of space weather, Journal of Computational Physics, Volume 231, Issue 3, 1 February 2012, Pages 795-821, ISSN 0021-9991, 10.1016/j.jcp.2011.03.035.
Studies of climate dynamics with innovative global-model simulations
NASA Astrophysics Data System (ADS)
Shi, Xiaoming
Climate simulations with different degrees of idealization are essential for the development of our understanding of the climate system. Studies in this dissertation employ carefully designed global-model simulations for the goal of gaining theoretical and conceptual insights into some problems of climate dynamics. Firstly, global warming-induced changes in extreme precipitation are investigated using a global climate model with idealized geography. The precipitation changes over an idealized north-south mid-latitude mountain barrier at the western margin of an otherwise flat continent are studied. The intensity of the 40 most intense events on the western slopes increases by about ~4°C of surface warming. In contrast, the intensity of the top 40 events on the eastern mountain slopes increases at about ~6°C. This higher sensitivity is due to enhanced ascent during the eastern-slope events, which can be explained in terms of linear mountain-wave theory relating to global warming-induced changes in the upper-tropospheric static stability and the tropopause level. Dominated by different dynamical factors, changes in the intensity of extreme precipitation events over plains and oceans might differ from changes over mountains. So the response of extreme precipitation over mountains and flat areas are further compared using larger data sets of simulated extreme events over the two types of surfaces. It is found that the sensitivity of extreme precipitation to increases in global mean surface temperature is 3% per °C lower over mountains than over the oceans or the plains. The difference in sensitivity among these regions is not due to thermodynamic effects, but rather to differences between the gravity-wave dynamics governing vertical velocities over the mountains and the cyclone dynamics governing vertical motions over the oceans and plains. The strengthening of latent heating in the storms over oceans and plains leads to stronger ascent in the warming climate
Simulating the global transport of nitrogen oxides emissions from aircraft
NASA Astrophysics Data System (ADS)
Sausen, R.; Köhler, I.
1994-05-01
With the atmosphere general circulation model ECHAM the passive transport of NOx emitted from global subsonic air traffic and the NOx concentration change due to these emissions are investigated. The source of NOx is prescribed according to an aircraft emission data base. The sink of NOx is parameterized as an exponential decay process with globally constant lifetime. Simulations in perpetual January and July modes are performed. Both the resulting mean and the standard deviation of the NOx mass mixing ratio are analysed. In January horizontal dispersion is more pronounced and vertical mixing is smaller than in July. In both cases the resulting quasi-stationary fields of the mass mixing ratio display a pronounced zonal asymmetry. The variability accounts up to 30% of the mean field.
Incorrectness of the usual gyrokinetic treatment in cylindrically symmetric systems
Linsker, R.
1980-07-01
It is shown that the usual gyrokinetic theory does not consistently retain all terms of leading order in the expansion parameter epsilon = gyroradius/equilibrium scale length. This is illustrated for cylindrically symmetric systems by comparing the perturbed distribution function calculated by the gyrokinetic method with that obtained by explicitly integrating the Vlasov equation over the unperturbed orbit. The integral equation used in some recent treatments of drift waves in sheared-slab geometry is shown to be incorrect. The correct calculation of the ion density perturbation for a collisionless ..beta.. = 0 plasma with cylindrical symmetry is presented.
A simulation of the global ocean circulation with resolved eddies
NASA Astrophysics Data System (ADS)
Semtner, Albert J.; Chervin, Robert M.
1988-12-01
A multilevel primitive-equation model has been constructed for the purpose of simulating ocean circulation on modern supercomputing architectures. The model is designed to take advantage of faster clock speeds, increased numbers of processors, and enlarged memories of machines expected to be available over the next decade. The model allows global eddy-resolving simulations to be conducted in support of the World Ocean Circulation Experiment. Furthermore, global ocean modeling is essential for proper representation of the full range of oceanic and climatic phenomena. The first such global eddy-resolving ocean calculation is reported here. A 20-year integration of a global ocean model with ½° grid spacing and 20 vertical levels has been carried out with realistic geometry and annual mean wind forcing. The temperature and salinity are constrained to Levitus gridded data above 25-m depth and below 710-m depth (on time scales of 1 month and 3 years, respectively), but the values in the main thermocline are unconstrained for the last decade of the calculation. The final years of the simulation allow the spontaneous formation of waves and eddies through the use of scale-selective viscosity and diffusion. A quasi-equilibrium state shows many realistic features of ocean circulation, including unstable separating western boundary currents, the known anomalous northward heat transport in the South Atlantic, and a global compensation for the abyssal spread of North Atlantic Deep Water via a long chain of thermocline mass transport from the tropical Pacific, through the Indonesian archipelago, across the Indian Ocean, and around the southern tip of Africa. This chain of thermocline transport is perhaps the most striking result from the model, and eddies and waves are evident along the entire 20,000-km path of the flow. The modeled Gulf Stream separates somewhat north of Cape Hatteras, produces warm- and cold-core rings, and maintains its integrity as a meadering thermal front
NASA Astrophysics Data System (ADS)
Xie, H. S.; Li, Y. Y.; Lu, Z. X.; Ou, W. K.; Li, B.
2017-07-01
To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on the integral equation, Euler initial value simulation, Euler matrix eigenvalue solution, and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift mode equation in Z-pinch with slab simplification and in tokamak with a ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at a strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas.
Mechanisms Affecting the Overturning Response in Global Warming Simulations.
NASA Astrophysics Data System (ADS)
Schweckendiek, U.; Willebrand, J.
2005-12-01
Climate models used to produce global warming scenarios exhibit widely diverging responses of the thermohaline circulation (THC). To investigate the mechanisms responsible for this variability, a regional Atlantic Ocean model driven with forcing diagnosed from two coupled greenhouse gas simulations has been employed. One of the coupled models (MPI) shows an almost constant THC, the other (GFDL) shows a declining THC in the twenty-first century.The THC evolution in the regional model corresponds rather closely to that of the respective coupled simulation, that is, it remains constant when driven with the forcing from the MPI model, and declines when driven with the GFDL forcing. These findings indicate that a detailed representation of ocean processes in the region covered by the Atlantic model may not be critical for the simulation of the overall THC changes in a global warming scenario, and specifically that the coupled model’s rather coarse representation of water mass formation processes in the subpolar North Atlantic is unlikely to be the primary cause for the large differences in the THC evolution.Sensitivity experiments have confirmed that a main parameter governing the THC response to global warming is the density of the intermediate waters in the Greenland Iceland Norwegian Seas, which in turn influences the density of the North Atlantic Deep Water, whereas changes in the air sea heat and freshwater fluxes over the subpolar North Atlantic are only of moderate importance, and mainly influence the interannual decadal variability of THC.Finally, as a consequence of changing surface fluxes, the Labrador Sea convection ceases by about 2030 under both forcings (i.e., even in a situation where the overall THC is stable) indicating that the eventual breakdown of the convection is likely but need not coincide with substantial THC changes.
Global simulation of the carbon isotope exchange of terrestrial ecosystems
NASA Astrophysics Data System (ADS)
Ito, A.; Terao, Y.; Mukai, H.
2009-12-01
There remain large uncertainties in our quantification of global carbon cycle, which has close interactions with the climate system and is subject to human-induced global environmental change. Information on carbon isotopes is expected to reduce the uncertainty by providing additional constraints on net atmosphere-ecosystem exchange. This study attempted to simulate the dynamics of carbon isotopes at the global scale, using a process-based terrestrial ecosystem model: Vegetation Integrative SImulator for Trace gases (VISIT). The base-model of carbon cycle (Sim-CYCLE, Ito 2003) has already considered stable carbon isotope composition (13C/12C), and here radioactive carbon isotope (14C) was included. The isotope ratios characterize various aspects of terrestrial carbon cycle, which is difficult to be constrained by sole mass balance. For example, isotopic discrimination by photosynthetic assimilation is closely related with leaf stomatal conductance and composition of C3 and C4 plant in grasslands. Isotopic disequilibrium represents mean residence time of terrestrial carbon pools. In this study, global simulations (spatial resolution 0.5-deg, time-step 1-month) were conducted during the period 1901 to 2100 on the basis of observed and projected atmospheric CO2, climate, and land-use conditions. As anthropogenic CO2 accumulates in the atmosphere, heavier stable carbon isotope (13C) was diluted, while radioactive carbon isotope (14C) is strongly affected by atomic bomb experiments mainly in the 1950s and 1960s. The model simulated the decadal change in carbon isotope compositions. Leaf carbon with shorter mean residence time responded rapidly to the atmospheric change, while plant stems and soil humus showed substantial time-lag, leading to large isotopic disequilibrium. In the future, the isotopic disequilibrium was estimated to augment, due to accelerated rate of anthropogenic CO2 accumulation. Spatial distribution of stable isotope composition (12C/13C, or d13C) was
Can Multimedia Make Kids Care about Social Studies? The GlobalEd Problem-Based Learning Simulation
ERIC Educational Resources Information Center
Ioannou, Andri; Brown, Scott W.; Hannafin, Robert D.; Boyer, Mark A.
2009-01-01
This study investigated whether using multimedia-based instructional material in a problem-based social studies simulation enhances student learning about world issues, increases interest in social studies, and generates positive attitudes toward the instruction. The GlobalEd Project, a Web-based international negotiation simulation embedded in…
Can Multimedia Make Kids Care about Social Studies? The GlobalEd Problem-Based Learning Simulation
ERIC Educational Resources Information Center
Ioannou, Andri; Brown, Scott W.; Hannafin, Robert D.; Boyer, Mark A.
2009-01-01
This study investigated whether using multimedia-based instructional material in a problem-based social studies simulation enhances student learning about world issues, increases interest in social studies, and generates positive attitudes toward the instruction. The GlobalEd Project, a Web-based international negotiation simulation embedded in…
First Radiation Magnetohydrodynamic Global Simulations Of Protoplanetary Disks
NASA Astrophysics Data System (ADS)
Flock, M.; Fromang, S.; González, M.; Commerçon, B.
2013-07-01
We present the turbulent and thermal evolution of a magnetized protoplanetary disks using full global 3D radiative MHD simulations including frequency dependent irradiation by the star. We perform classical 2D radiative viscous disk simulations to compare with the full model. The temperature evolution differs significantly between the two models, mainly due to the non uniform heating in case of the magneto rotational instability (MRI). In the full 3D model, the midplane temperature is flat and determined by the disk infrared surface temperature. The classical viscous models show the expected peak at the midplane due to the assumption of constant accretion stress. During the development of our method we focused on serial and parallel performance. As a result our method present high computational efficiency and we reach parallel scaling up to 70% using 1024 cpu's.
Simulating the global ozone distribution with ICON-ART
NASA Astrophysics Data System (ADS)
Schröter, Jennifer; Ruhnke, Roland
2015-04-01
Ozone is one of the most important atmospheric trace gases within the stratosphere as well as in the troposphere. Atmospheric chemistry is driven by solar radiation induced photodissociation of atmospheric trace gases. Thus, the calculation of the actinic flux and hence of the photodissociation frequencies is an essential part in the simulation of atmospheric trace gas distributions. The ICON-ART1 model is an extension of the non-hydrostatic modeling framework ICON2, jointly developed by the German Weather Service (DWD) and Max-Planck-Institute for Meteorology (MPI-M), and is used for numerical weather prediction as well as for future climate predictions. ICON-ART is developed with the goal to simulate interactions between trace substances and the state of the atmosphere. For the dynamics (transport and diffusion) of gaseous tracers, the original ICON tracer framework is used. For the model physics, numerical time integration follows a process splitting approach separating physical processes. Each process is called independently via an interface module. Currently, the processes of emission, dry and wet deposition, sedimentation, and first order chemical reactions are included. In this study we introduce a new gas-phase chemistry module for ICON-ART in combination with an online photolysis module. The new gas-phase chemical module uses the kpp formalism3 and the photolysis module is based on Fast-JX4, which provides online calculation of actinic flux for a wavelength region down to 170 nm, depending on the actual state of ozone, temperature, pressure, relative humidity and liquid water path, resulting in photolysis rates which are usable for the simulation of tropospheric as well as stratospheric trace gas distributions. We will present first simulations of global ozone distribution by using the new gas-phase chemistry module and photolysis module within ICON-ART to show the ability of ICON-ART to investigate chemical mechanisms and transport of chemical trace gas
NASA Astrophysics Data System (ADS)
Wiltberger, M. J.; Lyon, J.; Elkington, S. R.; Merkin, V. G.
2013-12-01
Global scale magnetohydrodynamic simulations have been used to successfully study the evolution of the magnetosphere-ionosphere system under a variety of solar wind conditions. Early studies with the Lyon-Fedder-Mobarry (LFM) model show the presence of flow channels in substorm simulations that had characteristics similar to those seen in observations of bursty bulk flows (BBFs) observed by numerous spacecraft, such as AMPTE and Geotail. More recently the THEMIS constellation has provided a unique opportunity to track the evolution of dipolarization fronts (DFs) from the mid-tail into the inner magnetosphere. Additionally, advances in high performance computing capability make it possible to conduct ultra-high resolution global simulations. In this paper we present comparisons between these ultra-high resolution simulations and the observations of THEMIS. The comparisons include a case study for a DF that was well observed on February 27, 2009 and statistical properties of the flow and electromagnetic field signatures seen in observations and MHD simulations with idealized solar wind conditions. In addition to these comparisons we will present results of using test-particle simulations of electrons driven by the simulated fields to study particle energization in regions around DFs.
Global Dynamic Numerical Simulations of Plate Tectonic Reorganizations
NASA Astrophysics Data System (ADS)
Morra, G.; Quevedo, L.; Butterworth, N.; Matthews, K. J.; Müller, D.
2010-12-01
We use a new numerical approach for global geodynamics to investigate the origin of present global plate motion and to identify the causes of the last two global tectonic reorganizations occurred about 50 and 100 million years ago (Ma) [1]. While the 50 Ma event is the most well-known global plate-mantle event, expressed by the bend in the Hawaiian-Emperor volcanic chain, a prominent plate reorganization at about 100 Ma, although presently little studied, is clearly indicated by a major bend in the fracture zones in the Indian Ocean and by a change in Pacific plate motion [2]. Our workflow involves turning plate reconstructions into surface meshes that are subsequently employed as initial conditions for global Boundary Element numerical models. The tectonic setting that anticipates the reorganizations is processed with the software GPlates, combining the 3D mesh of the paleo-plate morphology and the reconstruction of paleo-subducted slabs, elaborated from tectonic history [3]. All our models involve the entire planetary system, are fully dynamic, have free surface, are characterized by a spectacular computational speed due to the simultaneous use of the multi-pole algorithm and the Boundary Element formulation and are limited only by the use of sharp material property variations [4]. We employ this new tool to unravel the causes of plate tectonic reorganizations, producing and comparing global plate motion with the reconstructed ones. References: [1] Torsvik, T., Müller, R.D., Van der Voo, R., Steinberger, B., and Gaina, C., 2008, Global Plate Motion Frames: Toward a unified model: Reviews in Geophysics, VOL. 46, RG3004, 44 PP., 2008 [2] Wessel, P. and Kroenke, L.W. Pacific absolute plate motion since 145 Ma: An assessment of the fixed hot spot hypothesis. Journal of Geophysical Research, Vol 113, B06101, 2008 [3] L. Quevedo, G. Morra, R. D. Mueller. Parallel Fast Multipole Boundary Element Method for Crustal Dynamics, Proceeding 9th World Congress and 4th Asian
Global contrail coverage simulated by CAM5 with the inventory of 2006 global aircraft emissions
NASA Astrophysics Data System (ADS)
Chen, Chih-Chieh; Gettelman, Andrew; Craig, Cheryl; Minnis, Patrick; Duda, David P.
2012-02-01
This paper documents the incorporation of an inventory of the AEDT (Aviation Environmental Design Tool) global commercial aircraft emissions for the year of 2006 into the National Center for Atmospheric Research Community Earth System Model (CESM) version 1. The original dataset reports aircraft emission mass of ten species on an hourly basis which is converted to monthly emission mixing ratio tendencies as the released version of the dataset. We also describe how the released aircraft emission dataset is incorporated into CESM. A contrail parameterization is implemented in the CESM in which it is assumed that persistent contrails initially form when aircraft water vapor emissions experience a favorable atmospheric environment. Both aircraft emissions and ambient humidity are attributed to the formation of contrails. The ice water content of contrails is assumed to follow an empirical function of atmospheric temperature which determines the cloud fraction associated with contrails. Our modeling study indicates that the simulated global contrail coverage is sensitive to the vertical resolution of the GCMs in the upper troposphere and lower stratosphere because of model assumptions about the vertical overlap structure of clouds. Furthermore, the extent of global contrail coverage simulated by CESM exhibits a seasonal cycle which is in broad agreement with observations.
Hager, Robert; Chang, C. S.
2016-04-08
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Hager, Robert; Chang, C. S.
2016-04-08
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steepmore » edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.« less
NASA Astrophysics Data System (ADS)
Hager, Robert; Chang, C. S.
2016-04-01
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Hager, Robert Chang, C. S.
2016-04-15
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Global and local waveform simulations using the VERCE platform
NASA Astrophysics Data System (ADS)
Garth, Thomas; Saleh, Rafiq; Spinuso, Alessandro; Gemund, Andre; Casarotti, Emanuele; Magnoni, Federica; Krischner, Lion; Igel, Heiner; Schlichtweg, Horst; Frank, Anton; Michelini, Alberto; Vilotte, Jean-Pierre; Rietbrock, Andreas
2017-04-01
demonstrate the functionality of the VERCE platform with two use cases, one using the pre-loaded velocity model and mesh for the Maule area of Chile using the SPECFEM3D Cartesian workflow, and one showing the output of a global simulation using the SPECFEM3D globe workflow. It is envisioned that this tool will allow a much greater range of seismologists to access these full waveform inversion tools, and aid full waveform tomographic and source inversion, synthetic shakemap production and other full waveform applications, in a wide range of tectonic settings.
Physical Processes for Driving Ionospheric Outflows in Global Simulations
NASA Technical Reports Server (NTRS)
Moore, Thomas Earle; Strangeway, Robert J.
2009-01-01
We review and assess the importance of processes thought to drive ionospheric outflows, linking them as appropriate to the solar wind and interplanetary magnetic field, and to the spatial and temporal distribution of their magnetospheric internal responses. These begin with the diffuse effects of photoionization and thermal equilibrium of the ionospheric topside, enhancing Jeans' escape, with ambipolar diffusion and acceleration. Auroral outflows begin with dayside reconnexion and resultant field-aligned currents and driven convection. These produce plasmaspheric plumes, collisional heating and wave-particle interactions, centrifugal acceleration, and auroral acceleration by parallel electric fields, including enhanced ambipolar fields from electron heating by precipitating particles. Observations and simulations show that solar wind energy dissipation into the atmosphere is concentrated by the geomagnetic field into auroral regions with an amplification factor of 10-100, enhancing heavy species plasma and gas escape from gravity, and providing more current carrying capacity. Internal plasmas thus enable electromagnetic driving via coupling to the plasma, neutral gas and by extension, the entire body " We assess the Importance of each of these processes in terms of local escape flux production as well as global outflow, and suggest methods for their implementation within multispecies global simulation codes. We complete 'he survey with an assessment of outstanding obstacles to this objective.
Benchmark studies of the gyro-Landau-fluid code and gyro-kinetic codes on kinetic ballooning modes
NASA Astrophysics Data System (ADS)
Tang, T. F.; Xu, X. Q.; Ma, C. H.; Bass, E. M.; Holland, C.; Candy, J.
2016-03-01
A Gyro-Landau-Fluid (GLF) 3 + 1 model has been recently implemented in BOUT++ framework, which contains full Finite-Larmor-Radius effects, Landau damping, and toroidal resonance [Ma et al., Phys. Plasmas 22, 055903 (2015)]. A linear global beta scan has been conducted using the JET-like circular equilibria (cbm18 series), showing that the unstable modes are kinetic ballooning modes (KBMs). In this work, we use the GYRO code, which is a gyrokinetic continuum code widely used for simulation of the plasma microturbulence, to benchmark with GLF 3 + 1 code on KBMs. To verify our code on the KBM case, we first perform the beta scan based on "Cyclone base case parameter set." We find that the growth rate is almost the same for two codes, and the KBM mode is further destabilized as beta increases. For JET-like global circular equilibria, as the modes localize in peak pressure gradient region, a linear local beta scan using the same set of equilibria has been performed at this position for comparison. With the drift kinetic electron module in the GYRO code by including small electron-electron collision to damp electron modes, GYRO generated mode structures and parity suggest that they are kinetic ballooning modes, and the growth rate is comparable to the GLF results. However, a radial scan of the pedestal for a particular set of cbm18 equilibria, using GYRO code, shows different trends for the low-n and high-n modes. The low-n modes show that the linear growth rate peaks at peak pressure gradient position as GLF results. However, for high-n modes, the growth rate of the most unstable mode shifts outward to the bottom of pedestal and the real frequency of what was originally the KBMs in ion diamagnetic drift direction steadily approaches and crosses over to the electron diamagnetic drift direction.
Benchmark studies of the gyro-Landau-fluid code and gyro-kinetic codes on kinetic ballooning modes
Tang, T. F.; Xu, X. Q.; Ma, C. H.; Bass, E. M.; Candy, J.; Holland, C.
2016-03-15
A Gyro-Landau-Fluid (GLF) 3 + 1 model has been recently implemented in BOUT++ framework, which contains full Finite-Larmor-Radius effects, Landau damping, and toroidal resonance [Ma et al., Phys. Plasmas 22, 055903 (2015)]. A linear global beta scan has been conducted using the JET-like circular equilibria (cbm18 series), showing that the unstable modes are kinetic ballooning modes (KBMs). In this work, we use the GYRO code, which is a gyrokinetic continuum code widely used for simulation of the plasma microturbulence, to benchmark with GLF 3 + 1 code on KBMs. To verify our code on the KBM case, we first perform the beta scan based on “Cyclone base case parameter set.” We find that the growth rate is almost the same for two codes, and the KBM mode is further destabilized as beta increases. For JET-like global circular equilibria, as the modes localize in peak pressure gradient region, a linear local beta scan using the same set of equilibria has been performed at this position for comparison. With the drift kinetic electron module in the GYRO code by including small electron-electron collision to damp electron modes, GYRO generated mode structures and parity suggest that they are kinetic ballooning modes, and the growth rate is comparable to the GLF results. However, a radial scan of the pedestal for a particular set of cbm18 equilibria, using GYRO code, shows different trends for the low-n and high-n modes. The low-n modes show that the linear growth rate peaks at peak pressure gradient position as GLF results. However, for high-n modes, the growth rate of the most unstable mode shifts outward to the bottom of pedestal and the real frequency of what was originally the KBMs in ion diamagnetic drift direction steadily approaches and crosses over to the electron diamagnetic drift direction.
Grid-based Parallel Data Streaming Implemented for the Gyrokinetic Toroidal Code
S. Klasky; S. Ethier; Z. Lin; K. Martins; D. McCune; R. Samtaney
2003-09-15
We have developed a threaded parallel data streaming approach using Globus to transfer multi-terabyte simulation data from a remote supercomputer to the scientist's home analysis/visualization cluster, as the simulation executes, with negligible overhead. Data transfer experiments show that this concurrent data transfer approach is more favorable compared with writing to local disk and then transferring this data to be post-processed. The present approach is conducive to using the grid to pipeline the simulation with post-processing and visualization. We have applied this method to the Gyrokinetic Toroidal Code (GTC), a 3-dimensional particle-in-cell code used to study microturbulence in magnetic confinement fusion from first principles plasma theory.
Improving conservation properties of a 5D gyrokinetic semi-Lagrangian code
NASA Astrophysics Data System (ADS)
Latu, Guillaume; Grandgirard, Virginie; Abiteboul, Jérémie; Crouseilles, Nicolas; Dif-Pradalier, Guilhem; Garbet, Xavier; Ghendrih, Philippe; Mehrenberger, Michel; Sarazin, Yanick; Sonnendrücker, Eric
2014-11-01
In gyrokinetic turbulent simulations, the knowledge of some stationary states can help reducing numerical artifacts. Considering long-term simulations, the qualities of the Vlasov solver and of the radial boundary conditions have an impact on the conservation properties. In order to improve mass and energy conservation mainly, the following methods are investigated: fix the radial boundary conditions on a stationary state, use a 4D advection operator that avoids a directional splitting, interpolate with a delta-f approach. The combination of these techniques in the semi-Lagrangian code gysela leads to a net improvement of the conservation properties in 5D simulations. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.
Gyrokinetic Theory and Computational Methods for Electromagnetic Perturbations in Tokamaks
NASA Astrophysics Data System (ADS)
Qin, H.; Tang, W. M.; Rewoldt, G.
1998-11-01
A general gyrokinetic formalism and computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and the associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both MHD instabilities and electromagnetic drift waves(H. Qin, W. M. Tang, and G. Rewoldt, Phys. Plasmas 5), 1035 (1998). The gyrokinetic system of equations is derived by phase-space Lagrangian Lie perturbation methods. An important component missing from previous gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed. The corresponding numerical code, KIN-2DEM, has been systematically benchmarked against the high-n FULL code, the PEST code, and the NOVA-K code for kinetic ballooning modes, internal kink modes, and TAEs, respectively. For the internal kink mode, it is found that kinetic effects due to trapped ions can significantly modify the γ vs. q0 curve. For the destabilization of the TAEs by energetic particles, comparisons have been made between the non-perturbative, fully kinetic KIN-2DEM results and the perturbative hybrid NOVA-K results.
Magnetohydrodynamic simulations of global accretion disks with vertical magnetic fields
Suzuki, Takeru K.; Inutsuka, Shu-ichiro
2014-04-01
We report results of three-dimensional magnetohydrodynamical (MHD) simulations of global accretion disks threaded with weak vertical magnetic fields. We perform the simulations in the spherical coordinates with different temperature profiles and accordingly different rotation profiles. In the cases with a spatially constant temperature, because the rotation frequency is vertically constant in the equilibrium condition, general properties of the turbulence excited by magnetorotational instability are quantitatively similar to those obtained in local shearing box simulations. On the other hand, in the cases with a radially variable temperature profile, the vertical differential rotation, which is inevitable in the equilibrium condition, winds up the magnetic field lines in addition to the usual radial differential rotation. As a result, the coherent wound magnetic fields contribute to the Maxwell stress in the surface regions. We obtain nondimensional density and velocity fluctuations ∼0.1-0.2 at the midplane. The azimuthal power spectra of the magnetic fields show shallower slopes, ∼m {sup 0} – m {sup –1}, than those of velocity and density. The Poynting flux associated with the MHD turbulence drives intermittent and structured disk winds as well as sound-like waves toward the midplane. The mass accretion mainly occurs near the surfaces, and the gas near the midplane slowly moves outward in the time domain of the present simulations. The vertical magnetic fields are also dragged inward in the surface regions, while they stochastically move outward and inward around the midplane. We also discuss an observational implication of induced spiral structure in the simulated turbulent disks.
Weir, G. M.; Faber, B. J.; Likin, K. M.; Talmadge, J. N.; Anderson, D. T.; Anderson, F. S. B.
2015-05-15
Stiffness measurements are presented in the quasi-helically symmetric experiment (HSX), in which the neoclassical transport is comparable to that in a tokamak and turbulent transport dominates throughout the plasma. Electron cyclotron emission is used to measure the local electron temperature response to modulated electron cyclotron resonant heating. The amplitude and phase of the heat wave through the steep electron temperature gradient (ETG) region of the plasma are used to determine a transient electron thermal diffusivity that is close to the steady-state diffusivity. The low stiffness in the region between 0.2 ≤ r/a ≤ 0.4 agrees with the scaling of the steady-state heat flux with temperature gradient in this region. These experimental results are compared to gyrokinetic calculations in a flux-tube geometry using the gyrokinetic electromagnetic numerical experiment code with two kinetic species. Linear simulations show that the ETG mode may be experimentally relevant within r/a ≤ 0.2, while the Trapped Electron Mode (TEM) is the dominant long-wavelength microturbulence instability across most of the plasma. The TEM is primarily driven by the density gradient. Non-linear calculations of the saturated heat flux driven by the TEM and ETG bracket the experimental heat flux.
Numerical Instability in a 2D Gyrokinetic Code Caused by Divergent E × B Flow
NASA Astrophysics Data System (ADS)
Byers, J. A.; Dimits, A. M.; Matsuda, Y.; Langdon, A. B.
1994-12-01
In this paper, a numerical instability first observed in a 2D electrostatic gyrokinetic code is described. The instability should also be present in some form in many versons of particle-in-cell simulation codes that employ guiding center drifts. A perturbation analysis of the instability is given and its results agree quantitatively with the observations from the gyrokinetic code in all respects. The basic mechanism is a false divergence of the E × B flow caused by the interpolation between the grid and the particles as coupled with the specific numerical method for calculating E - ∇φ. Stability or instability depends in detail on the specific choice of particle interpolation method and field method. One common interpolation method, subtracted dipole, is stable. Other commonly used interpolation methods, linear and quadratic, are unstable when combined with a finite difference for the electric field. Linear and quadratic interpolation can be rendered stable if combined with another method for the electric field, the analytic differential of the interpolated potential.
NASA Astrophysics Data System (ADS)
Satoh, M.; Noda, A. T.; Kodama, C.; Yamada, Y.; Hashino, T.
2012-12-01
Global cloud distributions and properties simulated by the global nonhydrostatic model, NICAM (Nonhydrostatic Icosahedral Atmospheric Model), are evaluated and their future changes are discussed. First, we evaluated the simulated cloud properties produced by a case study of the 3.5km mesh experiment of NICAM using the satellite simulator package (the Joint-simulator) with cloud microphysics oriented approach (Hashino et al. 2012). Then, we analyzed future cloud changes using various sets of simulations under the present and the future global warming conditions. The results show that the zonal averaged ice water path (IWP) generally decreases or marginally unchanged in the tropics, while IWP in the extra-tropics increases. The upper cloud fraction increases both in the tropics and in the extra-tropics in general. We further analyzed contributions of cloud systems such as cloud clusters, tropical cyclones (TCs), and storm-tracks to these changes. Probability distribution of the larger cloud clusters decreases, while that of the smaller ones increases, consistent with the decrease in the number of tropical cyclones in the future climate. Average liquid water path (LWP) and IWP associated with each tropical cyclone are diagnosed, and it is found that both the associated LWP and IWP increase under the warmer condition. Even though, since the number of the intensive cloud systems decrease, the average IWP decreases. It should be remarked that the change in TC tracks largely contribute to the change in the horizontal distribution of clouds. The NICAM simulations also show that the storm-tracks shift poleward, and the storms become less frequent and stronger in the extra-tropics, similar to the results of other general circulation models. Both LWP and IWP associated with the storms also increase in the warmer climate in the NICAM simulations. This results in increase in the upper clouds under the warmer climate condition, as described by Miura et al. (2005). References
NASA Technical Reports Server (NTRS)
Chin, Mian; Rood, Richard B.; Lin, Shian-Jiann; Mueller, Jean-Francois; Thompson, Anne M.
2000-01-01
The Georgia Tech/Goddard Global Ozone Chemistry Aerosol Radiation and Transport (GOCART) model is used to simulate the atmospheric sulfur cycle. The model uses the simulated meteorological data from the Goddard Earth Observing System Data Assimilation System (GEOS DAS). Global sulfur budgets from a 6-year simulation for SO2, sulfate, dimethylsulfide (DMS), and methanesulfonic acid (MSA) are presented in this paper. In a normal year without major volcanic perturbations, about 20% of the sulfate precursor emission is from natural sources (biogenic and volcanic) and 80% is anthropogenic: the same sources contribute 339% and 67% respectively to the total sulfate burden. A sulfate production efficiency of 0.41 - 0.42 is estimated in the model, an efficiency which is defined as a ratio of the amount oi sulfate produced to the total amount of SO2 emitted and produced in the atmosphere. This value indicates that less than half of the SO2 entering the atmosphere contributes to the sulfate production, the rest being removed by dry and wet depositions. In a simulation for 1990, we estimate a total sulfate production of 39 Tg S /yr with 36% and 64% respectively from in-air and in-cloud oxidation of SO2. We also demonstrate that major volcanic eruptions, such as the Mt. Pinatubo eruption in 1991, can significantly change the sulfate formation pathways, distributions, abundance, and lifetime. Comparison with other models shows that the parameterizations for wet removal or wet production of sulfate are the most critical factors in determining the burdens of SO2 and sulfate. Therefore, a priority for future research should be to reduce the large uncertainties associated with the wet physical and chemical processes.
Global Adjoint Tomography: Combining Big Data with HPC Simulations
NASA Astrophysics Data System (ADS)
Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.
2014-12-01
The steady increase in data quality and the number of global seismographic stations have substantially grown the amount of data available for construction of Earth models. Meanwhile, developments in the theory of wave propagation, numerical methods and HPC systems have enabled unprecedented simulations of seismic wave propagation in realistic 3D Earth models which lead the extraction of more information from data, ultimately culminating in the use of entire three-component seismograms.Our aim is to take adjoint tomography further to image the entire planet which is one of the extreme cases in seismology due to its intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. We have started low resolution (T > 27 s, soon will be > 17 s) global inversions with 253 earthquakes for a transversely isotropic crust and mantle model on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Recent improvements in our 3D solvers, such as the GPU version of the SPECFEM3D_GLOBE package, will allow us perform higher-resolution (T > 9 s) and longer-duration (~180 m) simulations to take the advantage of high-frequency body waves and major-arc surface waves to improve imbalanced ray coverage as a result of uneven distribution of sources and receivers on the globe. Our initial results after 10 iterations already indicate several prominent features reported in high-resolution continental studies, such as major slabs (Hellenic, Japan, Bismarck, Sandwich, etc.) and enhancement in plume structures (the Pacific superplume, the Hawaii hot spot, etc.). Our ultimate goal is to assimilate seismic data from more than 6,000 earthquakes within the magnitude range 5.5 ≤ Mw ≤ 7.0. To take full advantage of this data set on ORNL's computational resources, we need a solid framework for managing big data sets during pre-processing (e.g., data requests and quality checks), gradient calculations, and post-processing (e
NASA Astrophysics Data System (ADS)
Gusakov, E. Z.; Altukhov, A. B.; Bulanin, V. V.; Gurchenko, A. D.; Heikkinen, J. A.; Janhunen, S. J.; Leerink, S.; Esipov, L. A.; Kantor, M. Yu; Kiviniemi, T. P.; Korpilo, T.; Kouprienko, D. V.; Lashkul, S. I.; Petrov, A. V.; Teplova, N. V.
2013-12-01
Quantitative reproduction of selected micro-, meso- and macro-scale transport phenomena as measured in the FT-2 tokamak is reached by Elmfire global full-f nonlinear gyrokinetic particle-in-cell simulation predictions. A detailed agreement with mean equilibrium flows, oscillating fine-scale zonal flows and turbulence radial correlation length observed by a set of sophisticated microwave backscattering techniques, as well as a good fit of the thermal diffusivity data in the central and gradient region of discharge are demonstrated. Both the shift and the broadening of the power spectrum of synthetic and experimental Doppler reflectometry diagnostics have been found to overlap perfectly at various radial positions, indicating similar rotation and spreading of the selected density fluctuations. At the same time similar radial electric field dynamics, spatial structure and outward geodesic acoustic mode (GAM) propagation have been observed by comparisons of the probability distribution function, the dominant frequency, the coherence and the cross-phase of the simulated and experimentally measured radial electric field fluctuations, identifying the turbulent driven GAM as a key contributor to the observed strong temporal variation of the radial electric field affected by impurity ions.
Global economic burden of Chagas disease: a computational simulation model
Lee, Bruce Y; Bacon, Kristina M; Bottazzi, Maria Elena; Hotez, Peter J
2013-01-01
Summary Background As Chagas disease continues to expand beyond tropical and subtropical zones, a growing need exists to better understand its resulting economic burden to help guide stakeholders such as policy makers, funders, and product developers. We developed a Markov simulation model to estimate the global and regional health and economic burden of Chagas disease from the societal perspective. Methods Our Markov model structure had a 1 year cycle length and consisted of five states: acute disease, indeterminate disease, cardiomyopathy with or without congestive heart failure, megaviscera, and death. Major model parameter inputs, including the annual probabilities of transitioning from one state to another, and present case estimates for Chagas disease came from various sources, including WHO and other epidemiological and disease-surveillance-based reports. We calculated annual and lifetime health-care costs and disability-adjusted life-years (DALYs) for individuals, countries, and regions. We used a discount rate of 3% to adjust all costs and DALYs to present-day values. Findings On average, an infected individual incurs US$474 in health-care costs and 0·51 DALYs annually. Over his or her lifetime, an infected individual accrues an average net present value of $3456 and 3·57 DALYs. Globally, the annual burden is $627·46 million in health-care costs and 806 170 DALYs. The global net present value of currently infected individuals is $24·73 billion in health-care costs and 29 385 250 DALYs. Conversion of this burden into costs results in annual per-person costs of $4660 and lifetime per-person costs of $27 684. Global costs are $7·19 billion per year and $188·80 billion per lifetime. More than 10% of these costs emanate from the USA and Canada, where Chagas disease has not been traditionally endemic. A substantial proportion of the burden emerges from lost productivity from cardiovascular disease-induced early mortality. Interpretation The economic burden
High resolution global climate modelling from the UPSCALE simulation campaign
NASA Astrophysics Data System (ADS)
Vidale, Pier-Luigi; Roberts, Malcolm; Mizielinski, Matthew; Demory, Marie-Estelle; Schiemann, Reinhard; Strachan, Jane
2014-05-01
A traceable hierarchy of global climate models (based on the Met Office Unified Model, GA3 formulation), with mesh sizes ranging from 130km to 25km, has been developed in order to study the impact of improved representation of small-scale processes on the mean climate, its variability and extremes. Five-member ensembles of atmosphere-only integrations were completed at these resolutions, each 27 years in length, using both present day forcing and a future climate scenario. These integrations, collectively known as the "UPSCALE campaign", were completed using time provided by the European PrACE project on supercomputer HERMIT (HLRS Stuttgart). A wide variety of processes are being studied to assess these integrations, in particular with regards to the role of resolution. Tropical cyclone characteristics are shown to improve as resolution is increased (in terms of spatial extent, frequency, structure and variability), particularly in the Atlantic basin, where ensemble correlations with observed interannual variability approach 0.8. Mid-latitude Atlantic jet positioning improves in some seasons, although the spread between ensemble members has a similar magnitude to the spread between ensembles means at resolution. The simulation of decadal trends in Sahel rainfall also improve as resolution is increased, which is very likely linked to processes such as African Easterly Waves. The simulation of polar lows and other processes also become more realistic in the higher resolution simulations. Some aspects of the relationship between the improved simulation of the current climate, and how this impacts on changes in the future climate, will also be discussed. In particular tropical cyclone frequency decreases robustly in the Southern Hemisphere, but changes in the Northern Hemisphere are more basin-dependent, with a decrease in the Atlantic but a shift in tracks in the Pacific.
Global Change Simulations Affect Potential Methane Oxidation in Upland Soils
NASA Astrophysics Data System (ADS)
Blankinship, J. C.; Hungate, B. A.
2004-12-01
Atmospheric concentrations of methane (CH4) are higher now than they have ever been during the past 420,000 years. However, concentrations have remained stable since 1999. Emissions associated with livestock husbandry are unlikely to have changed, so some combination of reduced production in wetlands, more efficient capture by landfills, or increased consumption by biological CH4 oxidation in upland soils may be responsible. Methane oxidizing bacteria are ubiquitous in upland soils and little is known about how these bacteria respond to anthropogenic global change, and how they will influence - or already are influencing - the radiative balance of the atmosphere. Might ongoing and future global changes increase biological CH4 oxidation? Soils were sampled from two field experiments to assess changes in rates of CH4 oxidation in response to global change simulations. Potential activities of CH4 oxidizing bacterial communities were measured through laboratory incubations under optimal temperature, soil moisture, and atmospheric CH4 concentrations (~18 ppm, or 10x ambient). The ongoing 6-year multifactorial Jasper Ridge Global Change Experiment (JRGCE) simulates warming, elevated precipitation, elevated atmospheric CO2, elevated atmospheric N deposition, and increased wildfire frequency in an annual grassland in a Mediterranean-type climate in central California. The ongoing 1-year multifactorial Merriam Climate Change Experiment (MCCE) simulates warming, elevated precipitation, and reduced precipitation in four different types of ecosystems along an elevational gradient in a semi-arid climate in northern Arizona. The high desert grassland, pinyon-juniper woodland, ponderosa pine forest, and mixed conifer forest ecosystems range in annual precipitation from 100 to 1000 mm yr-1, and from productivity being strongly water limited to strongly temperature limited. Among JRGCE soils, elevated atmospheric CO2 increased potential CH4 oxidation rates (p=0.052) and wildfire
Global Monte Carlo Simulation with High Order Polynomial Expansions
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-12-13
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, pos