Theory of Alfven wave heating in general toroidal geometry
Tataronis, J.A.; Salat, A.
1981-09-01
A general treatment of Alfven wave heating based on the linearized equations of ideal magnetohydrodynamics (MHD) is given. The conclusion of this study is that the geometry of the plasma equilium could play an important role on the effectiveness of this heating mechanism, and for certain geometries the fundamental equations may not possess solutions which satisfy prescribed boundary conditions.
X. Z. Tang
2000-12-18
Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given.
Particle simulations in toroidal geometry
Aydemir, A.Y.
1992-09-01
A computational tool to be used in kinetic simulations of toroidal plasmas is being developed. The initial goal of the project is to develop an electrostatic gyrokinetic model for studying transport and stability problems in tokamaks. In this brief report, preliminary results from the early stages of this effort are presented.
Reversed Field Pinch Dynamics in Toroidal and Cylindrical Geometries
NASA Astrophysics Data System (ADS)
Morales, Jorge A.; Bos, Wouter J. T.; Schneider, Kai; Montgomery, David C.
2014-10-01
The effect of the curvature of the imposed magnetic field on Reversed Field Pinch dynamics is investigated by comparing the flow of a magnetofluid in a torus with aspect ratio 1.83, with the flow in a periodic cylinder. It is found that an axisymmetric toroidal mode is always present in the toroidal, but absent in the cylindrical configuration. In particular, in contrast to the cylinder, the toroidal case presents a double poloidal recirculation cell with a shear localized at the plasma edge. Quasi-single-helicity states are found to be more persistent in toroidal than in periodic cylinder geometry. This work was supported by the contract SiCoMHD (ANR-Blanc 2011-045), computing time was supplied by IDRIS, project 22206.
Nonlinear particle simulation of ion cyclotron waves in toroidal geometry
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.
2015-12-10
Global particle simulation model has been developed in this work to provide a first-principles tool for studying the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation with realistic electron-to-ion mass ratio. Boris push scheme for the ion motion has been developed in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron and ion Bernstein waves in global gyrokinetic toroidal code (GTC). The nonlinear simulation capability is applied to study the parametric decay instability of a pump wave into an ion Bernstein wave side band and a low frequency ion cyclotron quasi mode.
General Linear Rf-Current Drive Calculation in Toroidal Plasma
NASA Astrophysics Data System (ADS)
Smirnov, A. P.; Harvey, R. W.; Prater, R.
2009-04-01
A new general linear calculation of RF current drive has been implemented in the GENRAY all-frequencies RF ray tracing code. This is referred to as the ADJ-QL package, and is based on the Karney, et al. [1] relativistic Green function calculator, ADJ, generalized to non-circular plasmas in toroidal geometry, and coupled with full, bounce-averaged momentum-space RF quasilinear flux [2] expressions calculated at each point along the RF ray trajectories. This approach includes momentum conservation, polarization effects and the influence of trapped electrons. It is assumed that the electron distribution function remains close to a relativistic Maxwellian function. Within the bounds of these assumptions, small banana width, toroidal geometry and low collisionality, the calculation is applicable for all-frequencies RF electron current drive including electron cyclotron, lower hybrid, fast waves and electron Bernstein waves. GENRAY ADJ-QL calculations of the relativistic momentum-conserving current drive have been applied in several cases: benchmarking of electron cyclotron current drive in ITER against other code results; and electron Bernstein and high harmonic fast wave current drive in NSTX. The impacts of momentum conservation on the current drive are also shown for these cases.
Neoclassical viscosity effects on resistive magnetohydrodynamic modes in toroidal geometry
Yang, J.G.; Oh, Y.H.; Choi, D.I. ); Kim, J.Y.; Horton, W. )
1992-03-01
The flux-surface-averaged linearized resistive magnetohydrodynamic (MHD) boundary-layer equations including the compressibility, diamagnetic drift, and neoclassical viscosity terms are derived in toroidal geometry. These equations describe the resistive layer dynamics of resistive MHD modes over the collisionality regime between the banana plateau and the Pfirsch--Schlueter. From the resulting equations, the effects of neoclassical viscosity on the stability of the tearing and resistive ballooning modes are investigated numerically. Also, a study is given for the problem of how the neoclassical resistive MHD mode is generated as the collisionality is reduced. It is shown that the neoclassical viscosity terms give a significant destabilizing effect for the tearing and resistive ballooning modes. This destabilization comes mainly from the reduction of the stabilizing effect of the parallel ion sound compression by the ion neoclassical viscosity. In the banana-plateau collisionality limit, where the compressibility is negligible, the dispersion relations of the tearing and resistive ballooning modes reduce to the same form, with the threshold value of the driving force given by {Delta}{sub {ital c}}=0. On the other hand, with the finite neoclassical effect it is found that the neoclassical resistive MHD instability is generated in agreement with previous results. Furthermore, it is shown that this later instability can be generated in a wide range of the collisionality including near the Pfirsch--Schlueter regime as well as the banana-plateau regime, suggesting that this mode is a probable cause of anomalous transport.
Ballooning mode spectrum in general toroidal systems
Dewar, R.L.; Glasser, A.H.
1982-04-01
A WKB formalism for constructing normal modes of short-wavelength ideal hydromagnetic, pressure-driven instabilities (ballooning modes) in general toroidal magnetic containment devices with sheared magnetic fields is developed. No incompressibility approximation is made. A dispersion relation is obtained from the eigenvalues of a fourth order system of ordinary differential equations to be solved by integrating along a line of force. Higher order calculations are performed to find the amplitude equation and the phase change at a caustic. These conform to typical WKB results. In axisymmetric systems, the ray equations are integrable, and semiclassical quantization leads to a growth rate spectrum consisting of an infinity of discrete eigenvalues, bounded above by an accumulation point. However, each eigenvalue is infinitely degenerate. In the nonaxisymmetric case, the rays are unbounded in a four dimensional phase space, and semiclassical quantization breaks down, leading to broadening of the discrete eigenvalues and accumulation point of the axisymmetric case into continuum bands. Analysis of a model problem indicates that the broadening of the discrete eigenvalues is numerically very small, the dominant effect being broadening of the accumulation point.
NASA Astrophysics Data System (ADS)
Taylor, Marika
2006-03-01
Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.
The universal instability in general geometry
Helander, P.; Plunk, G. G.
2015-09-15
The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.
Axisymmetric toroidal modes of general relativistic magnetized neutron star models
Asai, Hidetaka; Lee, Umin E-mail: lee@astr.tohoku.ac.jp
2014-07-20
We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Geometry of generalized depolarizing channels
Burrell, Christian K.
2009-10-15
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
Modeling of Feedback Stabilization of External MHD Modes in Toroidal Geometry
NASA Astrophysics Data System (ADS)
Chu, M. S.; Chance, M. S.; Okabayashi, M.
2000-10-01
The intelligent shell feedback scheme(C.M. Bishop, Plasma Phys. Contr. Nucl. Fusion 31), 1179 (1989). seeks to utilize external coils to suppress the unstable MHD modes slowed down by the resistive shell. We present a new formulation and numerical results of the interaction between the plasma and its outside vacuum region, with complete plasma response and the inclusion of a resistive vessel in general toroidal geometry. This is achieved by using the Green's function technique, which is a generalization of that previously used for the VACUUM(M.S. Chance, Phys. Plasmas 4), 2161 (1997). code and coupled with the ideal MHD code GATO. The effectiveness of different realizations of the intelligent shell concept is gauged by their ability to minimize the available free energy to drive the MHD mode. Computations indicate poloidal coverage of 30% of the total resistive wall surface area and 6 or 7 segments of ``intelligent coil'' arrays superimposed on the resistive wall will allow recovery of up to 90% the effectiveness of the ideal shell in stabilizing the ideal external kink.
MHD Stability Trends from Perturbed Equilibria: Possible Limitations with Toroidal Geometry
NASA Astrophysics Data System (ADS)
Comer, K. J.; Callen, J. D.; Hegna, C. C.; Turnbull, A. D.; Cowley, S.
2003-10-01
The effects of equilibrium changes on ideal MHD properties are usually studied using numerical parameter scans. Previously, we introduced a new technique to explore these dependencies: changes in the potential energy δ W due to equilibrium changes are found with an expansion of the energy principle, rather than an eigenvalue-solver code. Validation of the approach in toroidal geometry attempted to use GATO (an ideal MHD stability code) and DIII-D shot 87009. The approach should succeed with the global modes of 87009; however, ˜ 0.1% changes to qo predicted δ W rapidly increasing. Perturbing β of other toroidal equilibria resulted in similar behavior. We first review results for a cylindrical equilibrium and for 87009. Between the cylindrical case and 87009 lie several other equilibria, which should produce intermediate results. We examine several of these intermediate equilibria, starting with the cylindrical case and changing aspect ratio, shape and profiles until ending at 87009.
Role of geometry in optothermal response of toroidal ultra-high-Q cavities
NASA Astrophysics Data System (ADS)
Soltani, Soheil; Armani, Andrea M.
2015-03-01
Ultra-high quality factor (UHQ) resonant cavities are able to store light for long periods of time, resulting in high circulating intensities. As a result, numerous nonlinear optical phenomena appear, such as radiation pressure oscillations and lasing. However, deleterious behaviors also occur, such as optothermal broadening of the resonant linewidth. The degree of distortion is directly related to the circulating power in the cavity, the material absorption, and the thermo-optic coefficient of the cavity material. Specifically, a portion of the circulating power is absorbed by the material and converted to heat. This thermal energy is able to induce a refractive index change in the cavity which is experimentally observed as a resonant wavelength change. This behavior has been observed in numerous cavities, but one interesting case is the toroidal cavity, as it has a particularly complex geometry providing multiple thermal transport pathways. To accurately capture this complex behavior, we have developed a COMSOL Multiphysics model which combines the thermal and optical components. The model uses the non-uniform optical mode profile as the heat source. As such, changes in device geometry and wavelength are inherently captured. To verify the modeling, we characterize the optothermal threshold for a series of toroidal cavities across a range of wavelengths and device geometries. Additionally, the thermal time constant of the structure is explored. Of note, the membrane thickness is shown to play a critical role in the optothermal behaviors.
Solution of the Quiet Implicit Particle-In Moment Equations in Toroidal Geometry
NASA Astrophysics Data System (ADS)
Nystrom, William David
A computer program, QIP3D, has been developed to solve the Quiet Implicit Particle- in-cell (QIP) moment equations in three-dimensional toroidal geometry. This model provides an efficient algorithm for computing the time evolution of the full two-fluid (ion/electron) plasma. The coordinate system is based on a conformal mapping of the poloidal plane from a circular outer boundary and origin coincident with the magnetic axis to form a logically polar computational mesh. A Fourier, pseudospectral representation is employed for the poloidal and toroidal angles and finite differencing for the radial coordinate. The QIP equations are differenced implicitly in time and solved using a predictor -corrector algorithm. The implicit electric field equation (and other elliptic equations) are solved using advanced iterative methods. Efficient algorithms implement the required matrix-vector product and preconditioner. Two series of calculations in toroidal geometry with q_0 = 0.9 establish the two -fluid physics of the m = 1 internal kink mode where q _0 is the safety factor at the magnetic axis and m is the poloidal mode number. In each series, the mode is excited and exhibits the proper eigenmode structure. With the aspect ratio, A = R_0/a, constant at 10 and beta_0 varying from 0.0 to 0.01, the growth rate of the kink is found to increase with beta_0 and to be in quantitative agreement with previous calculations. Here, R _0 is the distance of the magnetic axis from the axis of rotational symmetry for the torus, a is the minor radius of the torus and beta_0 is the ratio of kinetic pressure to magnetic field pressure at the magnetic axis. With beta _0 = 0.0 and A varied from 5 to 10, the growth rate is found to be independent of A in agreement with theory.
Viscous damping of toroidal angular momentum in tokamaks
Stacey, W. M.
2014-09-15
The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various “neoclassical toroidal viscosity” mechanisms. In the process, it was verified that the parallel viscosity contribution to damping toroidal angular momentum still vanishes even in the presence of toroidal asymmetries, unless there are 3D radial magnetic fields.
Two-Dimensional x-y and r-z Geometry Multigroup Transport Code System for Large Toroidal Reactors.
Energy Science and Technology Software Center (ESTSC)
1980-06-16
Version: 00 Although TRIDENT-CTR is a follow-on code to TRIDENT, it has incorporated several features that make it significantly different. It can handle a wide range of irregular geometric domains in both x-y and r-z geometries. However, it was principally designed to solve shielding and blanket problems for large toroidal reactors. TRIDENT-CTR is a two-dimensional, x-y and r-z geometry, multigroup, neutral particle transport code. The use of triangular finite elements gives it the geometric flexibilitymore » to cope with the nonorthogonal shapes of many toroidal designs. The code is capable of handling a wide variety of problems having irregular domains in both x-y and r-z geometries.« less
Invisibility cloaks for toroids.
You, Yu; Kattawar, George W; Yang, Ping
2009-04-13
The material properties of toroidal invisibility cloaks are derived based on the coordinate transformation method. The permittivity and permeability tensors for toroidal cloaks are substantially different from those for spherical cloaks, but quite similar to those for 2D cylindrical cloaks because a singularity is involved at the inner boundary in both the cases. The cloaking effect is confirmed by the electric field distribution in the vicinity of toroidal cloaks simulated from the generalized discrete-dipole approximation (DDA) method. This study extends the concept of electromagnetic cloaking of arbitrarily-shaped objects to a complex geometry. PMID:19365485
Drift in toroidal configurations
NASA Astrophysics Data System (ADS)
Evangelidis, E. A.
1990-12-01
This paper considers possible mechanisms involved in amplifying the drift velocity of plasma particles, under conditions of toroidal geometry. It is shown that particles constrained to move on an axisymmetric circular spheroidal surface, develop a sinusoidal motion with a characteristic frequency which depends on the energy of the particles, the value of the isoflux surface, and the value of the general momentum. It is also shown that the incorporation of the effects of toroidal geometry in the Lorentz equation produces a nonambipolar charge-dependent particle flux amplified by a factor 2(q/epsilon) squared.
Modelling of 3D fields due to ferritic inserts and test blanket modules in toroidal geometry at ITER
NASA Astrophysics Data System (ADS)
Liu, Yueqiang; Äkäslompolo, Simppa; Cavinato, Mario; Koechl, Florian; Kurki-Suonio, Taina; Li, Li; Parail, Vassili; Saibene, Gabriella; Särkimäki, Konsta; Sipilä, Seppo; Varje, Jari
2016-06-01
Computations in toroidal geometry are systematically performed for the plasma response to 3D magnetic perturbations produced by ferritic inserts (FIs) and test blanket modules (TBMs) for four ITER plasma scenarios: the 15 MA baseline, the 12.5 MA hybrid, the 9 MA steady state, and the 7.5 MA half-field helium plasma. Due to the broad toroidal spectrum of the FI and TBM fields, the plasma response for all the n = 1–6 field components are computed and compared. The plasma response is found to be weak for the high-n (n > 4) components. The response is not globally sensitive to the toroidal plasma flow speed, as long as the latter is not reduced by an order of magnitude. This is essentially due to the strong screening effect occurring at a finite flow, as predicted for ITER plasmas. The ITER error field correction coils (EFCC) are used to compensate the n = 1 field errors produced by FIs and TBMs for the baseline scenario for the purpose of avoiding mode locking. It is found that the middle row of the EFCC, with a suitable toroidal phase for the coil current, can provide the best correction of these field errors, according to various optimisation criteria. On the other hand, even without correction, it is predicted that these n = 1 field errors will not cause substantial flow damping for the 15 MA baseline scenario.
Kelleher, W.P.
1987-01-01
In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field.
Fatigue life analysis for traction drives with application to a toroidal type geometry
NASA Technical Reports Server (NTRS)
Coy, J. J.; Loewenthal, S. H.; Zaretsky, E. V.
1976-01-01
A contact fatigue life analysis for traction drives was developed which was based on a modified Lundberg-Palmgren theory. The analysis was used to predict life for a cone-roller toroidal traction drive. A 90-percent probability of survival was assumed for the calculated life. Parametric results were presented for life and Hertz contact stress as a function of load, drive ratio, and size. A design study was also performed. The results were compared to previously published work for the dual cavity toroidal drive as applied to a typical compact passenger vehicle drive train. For a representative duty cycle condition wherein the engine delivers 29 horsepower at 2000 rpm with the vehicle moving at 48.3 km/hr (30 mph) the drive life was calculated to be 19,200 km (11 900 miles).
Kelleher, W.; Steiner, D.
1989-03-01
A personal computer system was developed for use in the assessment of magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement in toroidal axisymmetric geometry. This system involves two steps: first MHD equilibrium is calculated with the program PCEQ, then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment using the program PFDESIGN. The PCEQ/PFDESIGN system was used to examine equilibrium for the STARFIRE reactor concept, including the design of two different PFC arrangements. The MHD/PFC calculations agree to within a few percent of mainframe code results, demonstrating the utility and accuracy of PCEQ/PFDESIGN, proving it to be an ideal tool for scoping studies.
Yang, Yi; Aisa, Haji Akber; Ito, Yoichiro
2010-01-01
The toroidal column using a zigzag pattern has been improved in both retention of the stationary phase and peak resolution. To further improve the retention of stationary phase and peak resolution, a series of novel geometric designs of tubing (plain, mid-clamping, flattened and flat-twisted tubing) was evaluated their performance in CCC. The results showed that the tubing which was flattened vertically against centrifugal force (vert-flattened tubing) produced the best peak resolution among them. Using vert-flattened tubing a series of experiments was performed to study the effects of column capacity and sample size. The results indicated that a 0.25 ml capacity column is ideal for analysis of small amount samples. PMID:20454530
Velocity-Space Diffusion Coefficients Due to Full-Wave ICRF Fields in Toroidal Geometry
Harvey, R.W.; Jaeger, F.; Berry, L.A.; Batchelor, D.B.; D'Azevedo, E.; Carter, M.D.; Ershov, N.M.; Smirnov, A.P.; Bonoli, P.; Wright, J.C.; Smithe, D.N.
2005-09-26
Jaeger et al. have calculated bounce-averaged QL diffusion coefficients from AORSA full-wave fields, based on non-Maxwellian distributions from CQL3D Fokker-Planck code. A zero banana-width approximation is employed. Complementing this calculation, a fully numerical calculation of ion velocity diffusion coefficients using the full-wave fields in numerical tokamak equilibria has been implemented to determine the finite orbit width effects. The un-approximated Lorentz equation of motion is integrated to obtain the change in velocity after one complete poloidal transit of the tokamak. Averaging velocity changes over initial starting gyro-phase and toroidal angle gives bounce-averaged diffusion coefficients. The coefficients from the full-wave and Lorentz orbit methods are compared for an ITER DT second harmonic tritium ICRF heating case: the diffusion coefficients are similar in magnitude but reveal substantial finite orbit effects.
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.
NASA Astrophysics Data System (ADS)
Fernandez-Nieves, Alberto
We will discuss how nematic liquid crystals organize inside toroidal droplets. When the director is parallel to the bounding surface, we find spontaneous reflection symmetry breaking, which we attribute to the role played by saddle-splay contributions to the Frank free energy. When the director is perpendicular to the bounding surface, we find that the structure is reminiscent of the escape radial configuration seen in cylinders, but with a central doubly-twisted organization, which we attribute to the geometry of the torus. We will end by presenting recent experiments with active nematics on the toroidal surface. In this case, topology and activity both affect the structure and dynamics of the material.
GGADT: Generalized Geometry Anomalous Diffraction Theory
NASA Astrophysics Data System (ADS)
Hoffman, John; Tarczon, Michael; Draine, Bruce T.
2015-10-01
GGADT uses anomalous diffraction theory (ADT) to compute the differential scattering cross section (or the total cross sections as a function of energy) for a specified grain of arbitrary geometry (natively supports spheres, ellipsoids, and clusters of spherical monomers). It is written in Fortran 95. ADT is valid when the grain is large compared to the wavelength of incident light. GGADT can calculate either the integrated cross sections (absorption, scattering, extinction) as a function of energy, or it can calculate the differential scattering cross section as a function of scattering angle.
NASA Astrophysics Data System (ADS)
Chu, M. S.; Guo, Wenfeng
2016-06-01
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
8. General view of truss geometry at center of span ...
8. General view of truss geometry at center of span from lower parking lot, looking northwest - Lower Rollstone Street Bridge, Spanning Nashua River on Rollstone Street, Fitchburg, Worcester County, MA
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Pulsed Laser Nonlinear Thomson Scattering for General Scattering Geometries
Geoffrey Krafft; A. Doyuran; James Rosenzweig
2005-05-01
In a recent paper it has been shown that single electron Thomson backscatter calculations can be performed including the effects of pulsed high intensity lasers. In this paper we present a more detailed treatment of the problem and present results for more general scattering geometries. In particular, we present new results for 90 degree Thomson scattering. Such geometries have been increasingly studied as X-ray sources of short-pulse radiation. Also, we present a clearer physical basis for these different cases.
Sugama, H.; Nishimura, S.
2008-04-15
A detailed comparison is made between moment-equation methods presented by H. Sugama and S. Nishimura [Phys. Plasmas 9, 4637 (2002)] and by M. Taguchi [Phys. Fluids B 4, 3638 (1992)] for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic equation with the same collision model used for correctly taking account of collisional momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the moment equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the Laguerre-polynomial expansion is truncated up to a finite order because different weight functions are used in them to derive the moment equations. At each order of the truncation, the neoclassical transport coefficients obtained from the Sugama-Nishimura method show the Onsager symmetry and satisfy the ambipolar-diffusion condition intrinsically for symmetric systems. Also, numerical examples are given to show how the transport coefficients converge with the truncation number increased for the two methods.
Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.
2007-06-29
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.
Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.
2014-06-15
An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.
Generalization of the electronic susceptibility for arbitrary molecular geometries
NASA Astrophysics Data System (ADS)
Scherrer, Arne; Dreßler, Christian; Ahlert, Paul; Sebastiani, Daniel
2016-04-01
We generalize the explicit representation of the electronic susceptibility χ[R](r, r') for arbitrary molecular geometries R. The electronic susceptibility is a response function that yields the response of the molecular electronic charge density at linear order to an arbitrary external perturbation. We address the dependence of this response function on the molecular geometry. The explicit representation of the molecular geometry dependence is achieved by means of a Taylor expansion in the nuclear coordinates. Our approach relies on a recently developed low-rank representation of the response function χ[R](r, r') which allows a highly condensed storage of the expansion and an efficient application within dynamical chemical environments. We illustrate the performance and accuracy of our scheme by computing the vibrationally induced variations of the response function of a water molecule and its resulting Raman spectrum.
Generalized quantum gravity condensates for homogeneous geometries and cosmology
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Pranzetti, Daniele; Ryan, James P.; Sindoni, Lorenzo
2015-12-01
We construct a generalized class of quantum gravity condensate states that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction also lends itself easily to application to the case of spherically symmetric quantum geometries.
Electrostatic toroidal drift mode turbulence in tokamaks
Hirshman, S.P.; Diamond, P.H.; Rosenbluth, M.N.; Chen, L.; Molvig, K.; Whitson, J.C.; Smith, J.
1980-01-01
The kinetic theory of turbulent effects due to electron orbit stochasticity was combined with linear response in toroidal geometry. A review of the linear theory is given. The toroidal electron response is given in the ballooning representation. (MOW)
Generalized -deformed correlation functions as spectral functions of hyperbolic geometry
NASA Astrophysics Data System (ADS)
Bonora, L.; Bytsenko, A. A.; Guimarães, M. E. X.
2014-08-01
We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with , is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to . With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry.
Electron cyclotron current drive efficiency in general tokamak geometry
Lin-Liu, Y. R.; Chan, V. S.; Prater, R.
2003-01-01
Green's-function techniques are used to calculate electron cyclotron current drive (ECCD) efficiency in general tokamak geometry in the low-collisionality regime. Fully relativistic electron dynamics is employed in the theoretical formulation. The high-velocity collision model is used to model Coulomb collisions and a simplified quasi-linear rf diffusion operator describes wave-particle interactions. The approximate analytic solutions which are benchmarked with a widely used ECCD model, facilitate time-dependent simulations of tokamak operational scenarios using the non-inductive current drive of electron cyclotron waves.
Third Elementary Dipole Moment: Toroidal
NASA Astrophysics Data System (ADS)
Cordrey, Vincent; Eshete, Amanuel; Majewski, Walerian
2015-04-01
In this paper we study the generally unknown characteristics of toroids, magnets without magnetic poles. Toroids have never seemed interesting enough to be studied for their physical features in labs due to the fact that they have no magnetic fields on the outside, but rather a very strong magnetic field trapped inside. Toroidal solenoids or magnets (rings magnetized circumferentially) interact with the external magnetic field only through its curl, which can be created either by an electric current, or by a time-dependent electric flux. We confirmed a theoretical prediction, that a toroid would not interact with the curl-less magnetic field of a current-carrying wire running outside of the torus's hole. We used our toroids as magnetic curlmeters, measuring the torque on the toroid, when the current-carrying wire runs through the toroid. From this torque we found the toroidal dipole moment. We are experimenting on detecting the escape of the inner magnetic field of the toroid outside of it, when magnetic toroid rotates or when electric toroid is driven by AC voltage. We also will discuss toroidal (or anapole) moments of fundamental particles, nuclei and atoms, and toroids' applications in metamaterials.
Nishimura, S.; Sugama, H.; Maassberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-15
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Fixed boundary toroidal plasma equilibria with toroidal flows
NASA Astrophysics Data System (ADS)
Hu, Yanqiang; Hu, Yemin; Xiang, Nong
2016-04-01
The fixed boundary toroidal plasma equilibria with toroidal flows are investigated by solving the modified Grad-Shafranov equation numerically in the cylindrical coordinate system. For normal equilibrium configurations with geometry and profiles similar to usual tokamaks with no flow, it is found that the effect of flow is to lead to an outward shift of the magnetic flux surfaces, together with the profiles of pressure, and mass and current densities. The shifts could become significant when the toroidal flow Mach number exceeds 0.5. For non-conventional current profiles, even for the usual tokamak geometry, novel current reversal equilibrium configurations may result, sometimes with changed topology in the poloidal flux function. This change in the topology of plasma equilibrium can be attributed to the large toroidal flow. The computed results may correspond to situations of intense tangential injection during the low toroidal current phase in expected experimental situations.
Intrinsic rotation of toroidally confined magnetohydrodynamics.
Morales, Jorge A; Bos, Wouter J T; Schneider, Kai; Montgomery, David C
2012-10-26
The spatiotemporal self-organization of viscoresistive magnetohydrodynamics in a toroidal geometry is studied. Curl-free toroidal magnetic and electric fields are imposed. It is observed in our simulations that a flow is generated, which evolves from dominantly poloidal to toroidal when the Lundquist numbers are increased. It is shown that this toroidal organization of the flow is consistent with the tendency of the velocity field to align with the magnetic field. Up-down asymmetry of the geometry causes the generation of a nonzero toroidal angular momentum. PMID:23215195
Geometry of the generalized Bloch sphere for qutrits
NASA Astrophysics Data System (ADS)
Goyal, Sandeep K.; Neethi Simon, B.; Singh, Rajeev; Simon, Sudhavathani
2016-04-01
The geometry of the generalized Bloch sphere Ω3, the state space of a qutrit, is studied. Closed form expressions for Ω3, its boundary ∂Ω3, and the set of extremals {{{Ω }}}3{{ext}} are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU(3), the symmetry underlying Ω3, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .
Dawson, John M.; Furth, Harold P.; Tenney, Fred H.
1988-12-06
Method for producing fusion power wherein a neutral beam is injected into a toroidal bulk plasma to produce fusion reactions during the time permitted by the slowing down of the particles from the injected beam in the bulk plasma.
Generalization in Place Learning and Geometry Knowledge in Rats
ERIC Educational Resources Information Center
Tommasi, Luca; Thinus-Blanc, Catherine
2004-01-01
Rats were trained to search for a food reward hidden under sawdust in the center of a square-shaped enclosure designed to force orientation on the basis of the overall geometry of the environment. They were then tested in a number of enclosures differing in shape and in size (rectangular-, double-side square-, and equilateral triangle-shaped…
Magnetic Properties of 3D Printed Toroids
NASA Astrophysics Data System (ADS)
Bollig, Lindsey; Otto, Austin; Hilpisch, Peter; Mowry, Greg; Nelson-Cheeseman, Brittany; Renewable Energy; Alternatives Lab (REAL) Team
Transformers are ubiquitous in electronics today. Although toroidal geometries perform most efficiently, transformers are traditionally made with rectangular cross-sections due to the lower manufacturing costs. Additive manufacturing techniques (3D printing) can easily achieve toroidal geometries by building up a part through a series of 2D layers. To get strong magnetic properties in a 3D printed transformer, a composite filament is used containing Fe dispersed in a polymer matrix. How the resulting 3D printed toroid responds to a magnetic field depends on two structural factors of the printed 2D layers: fill factor (planar density) and fill pattern. In this work, we investigate how the fill factor and fill pattern affect the magnetic properties of 3D printed toroids. The magnetic properties of the printed toroids are measured by a custom circuit that produces a hysteresis loop for each toroid. Toroids with various fill factors and fill patterns are compared to determine how these two factors can affect the magnetic field the toroid can produce. These 3D printed toroids can be used for numerous applications in order to increase the efficiency of transformers by making it possible for manufacturers to make a toroidal geometry.
GASP- General Aviation Synthesis Program. Volume 2: Geometry
NASA Technical Reports Server (NTRS)
Hague, D.
1978-01-01
The gross characteristics of an aircraft under study are specified to the subroutines SIZE. The principal quantities specified are both geometric (lengths and areas) and operational (altitude and Mach number). The sequence of computations carried out by SIZE is controlled by the parameter NPC which is passed into SIZE by COMMON. When NPC-0, the computation is initialized. Subsequently, NPC is set to 2 and the program advances through the geometric computations. Geometry models for the fuselage, wing, empennage, cabin pressurization, and nacelle area are examined.
Cosmology for quadratic gravity in generalized Weyl geometry
NASA Astrophysics Data System (ADS)
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.
2016-04-01
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.
Toroidal Theory of MHD Instabilities
Goedbloed, J.P.
2004-03-15
We continue with the adventures of the Alfven wave and its two magnetosonic companions as they travel in the curved space of magnetic surfaces and field lines (Sec. 2), find themselves trapped in singularities of an unprecedented richness (Sec. 3), decide to get themselves better maps of the landscape to do the required twisting while some of their youthful energy is leaking away (Sec. 4), cause trouble at the edge of a powerful empire (Sec. 5), and finally see the light in a distant future (Sec. 6). Needed on the trip are the evolution equations of both ideal and resistive MHD 'derived' in reference [1], the solutions to the toroidal equilibrium equations discussed in reference [2], the general background on spectral theory of inhomogeneous plasmas presented in reference [3], which is extended in the two directions of toroidal geometry and resistivity in this lecture [4]. This leads to such intricate dynamics that numerical techniques are virtually the only way to proceed. This aspect is further elaborated in reference [5] on numerical techniques.
Toroidal Alfven wave stability in ignited tokamaks
Cheng, C.Z.; Fu, G.Y.; Van Dam, J.W.
1989-01-01
The effects of fusion-product alpha particles on the stability of global-type shear Alfven waves in an ignited tokamak plasma are investigated in toroidal geometry. Finite toroidicity can lead to stabilization of the global Alfven eigenmodes, but it induces a new global shear Alfven eigenmodes, which is strongly destabilized via transit resonance with alpha particles. 8 refs., 2 figs.
Multidimensional Plasma Sheath Modeling Using The Three Fluid Plasma Model in General Geometries
NASA Astrophysics Data System (ADS)
Lilly, Robert; Shumlak, Uri
2012-10-01
There has been renewed interest in the use of plasma actuators for high speed flow control applications. In the plasma actuator, current is driven through the surrounding weakly ionized plasma to impart control moments on the hypersonic vehicle. This expanded general geometry study employs the three-fluid (electrons, ions,neutrals) plasma model as it allows the capture of electron inertial effects, as well as energy and momentum transfer between the charged and neutral species. Previous investigations have typically assumed an electrostatic electric field. This work includes the full electrodynamics in general geometries. Past work utilizing the research code WARPX (Washington Approximate Riemann Problem) employed cartesian grids. In this work, the problem is expanded to general geometries with the euler fluid equations employing Braginskii closure. In addition, WARPX general geometry grids are generated from Cubit or CAD files. Comparisons are made against AFRL magnetized plasma actuator experiments.
J Selvaggi; S Salon; O Kwon CVK Chari
2006-02-14
An alternative method is developed to compute the magnetic field from a circular cylindrical magnetic source. Specifically, a Fourier series expansion whose coefficients are toroidal functions is introduced which yields an alternative to the more familiar spherical harmonic solution or the Elliptic integral solution. This alternate formulation coupled with a method called charge simulation allows one to compute the external magnetic field from an arbitrary magnetic source in terms of a toroidal expansion. This expansion is valid on any finite hypothetical external observation cylinder. In other words, the magnetic scalar potential or the magnetic field intensity is computed on a exterior cylinder which encloses the magnetic source. This method can be used to accurately compute the far field where a finite element formulation is known to be inaccurate.
Generalized Particle Swarm Algorithm for HCR Gearing Geometry Optimization
NASA Astrophysics Data System (ADS)
Kuzmanović, Siniša; Vereš, Miroslav; Rackov, Milan
2012-12-01
Logically rectangular mixed methods for Darcy flow on general geometry
Arbogast, T.; Keenan, P.T.; Wheeler, M.F.; Yotov, I.
1995-12-31
The authors consider an expanded mixed finite element formulation (cell centered finite difference) for Darcy flow with a tensor absolute permeability. The reservoir can be geometrically general with internal features, but the computational domain is rectangular. The method is defined on a curvilinear grid that need not be orthogonal, obtained by mapping the rectangular, computational grid. The original flow problem becomes a similar problem with a modified permeability on the computational grid. Quadrature rules turn the mixed method into a cell-centered finite difference method with a 9 point stencil in 2-D and 19 in 3-D. As shown by theory and experiment, if the modified permeability on the computational domain is smooth, then the convergence rate is optimal and both pressure and velocity are superconvergent at certain points. If not, Lagrange multiplier pressures can be introduced on boundaries of elements so that optimal convergence is retained. This modification presents only small changes in the solution process; in fact, the same parallel domain decomposition algorithms can be applied with little or no change to the code if the modified permeability is smooth over the subdomains. This Lagrange multiplier procedure can be used to extend the difference scheme to multi-block domains, and to give a coupling with unstructured grids. In all cases, the mixed formulation is locally conservative. Computational results illustrate the advantage and convergence of this method.
Bonanos, Peter
1983-01-01
A toroidal magnet for confining a high magnetic field for use in fusion reactor research and nuclear particle detection. The magnet includes a series of conductor elements arranged about and fixed at its small major radius portion to the outer surface of a central cylindrical support each conductor element having a geometry such as to maintain the conductor elements in pure tension when a high current flows therein, and a support assembly which redistributes all or part of the tension which would otherwise arise in the small major radius portion of each coil element to the large major radius portion thereof.
Toroidal linear force-free magnetic fields with axial symmetry
NASA Astrophysics Data System (ADS)
Vandas, M.; Romashets, E.
2016-01-01
Aims: Interplanetary magnetic flux ropes are often described as linear force-free fields. To account for their curvature, toroidal configurations must be used. The aim is to find an analytic description of a linear force-free magnetic field of the toroidal geometry in which the cross section of flux ropes can be controlled. Methods: The solution is found as a superposition of fields given by linear force-free cylinders tangential to a generating toroid. The cylindrical field is expressed in a series of terms that are not all cylindrically symmetric. Results: We found the general form of a toroidal linear force-free magnetic field. The field is azimuthally symmetric with respect to the torus axis. It depends on a set of coefficients that enables controlling the flux rope shape (cross section) to some extent. By varying the coefficients, flux ropes with circular and elliptic cross sections were constructed. Numerical comparison suggests that the simple analytic formula for calculating the helicity in toroidal flux ropes of the circular cross section can be used for flux ropes with elliptic cross sections if the minor radius in the formula is set to the geometric mean of the semi-axes of the elliptic cross section.
Inflatable nested toroid structure
NASA Technical Reports Server (NTRS)
Johnson, Christopher J. (Inventor); Raboin, Jasen L. (Inventor); Spexarth, Gary R. (Inventor)
2011-01-01
An inflatable structure comprises at least two generally toroidal, inflatable modules. When in a deployed mode, the first, inner module has a major diameter less than that of a second, outer module and is positioned within the inner circumference of the outer module such that the first module is nested circumferentially alongside the second module. The inflatable structure, in a non-deployed, non-inflated mode, is of compact configuration and adapted to be transported to a site of deployment. When deployed, the inflatable structure is of substantially increased interior volume. In one embodiment, access between the interior of the first module and the second module is provided by at least one port or structural pass-through. In another embodiment, the inflatable structure includes at least one additional generally toroidal module external of and circumferentially surrounding the second module.
KEELE BD
2005-02-01
A collimated portable gamma-ray detector will be used to quantify the plutonium content of items that can be approximated as a point, line, or area geometry with respect to the detector. These items can include ducts, piping, glove boxes, isolated equipment inside of gloveboxes, and HEPA filters. The Generalized Geometry Holdup (GGH) model is used for the reduction of counting data. This document specifies the calculations to reduce counting data into contained plutonium and the associated total measurement uncertainty.
Kelleher, W.P. ); Steiner, D. . Dept. of Nuclear Science)
1989-07-01
A personal-computer (PC)-based calculational approach assesses magnetohydrodynamic (MHD) equilibrium and poloidal field (PF) coil arrangement in a highly interactive mode, well suited for tokamak scoping studies. The system developed involves a two-step process: the MHD equilibrium is calculated and then a PF coil arrangement, consistent with the equilibrium is determined in an interactive design environment. In this paper the approach is used to examine four distinctly different toroidal configurations: the STARFIRE rector, a spherical torus (ST), the Big Dee, and an elongated tokamak. In these applications the PC-based results are benchmarked against those of a mainframe code for STARFIRE, ST, and Big Dee. The equilibrium and PF coil arrangement calculations obtained with the PC approach agree within a few percent with those obtained with the mainframe code.
Yang, X.; Satvat, N.
2012-07-01
A transport theory code MOCUM based on the Method of Characteristics (MOC) as the flux solver with an advanced general geometry processor is developed for two-dimensional lattice and full core neutronics modeling. The core structure is represented by Constructive Solid Geometry (CSG) that uses Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building CSG objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a conforming Delaunay triangulation to ensure the quality of the meshes. The MOC solver kernel is fully paralleled using OpenMP and the developed numerical code is validated by several benchmarks representing various core geometries. For the cases modeled, the maximum percentage error for multiplication factor and the pin power compared to reference values are 0.1% and 0.7% respectively. (authors)
KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry
Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.
1993-07-01
This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code`s flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array.
NASA Astrophysics Data System (ADS)
Auluck, S. K. H.
2014-10-01
Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects the shape of the DPF current sheath. Locally unidirectional shock propagation in this coordinate system enables construction of a system of 7 one-dimensional hyperbolic conservation law equations with geometric source terms, taking into account all the components of magnetic field and flow velocity. Rankine-Hugoniot jump conditions for this system lead to expressions for the axial magnetic field and three components of fluid velocity having high ion kinetic energy.
Auluck, S. K. H.
2014-10-15
Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects the shape of the DPF current sheath. Locally unidirectional shock propagation in this coordinate system enables construction of a system of 7 one-dimensional hyperbolic conservation law equations with geometric source terms, taking into account all the components of magnetic field and flow velocity. Rankine-Hugoniot jump conditions for this system lead to expressions for the axial magnetic field and three components of fluid velocity having high ion kinetic energy.
Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries
NASA Astrophysics Data System (ADS)
Batle, J.; Bagdasaryan, Armen; Abdel-Aty, M.; Abdalla, S.
2016-06-01
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the S d - 1 -sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.
Kinetic studies of microinstabilities in toroidal plasmas: Simulation and theory
Lee, W.W.; Haham, T.S.; Parker, S.E.; Perkins, F.W.; Rath, S.; Rewoldt, G.; Reynders, J.V.W.; Santoro, R.A.; Tang, W.M.
1992-12-01
A comprehensive program for the development and use of particle simulation techniques for solving the gyrokinetic Vlasov-Maxwell equations on massively parallel computers has been carried out at Princeton Plasma Physics Laboratory. This is a key element of our ongoing theoretical efforts to systematically investigate physics issues vital to understanding tokamak plasmas. In this paper, our focus is on spatial-gradient-driven microinstabilities. Their importance is supported by the recent progress in achieving a physics-based understanding of anomalous transport in toroidal systems which has been based on the proposition that these drift-type electrostatic modes dependent on ion temperature gradient (ITG) and trapped particle effects are dominant in the bulk ( confinement'') region. Although their presence is consistent with a number of significant confinement trends, results from high temperature tokamaks such as TFTR have highlighted the need for better insight into the nonlinear properties of such instabilities in long-mean-free-path plasmas. In addressing this general issue, we report important new results including (i) the first fully toroidal 3D gyrokinetic simulation of ITG modes and (ii) realistic toroidal eigenmode calculations demonstrating the unique capability to deal with large scale kinetic behavior extending over many rational surfaces. The effects of ITG modes (iii) on the inward pinch of impurities in 3D slab geometry and (iv) on the existence of microtearing modes in 2D slab are also discussed. Finally, (v) sheared toroidal flow effects on trapped-particle modes are presented.
Kinetic studies of microinstabilities in toroidal plasmas: Simulation and theory
Lee, W.W.; Haham, T.S.; Parker, S.E.; Perkins, F.W.; Rath, S.; Rewoldt, G.; Reynders, J.V.W.; Santoro, R.A.; Tang, W.M.
1992-12-01
A comprehensive program for the development and use of particle simulation techniques for solving the gyrokinetic Vlasov-Maxwell equations on massively parallel computers has been carried out at Princeton Plasma Physics Laboratory. This is a key element of our ongoing theoretical efforts to systematically investigate physics issues vital to understanding tokamak plasmas. In this paper, our focus is on spatial-gradient-driven microinstabilities. Their importance is supported by the recent progress in achieving a physics-based understanding of anomalous transport in toroidal systems which has been based on the proposition that these drift-type electrostatic modes dependent on ion temperature gradient (ITG) and trapped particle effects are dominant in the bulk (``confinement``) region. Although their presence is consistent with a number of significant confinement trends, results from high temperature tokamaks such as TFTR have highlighted the need for better insight into the nonlinear properties of such instabilities in long-mean-free-path plasmas. In addressing this general issue, we report important new results including (i) the first fully toroidal 3D gyrokinetic simulation of ITG modes and (ii) realistic toroidal eigenmode calculations demonstrating the unique capability to deal with large scale kinetic behavior extending over many rational surfaces. The effects of ITG modes (iii) on the inward pinch of impurities in 3D slab geometry and (iv) on the existence of microtearing modes in 2D slab are also discussed. Finally, (v) sheared toroidal flow effects on trapped-particle modes are presented.
Generalized functional formulation for multi-fractal representation of basin hydraulic geometry
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Natural rivers exhibit power-functional variability in their width, depth, and velocity with flow discharge (Leopold and Maddock, 1953). This relation named hydraulic geometry has been empirically supported by many field studies across the world (e.g., Leopold et al., 1964; Stall and Fok, 1968). The relationship appears either at a fixed cross-section, showing temporal variability, or along a downstream direction across an entire basin, showing spatial variability, the latter named downstream or basin hydraulic geometry. Theoretical studies that attempt to explain the power-law phenomenon (fractal), have assumed that the watershed is homogeneous hydrologically and geologically. Nevertheless, real watersheds are often subject to spatially heterogeneous conditions, due to various reasons including partial area storm coverage (Sólyom and Tucker, 2004) and transmission losses on bed and banks (Lane et al., 1997). In this setting, hydraulic geometry relationships are likely to deviate from monotonic power-law relationship and to follow rather more complex multi-fractal characteristics. In fact, deviation from single power-law was reported for at-a-station relationship of midwest rivers in US (Dodov and Foufoula-Georgiou, 2004). In the case of downstream variation, we identify significant multi-fractal characteristics over the Colorado River basin where strong heterogeneity in geological and hydrological settings presents. Conventional power-law hydraulic geometry relationships cannot express the functional variability for these cases. Motivated by this fact, we generalize the hydraulic geometry functional formulation in this study to express multi-fractal relationships. To do so, we couple the formulation of Paik and Kumar (2004), which generalized at-a-station and downstream relationships, with the formulation of Dodov and Foufoula-Georgiou (2004) which was proposed for multi-scaling in at-a-station relationship. The proposed formulation is successfully evaluated with
T-duality and exceptional generalized geometry through symmetries of dg-manifolds
NASA Astrophysics Data System (ADS)
Lupercio, Ernesto; Rengifo, Camilo; Uribe, Bernardo
2014-09-01
We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T-dual dg-manifolds. Within this framework, we construct the T-duality map as a degree -1 map between the cohomologies of the T-dual dg-manifolds and we show an explicit isomorphism between the differential graded algebra of the symmetries of the T-dual dg-manifolds. We, furthermore, show how the algebraic structure underlying Bn generalized geometry could be recovered as derived dg-Leibniz algebra of the fixed points of the T-dual automorphism acting on the symmetries of a self T-dual dg-manifold, and we show how other types of algebraic structures underlying exceptional generalized geometry could be obtained as derived symmetries of certain dg-manifolds.
NASA Astrophysics Data System (ADS)
Contreras, Ernesto; Villalba, Fabián D.; Bargueño, Pedro
2016-06-01
In this work we construct several black-hole metrics which are consistent with the generalized uncertainty principle logarithmic correction to the Bekenstein-Hawking entropy formula. After preserving the event horizon at the usual position, a singularity at the Planck scale is found. Finally, these geometries are shown to be realized by certain model of non-linear electrodynamics, which resembles previously studied regular black-hole solutions.
Generalized complex geometry of pure backgrounds in 10 and 11 dimensions
NASA Astrophysics Data System (ADS)
Prins, Daniël; Tsimpis, Dimitrios
2015-04-01
Pure backgrounds are a natural generalization of supersymmetric Calabi-Yau compactifications in the presence of flux. They are described in the language of generalized SU(d)× SU(d) structures and generalized complex geometry, and they exhibit some interesting general patterns: the internal manifold is generalized Calabi-Yau, whereas the Ramond-Ramond flux is exact in a precise sense, as discussed in this paper. We have shown that although these two characteristics do persist in the case of generic 10-dimensional Euclidean type II pure backgrounds, they do not capture the full content of supersymmetry. We also discuss the uplift of real Euclidean type IIA pure backgrounds to supersymmetric backgrounds of Lorentzian 11-dimensional supergravity.
Internal connectivity of meandering rivers: Statistical generalization of channel hydraulic geometry
NASA Astrophysics Data System (ADS)
Czapiga, M. J.; Smith, V. B.; Nittrouer, J. A.; Mohrig, D.; Parker, G.
2015-09-01
The geometry of rivers has been characterized in terms of downstream and at-a-station hydraulic geometry, based on individual cross sections. Such analyses do not, however, provide insight as to how these cross sections are connected. We generalize the concept of hydraulic geometry, using data on bathymetry from four reaches of meandering rivers that include at least five bends. We quantify connectivity in terms of the probability that a connected path exists such that a given attribute remains within specified bounds along it. While the concept is general, here we apply it to vessel navigability. We develop a predictor for navigability in meandering rivers, which requires only the following, relatively easily obtained input: vessel draft, vessel width, bankfull depth, bankfull width, relative difference between current and bankfull water surface elevation, and length of desired navigation path. The predictor is applicable to both bankfull and below-bankfull stage. A key input parameter is the standard deviation of the probability distribution of depth. This parameter, in and of itself, yields no information on connectivity as it does not capture the spatial orientation of depth variation. We find, however, that (a) the probability function for connectivity does depend on this parameter, and (b) its use allows for an approximate similarity collapse of the probability function, so providing a quasi-universal predictive relation applying to all four reaches. The results also suggest potential application to more complex forms for connectivity that involve other or multiple in-stream physical variables.
Xu, Lei
2004-07-01
The nature of Bayesian Ying-Yang harmony learning is reexamined from an information theoretic perspective. Not only its ability for model selection and regularization is explained with new insights, but also discussions are made on its relations and differences from the studies of minimum description length (MDL), Bayesian approach, the bit-back based MDL, Akaike information criterion (AIC), maximum likelihood, information geometry, Helmholtz machines, and variational approximation. Moreover, a generalized projection geometry is introduced for further understanding such a new mechanism. Furthermore, new algorithms are also developed for implementing Gaussian factor analysis (FA) and non-Gaussian factor analysis (NFA) such that selecting appropriate factors is automatically made during parameter learning. PMID:15461081
NASA Astrophysics Data System (ADS)
Raybould, T. A.; Fedotov, V. A.; Papasimakis, N.; Kuprov, I.; Youngs, I. J.; Chen, W. T.; Tsai, D. P.; Zheludev, N. I.
2016-07-01
We demonstrate that the induced toroidal dipole, represented by currents flowing on the surface of a torus, makes a distinct and indispensable contribution to circular dichroism. We show that toroidal circular dichroism supplements the well-known mechanism involving electric dipole and magnetic dipole transitions. We illustrate this with rigorous analysis of the experimentally measured polarization-sensitive transmission spectra of an artificial metamaterial, constructed from elements of toroidal symmetry. We argue that toroidal circular dichroism will be found in large biomolecules with elements of toroidal symmetry and should be taken into account in the interpretation of circular dichroism spectra of organics.
Lindenmeyer, Carl W.
1981-01-01
A lower support receives a toroid at a winding station with the axis of the toroid aligned with a slot in the support. An upper guide member applies an axial force to hold the toroid against the lower support. A pair of movable jaws carried by an indexing mechanism engage the outer surface of the toroid to apply a radial holding force. While the toroid is thus held, a wire is placed axially through the toroid, assisted by a funnel-shaped surface in the upper guide member, and is drawn tight about the toroid by a pair of cooperating draw rollers. When operated in the "full cycle" mode, the operator then actuates a switch which energizes a power drive to release the axial clamp and to drive the indexing mechanism and the jaws to rotate the toroid about its axis. At the same time, the wire is ejected from the draw rollers beneath the toroid so that the operator may grasp it to form another loop. When the toroid is fully indexed, the jaws release it, and the upper guide member is returned to clamp the toroid axially while the indexing mechanism is returned to its starting position. The apparatus may also be operated in a "momentary contact" mode in which the mechanism is driven only for the time a switch is actuated.
Experimental Investigation of the Natural Frequencies of Liquids in Toroidal Tanks
NASA Technical Reports Server (NTRS)
McCarty, John Locke; Leonard, H. Wayne; Walton, William C., Jr.
1960-01-01
Several toroidal configurations applicable to missile and space-vehicle liquid storage systems were oscillated to study the natural frequencies of the antisymmetric modes of contained liquids over a range of liquid depths and tank sizes. Natural frequencies for tank oscillations parallel to the free surface of both vertical and horizontal tank orientations. Natural frequencies were obtained. The data are presented in terms of dimensionless parameters which are obtained by relating experimentally determined natural liquid frequencies to analytical expressions developed through consideration of the physics of the problem and from existing solutions for liquids in tanks having similar boundaries at the liquid surface. The experimental results obtained for the toroids indicate that these parameters are applicable to the prediction of the natural frequencies of fluids in toroids of general geometry and size.
General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry
NASA Astrophysics Data System (ADS)
Savickas, David
2014-03-01
The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.
A versatile and low order hybrid stress element for general shell geometry
NASA Technical Reports Server (NTRS)
Kang, David S.; Pian, Theodore H. H.
1987-01-01
A hybrid stress general shell element is developed based on the Hellinger-Reissner principle modified for relaxed element compatibility conditions. The element is based on a consistent first order thin shell theory with Love Kirchhoff hypotheses. It is of quadrilateral shape with only four corner nodes and five degrees of freedom per node. The geometry of the element is approximated through a bi-cubic polynomial surface patch. Numerical examples consist of torsion-loaded slit cylinder and pinched cylinder with open ends and rigid diaphragmed ends. Also, the representation of the rigid body motion is studied by series of parametric eigenvalue analysis of the stiffness matrix.
Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries
NASA Astrophysics Data System (ADS)
Savickas, David
2015-04-01
General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).
The effect of toroidicity on reversed field pinch dynamics
NASA Astrophysics Data System (ADS)
Morales, Jorge A.; Bos, Wouter J. T.; Schneider, Kai; Montgomery, David C.
2014-09-01
The influence of the curvature of the imposed magnetic field on reversed field pinch dynamics is investigated by comparing the flow of a magnetofluid in a torus with aspect ratio 1.83, with the flow in a periodic cylinder. It is found that an axisymmetric toroidal mode is always present in the toroidal, but absent in the cylindrical configuration. In particular, in contrast to the cylinder, the toroidal case presents a double poloidal recirculation cell with a shear localized at the plasma edge. Quasi-single-helicity states are found to be more persistent in toroidal than in periodic cylinder geometry.
Huang, Yao-Wei; Chen, Wei Ting; Wu, Pin Chieh; Fedotov, Vassili A.; Zheludev, Nikolay I.; Tsai, Din Ping
2013-01-01
Toroidal shapes are often found in bio-molecules, viruses, proteins and fats, but only recently it was proved experimentally that toroidal structures can support exotic high-frequency electromagnetic excitations that are neither electric or magnetic multipoles. Such excitations, known as toroidal moments, could be playing an important role in enhancing inter-molecular interaction and energy transfer due to its higher electromagnetic energy confinement and weaker coupling to free space. Using a model toroidal metamaterial system, we show that coupling optical gain medium with high Q-factor toroidal resonance mode can enhance the single pass amplification to up to 65 dB. This offers an opportunity of creating the “toroidal” lasing spaser, a source of coherent optical radiation that is fueled by toroidal plasmonic oscillations in the nanostructure. PMID:23393619
NASA Technical Reports Server (NTRS)
Egolf, T. A.; Landgrebe, A. J.
1983-01-01
An analytic investigation to generalize wake geometry of a helicopter rotor in steady level forward flight and to demonstrate the influence of wake deformation in the prediction of rotor airloads and performance is described. Volume 1 presents a first level generalized wake model based on theoretically predicted tip vortex geometries for a selected representative blade design. The tip vortex distortions are generalized in equation form as displacements from the classical undistorted tip vortex geometry in terms of vortex age, blade azimuth, rotor advance ratio, thrust coefficient, and number of blades. These equations were programmed to provide distorted wake coordinates at very low cost for use in rotor airflow and airloads prediction analyses. The sensitivity of predicted rotor airloads, performance, and blade bending moments to the modeling of the tip vortex distortion are demonstrated for low to moderately high advance ratios for a representative rotor and the H-34 rotor. Comparisons with H-34 rotor test data demonstrate the effects of the classical, predicted distorted, and the newly developed generalized wake models on airloads and blade bending moments. Use of distorted wake models results in the occurrence of numerous blade-vortex interactions on the forward and lateral sides of the rotor disk. The significance of these interactions is related to the number and degree of proximity to the blades of the tip vortices. The correlation obtained with the distorted wake models (generalized and predicted) is encouraging.
A geometry and texture coupled flexible generalization of urban building models
NASA Astrophysics Data System (ADS)
Zhang, Man; Zhang, Liqiang; Takis Mathiopoulos, P.; Xie, Wenqing; Ding, Yusi; Wang, Hao
2012-06-01
In the past, numerous research efforts have focused on generalization of city building models. However, a generic procedure for creating flexible generalization results supporting the fast and efficient update of original building models with various complexities is still an open problem. Moreover, building clusters created in previously published generalization methods are not flexible enough to meet the various requirements for both legible and realistic visualization. Motivated by these observations, this paper proposes a new method for generating a flexible generalization outcome which enables convenient updating of original building models. It also proposes a flexible preprocessing of this generalized information to render a legible and realistic urban scene. This is accomplished by introducing a novel component structure, termed as FEdge, particularly designed for efficiently managing the geometry and texture information in building cluster instances (both original building models and building clusters) during the generalization, visualization and updating processes. Furthermore, a multiple representation structure, referred to as Evolved Buffer-Tree (EBT), is also introduced. The purpose of the EBT is to organize building cluster instances and to employ more flexible LODs for both legible and realistic visualization of urban scenes. FEdge has an intuitive planar shape which can be effectively used in representing rough 3D facade composed by detailed continuous meshes. Each FEdge is given a unique identifier, referred to as FEdge Index. In the proposed generalization scheme, firstly each original building model treated as a building cluster instance is abstracted and presented as FEdge Indices. These FEdge Indices are then used for producing generalized building cluster instances in the EBT portably, and to support convenient model updating and flexible preprocessing of the generalization results for renderable building cluster instances. Secondly, to achieve
NASA Astrophysics Data System (ADS)
Khawaja, Aly Salim
A general prismatic mesh generator capable of discretizing flow domains for arbitrary 3-D geometries is presented. The overall project objective was to be able to perform routine viscous flow simulations for engineering design and analysis. The suitability of the hybrid prismatic/tetrahedral grid generation approach for numerical computations of flow phenomena over complex bodies was to be authenticated. The prismatic elements are used in close proximity to the body surface to resolve the viscous stresses whereas tetrahedral elements tessellate the rest of the domain. Such an approach allows the exploitation of the best of both, structured and unstructured grid generation approaches. A special algorithm is developed to allow the prisms to march along general splined boundary surfaces. The method uses a 2-D marching scheme in the parametric domain and performs coordinate transfers to the real space. The inclusion of such a scheme allows the use of periodic boundary conditions to reduce solver memory requirements and broaden the range of applicability of the grid generator. The work also introduces the novel ideas of multi-zone and unstructured prismatic mesh generation to allow different levels of grid resolution within the same geometry and to treat disparate length scales. Both these developments are aimed at optimizing the discretized flow domain with the fewest elements and reducing the time step restrictions of the solver by increasing the volumes of the individual cells. Several quality enhancement and validity checks are presented along with an automatic mesh regeneration mechanism for improved overall quality. The combination of the developed algorithms allows for the discretization of realistic 3-D geometries without much user intervention. Applications of the hybrid prismatic/tetrahedral grid generator are presented from various fields such as the aerospace, turbomachinery and offshore industries. The robustness and efficiency of the prismatic grid
Unifying the Geometry of General Relativity with the Virtual Particle Nature of Quantum Theory
NASA Astrophysics Data System (ADS)
Laubenstein, John
2007-03-01
General Relativity (GR) and Quantum Electro-Dynamics (QED) utilize different underlying assumptions regarding the nature of vacuum and space-time. GR requires the actual geometry of space-time to change in the presence of mass resulting in gravitation. QED operates within flat space-time and propagates forces through the exchange of virtual photons. Efforts to unify these theories are -- despite their mathematical elegance -- complex, cumbersome and incomplete. The inability to achieve unification may suggest a need to re-think basic conceptual models. The IWPD Research Center has found evidence suggesting that time -- as a unique degree of freedom -- may be illusionary. Our research suggests that time may be ``embedded'' within a spatial dimension through a geometric manipulation of the light cone in Minkowski space-time. This interpretation of space-time provides predictions that are experimentally verifiable and suggests a conceptual path for the unification of GR and QED.
Development of a general method for obtaining the geometry of microfluidic networks
Razavi, Mohammad Sayed Salimpour, M. R.; Shirani, Ebrahim
2014-01-15
In the present study, a general method for geometry of fluidic networks is developed with emphasis on pressure-driven flows in the microfluidic applications. The design method is based on general features of network's geometry such as cross-sectional area and length of channels. Also, the method is applicable to various cross-sectional shapes such as circular, rectangular, triangular, and trapezoidal cross sections. Using constructal theory, the flow resistance, energy loss and performance of the network are optimized. Also, by this method, practical design strategies for the fabrication of microfluidic networks can be improved. The design method enables rapid prediction of fluid flow in the complex network of channels and is very useful for improving proper miniaturization and integration of microfluidic networks. Minimization of flow resistance of the network of channels leads to universal constants for consecutive cross-sectional areas and lengths. For a Y-shaped network, the optimal ratios of consecutive cross-section areas (A{sub i+1}/A{sub i}) and lengths (L{sub i+1}/L{sub i}) are obtained as A{sub i+1}/A{sub i} = 2{sup −2/3} and L{sub i+1}/L{sub i} = 2{sup −1/3}, respectively. It is shown that energy loss in the network is proportional to the volume of network. It is also seen when the number of channels is increased both the hydraulic resistance and the volume occupied by the network are increased in a similar manner. Furthermore, the method offers that fabrication of multi-depth and multi-width microchannels should be considered as an integral part of designing procedures. Finally, numerical simulations for the fluid flow in the network have been performed and results show very good agreement with analytic results.
General relativity exactly described in terms of Newton's laws within curved geometries
NASA Astrophysics Data System (ADS)
Savickas, D.
2014-07-01
Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.
DeHart, M.D.
1992-12-01
A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.
tt * geometry in 3 and 4 dimensions
NASA Astrophysics Data System (ADS)
Cecotti, Sergio; Gaiotto, Davide; Vafa, Cumrun
2014-05-01
We consider the vacuum geometry of supersymmetric theories with 4 supercharges, on a flat toroidal geometry. The 2 dimensional vacuum geometry is known to be captured by the tt * geometry. In the case of 3 dimensions, the parameter space is ( T 2 × ) N and the vacuum geometry turns out to be a solution to a generalization of monopole equations in 3 N dimensions where the relevant topological ring is that of line operators. We compute the generalization of the 2d cigar amplitudes, which lead to S 2 × S 1 or S 3 partition functions which are distinct from the supersymmetric partition functions on these spaces, but reduce to them in a certain limit. We show the sense in which these amplitudes generalize the structure of 3d Chern-Simons theories and 2d RCFT's. In the case of 4 dimensions the parameter space is of the form X M,N = ( T 3 × ) M × T 3 N , and the vacuum geometry is a solution to a mixture of generalized monopole equations and generalized instanton equations (known as hyper-holomorphic connections). In this case the topological rings are associated to surface operators. We discuss the physical meaning of the generalized Nahm transforms which act on all of these geometries.
A generalization of the Drude-Smith formula for magneto-optical conductivities in Faraday geometry
NASA Astrophysics Data System (ADS)
Han, F. W.; Xu, W.; Li, L. L.; Zhang, C.
2016-06-01
In this study, we generalize the impulse response approach and Poisson statistics proposed by Smith [Phys. Rev. B 64, 155106 (2001)] to evaluate the longitudinal and transverse magneto-optical conductivities in an electron gas system in Faraday geometry. Comparing with the standard Drude model, the coefficients an are introduced in the Drude-Smith formula to describe the backscattering or localization effect for the nth electronic scattering event. Such a formula can also be applied to study the elements of the dielectric function matrix in the presence of magnetic and radiation fields in electron gas systems. This theoretical work is primely motivated by recent experimental activities in measuring the real and imaginary parts of longitudinal and transverse magneto-optical conductivities in condensed matter materials and electronic devices using terahertz time-domain spectroscopy. We believe that the results obtained from this study can provide an appropriate theoretical tool in reproducing the experimental findings and in fitting with experimental data to determine the important sample and material parameters.
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Induced toroid structures and toroid polarizabilities
Costescu, A.; Radescu, E.E.
1987-06-01
The frequency-dependent toroid dipole polarizability ..gamma..(..omega..) of a (nonrelativistic, spinless) hydrogenlike atom in its ground state is calculated analytically in terms of two Gauss hypergeometric functions. The static result reads ..gamma..(..omega.. = 0) = (23/60)..cap alpha../sup 2/Z/sup -4/a/sub 0/ /sup 5/(..cap alpha.. = fine-structure constant, Z = nucleus charge number, a/sub 0/ = Bohr radius). Comparing the present evaluations for atoms with previous ones for pions, one sees that the role of the induced toroid moments (as against that of the usual electric ones) increases considerably towards smaller distances (or higher characteristic excitation energies). It might become dramatic at the subhadronic level.
Potthoff, Clifford M.
1978-01-01
The disclosure is directed to an apparatus for placing wire windings on a toroidal body, such as a transformer core, having an orifice in its center. The apparatus comprises a wire storage spool, a wire loop holding continuous belt maintained in a C-shaped loop by a belt supporting structure and provision for turning the belt to place and tighten loops of wire on a toroidal body, which is disposed within the gap of the C-shaped belt loop.
Westerly, David C.; Mo, Xiaohu; Tomé, Wolfgang A.; Mackie, Thomas R.; DeLuca, Paul M.
2013-01-01
Purpose: Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke [“Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media,” Phys. Med. Biol. 47, 3313–3330 (2002)10.1088/0031-9155/47/18/304] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth. Methods: Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Molière scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam. Results: Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as
Ames, B.; Ferguson, D.
1996-12-31
The DT-NURBS spline geometry subroutine library is a Non-Uniform Rational B-spline library developed with the goal of providing a common mathematical base for integrating geometrically dependent analysis tools with design geometry; and as a tool for use in the development of multi-disciplinary applications. In this paper we will describe the approach taken with the DT-NURBS library, the basic library entities themselves and how they can be used to affect the integration of diverse geometries and analyses.
Heterotic free fermionic and symmetric toroidal orbifold models
NASA Astrophysics Data System (ADS)
Athanasopoulos, P.; Faraggi, A. E.; Nibbelink, S. Groot; Mehta, V. M.
2016-04-01
Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z_2× Z_2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: we give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z_2× Z_2 orbifold geometries in six dimensions.
ERIC Educational Resources Information Center
Stallings, William M.
It was hypothesized that instruction in descriptive geometry produces an increase in SRT scores. The resultant data do not firmly support this hypothesis. It is suggested that this study be replicated with the use of randomly selected control groups. (MS)
NASA Astrophysics Data System (ADS)
Bae, Cheonho; Stacey, Weston
2015-11-01
Braginskii's flow rate of strain tensor formalism, as extended first to low collisional plasmas in axisymmetric circular toroidal flux surface geometry, then to elongated axisymmetric flux surface geometry, has recently been extended to 3-D non-axisymmetric toroidal flux surface geometry. In toroidally non-axisymmetric plasmas, the leading order neoclassical parallel viscosity terms in the flow rate of strain tensor do not vanish to cause flux surface averaged toroidal angular momentum damping and eventually slow down the plasma rotation. The formalism of Ref. 5 provides a means to systematically evaluate the ``neoclassical toroidal viscosity (NTV)'' in curvilinear plasma geometry based on the plasma fluid equations. As the first step of its application, a practical formalism for circular plasmas, given in the appendix of Ref. 5, will be applied to KSTAR discharges to predict the rotation and NTV, which can also be compared with actual rotation measurements to numerically validate the NTV damping effects.
Gerald, Rex E. II; Sanchez, Jairo; Rathke, Jerome W.
2004-08-10
A video toroid cavity imager for in situ measurement of electrochemical properties of an electrolytic material sample includes a cylindrical toroid cavity resonator containing the sample and employs NMR and video imaging for providing high-resolution spectral and visual information of molecular characteristics of the sample on a real-time basis. A large magnetic field is applied to the sample under controlled temperature and pressure conditions to simultaneously provide NMR spectroscopy and video imaging capabilities for investigating electrochemical transformations of materials or the evolution of long-range molecular aggregation during cooling of hydrocarbon melts. The video toroid cavity imager includes a miniature commercial video camera with an adjustable lens, a modified compression coin cell imager with a fiat circular principal detector element, and a sample mounted on a transparent circular glass disk, and provides NMR information as well as a video image of a sample, such as a polymer film, with micrometer resolution.
Ohkawa, Tihiro; Baker, Charles C.
1981-01-01
In a plasma device having a toroidal plasma containment vessel, a toroidal field-generating coil system includes fixed linking coils each formed of first and second sections with the first section passing through a central opening through the containment vessel and the second section completing the linking coil to link the containment vessel. A plurality of removable unlinked coils are each formed of first and second C-shaped sections joined to each other at their open ends with their bights spaced apart. The second C-shaped section of each movable coil is removably mounted adjacent the second section of a linking coil, with the containment vessel disposed between the open ends of the first and second C-shaped sections. Electric current is passed through the linking and removable coils in opposite sense in the respective adjacent second sections to produce a net toroidal field.
The geometrical structure of quantum theory as a natural generalization of information geometry
Reginatto, Marcel
2015-01-13
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
The geometrical structure of quantum theory as a natural generalization of information geometry
NASA Astrophysics Data System (ADS)
Reginatto, Marcel
2015-01-01
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Progress in Compact Toroid Experiments
Dolan, Thomas James
2002-09-01
The term "compact toroids" as used here means spherical tokamaks, spheromaks, and field reversed configurations, but not reversed field pinches. There are about 17 compact toroid experiments under construction or operating, with approximate parameters listed in Table 1.
Appearance of toroidal structure in dissipating laser-generated sparks
NASA Astrophysics Data System (ADS)
Nassif, D.; Hüwel, L.
2000-03-01
We have investigated the temporal and spatial evolution of laser-induced plasmas in pure nitrogen. A 1064 nm, 20 ns pulse from a neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser with pulse energies ranging from 175 to 500 mJ is tightly focused to produce a spark at various, near-atmospheric pressures. Spatially resolved Rayleigh scattered light from a time-delayed, 355 nm Nd:YAG laser pulse traversing the spark at right angles is collected with an image intensifier gated, linear diode array. At a delay time of 30 μs, the laser plasma remnant appears as a nearly spherically symmetric region with a center temperature of about 4500 K. After around 100 μs, the hot gas starts to change into a toroidal shape expanding radially at an average speed of a few meters per second. The final torus size increases with decreasing pressure and increasing laser power. This general behavior of the plasma afterglow can be reconciled with a numerical model, where in the aftermath of the spark shock wave a pair of vortices is produced which in turn moves the residual hot gas into the observed toroidal geometry.
NASA Astrophysics Data System (ADS)
Chung, Kyung Tae; Lee, Jong Woo
1989-08-01
A connection which is both Einstein and semisymmetric is called an SE connection, and a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by g λμ through an SE connection is called an n-dimensional SE manifold and denoted by SEXn. This paper is a direct continuation of earlier work. In this paper, we derive the generalized fundamental equations for the hypersubmanifold of SEXn, including generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations.
Applications of a generalized pressure correction algorithm for flows in complicated geometries
NASA Astrophysics Data System (ADS)
Shyy, W.; Braaten, M. E.
An overview is given of recent progress in developing a unified numerical algorithm capable of solving flow over a wide range of Mach and Reynolds numbers in complex geometries. The algorithm is based on the pressure correction method, combined treatment of the Cartesian and contravariant velocity components on arbitrary coordinates, and second-order accurate discretization. A number of two- and three-dimensional flow problems including the effects of electric currents, turbulence, combustion, multiple phases, and compressibility are presented to demonstrate the capability of the present algorithm. Some related technical issues, such as the skewness of the grid distribution and the promise of parallel computation, are also addressed.
Diffusiophoresis of a charged toroidal polyelectrolyte.
Tseng, Shiojenn; Hsu, Yen-Rei; Hsu, Jyh-Ping
2016-06-01
Considering recent application of concentration driven motion of charged nanoparticles in sensing technology, we model the diffusiophoresis of an isolated toroidal polyelectrolyte (PE) for the first time. Choosing an aqueous KCl solution for illustration, its behavior under various conditions is simulated by varying the double layer thickness, the size of toroid, and its softness and fixed charge density. We show that the behavior of the present PE can be different both quantitatively and qualitatively from that of the corresponding spherical PE. This arises from the competition of the hydrodynamic force and the electric force acting on a PE. The geometry and the nature of a PE can also influence appreciably its behavior, yielding complicated and interesting results. PMID:26970033
Influence of toroidal rotation on resistive tearing modes in tokamaks
NASA Astrophysics Data System (ADS)
Wang, S.; Ma, Z. W.
2015-12-01
Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τR/τV ≫ 1, where τR and τV represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τR/τV ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.
Influence of toroidal rotation on resistive tearing modes in tokamaks
Wang, S.; Ma, Z. W.
2015-12-15
Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τ{sub R}/τ{sub V} ≫ 1, where τ{sub R} and τ{sub V} represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τ{sub R}/τ{sub V} ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.
Polytope ARTMAP: pattern classification without vigilance based on general geometry categories.
Gomes Amorim, Dinani; Fernández Delgado, Manuel; Barro Ameneiro, Senén
2007-09-01
This paper proposes polytope ARTMAP (PTAM), an adaptive resonance theory (ART) network for classification tasks which does not use the vigilance parameter. This feature is due to the geometry of categories in PTAM, which are irregular polytopes whose borders approximate the borders among the output predictions. During training, the categories expand only towards the input pattern without category overlap. The category expansion in PTAM is naturally limited by the other categories, and not by the category size, so the vigilance is not necessary. PTAM works in a fully automatic way for pattern classification tasks, without any parameter tuning, so it is easier to employ for nonexpert users than other classifiers. PTAM achieves lower error than the leading ART networks on a complete collection of benchmark data sets, except for noisy data, without any parameter optimization. PMID:18220182
Tokamak with liquid metal toroidal field coil
Ohkawa, Tihiro; Schaffer, Michael J.
1981-01-01
Tokamak apparatus includes a pressure vessel for defining a reservoir and confining liquid therein. A toroidal liner disposed within the pressure vessel defines a toroidal space within the liner. Liquid metal fills the reservoir outside said liner. Electric current is passed through the liquid metal over a conductive path linking the toroidal space to produce a toroidal magnetic field within the toroidal space about the major axis thereof. Toroidal plasma is developed within the toroidal space about the major axis thereof.
Method to integrate full particle orbit in toroidal plasmas
NASA Astrophysics Data System (ADS)
Wei, X. S.; Xiao, Y.; Kuley, A.; Lin, Z.
2015-09-01
It is important to integrate full particle orbit accurately when studying charged particle dynamics in electromagnetic waves with frequency higher than cyclotron frequency. We have derived a form of the Boris scheme using magnetic coordinates, which can be used effectively to integrate the cyclotron orbit in toroidal geometry over a long period of time. The new method has been verified by a full particle orbit simulation in toroidal geometry without high frequency waves. The full particle orbit calculation recovers guiding center banana orbit. This method has better numeric properties than the conventional Runge-Kutta method for conserving particle energy and magnetic moment. The toroidal precession frequency is found to match that from guiding center simulation. Many other important phenomena in the presence of an electric field, such as E × B drift, Ware pinch effect and neoclassical polarization drift are also verified by the full orbit simulation.
Amundsen, Morten; Linder, Jacob
2016-01-01
An extension of quasiclassical Keldysh-Usadel theory to higher spatial dimensions than one is crucial in order to describe physical phenomena like charge/spin Hall effects and topological excitations like vortices and skyrmions, none of which are captured in one-dimensional models. We here present a numerical finite element method which solves the non-linearized 2D and 3D quasiclassical Usadel equation relevant for the diffusive regime. We show the application of this on three model systems with non-trivial geometries: (i) a bottlenecked Josephson junction with external flux, (ii) a nanodisk ferromagnet deposited on top of a superconductor and (iii) superconducting islands in contact with a ferromagnet. In case (i), we demonstrate that one may control externally not only the geometrical array in which superconducting vortices arrange themselves, but also to cause coalescence and tune the number of vortices. In case (iii), we show that the supercurrent path can be tailored by incorporating magnetic elements in planar Josephson junctions which also lead to a strong modulation of the density of states. The finite element method presented herein paves the way for gaining insight in physical phenomena which have remained largely unexplored due to the complexity of solving the full quasiclassical equations in higher dimensions. PMID:26961921
Amundsen, Morten; Linder, Jacob
2016-01-01
An extension of quasiclassical Keldysh-Usadel theory to higher spatial dimensions than one is crucial in order to describe physical phenomena like charge/spin Hall effects and topological excitations like vortices and skyrmions, none of which are captured in one-dimensional models. We here present a numerical finite element method which solves the non-linearized 2D and 3D quasiclassical Usadel equation relevant for the diffusive regime. We show the application of this on three model systems with non-trivial geometries: (i) a bottlenecked Josephson junction with external flux, (ii) a nanodisk ferromagnet deposited on top of a superconductor and (iii) superconducting islands in contact with a ferromagnet. In case (i), we demonstrate that one may control externally not only the geometrical array in which superconducting vortices arrange themselves, but also to cause coalescence and tune the number of vortices. In case (iii), we show that the supercurrent path can be tailored by incorporating magnetic elements in planar Josephson junctions which also lead to a strong modulation of the density of states. The finite element method presented herein paves the way for gaining insight in physical phenomena which have remained largely unexplored due to the complexity of solving the full quasiclassical equations in higher dimensions. PMID:26961921
A test of general relativity from the three-dimensional orbital geometry of a binary pulsar.
van Straten, W; Bailes, M; Britton, M; Kulkarni, S R; Anderson, S B; Manchester, R N; Sarkissian, J
2001-07-12
Binary pulsars provide an excellent system for testing general relativity because of their intrinsic rotational stability and the precision with which radio observations can be used to determine their orbital dynamics. Measurements of the rate of orbital decay of two pulsars have been shown to be consistent with the emission of gravitational waves as predicted by general relativity, but independent verification was not possible. Such verification can in principle be obtained by determining the orbital inclination in a binary pulsar system using only classical geometrical constraints. This would permit a measurement of the expected retardation of the pulse signal arising from the general relativistic curvature of space-time in the vicinity of the companion object (the 'Shapiro delay'). Here we report high-precision radio observations of the binary millisecond pulsar PSR J0437-4715, which establish the three-dimensional structure of its orbit. We see the Shapiro delay predicted by general relativity, and we determine the mass of the neutron star and its white dwarf companion. The determination of such masses is necessary in order to understand the origin and evolution of neutron stars. PMID:11449265
ERIC Educational Resources Information Center
Linenberger, Kimberly J.; Cole, Renee S.; Sarkar, Somnath
2011-01-01
We present a guided-inquiry experiment using Spartan Student Version, ready to be adapted and implemented into a general chemistry laboratory course. The experiment provides students an experience with Spartan Molecular Modeling software while discovering the relationships between the structure and properties of molecules. Topics discussed within…
Simulated Textures of Toroidal Nematic Liquid Crystal Droplets
NASA Astrophysics Data System (ADS)
Ellis, Perry; Fernandez-Nieves, Alberto
2014-03-01
Nematic liquid crystals under confinement by curved surfaces can produce complex hierarchical structures whose design principles and properties have yet to be unraveled. Here we focus on toroidal geometries and perform computer simulations of the nematic textures seen between crossed-polarizers. We find agreement with experiments using director fields that exhibit pronounced twist deformations with contributions from bend and splay.
Boerger, D.M.; Kramer, J.J.; Partain, L.D.
1981-01-01
A rigorous derivation is given to generalize the allowed, Hall effect, sample shapes from the restrictive, rectangular parallelepiped configurations to a much more general class of geometries characterized by mirror symmetry for materials whose mobile carriers have surfaces of constant energy in k-bar space that are well described by ellipsoids. However, this mirror symmetry condition is more restrictive than the almost arbitrary sample shapes proposed with the van der Pauw technique for thin films. Experimental data taken on n-type CdS at liquid-nitrogen temperatures in magnetic field strengths of 8 and 145 kG show that errors ranging from 1 to 600% can result from van der Pauw-type geometries depending on how much the sample shape and/or contact arrangement differs from the mirror symmetry. An empirically derived averaging technique is described that reduces the observed errors to less than 13% even with van der Pauw-type shapes that do not meet the mirror symmetry conditions.
A generalized reverse projection method for fan beam geometry under partially coherent illumination
NASA Astrophysics Data System (ADS)
Wu, Z.; Wang, Z. L.; Gao, K.; Zhang, K.; Ge, X.; Wang, D. J.; Wang, S. H.; Chen, J.; Pan, Z. Y.; Zhu, P. P.; Wu, Z. Y.
2014-02-01
In this paper, a generalized reverse projection (RP) method for grating-based fan beam phase contrast imaging is presented. Compared to the original RP method, rays rather than projection images are taken into account during the information extraction process. We also discuss the influence of partial coherence on the extracted information. Theoretical derivations and numerical simulations are performed to confirm the validity of the method.
The Segmented Bifilar Contrawound Toroidal Helical Antenna.
NASA Astrophysics Data System (ADS)
Vanvoorhies, Kurt Louis
The segmented bifilar contrawound toroidal helical antenna, a.k.a. QuadContra antenna creates a toroidal magnetic current whose radiated electromagnetic fields emulate those of an electric dipole located normal to the plane of the toroidal helix. This antenna is a magnetic dual of the constant current electric loop antenna. Its principal advantages of reduced size and low profile result from both its circular geometry and from the velocity factor of its slow wave contrawound helical structure. This antenna is constructed by winding two conductors in contrawound relation to each other on a toroidal form, dividing the winding into an even number of segments, and reversing the pitch sense of each conductor from one segment to another. Feed ports are located on the conductors at the segment boundaries, and are connected in alternate phase to a central signal terminal via balanced and tuned transmission line elements. At resonance, each winding segment supports a quarter-wave sinusoidal current distribution. Toroidal electric current components are canceled, and poloidal current components are enhanced in the resulting anti-symmetric mode current distribution. This study measured and simulated the velocity factor, input impedance, bandwidth and simulated the radiation gain and pattern for a variety of linear and toroidal structures. The velocity factor, modeled as a power function of the ratio of axial winding length to wire length, was two to three times slower for the anti-symmetric mode contrawound helix than for a comparable monofilar helix. The radiation characteristics of the antenna were simulated using the OSU ESP4 Moment Method based program, after making extensive improvements to accommodate a wide variety of antenna configurations and to automatically find resonant frequencies. The simulated QuadContra antenna radiates with vertically polarization in a dipole-like pattern having a gain about 2 dB less than the dipole. The gain falls off dramatically for
Deformation energy of a toroidal nucleus and plane fragmentation barriers
NASA Astrophysics Data System (ADS)
Fauchard, C.; Royer, G.
1996-02-01
The path leading to pumpkin-like configurations and toroidal shapes is investigated using a one-parameter shape sequence. The deformation energy is determined within the analytical expressions obtained for the various shape-dependent functions and the generalized rotating liquid drop model taking into account the proximity energy and the temperature. With increasing mass and angular momentum, a potential well appears in the toroidal shape path. For the heaviest systems, the pocket is large and locally favourable with respect to the plane fragmentation barriers which might allow the formation of evanescent toroidal systems which would rapidly decay in several fragments to minimize the surface tension.
Johnson, R.L.
1985-01-01
The Advanced Toroidal Facility (ATF) is a new magnetic confinement plasma device under construction at the Oak Ridge National Laboratory (ORNL) that will lead to improvements in toroidal magnetic fusion reactors. The ATF is a type of stellerator, known as a ''torsatron'' which theoretically has the capability to operate at greater than or equal to8% beta in steady state. The ATF plasma has a major radius of 2.1 m, an average minor radius of 0.3 m, and a field of 2 T for a 2 s duration or 1 T steady state. The ATF device consists of a helical field (HF) coil set, a set of poloidal field (PF) coils, an exterior shell structure to support the coils, and a thin, helically contoured vacuum vessel inside the coils. The ATF replaces the Impurities Studies Experiment (ISX-B) tokamak at ORNL and will use the ISX-B auxiliary systems including 4 MW of electron cyclotron heating. The ATF is scheduled to start operation in late 1986. An overview of the ATF device is presented, including details of the construction process envisioned. 9 refs., 7 figs., 3 tabs.
Equivalent plate analysis of aircraft wing box structures with general planform geometry
NASA Technical Reports Server (NTRS)
Giles, G. L.
1986-01-01
A new equivalent plate analysis formulation is described which is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. Multiple trapezoidal segments are used to represent such planforms. A Ritz solution technique is used in conjunction with global displacement functions which encompass all the segments. This Ritz solution procedure is implemented efficiently into a computer program so that it can be used by rigorous optimization algorithms for application in early preliminary design. A direct method to interface this structural analysis procedure with aerodynamic programs for use in aeroelastic calculations is described. This equivalent plate analysis procedure is used to calculate the static deflections and stresses and vibration frequencies and modes of an example wing configuration. The numerical results are compared with results from a finite element model of the same configuration to illustrate typical levels of accuracy and computation times resulting from use of this procedure.
Equivalent plate analysis of aircraft wing box structures with general planform geometry
NASA Technical Reports Server (NTRS)
Giles, G. L.
1986-01-01
A new equilvalent plate analysis formulation is described which is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. Multiple trapezoidal segments are used to represent such planforms. A Ritz solution technique is used in conjunction with global displacement functions which encompass all the segments. This Ritz solution procedure is implemented efficiently into a computer program so that it can be used by rigorous optimization algorithms for application in early preliminary design. A direct method to interface this structural analysis procedure with aerodynamic programs for use in aeroelastic calculations is described. This equivalent plate analysis procedure is used to calculate the static deflections and stresses and vibration frequencies and modes of an example wing configuration. The numerical results are compared with results from a finite element model of the same configuration to illustrate typical levels of accuracy and computation times resulting from use of this procedure.
Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves
NASA Technical Reports Server (NTRS)
Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.
1992-01-01
The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.
NASA Astrophysics Data System (ADS)
Rong, Y. M.; Chang, Y.; Huang, Y.; Zhang, G. J.; Shao, X. Y.
2015-12-01
There are few researches that concentrate on the prediction of the bead geometry for laser brazing with crimping butt. This paper addressed the accurate prediction of the bead profile by developing a generalized regression neural network (GRNN) algorithm. Firstly GRNN model was developed and trained to decrease the prediction error that may be influenced by the sample size. Then the prediction accuracy was demonstrated by comparing with other articles and back propagation artificial neural network (BPNN) algorithm. Eventually the reliability and stability of GRNN model were discussed from the points of average relative error (ARE), mean square error (MSE) and root mean square error (RMSE), while the maximum ARE and MSE were 6.94% and 0.0303 that were clearly less than those (14.28% and 0.0832) predicted by BPNN. Obviously, it was proved that the prediction accuracy was improved at least 2 times, and the stability was also increased much more.
Quantum fields in toroidal topology
Khanna, F.C.; Malbouisson, A.P.C.; Santana, A.E.
2011-10-15
The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type {Gamma}{sub D}{sup d}=(S{sup 1}){sup d}xM{sup D-d}. The modular operator is generalized to introduce representations of isometry groups. The Poincare symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2x2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein-Gordon and Dirac fields, and then formulate non-abelian gauge theories in {Gamma}{sub D}{sup d}. Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification. - Highlights: > C*-algebra is used to describe fields in compactified space-time dimensions. > The space-time is characterized by toroidal topologies. > Representations of the Poincare group are studied by using the modular operator. > We derive non-abelian gauge theories in compactified regions of space-time. > We show the compactification effect in the decay of particles using the S-matrix.
Dynamics of the Disruption Halo Current Toroidal Asymmetry in NSTX
S.P. Gerhardt
2012-09-27
This paper describes the dynamics of disruption halo current non-axisymmetries in the lower divertor of the National Spherical Torus Experiment [M. Ono, et al. Nuclear Fusion 40, 557 (2000)]. While. The halo currents typically have a strongly asymmetric structure where they enter the divertor floor, and this asymmetry has been observed to complete up to 7 toroidal revolutions over the duration of the halo current pulse. However, the rotation speed and toroidal extend of the asymmetry can vary significantly during the pulse. The rotation speed, halo current pulse duration, and total number of revolutions tend to be smaller in cases with large halo currents. The halo current pattern is observed to become toroidally symmetric at the end of the halo current pulse. It is proposed that this symmeterization is due to the loss of most or all of the closed field line geometry in the final phase of the vertical displacement event.
Visualizing the Formation and Collapse of DNA Toroids
van den Broek, Bram; Noom, Maarten C.; van Mameren, Joost; Battle, Christopher; MacKintosh, Fred C.; Wuite, Gijs J.L.
2010-01-01
Abstract In living organisms, DNA is generally confined into very small volumes. In most viruses, positively charged multivalent ions assist the condensation of DNA into tightly packed toroidal structures. Interestingly, such cations can also induce the spontaneous formation of DNA toroids in vitro. To resolve the condensation dynamics and stability of DNA toroids, we use a combination of optical tweezers and fluorescence imaging to visualize in real-time spermine-induced (de)condensation in single DNA molecules. By actively controlling the DNA extension, we are able to follow (de)condensation under tension with high temporal and spatial resolution. We show that both processes occur in a quantized manner, caused by individual DNA loops added onto or removed from a toroidal condensate that is much smaller than previously observed in similar experiments. Finally, we present an analytical model that qualitatively captures the experimentally observed features, including an apparent force plateau. PMID:20441754
Instability of Toroidal Magnetic Field in Jets and Plerions
NASA Astrophysics Data System (ADS)
Begelman, Mitchell C.
1998-01-01
Astrophysical jets and pulsar-fed supernova remnants (plerions) are expected to develop highly organized magnetic structures dominated by concentric loops of toroidal field, Bφ. It has been argued that such structures could explain the polarization properties of some jets and contribute to their lateral confinement through magnetic tension forces. A concentric toroidal field geometry is also central to the Rees-Gunn model for the Crab Nebula, the archetypal plerion, and leads to the deduction that the Crab pulsar's wind must have a weak magnetic field. Yet this kind of equilibrium between magnetic and gas pressure forces, the ``equilibrium Z-pinch'' of the controlled fusion literature, is well known to be susceptible to disruptive localized instabilities, even when the magnetic field is weak and/or boundary conditions (e.g., a dense external medium) slow or suppress global modes. Thus, the magnetic field structures imputed to the interiors of jets and plerions are unlikely to persist for very long. To determine the growth rates of Z-pinch instabilities under astrophysical conditions, I derive a dispersion relation that is valid for the relativistic fluids of which jets and plerions may be composed, in the ideal magnetohydrodynamics (MHD) limit. The dominant instabilities are kink (m = 1) and pinch (m = 0) modes. The former generally dominate, destroying the concentric field structure and probably driving the system toward a more chaotic state in which the mean field strength is independent of radius (and in which resistive dissipation of the field may be enhanced). I estimate the timescales over which the field structure is likely to be rearranged and relate these to distances along relativistic jets and radii from the central pulsar in a plerion. I conclude that the central tenet of the Rees-Gunn model for the Crab Nebula, the existence of a concentric toroidal field well outside the pulsar wind's termination shock, is physically unrealistic. With this assumption
Seol, J; Lee, S G; Park, B H; Lee, H H; Terzolo, L; Shaing, K C; You, K I; Yun, G S; Kim, C C; Lee, K D; Ko, W H; Kwak, J G; Kim, W C; Oh, Y K; Kim, J Y; Kim, S S; Ida, K
2012-11-01
It is observed that the magnitude of the toroidal rotation speed is reduced by the central electron cyclotron resonance heating (ECRH) regardless of the direction of the toroidal rotation. The magnetohydrodynamics activities generally appear with the rotation change due to ECRH. It is shown that the internal kink mode is induced by the central ECRH and breaks the toroidal symmetry. When the magnetohydrodynamics activities are present, the toroidal plasma viscosity is not negligible. The observed effects of ECRH on the toroidal plasma rotation are explained by the neoclassical toroidal viscosity in this Letter. It is found that the neoclassical toroidal viscosity torque caused by the internal kink mode damps the toroidal rotation. PMID:23215391
Grinding Inside A Toroidal Cavity
NASA Technical Reports Server (NTRS)
Mayer, Walter; Adams, James F.; Burley, Richard K.
1987-01-01
Weld lines ground smooth within about 0.001 in. Grinding tool for smoothing longitudinal weld lines inside toroidal cavity includes curved tunnel jig to guide grinding "mouse" along weld line. Curvature of tunnel jig matched to shape of toroid so grinding ball in mouse follows circular arc of correct radius as mouse is pushed along tunnel. Tool enables precise control of grindout shape, yet easy to use.
PEGASUS Toroidal Experimental Facility*
NASA Astrophysics Data System (ADS)
Lewicki, B.; Pegasus Group
1998-11-01
P EGASUS began operations in June 98 and will study the characteristics of Extremely Low-Aspect Ratio Tokamak (ELART) plasmas. The 2.0m diameter, thin-walled (6.35 mm) vacuum vessel is a continuous stainless steel shell with generous port access. Initial pump down base pressure was 5 × 10-8 torr. The high stress ohmic solenoid is powered by a 15 kV, 4.5 MJ capacitor bank and will be impedance-matched through a 10:1 step-down transformer to extend the pulse length. Operating at peak fields of 13 - 20 T, the solenoid can achieve a flux swing of up to 190mV-s over 60 ms. The toroidal field of 0.1 T on axis is powered by a 3 MVA AC/DC converter capable of 3.5 kA at 600 VDC. The equilibrium and shaping field magnets are powered by 2.2 F of commutated capacitor banks plus a 0.5 MVA programmable switching supply. Modest waveform control is available to compensate for the resistive vacuum vessel and aid in plasma shaping for elongated and diverted plasmas. Operational diagnostics include internal magnetic pickup loops, high resolution and fast framing cameras, and impurity monitoring systems. * *Supported by U.S. DoE grant No. DE-FG02-96ER54375
PARTICLE-HOLE NATURE OF THE LIGHT HIGH-SPIN TOROIDAL ISOMERS
Staszczak, A.; Wong, Cheuk-Yin
2015-01-01
Nuclei under non-collective rotation with a large angular momentum above some threshold can assume a toroidal shape. In our previous work, we showed by using cranked Skyrme Hartree Fock approach that even even, N = Z, high-K, toroidal isomeric states may have general occurrences for light nuclei with 28 < A < 52. We present here some additional results and systematics on the particle-hole nature of these high-spin toroidal isomers.
Toroidal plasma enhanced CVD of diamond films
Zvanya, John Cullen, Christopher Morris, Thomas Krchnavek, Robert R.; Holber, William Basnett, Andrew Basnett, Robert; Hettinger, Jeffrey
2014-09-01
An inductively coupled toroidal plasma source is used as an alternative to microwave plasmas for chemical vapor deposition of diamond films. The source, operating at a frequency of 400 kHz, synthesizes diamond films from a mixture of argon, methane, and hydrogen. The toroidal design has been adapted to create a highly efficient environment for diamond film deposition: high gas temperature and a short distance from the sample to the plasma core. Using a toroidal plasma geometry operating in the medium frequency band allows for efficient (≈90%) coupling of AC line power to the plasma and a scalable path to high-power and large-area operation. In test runs, the source generates a high flux of atomic hydrogen over a large area, which is favorable for diamond film growth. Using a deposition temperature of 900–1050 °C and a source to sample distance of 0.1–2.0 cm, diamond films are deposited onto silicon substrates. The results showed that the deposition rate of the diamond films could be controlled using the sample temperature and source to sample spacing. The results also show the films exhibit good-quality polycrystalline diamond as verified by Raman spectroscopy, x-ray diffraction, and scanning electron microscopy. The scanning electron microscopy and x-ray diffraction results show that the samples exhibit diamond (111) and diamond (022) crystallites. The Raman results show that the sp{sup 3} peak has a narrow spectral width (FWHM 12 ± 0.5 cm{sup −1}) and that negligible amounts of the sp{sup 2} band are present, indicating good-quality diamond films.
Toroidal Simulations of Sawteeth with Diamagnetic Effects
NASA Astrophysics Data System (ADS)
Beidler, Matthew; Cassak, Paul; Jardin, Stephen
2014-10-01
The sawtooth crash in tokamaks limits the core temperature, adversely impacts confinement, and seeds disruptions. Adequate knowledge of the physics governing the sawtooth crash and a predictive capability of its ramifications has been elusive, including an understanding of incomplete reconnection, i.e., why sawteeth often cease prematurely before processing all available magnetic flux. There is an indication that diamagnetic suppression could play an important role in this phenomenon. While computational tools to study toroidal plasmas have existed for some time, extended-MHD physics have only recently been integrated. Interestingly, incomplete reconnection has been observed in simulations when diamagnetic effects are present. In the current study, we employ the three-dimensional, extended-MHD code M3D-C1 to study the sawtooth crash in a toroidal geometry. In particular, we describe how magnetic reconnection at the q = 1 rational surface evolves when self-consistently increasing diamagnetic effects are present. We also explore how the termination of reconnection may lead to core-relaxing ideal-MHD instabilities.
Drift Mode Calculations in Nonaxisymmetric Geometry
G. Rewoldt; L.-P. Ku; W.A. Cooper; W.M. Tang
1999-07-01
A fully kinetic assessment of the stability properties of toroidal drift modes has been obtained for nonaxisymmetric (stellarator) geometry, in the electrostatic limit. This calculation is a comprehensive solution of the linearized gyrokinetic equation, using the lowest-order ''ballooning representation'' for high toroidal mode number instabilities, with a model collision operator. Results for toroidal drift waves destabilized by temperature gradients and/or trapped particle dynamics are presented, using three-dimensional magnetohydrodynamic equilibria generated as part of a design effort for a quasiaxisymmetric stellarator. Comparisons of these results with those obtained for typical tokamak cases indicate that the basic trends are similar.
NASA Astrophysics Data System (ADS)
Bergmann, Ryan
general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP ha
Reduced-magnetohydrodynamic simulations of toroidally and poloidally localized edge localized modes
Hoelzl, M.; Guenter, S.; Mueller, W.-C.; Lackner, K.; Krebs, I.; Wenninger, R. P.; Huysmans, G. T. A.; Collaboration: ASDEX Upgrade Team
2012-08-15
We use the non-linear reduced-magnetohydrodynamic code JOREK to study edge localized modes (ELMs) in the geometry of the ASDEX Upgrade tokamak. Toroidal mode numbers, poloidal filament sizes, and radial propagation speeds of filaments into the scrape-off layer are in good agreement with observations for type-I ELMs in ASDEX Upgrade. The observed instabilities exhibit a toroidal and poloidal localization of perturbations which is compatible with the 'solitary magnetic perturbations' recently discovered in ASDEX Upgrade [R. Wenninger et al., 'Solitary magnetic perturbations at the ELM onset,' Nucl. Fusion (accepted)]. This localization can only be described in numerical simulations with high toroidal resolution.
Progress in toroidal confinement and fusion research
Furth, H.P.
1987-10-01
During the past 30 years, the characteristic T/sub i/n tau/sub E/-value of toroidal-confinement experiments has advanced by more than seven orders of magnitude. Part of this advance has been due to an increase of gross machine parameters. Most of this advance has been due to an increase of gross machine parameters. Most of the advance is associated with improvements in the ''quality of plasma confinement.'' The combined evidence of spherator and tokamak research clarifies the role of magnetic-field geometry in determining confinement and points to the importance of shielding out plasma edge effects. A true physical understanding of anomalous transport remains to be achieved. 39 refs., 11 figs., 1 tab.
Report for collisional and chaotic transport of energetic particles in toroidal plasma
Cary, J.R.; Shasharina, S.G.
1995-04-01
The authors have made progress in two general areas of confinement plasma physics. (1) We studies a new loss mechanism of the toroidally trapped particles related to the up-down asymmetry of ripple in a tokamak. (2) We estimated the bootstrap current of the particles making transitions between the toroidally and locally states in non-axisymmetric tori, stellarators and tokamaks.
Concentric Nested Toroidal Inflatable Structures
NASA Technical Reports Server (NTRS)
Johnson, Christopher J.; Raboin, Jasen L.; Spexarth, Gary R.
2010-01-01
Assemblies comprising multiple limited- height toroidal inflatable structures nested in a concentric arrangement have been invented to obtain more design flexibility than can be obtained in single taller, wider toroidal inflatable structures (see figure). Originally intended for use as containers for habitats for humans in outer space or on remote planets, these and related prior inflatable structures could also be useful on Earth as lightweight, compactly stowable, portable special-purpose buildings that could be transported to remote locations and there inflated to full size and shape. In the case of a single inflatable toroidal structure, one important source of lack of design flexibility is the fact that an increase in outer diameter (which is sometimes desired) is necessarily accompanied by an increase in height (which is sometimes undesired). Increases in diameter and height can also cause difficulty in utilization of the resulting larger volume, in that it can become necessary to partition the volume by means of walls and floors, and features (e.g., stairs or ladders) must be added to enable vertical movement between floors. Moreover, ascending and descending between floors in a gravitational environment could pose unacceptable difficulty for the inhabitants under some circumstances. Another source of lack of design flexibility in a single toroidal inflatable structure is that for a given inflation pressure, an increase in the outer diameter of the structure necessarily entails an increase in the maximum stress in the structure. Because it is necessary to keep the maximum stress within the load-bearing capability of the structural materials, consistent with other aspects of the design, this may translate to a limit on the outer diameter. In an assembly comprising concentric nested toroidal structures, an increase in outer diameter does not necessarily entail an increase in height or a maximum stress in excess of the load-bearing capability of the structural
Quantum toroidal moments of nanohelix eigenstates
NASA Astrophysics Data System (ADS)
Williamson, Johnny; Encinosa, Mario
2015-09-01
Developments in the area of metamaterial research have generated interest in toroidal moments and their treatment in the quantum regime. A quantum mechanical method of determining toroidal moments due to current circulating on a toroidal helix is presented. The Hamiltonian of a negatively charged spinless particle constrained to motion in the vicinity of a toroidal helix having loops of arbitrary eccentricity is developed. The resulting three dimensional Schr¨odinger equation is reduced to a one dimensional form inclusive of curvature effects. Low-lying eigenfunctions of the toroidal helix system are determined along with corresponding toroidal moments. A disagreement, not predicted by a classical treatment, arises between toroidal moments of elliptic toroidal helix systems when vertical and horizontal eccentricity are transposed.
NASA Astrophysics Data System (ADS)
Bergmann, Ryan
general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP has limited capabilities. Despite WARP's lack of features, its novel algorithm implementations show that high performance can be achieved on a GPU despite the inherently divergent program flow and sparse data access patterns. WARP is not ready for everyday nuclear reactor calculations, but is a good platform for further development of GPU-accelerated Monte Carlo neutron transport. In it's current state, it may be a useful tool for multiplication factor searches, i.e. determining reactivity coefficients by perturbing material densities or temperatures, since these types of calculations typically do not require many flux tallies. (Abstract shortened by UMI.)
Toroidal Tank Development for Upper-stages
NASA Technical Reports Server (NTRS)
DeLay, Tom; Roberts, Keith
2003-01-01
The advantages, development, and fabrication of toroidal propellant tanks are profiled in this viewgraph presentation. Several images are included of independent research and development (IR&D) of toroidal propellant tanks at Marshall Space Flight Center (MSFC). Other images in the presentation give a brief overview of Thiokol conformal tank technology development. The presentation describes Thiokol's approach to continuous composite toroidal tank fabrication in detail. Images are shown of continuous and segmented toroidal tanks fabricated by Thiokol.
Transport and dynamics in toroidal fusion systems. Report of second year progress, 1993--1994
Schnack, D.D.
1994-05-09
In this document the author describes an extension of the spatial gridding techniques to an MHD model suitable for the description of the dynamics of toroidal fusion devices. Since the dominant MHD modes in these devices have relatively long toroidal wavelength, the toroidal coordinate is approximated with finite Fourier series. The unstructured, triangular mesh is used to describe the details of the poloidal geometry. With some exceptions, the hydrodynamic variables are treated in a manner analogous to that used in CFD. These quantities (mass, energy, and momentum) are volume based densities that satisfy scalar or vector conservation laws. The electromagnetic variables (the magnetic flux density B and the electric current density J) are area based densities that satisfy pseudo-vector conservation laws, and have no counterpart in fluid dynamics. These variables are also constrained to remain solenoidal. These quantities are represented on the triangular mesh in a new manner that is an extension of that used on rectangular, structured meshes. In this work the author has chosen to solve the primitive MHD equations in order to make the resulting codes and techniques more generally applicable to problems beyond the narrow scope of tokamak plasmas. The temporal stiffness problems inherent in this description of tokamak dynamics that motivate the reduced MHD model are addressed here with the semi-implicit method of time integration. Finally, the author remarks that, while the present work deals strictly with the MHD equations, other volume based fluid descriptions, such as diffusive transport could easily be adapted to these techniques and coupled with the description of the electromagnetic field presented here.
Physics models in the toroidal transport code PROCTR
Howe, H.C.
1990-08-01
The physics models that are contained in the toroidal transport code PROCTR are described in detail. Time- and space-dependent models are included for the plasma hydrogenic-ion, helium, and impurity densities, the electron and ion temperatures, the toroidal rotation velocity, and the toroidal current profile. Time- and depth-dependent models for the trapped and mobile hydrogenic particle concentrations in the wall and a time-dependent point model for the number of particles in the limiter are also included. Time-dependent models for neutral particle transport, neutral beam deposition and thermalization, fusion heating, impurity radiation, pellet injection, and the radial electric potential are included and recalculated periodically as the time-dependent models evolve. The plasma solution is obtained either in simple flux coordinates, where the radial shift of each elliptical, toroidal flux surface is included to maintain an approximate pressure equilibrium, or in general three-dimensional torsatron coordinates represented by series of helical harmonics. The detailed coupling of the plasma, scrape-off layer, limiter, and wall models through the neutral transport model makes PROCTR especially suited for modeling of recycling and particle control in toroidal plasmas. The model may also be used in a steady-state profile analysis mode for studying energy and particle balances starting with measured plasma profiles.
ERIC Educational Resources Information Center
Fahlgren, Maria; Brunström, Mats
2014-01-01
The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…
Topology of tokamak plasma equilibria with toroidal current reversal
Rodrigues, Paulo; Bizarro, Joao P. S.
2012-01-15
Some general principles about scalar functions with critical points are used to rigorously ascertain that magnetic equilibria with both toroidal current reversal and nested magnetic surfaces are atypical solutions and highly unstable to arbitrary perturbations of boundary conditions and other parameters. The cause for such is shown to lie in the condition of nested magnetic surfaces and not in the possibility of current reversal and consequent vanishing of the poloidal field inside the plasma. Rather than supporting the claim that instability against experimentally driven perturbations forbids configurations with toroidal current reversal, it is argued that these can be attained if an axisymmetric island system is allowed for in order to break the condition of nested magnetic surfaces. A number of results previously reported in the literature are discussed and reinterpreted under the proposed framework, providing some physical insight on the nature of equilibria with toroidal current reversal.
Experimental tests of a toroidal electrostatic analyzer
Young, D.T.; Ghielmetti, A.G.; Shelley, E.G.; Marshall, J.A.; Burch, J.L.; Booker, T.L.
1987-04-01
A toroidal electrostatic analyzer of a design suitable for space plasma instrumentation has been constructed and tested. Experimental results are compared with second-order ion optical theory and are in good agreement. Verifying the ion optics of the toroid was simplified by use of a position-sensing microchannel-plate detector mounted on a positioning system with three translational degrees of freedom located at the toroid exit. The toroidal analyzer described here is the first optical element in a fully toroidal mass spectrograph intended for analysis of kilovolt magnetospheric plasmas.
Electromagnetic effects on toroidal momentum transport
Mahmood, M. Ansar; Eriksson, A.; Weiland, J.
2010-12-15
A parametric study of electromagnetic effects on toroidal momentum transport has been performed. The work is based on a new version of the Weiland model where symmetry breaking toroidicity effects derived from the stress tensor have been taken into account. The model includes a self-consistent calculation of the toroidal momentum diffusivity, which contains both diagonal and off-diagonal contributions to the momentum flux. It is found that electromagnetic effects considerably increase the toroidal momentum pinch. They are sometimes strong enough to make the total toroidal momentum flux inward.
Perturbing macroscopic magnetohydrodynamic stability for toroidal plasmas
NASA Astrophysics Data System (ADS)
Comer, Kathryn J.
We have introduced a new perturbative technique to rapidly explore the dependence of long wavelength ideal magnetohydrodynamic (MHD) instabilities on equilibrium profiles, shaping properties, and wall parameters. Traditionally, these relations are studied with numerical parameter scans using computationally intensive stability codes. Our perturbative technique first finds the equilibrium and stability using traditional methods. Subsequent small changes in the original equilibrium parameters change the stability. We quickly find the new stability with an expansion of the energy principle, rather than with another run of the stability codes. We first semi-analytically apply the technique to the screw pinch after eliminating compressional Alfven wave effects. The screw pinch results validate the approach, but also indicate that allowable perturbations to equilibria with certain features may be restricted. Next, we extend the approach to toroidal geometry using experimental equilibria and a simple constructed equilibrium, with the ideal MHD stability code GATO. Stability properties are successfully predicted from perturbed toroidal equilibria when only the vacuum beyond the plasma is perturbed (through wall parameter variations), rather than the plasma itself. Small plasma equilibrium perturbations to both experimental and simple equilibria result in very large errors to the predicted stability, and valid results are found only over a narrow range of most perturbations. Despite the large errors produced when changing plasma parameters, the wall perturbations revealed two useful applications of this technique. Because the calculations are non-iterative matrix multiplications, the convergence issues that can disrupt a full MHD stability code are absent. Marginal stability, therefore, is much easier to find with the perturbative technique. Also, the perturbed results can be input as the initial guess for the eigenvalue for a full stability code, and improve subsequent
Electromagnetic Torque in Tokamaks with Toroidal Asymmetries
NASA Astrophysics Data System (ADS)
Logan, Nikolas Christopher
Toroidal rotation and rotation shear strongly influences stability and confinement in tokamaks. Breaking of the toroidal symmetry by fields orders of magnitude smaller than the axisymmetric field can, however, produce electromagnetic torques that significantly affect the plasma rotation, stability and confinement. These electromagnetic torques are the study of this thesis. There are two typical types of electromagnetic torques in tokamaks: 1) "resonant torques" for which a plasma current defined by a single toroidal and single poloidal harmonic interact with external currents and 2) "nonresonant torques" for which the global plasma response to nonaxisymmetric fields is phase shifted by kinetic effects that drive the rotation towards a neoclassical offset. This work describes the diagnostics and analysis necessary to evaluate the torque by measuring the rate of momentum transfer per unit area in the vacuum region between the plasma and external currents using localized magnetic sensors to measure the Maxwell stress. These measurements provide model independent quantification of both the resonant and nonresonant electromagnetic torques, enabling direct verification of theoretical models. Measured values of the nonresonant torque are shown to agree well with the perturbed equilibrium nonambipolar transport (PENT) code calculation of torque from cross field transport in nonaxisymmetric equilibria. A combined neoclassical toroidal viscosity (NTV) theory, valid across a wide range of kinetic regimes, is fully implemented for the first time in general aspect ratio and shaped plasmas. The code captures pitch angle resonances, reproducing previously inaccessible collisionality limits in the model. The complete treatment of the model enables benchmarking to the hybrid kinetic MHD stability codes MARS-K and MISK, confirming the energy-torque equivalency principle in perturbed equilibria. Experimental validations of PENT results confirm the torque applied by nonaxisymmetric
Toroidal momentum transport in a tokamak due to profile shearing
Buchholz, R.; Grosshauser, S. R.; Hornsby, W. A.; Migliano, P.; Peeters, A. G.; Camenen, Y.; Casson, F. J.
2014-06-15
The effect of profile shearing on toroidal momentum transport is studied in linear and non-linear gyro-kinetic simulations. Retaining the radial dependence of both plasma and geometry parameters leads to a momentum flux that has contributions both linear in the logarithmic gradients of density and temperature, as well as contributions linear in the derivatives of the logarithmic gradients. The effect of the turbulence intensity gradient on momentum transport is found to be small for the studied parameters. Linear simulations at fixed normalized toroidal wave number predict a weak dependence of the momentum flux on the normalized Larmor radius ρ{sub *}=ρ/R. Non-linear simulations, however, at sufficiently small ρ{sub *} show a linear scaling of the momentum flux with ρ{sub *}. The obtained stationary rotation gradients are in the range of, although perhaps smaller than, current experiments. For a reactor plasma, however, a rather small rotation gradient should result from profile shearing.
NASA Astrophysics Data System (ADS)
Yazgan, Efe; Taşci, Emre; Erkoç, Şakir
An algorithm to generate toroidal or helical cage structures has been developed. Any toroidal or helical structure can be generated following four stages. In the first stage a Fonseca type unit cell and its symmetrical counterpart is formed which represents one-fifth of a toroid. In the second stage one-fifth fragment of the torus is fully obtained by applying geometry optimization to the structure obtained in the first stage. In the third stage the torus fragment obtained in the second stage is reproduced five times and connected to each other to generate either toroidal or helical structure. In the last stage a final optimization process is reapplied to get the complete structure desired.
From non- to super-radiating manipulation of a dipolar emitter coupled to a toroidal metastructure.
Li, Jie; Xin, Xing-Xing; Shao, Jian; Wang, Ying-Hua; Li, Jia-Qi; Zhou, Lin; Dong, Zheng-Gao
2015-11-16
Toroidal dipolar response in a metallic metastructure, composed of double flat rings, is utilized to manipulate the radiation pattern of a single dipolar emitter (e.g., florescent molecule/atom or quantum dot). Strong Fano-type radiation spectrum can be obtained when these two coupling dipoles are spatially overlapped, leading to significant radiation suppression (so-called nonradiating source) attributed to the dipolar destructive interference. Moreover, this nonradiating configuration will become a directionally super-radiating nanoantenna after a radial displacement of the emitter with respect to the toroidal flat-ring geometry, which emits linearly polarized radiation with orders of power enhancement in a particular orientation. The demonstrated radiation characteristics from a toroidal-dipole-mediated dipolar emitter indicate a promising manipulation capability of the dipolar emission source by intriguing toroidal dipolar response. PMID:26698422
Toroidal modeling of plasma response and resonant magnetic perturbation field penetration
NASA Astrophysics Data System (ADS)
Liu, Y. Q.; Kirk, A.; Sun, Y.; Cahyna, P.; Chapman, I. T.; Denner, P.; Fishpool, G.; Garofalo, A. M.; Harrison, J. R.; Nardon, E.; the MAST Team
2012-12-01
The penetration dynamics of the resonant magnetic perturbation (RMP) field is simulated in the full toroidal geometry, under realistic plasma conditions in MAST experiments. The physics associated with several aspects of the RMP penetration—the plasma response and rotational screening, the resonant and non-resonant torques and the toroidal momentum balance—are highlighted. In particular, the plasma response is found to significantly amplify the non-resonant component of the RMP field for some of the MAST plasmas. A fast rotating plasma, in response to static external magnetic fields, experiences a more distributed electromagnetic torque due to the resonance with continuum waves in the plasma. At fast plasma flow (such as for the MAST plasma), the electromagnetic torque is normally dominant over the neoclassical toroidal viscous (NTV) torque. However, at sufficiently slow plasma flow, the NTV torque can play a significant role in the toroidal momentum balance, thanks to the precession drift resonance enhanced, so-called superbanana plateau regime.
NASA Astrophysics Data System (ADS)
Pfefferlé, D.; Graves, J. P.; Cooper, W. A.
2015-05-01
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).
Hollow nanotubular toroidal polymer microrings
NASA Astrophysics Data System (ADS)
Lee, Jiyeong; Baek, Kangkyun; Kim, Myungjin; Yun, Gyeongwon; Ko, Young Ho; Lee, Nam-Suk; Hwang, Ilha; Kim, Jeehong; Natarajan, Ramalingam; Park, Chan Gyung; Sung, Wokyung; Kim, Kimoon
2014-02-01
Despite the remarkable progress made in the self-assembly of nano- and microscale architectures with well-defined sizes and shapes, a self-organization-based synthesis of hollow toroids has, so far, proved to be elusive. Here, we report the synthesis of polymer microrings made from rectangular, flat and rigid-core monomers with anisotropically predisposed alkene groups, which are crosslinked with each other by dithiol linkers using thiol-ene photopolymerization. The resulting hollow toroidal structures are shape-persistent and mechanically robust in solution. In addition, their size can be tuned by controlling the initial monomer concentrations, an observation that is supported by a theoretical analysis. These hollow microrings can encapsulate guest molecules in the intratoroidal nanospace, and their peripheries can act as templates for circular arrays of metal nanoparticles.
Prospects for toroidal fusion reactors
Sheffield, J.; Galambos, J.D.
1994-06-01
Work on the International Thermonuclear Experimental Reactor (ITER) tokamak has refined understanding of the realities of a deuterium-tritium (D-T) burning magnetic fusion reactor. An ITER-like tokamak reactor using ITER costs and performance would lead to a cost of electricity (COE) of about 130 mills/kWh. Advanced tokamak physics to be tested in the Toroidal Physics Experiment (TPX), coupled with moderate components in engineering, technology, and unit costs, should lead to a COE comparable with best existing fission systems around 60 mills/kWh. However, a larger unit size, {approximately}2000 MW(e), is favored for the fusion system. Alternative toroidal configurations to the conventional tokamak, such as the stellarator, reversed-field pinch, and field-reversed configuration, offer some potential advantage, but are less well developed, and have their own challenges.
Experimental studies of compact toroids
Not Available
1991-01-01
The Berkeley Compact Toroid Experiment (BCTX) device is a plasma device with a Marshall-gun generated, low aspect ratio toroidal plasma. The device is capable of producing spheromak-type discharges and may, with some modification, produce low-aspect ratio tokamak configurations. A unique aspect of this experimenal devie is its large lower hybrid (LH) heating system, which consists of two 450MHz klystron tubes generating 20 megawatts each into a brambilla-type launching structure. Successful operation with one klystron at virtually full power (18 MW) has been accomplished with 110 {mu}s pulse length. A second klystron is currently installed in its socket and magnet but has not been added to the RF drive system. This report describes current activities and accomplishments and describes the anticipated results of next year's activity.
Toroidal midplane neutral beam armor and plasma limiter
Kugel, H.W.; Hand, S.W. Jr.; Ksayian, H.
1985-05-31
This invention contemplates an armor shield/plasma limiter positioned upon the inner wall of a toroidal vacuum chamber within which is magnetically confined an energetic plasma in a tokamak nuclear fusion reactor. The armor shield/plasma limiter is thus of a general semi-toroidal shape and is comprised of a plurality of adjacent graphite plates positioned immediately adjacent to each other so as to form a continuous ring upon and around the toroidal chamber's inner wall and the reactor's midplane coil. Each plate has a generally semi-circular outer circumference and a recessed inner portion and is comprised of upper and lower half sections positioned immediately adjacent to one another along the midplane of the plate. With the upper and lower half sections thus joined, a channel or duct is provided within the midplane of the plate in which a magnetic flux loop is positioned. The magnetic flux loop is thus positioned immediately adjacent to the fusing toroidal plasma and serves as a diagnostic sensor with the armor shield/plasma limiter minimizing the amount of power from the energetic plasma as well as from the neutral particle beams heating the plasma incident upon the flux loop.
Transport and Dynamics in Toroidal Fusion Systems
Schnack, Dalton D
2006-05-16
This document reports the successful completion of the OFES Theory Milestone for FY2005, namely, Perform parametric studies to better understand the edge physics regimes of laboratory experiments. Simulate at increased resolution (up to 20 toroidal modes), with density evolution, late into the nonlinear phase and compare results from different types of edge modes. Simulate a single case including a study of heat deposition on nearby material walls. The linear stability properties and nonlinear evolution of Edge Localized Modes (ELMs) in tokamak plasmas are investigated through numerical computation. Data from the DIII-D device at General Atomics (http://fusion.gat.com/diii-d/) is used for the magnetohydrodynamic (MHD) equilibria, but edge parameters are varied to reveal important physical effects. The equilibrium with very low magnetic shear produces an unstable spectrum that is somewhat insensitive to dissipation coefficient values. Here, linear growth rates from the non-ideal NIMROD code (http://nimrodteam.org) agree reasonably well with ideal, i.e. non-dissipative, results from the GATO global linear stability code at low toroidal mode number (n) and with ideal results from the ELITE edge linear stability code at moderate to high toroidal mode number. Linear studies with a more realistic sequence of MHD equilibria (based on DIII-D discharge 86166) produce more significant discrepancies between the ideal and non-ideal calculations. The maximum growth rate for the ideal computations occurs at toroidal mode index n=10, whereas growth rates in the non-ideal computations continue to increase with n unless strong anisotropic thermal conduction is included. Recent modeling advances allow drift effects associated with the Hall electric field and gyroviscosity to be considered. A stabilizing effect can be observed in the preliminary results, but while the distortion in mode structure is readily apparent at n=40, the growth rate is only 13% less than the non-ideal MHD
Toroidal cell and battery. [Patent application
Nagle, W.J.
1981-04-01
A toroidal storage battery designed to handle relatively high amp-hour loads is described. The cell includes a wound core disposed within a pair of toroidal channel shaped electrodes spaced apart by nylon insulator. The shape of the case electrodes of this toroidal cell allows a first planar doughnut shaped surface and the inner cylindrical case wall to be used as a first electrode and a second planar doughnut shaped surface and the outer cylindrical case wall to be used as a second electrode. Connectors may be used to stack two or more toroidal cells together by connecting substantially the entire surface area of the first electrode of a first cell to substantially the entire surface area of the second electrode of a second cell. The central cavity of each toroidal cell may be used as a conduit for pumping a fluid through the toroidal cell to thereby cool the cell. Official Gazette of the U.S. Patent and Trademark Office
ATF (Advanced Toroidal Facility) data management
Kannan, K.L.; Baylor, L.R.
1988-01-01
Data management for the Advanced Toroidal Facility (ATF), a stellarator located at Oak Ridge National Laboratory (ORNL), is provided by DMG, a locally developed, VAX-based software system. DMG is a data storage and retrieval software system that provides the user interface to ATF raw and analyzed data. Data are described in terms of data models and data types and are organized as signals into files, which are internally documented. The system was designed with user accessibility, software maintainability, and extensibility as primary goals. Extensibility features include compatibility with ATF as it moves from pulsed to steady-state operation and capability for use of the DMG system with experiments other than ATF. DMG is implemented as a run-time library of routines available as a shareable image. General-purpose and specialized data acquisition and analysis applications have been developed using the DMG system. This paper describes the DMG system and the interfaces to it. 4 refs., 2 figs.
Toroidal transformer design program with application to inverter circuitry
NASA Technical Reports Server (NTRS)
Dayton, J. A., Jr.
1972-01-01
Estimates of temperature, weight, efficiency, regulation, and final dimensions are included in the output of the computer program for the design of transformers for use in the basic parallel inverter. The program, written in FORTRAN 4, selects a tape wound toroidal magnetic core and, taking temperature, materials, core geometry, skin depth, and ohmic losses into account, chooses the appropriate wire sizes and number of turns for the center tapped primary and single secondary coils. Using the program, 2- and 4-kilovolt-ampere transformers are designed for frequencies from 200 to 3200 Hz and the efficiency of a basic transistor inverter is estimated.
Atomic physics effects on dissipative toroidal drift wave stability
Beer, M.A.; Hahm, T.S.
1992-02-01
The effects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissipative drift waves are investigated in toroidal geometry both numerically and analytically. For typical TFTR and TEXT edge parameters, overall linear stability is determined by the competition between the destabilizing influence of ionization and the stabilizing effect due to the electron temperature gradient. An analytical expression for the linear marginal stability condition, {eta}{sub e}{sup crit}, is derived. The instability is most likely to occur at the extreme edge of tokamaks with a significant ionization source and a steep electron density gradient.
Fabrication of toroidal composite pressure vessels. Final report
Dodge, W.G.; Escalona, A.
1996-11-24
A method for fabricating composite pressure vessels having toroidal geometry was evaluated. Eight units were fabricated using fibrous graphite material wrapped over a thin-walled aluminum liner. The material was wrapped using a machine designed for wrapping, the graphite material was impregnated with an epoxy resin that was subsequently thermally cured. The units were fabricated using various winding patterns. They were hydrostatically tested to determine their performance. The method of fabrication was demonstrated. However, the improvement in performance to weight ratio over that obtainable by an all metal vessel probably does not justify the extra cost of fabrication.
Implications of polarized DT plasmas for toroidal fusion reactors
Micklich, B.J.; Jassby, D.L.
1983-05-01
Spin polarization of the deuterons and tritons in a reacting plasma can result in an increase in the fusion reactivity and variation of the angular distribution of emission of the fusion neutrons. The increased fusion reactivity relaxes the confinement-temperature conditions for breakeven and ignition. We have determined the effect of varying the angular distribution of the fusion neutrons on the spatial distribution of fusion neturon current and flux at the first wall, on the global tritium breeding ratio, and on the first-wall radiation damage in low-aspect-ratio toroidal geometry.
Plastic Finite Element Analysis of D0 Toroid Iron Welds
Wands, R.; /Fermilab
1987-11-23
The assembly of the DO toroid iron involves the use of large groove welds to connect massive blocks of steel. These welds are very heavily constrained, and large thermal strains develop which have produced large cracks in the base metal near the weld. The effort to solve these problems has involved investigations of weld geometry, weld preparation, and the metallurgy of both the base metal and the welding rod. The purpose of this analysis was to compare the effects of two welding rods with markedly different yield strengths and post-yieding behaviour on the plastic strains developed in the base metal near the weld.
Two-Dimensional Ballooning Transformation with Applications to Toroidal Alfven Eigenmodes.
NASA Astrophysics Data System (ADS)
Zhang, Xiao-Dong
A general formulation for high-n (n is the toroidal mode number) modes in an axisymmetric toroidal plasma is presented, based on the two dimensional (2-D) ballooning transformation. It is shown that this formulation is more general than the conventional ballooning theory, and reduces to the conventional theory in a special case. Toroidal Alfven waves are studied using the 2 -D ballooning formulation. A perturbation theory is systematically developed for the continuum damping of the toroidal Alfven eigenmode (TAE). A formula, similar to the Fermi golden rule for decaying systems in quantum mechanics, is derived for the continuum damping rate of the TAE; the decay (damping) rate is expressed explicitly in terms of the coupling of the TAE to the continuum spectrum. Numerical results are obtained and compared to previous calculations. Kinetic effects on toroidal Alfven waves are studied. Multiple -gap coupling is included automatically by the 2-D ballooning formulation. A new branch of modes, the kinetic toroidal Alfven eigenmodes (KTAE), emerges as a result of kinetic effects. This mode resides just above the toroidal shear Alfven gap, and has a structure similar to the TAE. Numerical results for the kinetic damping rates for the TAE and the KTAE are obtained, and multiple-gap coupling effects are studied by comparing with the single gap theory of Mett and Mahajan (Phys. Fluids B 4 2885 (1992)).
Turbulent Equipartition Theory of Toroidal Momentum Pinch
T.S. Hahm, P.H. Diamond, O.D. Gurcan, and G. Rewaldt
2008-01-31
The mode-independet part of magnetic curvature driven turbulent convective (TuroCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14,072302 (2007)] which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of "magnetically weighted angular momentum density," nmi U|| R/B2, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustratd that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms which exist in a simpler geometry.
Turbulent equipartition theory of toroidal momentum pinch
Hahm, T. S.; Rewoldt, G.; Diamond, P. H.; Gurcan, O. D.
2008-05-15
The mode-independent part of the magnetic curvature driven turbulent convective (TurCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14, 072302 (2007)], which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of 'magnetically weighted angular momentum density', nm{sub i}U{sub parallel}R/B{sup 2}, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustrated that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms that exist in a simpler geometry.
Dynamics of toroidal spiral strings around five-dimensional black holes
Igata, Takahisa; Ishihara, Hideki
2010-02-15
We examine the separability of the Nambu-Goto equation for test strings in a shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In particular, for a 'Hopf loop' string which is a special class of the toroidal spiral strings, we show the complete separation of variables occurs in two cases, Kerr background and Kerr-AdS background with equal angular momenta. We also obtain the dynamical solution for the Hopf loop around a black hole and for the general toroidal spiral in Minkowski background.
NASA Astrophysics Data System (ADS)
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A.; Plecháč, Petr
2015-08-01
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Plecháč, Petr
2015-08-28
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
From the generalized uncertainty relations on fuzzy AdS 2 to the Poincaré geometry
NASA Astrophysics Data System (ADS)
Fakhri, H.; Hashemi, A.; Lotfizadeh, M.
2012-03-01
The positive and discrete unitary irreps of SU(1,1) are used to construct fuzzy (Euclidean) AdS 2. Two different types of uncertainty relation involving the Weyl-Heisenberg and a weaker type are studied. It is shown that there are no generalized coherent states which simultaneously minimize the Weyl-Heisenberg uncertainty relations among three non-commuting embedding coordinates of the fuzzy AdS 2. However, generalized squeezed states that simultaneously satisfy the three weaker uncertainty relations do exist, and reproduce some properties of the classical AdS 2. Up to a common scaling factor in terms of the irrep label, the expectation values of the non-commuting coordinates over such states are described in the same manner as the classical AdS 2, in terms of the Poincaré coordinates. The expectation values on the fuzzy AdS 2 tend to their corresponding values in the commutative limit.
Toroidal current asymmetry in tokamak disruptions
Strauss, H. R.
2014-10-15
It was discovered on JET that disruptions were accompanied by toroidal asymmetry of the toroidal plasma current I{sub ϕ}. It was found that the toroidal current asymmetry was proportional to the vertical current moment asymmetry with positive sign for an upward vertical displacement event (VDE) and negative sign for a downward VDE. It was observed that greater displacement leads to greater measured I{sub ϕ} asymmetry. Here, it is shown that this is essentially a kinematic effect produced by a VDE interacting with three dimensional MHD perturbations. The relation of toroidal current asymmetry and vertical current moment is calculated analytically and is verified by numerical simulations. It is shown analytically that the toroidal variation of the toroidal plasma current is accompanied by an equal and opposite variation of the toroidal current flowing in a thin wall surrounding the plasma. These currents are connected by 3D halo current, which is π/2 radians out of phase with the n = 1 toroidal current variations.
Electrostatics of a Family of Conducting Toroids
ERIC Educational Resources Information Center
Lekner, John
2009-01-01
An exact solution is found for the electrostatic potential of a family of conducting charged toroids. The toroids are characterized by two lengths "a" and "b", with "a" greater than or equal to "2b". They are closed, with no hole in the "doughnut". The results are obtained by considering the potential of two equal charges, displaced from the…
Closed expressions for the magnetic field of toroidal multipole configurations
Sheffield, G.V.
1983-04-01
Closed analytic expressions for the vector potential and the magnetic field for the lower order toroidal multipoles are presented. These expressions can be applied in the study of tokamak plasma cross section shaping. An example of such an application is included. These expressions also allow the vacuum fields required for plasma equilibrium to be specified in a general form independent of a particular coil configuration.
Antenna excitation of drift wave in a toroidal plasma
Diallo, A.; Ricci, P.; Fasoli, A.; Furno, I.; Labit, B.; Mueller, S. H.; Podesta, M.; Poli, F. M.; Skiff, F.
2007-10-15
In a magnetized toroidal plasma, an antenna tunable in vertical wave number is used to excite density perturbations. Coherent detection is performed by means of Langmuir probes to directly determine both the wave vector and the plasma response induced by the antenna. Comparison between the theoretical density response predicted by the generalized Hasegawa-Wakatani model, and the experimentally determined density response enables us the identification of one peak of the plasma response as a drift wave.
Radial Eigenmodes for a Toroidal Waveguide with Rectangular Cross Section
Rui Li
2012-07-01
In applying mode expansion to solve the CSR impedance for a section of toroidal vacuum chamber with rectangular cross section, we identify the eigenvalue problem for the radial eigenmodes which is different from that for cylindrical structures. In this paper, we present the general expressions of the radial eigenmodes, and discuss the properties of the eigenvalues on the basis of the Sturm-Liouville theory.
Cutoff frequency of toroidal plasma waveguide
Zakeri-Khatir, H.; Aghamir, F. M.
2015-02-15
The cutoff frequencies of E and H-modes of empty and plasma filled toroidal waveguides are evaluated. The effects of space curvature and plasma density on cutoff frequencies for both modes are investigated. Using a suitable variable change, a scalar wave equation in the direction of propagation was obtained. The study indicates that the curvature in the direction of wave propagation in toroidal waveguide has an analogous effect as a straight waveguide filled with anisotropic media. The Rayleigh-Schrodinger perturbation method was employed to solve for cutoff frequencies in the first order of approximation. In the limit of small space curvature, the toroidal waveguide cutoff frequencies for both E and H-modes approach those of TM and TE modes of empty cylindrical waveguide with a radius equal to toroidal waveguide minor radius. The analysis shows that the curvature in the direction of propagation in toroidal waveguides leads to the removal of the degeneracy between E and H-modes.
Asymmetric Magnon Excitation by Spontaneous Toroidal Ordering
NASA Astrophysics Data System (ADS)
Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi
2016-05-01
The effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from the antisymmetric spin-orbit coupling and the multiorbital correlation effect. We show that the model exhibits a Néel-type antiferromagnetic order, which simultaneously accompanies a ferroic toroidal order. We find that the occurrence of toroidal order modulates the magnon dispersion in an asymmetric way with respect to the wave number: a toroidal dipole order on the zigzag chain leads to a band-bottom shift, while a toroidal octupole order on the honeycomb lattice gives rise to a valley splitting. These asymmetric magnon excitations could be a source of unusual magnetic responses, such as nonreciprocal magnon transport. A variety of modulations are discussed while changing the lattice and magnetic symmetries. The implications regarding candidate materials for asymmetric magnon excitations are presented.
Development of Toroidal Core Transformers
Leon, Francisco
2014-05-31
The original objective of this project was to design, build and test a few prototypes of singlephase dry-type distribution transformers of 25 kVA, 2.4 kV primary to 120 V transformers using cores made of a continuous steel strip shaped like a doughnut (toroid). At different points during the development of the project, the scope was enhanced to include the more practical case of a 25 kVA transformer for a 13.8 kV primary system voltage. Later, the scope was further expanded to design and build a 50 kVA unit to transformer voltage from 7.62 kV to 2x120 V. This is a common transformer used by Con Edison of New York and they are willing to test it in the field. The project officially started in September 2009 and ended in May 2014. The progress was reported periodically to DOE in eighteen quarterly reports. A Continuation Application was submitted to DOE in June 2010. In May 2011 we have requested a non-cost extension of the project. In December 2011, the Statement of Project Objectives (SOPO) was updated to reflect the real conditions and situation of the project as of 2011. A second Continuation Application was made and funding was approved in 2013 by DOE and the end date was extended to May 2014.The technical challenges that were overcome in this project include: the development of the technology to pass the impulse tests, derive a model for the thermal performance, produce a sound mechanical design, and estimate the inrush current. However, the greatest challenge that we faced during the development of the project was the complications of procuring the necessary parts and materials to build the transformers. The actual manufacturing process is relatively fast, but getting all parts together is a very lengthy process. The main products of this project are two prototypes of toroidal distribution transformers of 7.62 kV (to be used in a 13.8 kV system) to 2x120 V secondary (standard utilization voltage); one is rated at 25 kVA and the other at 50 kVA. The 25 k
Turbulent Transport in Fusion Plasmas, Effects of Toroidicity and Fluid Closure
Weiland, Jan
2009-11-10
Basic aspects of turbulent transport in toroidal magnetized plasmas are discussed. In particular Kadomtsev's mixing length estimate is found to work well for the Cyclone base case at the experimental gradient. Generalizations to include non-Markovian effects and off diagonal fluxes are given. The importance of toroidal effects is stressed These enter particularly strongly in convective or off diagonal fluxes. This feature applies also to momentum ttransport.
Tokamak with mechanical compression of toroidal magnetic field
Ohkawa, Tihiro
1981-01-01
A tokamak apparatus includes a pressure vessel for defining a reservoir and confining liquid therein. A collapsible toroidal liner disposed within the pressure vessel defines a toroidal space within the liner. Liquid metal fills the reservoir outside said liner. A toroidal magnetic field is developed within the toroidal space about the major axis thereof. A toroidal plasma is developed within the toroidal space about the major axis thereof. Pressure is applied to the liquid metal to collapse the liner and reduce the volume of the toroidal space, thereby increasing the toroidal magnetic flux density therein.
NCSX Toroidal Field Coil Design
Kalish, M.; Rushinski, J.; Myatt, L.; Brooks, A.; Dahlgren, F.; Chrzanowski, J.; Reiersen, W.; Freudenberg, K.
2005-10-07
The National Compact Stellarator Experiment (NCSX) is an experimental device whose design and construction is underway at the Department of Energy's Princeton Plasma Physics Laboratory (PPPL). The primary coil systems for the NCSX device consist of the twisted plasma-shaping Modular Coils, the Poloidal Field Coils, and the Toroidal Field (TF) Coils. The TF Coils are D-shaped coils wound from hollow copper conductor, and vacuum impregnated with a glass-epoxy resin system. There are 18 identical, equally spaced TF coils providing 1/R field at the plasma. They operate within a cryostat, and are cooled by LN2, nominally, to 80K. Wedge shaped castings are assembled to the inboard face of these coils, so that inward radial loads are reacted via the nesting of each of the coils against their adjacent partners. This paper outlines the TF Coil design methodology, reviews the analysis results, and summarizes how the design and analysis support the design requirements.
Davies, J. A.; Perry, C. H.; Harrison, R. A.; Trines, R. M. G. M.; Lugaz, N.; Möstl, C.; Liu, Y. D.; Steed, K.
2013-11-10
The twin-spacecraft STEREO mission has enabled simultaneous white-light imaging of the solar corona and inner heliosphere from multiple vantage points. This has led to the development of numerous stereoscopic techniques to investigate the three-dimensional structure and kinematics of solar wind transients such as coronal mass ejections (CMEs). Two such methods—triangulation and the tangent to a sphere—can be used to determine time profiles of the propagation direction and radial distance (and thereby radial speed) of a solar wind transient as it travels through the inner heliosphere, based on its time-elongation profile viewed by two observers. These techniques are founded on the assumption that the transient can be characterized as a point source (fixed φ, FP, approximation) or a circle attached to Sun-center (harmonic mean, HM, approximation), respectively. These geometries constitute extreme descriptions of solar wind transients, in terms of their cross-sectional extent. Here, we present the stereoscopic expressions necessary to derive propagation direction and radial distance/speed profiles of such transients based on the more generalized self-similar expansion (SSE) geometry, for which the FP and HM geometries form the limiting cases; our implementation of these equations is termed the stereoscopic SSE method. We apply the technique to two Earth-directed CMEs from different phases of the STEREO mission, the well-studied event of 2008 December and a more recent event from 2012 March. The latter CME was fast, with an initial speed exceeding 2000 km s{sup –1}, and highly geoeffective, in stark contrast to the slow and ineffectual 2008 December CME.
NASA Astrophysics Data System (ADS)
Davies, J. A.; Perry, C. H.; Trines, R. M. G. M.; Harrison, R. A.; Lugaz, N.; Möstl, C.; Liu, Y. D.; Steed, K.
2013-11-01
The twin-spacecraft STEREO mission has enabled simultaneous white-light imaging of the solar corona and inner heliosphere from multiple vantage points. This has led to the development of numerous stereoscopic techniques to investigate the three-dimensional structure and kinematics of solar wind transients such as coronal mass ejections (CMEs). Two such methods—triangulation and the tangent to a sphere—can be used to determine time profiles of the propagation direction and radial distance (and thereby radial speed) of a solar wind transient as it travels through the inner heliosphere, based on its time-elongation profile viewed by two observers. These techniques are founded on the assumption that the transient can be characterized as a point source (fixed phi, FP, approximation) or a circle attached to Sun-center (harmonic mean, HM, approximation), respectively. These geometries constitute extreme descriptions of solar wind transients, in terms of their cross-sectional extent. Here, we present the stereoscopic expressions necessary to derive propagation direction and radial distance/speed profiles of such transients based on the more generalized self-similar expansion (SSE) geometry, for which the FP and HM geometries form the limiting cases; our implementation of these equations is termed the stereoscopic SSE method. We apply the technique to two Earth-directed CMEs from different phases of the STEREO mission, the well-studied event of 2008 December and a more recent event from 2012 March. The latter CME was fast, with an initial speed exceeding 2000 km s-1, and highly geoeffective, in stark contrast to the slow and ineffectual 2008 December CME.
Toroidal solar collection and energy storage apparatus
Wasserman, K.J.
1980-09-23
Vehicular tires are generally toroidal heat collection elements of a solar heating system. Liquid or gaseous fluid flow is circulated between the tires and a space to be heated for transferring the heat from the tires to the space. The tires are generally vertically stacked within a thermally insulated enclosure which includes a double glazed window located so that solar rays impinge on and heat the tires. Heat storage media such as water, rock or pebble beds, or phase change material in an elongated coiled jacket may be provided within the tires. Downwardly inclined vanes either partially cut from the tire walls or attached to the tires or attached to separators between the tires, provide additional surface area to absorb the solar radiation and to also direct airflow radially inward into the center of the tires. When the vanes are formed by cutting from the tires, they are naturally hinged for elevational angulation and a cable linkage is provided to simultaneously adjust the elevation of the vanes or to close the apertures in the tire walls formed by the cutting out of the vanes. The window is selectively obstructed from light and heat transfer therethrough either by means of a removeable cover or by thermally insulating sliding opaque sheets within the walls of the enclosure which are selectively positionable between the double glazing.
Poloidal field amplification in a coaxial compact toroid accelerator
NASA Astrophysics Data System (ADS)
Horton, R. D.; Hwang, D. Q.; Howard, S.; Brockington, S. J.; Evans, R. W.
2008-09-01
The Compact Toroid Injection Experiment (CTIX) produces spheromak-like compact toroids (SCTs) without external power switching, initiating a discharge by pulsed gas injection into a formation region containing a seed magnetic field generated by a solenoidal coil. After formation, the plasma is driven by an inductively delayed capacitor bank into an acceleration region, where surface axial and toroidal magnetic fields are measured at several axial positions. Due to strong eddy-current effects, formation-region magnetic field cannot be simply computed; instead, it is measured using the response of axial and radial test coils in the formation region to short solenoid test current pulses. A temporal and spatial reconstruction method is developed allowing formation-region field to be computed from the test-coil data for any CTIX discharge of identical solenoid geometry. By varying the peak value and timing of solenoidal current, curves of peak accelerator-region field as a function of initial formation-region field are developed. Curves of peak accelerator-region axial magnetic field are thereby found to be highly nonlinear functions of formation-region field, showing a threshold value for the formation-region field of approximately 5 G, above which acceleration-region field saturates at values between 2 and 12 kG. The direction of acceleration-region axial field reverses sign when the direction of solenoid current is reversed. Saturated accelerator-region axial field is a function of axial position and accelerator voltage, and is typically comparable to toroidal field at the same location. The ratio of accelerator-region to formation-region axial field commonly exceeds 1000 near the onset of saturation. This large amplification is of practical advantage for delayed plasma breakdown on CTIX, allowing a modest seed field to produce high poloidal fields, which are necessary for intense SCT acceleration. The results may also provide a useful benchmark for numerical
Li, Hai-ming; Liu, Shao-bin Liu, Si-yuan; Ding, Guo-wen; Yang, Hua; Yu, Zhi-yang; Zhang, Hai-feng; Wang, Shen-yun
2015-02-23
In this paper, a low-loss and high transmission analogy of electromagnetically induced transparency based on electric toroidal dipolar response is numerically and experimentally demonstrated. It is obtained by the excitation of the low-loss electric toroidal dipolar response, which confines the magnetic field inside a dielectric substrate with toroidal geometry. The metamaterial electromagnetically induced transparency (EIT) structure is composed of the cut wire and asymmetric split-ring resonators. The transmission level is as high as 0.88, and the radiation loss is greatly suppressed, which can be proved by the surface currents distributions, the magnetic field distributions, and the imaginary parts of the effective permeability and permittivity. It offers an effective way to produce low-loss and high transmission metamaterial EIT.
Dual-band toroidal-dipole-induced transparency in optical regime
NASA Astrophysics Data System (ADS)
Li, Jie; Dong, Zheng-Gao; Zhu, Ming-Jie; Shao, Jian; Wang, Ying-Hua; Li, Jia-Qi
2016-09-01
The interference between toroidal and electric dipoles in the optical regime is investigated in a metallic composite metastructure composed of a 12-fold double-bar and an upright rod. It shows that toroidal and electric dipoles can be simultaneously excited, exhibiting a plasmon analog of electromagnetically induced transparency (EIT) and suppressing the far-field radiation. By shifting the upright rod transversally, another transparency window emerges due to the asymmetry of the geometry, resulting in dual-band EIT-like behavior. The result not only contributes to the understanding of optical toroidal dipoles, but also creates the possibility of designing optical devices based on the dual-band EIT-like effect.
Energy Science and Technology Software Center (ESTSC)
1991-05-01
Version 00 MORSE-CGA was developed to add the capability of modelling rectangular lattices for nuclear reactor cores or for multipartitioned structures. It thus enhances the capability of the MORSE code system. The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. It has been designed as a tool for solving most shielding problems. Through the use of multigroup cross sections, the solution of neutron, gamma-ray, or coupled neutron-gamma-ray problems may be obtainedmore » in either the forward or adjoint mode. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry may be used with an albedo option available at any material surface. Isotropic or anisotropic scattering up to a P16 expansion of the angular distribution is allowed.« less
Zonal Toroidal Harmonic Expansions of External Gravitational Fields for Ring-like Objects
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2016-08-01
We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace’s equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000–10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.
NASA Astrophysics Data System (ADS)
Lee, H. H.; Seol, J.; Ko, W. H.; Terzolo, L.; Aydemir, A. Y.; In, Y.; Ghim, Y.-c.; Lee, S. G.
2016-08-01
Effects of neoclassical toroidal viscosity (NTV) induced by intrinsic error fields and toroidal field ripple on cocurrent toroidal rotation in H-mode tokamak plasmas are investigated. It is expected that large NTV torque can be localized at the edge region through the 1/ν-regime in the vicinity of E r ˜ 0 in the cocurrent rotating H-mode plasma. Numerical simulation on toroidal rotation demonstrates that the edge localized NTV torque determined by the intrinsic error fields and toroidal field ripples in the level of most tokamaks can damp the toroidal rotation velocity over the whole region while reducing the toroidal rotation pedestal which is clearly observed in Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak. It is found that the NTV torque changes the toroidal rotation gradient in the pedestal region dramatically, but the toroidal rotation profile in the core region responds rigidly without a change in the gradient. On the other hand, it shows that the NTV torque induced by the intrinsic error fields and toroidal field ripple in the level of the KSTAR tokamak, which are expected to be smaller than most tokamaks by at least one order of magnitude, is negligible in determining the toroidal rotation velocity profile. Experimental observation on the toroidal rotation change by the externally applied nonaxisymmetric magnetic fields on KSTAR also suggests that NTV torque arising from nonaxisymmetric magnetic fields can damp the toroidal rotation over the whole region while diminishing the toroidal rotation pedestal.
Axisymmetric curvature-driven instability in a model divertor geometry
Farmer, W. A.; Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, California 94550 ; Ryutov, D. D.
2013-09-15
A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.
Tokamak with in situ magnetohydrodynamic generation of toroidal magnetic field
Schaffer, Michael J.
1986-01-01
A tokamak apparatus includes an electrically conductive metal pressure vessel for defining a chamber and confining liquid therein. A liner disposed within said chamber defines a toroidal space within the liner and confines gas therein. The metal vessel provides an electrically conductive path linking the toroidal space. Liquid metal is forced outwardly through the chamber outside of the toroidal space to generate electric current in the conductive path and thereby generate a toroidal magnetic field within the toroidal space. Toroidal plasma is developed within the toroidal space about the major axis thereof.
Steady state compact toroidal plasma production
Turner, William C.
1986-01-01
Apparatus and method for maintaining steady state compact toroidal plasmas. A compact toroidal plasma is formed by a magnetized coaxial plasma gun and held in close proximity to the gun electrodes by applied magnetic fields or magnetic fields produced by image currents in conducting walls. Voltage supply means maintains a constant potential across the electrodes producing an increasing magnetic helicity which drives the plasma away from a minimum energy state. The plasma globally relaxes to a new minimum energy state, conserving helicity according to Taylor's relaxation hypothesis, and injecting net helicity into the core of the compact toroidal plasma. Controlling the voltage so as to inject net helicity at a predetermined rate based on dissipative processes maintains or increases the compact toroidal plasma in a time averaged steady state mode.
Bow-shaped toroidal field coils
Bonanos, P.
1981-05-01
Design features of Bow-Shaped Toroidal Field Coils are described and compared with circular and D shaped coils. The results indicate that bow coils can produce higher field strengths, store more energy and be made demountable. The design offers the potential for the production of ultrahigh toroidal fields. Included are representative coil shapes and their engineering properties, a suggested structural design and an analysis of a specific case.
A toroidal trap for cold {}^{87}{Rb} atoms using an rf-dressed quadrupole trap
NASA Astrophysics Data System (ADS)
Chakraborty, A.; Mishra, S. R.; Ram, S. P.; Tiwari, S. K.; Rawat, H. S.
2016-04-01
We demonstrate the trapping of cold {}87{Rb} atoms in a toroidal geometry using a radio frequency (rf) dressed quadrupole magnetic trap formed by superposing a strong rf-field on a quadrupole trap. This rf-dressed quadrupole trap has the minimum potential away from the quadrupole trap centre on a circular path which facilitates trapping in toroidal geometry. In these experiments, the laser cooled atoms were first trapped in a quadrupole trap, then cooled evaporatively using a weak rf-field, and finally trapped in an rf-dressed quadrupole trap. The radius of the toroid could be varied by varying the frequency of the dressing rf-field. It has also been demonstrated that a single rf source and an antenna can be used for the rf-evaporative cooling as well as for the rf-dressing of atoms. The atoms trapped in the toroidal trap may have applications in the realization of an atom gyroscope as well as in studying the quantum gases in low dimensions.
NASA Astrophysics Data System (ADS)
Beidler, Matthew; Cassak, Paul; Jardin, Stephen; Ferraro, Nathaniel
2015-11-01
The sawtooth crash in tokamaks limits the core temperature, harms confinement, and seeds disruptions. A predictive capability of its ramifications has been elusive. Extended-MHD physics is needed to properly analyze the magnetic reconnection that occurs during the crash phase, but it has only recently been integrated into codes using a toroidal geometry. In this study, we employ the three-dimensional toroidal, extended-MHD code M3D-C1 to study reconnection during the sawtooth crash. We study the nonlinear evolution of a test equilibrium in a non-reduced field representation for resistive-MHD and the two-fluid model. We find that the toroidal mode growth rates for the two-fluid reconnection process exhibit a nonlinear acceleration and greatly exceed that of a similar resistive MHD model, more closely in line with experimental results. Furthermore, by sampling the two-fluid simulation data in the plane perpendicular to the helical (m,n) =(1,1) mode, we present the first observation of the quadrupole out-of-plane magnetic field appearing during sawtooth reconnection with the Hall term. We also explore how reconnection as viewed in the helically perpendicular plane varies toroidally, which affects the symmetry of the reconnection geometry and the local diamagnetic effects.
Low-n shear Alfven spectra in axisymmetric toroidal plasmas
Cheng, C.Z.; Chance, M.S.
1985-11-01
In toroidal plasmas, the toroidal magnetic field is nonuniform over a magnetic surface and causes coupling of different poloidal harmonics. It is shown both analytically and numerically that the toroidicity not only breaks up the shear Alfven continuous spectrum, but also creates new, discrete, toroidicity-induced shear Alfven eigenmodes with frequencies inside the continuum gaps. Potential applications of the low-n toroidicity-induced shear Alfven eigenmodes on plasma heating and instabilities are addressed. 17 refs., 4 figs.
Finite beta plasma equilibrium in toroidally linked mirrors
Ilgisonis, V.I.; Berk, H.L.; Pastukhov, V.P.
1993-07-01
The problem of finite pressure plasma equilibrium in a system with closed magnetic field lines consisting of quadrupole mirrors linked by simple toroidal cells with elliptical cross-sections is analyzed. An appropriate analytical procedure is developed, that uses conformal mapping techniques, which enables one to obtain the magnetic field structure for the free boundary equilibrium problem. This method has general applicability for finding analytic solutions of the two-dimensional Dirichlet problem outside of an arbitrary closed contour. Using this method, the deformations of the plasma equilibrium configuration due to finite plasma pressure in the toroidal cell are calculated analytically to the second order in {lambda}-expansion, where {lambda} {approximately} {beta}/{epsilon}E, {beta} is the ratio of plasma pressure to the magnetic field pressure, {epsilon} is the inverse aspect ratio and E is the ellipticity of the plasma cross-section. The outer displacement of the plasma column is shown to depend nonlinearly on the increase of plasma pressure, and does not prevent the achievement of substantial {beta} {approximately} 10% in the toroidal cells.
Varma, Archana; Huang, Kerwyn Casey; Young, Kevin D
2008-03-01
In Escherichia coli, division site placement is regulated by the dynamic behavior of the MinCDE proteins, which oscillate from pole to pole and confine septation to the centers of normal rod-shaped cells. Some current mathematical models explain these oscillations by considering interactions among the Min proteins without recourse to additional localization signals. So far, such models have been applied only to regularly shaped bacteria, but here we test these models further by employing aberrantly shaped E. coli cells as miniature reactors. The locations of MinCDE proteins fused to derivatives of green fluorescent protein were monitored in branched cells with at least three conspicuous poles. MinCDE most often moved from one branch to another in an invariant order, following a nonreversing clockwise or counterclockwise direction over the time periods observed. In cells with two short branches or nubs, the proteins oscillated symmetrically from one end to the other. The locations of FtsZ rings were consistent with a broad MinC-free zone near the branch junctions, and Min rings exhibited the surprising behavior of moving quickly from one possible position to another. Using a reaction-diffusion model that reproduces the observed MinCD oscillations in rod-shaped and round E. coli, we predict that the oscillation patterns in branched cells are a natural response of Min behavior in cellular geometries having different relative branch lengths. The results provide further evidence that Min protein oscillations act as a general cell geometry detection mechanism that can locate poles even in branched cells. PMID:18178745
Rotation shear induced fluctuation decorrelation in a toroidal plasma
Hahm, T.S.
1994-06-01
The enhanced decorrelation of fluctuations by the combined effects of the E {times} B flow (V{sub E}) shear, the parallel flow (V{sub {parallel}}) shear, and the magnetic shear is studied in toroidal geometry. A two-point nonlinear analysis previously utilized in a cylindrical model shows that the reduction of the radial correlation length below its ambient turbulence value ({Delta}r{sub 0}) is characterized by the ratio between the shearing rate {omega}{sub s} and the ambient turbulence scattering rate {Delta}{omega}{sub T}. The derived shearing rate is given by {omega}{sub s}{sup 2} = ({Delta}r{sub 0}){sup 2}[1/{Delta}{phi}{sup 2}{l_brace}{partial_derivative}/{partial_derivative}r(qV{sub E}/r){r_brace}{sup 2} + 1/{Delta}{eta}{sup 2}{l_brace}{partial_derivative}/{partial_derivative}r(V{parallel}/qR){r_brace}{sup 2}], where {Delta}{phi} and {Delta}{eta} are the correlation angles of the ambient turbulence along the toroidal and parallel directions. This result deviates significantly from the cylindrical result for high magnetic shear or for ballooning-like fluctuations. For suppression of flute-like fluctuations, only the radial shear of qV{sub E}/r contributes, and the radial shear of V{parallel}/qR is irrelevant regardless of the plasma rotation direction.
Noncommutative Geometry and Physics
NASA Astrophysics Data System (ADS)
Connes, Alain
2006-11-01
In this very short essay we shall describe a "spectral" point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a "sum over geometries" on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of "observables" in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.
Neoclassical transport in toroidal plasmas with nonaxisymmetric flux surfaces
NASA Astrophysics Data System (ADS)
Belli, E. A.; Candy, J.
2015-05-01
The capability to treat nonaxisymmetric flux surface geometry has been added to the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010). Geometric quantities (i.e. metric elements) are supplied by a recently-developed local 3D equilibrium solver, allowing neoclassical transport coefficients to be systematically computed while varying the 3D plasma shape in a simple and intuitive manner. Code verification is accomplished via detailed comparison with 3D Pfirsch-Schlüter theory. A discussion of the various collisionality regimes associated with 3D transport is given, with an emphasis on non-ambipolar particle flux, neoclassical toroidal viscosity, energy flux and bootstrap current. Finally, we compute the transport in the presence of ripple-type perturbations in a DIII-D-like H-mode edge plasma.
Compact toroidal ion-trap design and optimization
Madsen, M. J.; Gorman, C. H.
2010-10-15
We present the design of a type of compact toroidal, or 'halo', ion trap. Such traps may be useful for mass spectrometry, studying small Coulomb cluster rings, quantum-information applications, or other quantum simulations where a ring topology is of interest. We present results from a Monte Carlo optimization of the trap design parameters using finite-element analysis simulations that minimize higher-order anharmonic terms in the trapping pseudopotential, while maintaining complete control over ion placement at the pseudopotential node in three dimensions using static bias fields. These simulations are based on a practical electrode design using readily available parts, yet can be easily scaled to any size trap with similar electrode spacings. We also derive the conditions for a crystal structure transition for two ions in the compact halo trap, the first nontrivial transition for Coulomb crystals in this geometry.
Long-wavelength microinstabilities in toroidal plasmas
Tang, W.W.; Rewoldt, G.
1993-01-01
Realistic kinetic toroidal eigenmode calculations have been carried out to support a proper assessment of the influence of long-wavelength microturbulence on transport in tokamak plasmas. In order to efficiently evaluate large-scale kinetic behavior extending over many rational surfaces, significant improvements have been made to a toroidal finite element code used to analyze the fully two-dimensional (r,[theta]) mode structures of trapped-ion and toroidal ion temperature gradient (ITG) instabilities. It is found that even at very long wavelengths, these eigenmodes exhibit a strong ballooning character with the associated radial structure relatively insensitive to ion Landau damping at the rational surfaces. In contrast to the long-accepted picture that the radial extent of trapped-ion instabilities is characterized by the ion-gyroradius-scale associated with strong localization between adjacent rational surfaces, present results demonstrate that under realistic conditions, the actual scale is governed by the large-scale variations in the equilibrium gradients. Applications to recent measurements of fluctuation properties in TFTR L-mode plasmas indicate that the theoretical trends appear consistent with spectral characteristics as well as rough heuristic estimates of the transport level. Benchmarking calculations in support of the development of a three-dimensional toroidal gyrokinetic code indicate reasonable agreement with respect to both the properties of the eigenfunctions and the magnitude of the eigenvalues during the linear phase of the simulations of toroidal ITG instabilities.
Long-wavelength microinstabilities in toroidal plasmas
Tang, W.W.; Rewoldt, G.
1993-01-01
Realistic kinetic toroidal eigenmode calculations have been carried out to support a proper assessment of the influence of long-wavelength microturbulence on transport in tokamak plasmas. In order to efficiently evaluate large-scale kinetic behavior extending over many rational surfaces, significant improvements have been made to a toroidal finite element code used to analyze the fully two-dimensional (r,{theta}) mode structures of trapped-ion and toroidal ion temperature gradient (ITG) instabilities. It is found that even at very long wavelengths, these eigenmodes exhibit a strong ballooning character with the associated radial structure relatively insensitive to ion Landau damping at the rational surfaces. In contrast to the long-accepted picture that the radial extent of trapped-ion instabilities is characterized by the ion-gyroradius-scale associated with strong localization between adjacent rational surfaces, present results demonstrate that under realistic conditions, the actual scale is governed by the large-scale variations in the equilibrium gradients. Applications to recent measurements of fluctuation properties in TFTR L-mode plasmas indicate that the theoretical trends appear consistent with spectral characteristics as well as rough heuristic estimates of the transport level. Benchmarking calculations in support of the development of a three-dimensional toroidal gyrokinetic code indicate reasonable agreement with respect to both the properties of the eigenfunctions and the magnitude of the eigenvalues during the linear phase of the simulations of toroidal ITG instabilities.
Tokamak with liquid metal for inducing toroidal electrical field
Ohkawa, Tihiro
1981-01-01
A tokamak apparatus includes a vessel for defining a reservoir and confining liquid therein. A toroidal liner disposed within said vessel defines a toroidal space within the liner confines gas therein. Liquid metal fills the reservoir outside the liner. A magnetic field is established in the liquid metal to develop magnetic flux linking the toroidal space. The gas is ionized. The liquid metal and the toroidal space are moved relative to one another transversely of the space to generate electric current in the ionized gas in the toroidal space about its major axis and thereby heat plasma developed in the toroidal space.
Bose-Einstein condensates in toroidal traps: Instabilities, swallow-tail loops, and self-trapping
NASA Astrophysics Data System (ADS)
Baharian, Soheil; Baym, Gordon
2013-01-01
We study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a “disorder” potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.
Toroidal equilibrium with low frequency wave driven currents
Ehst, D.A.
1984-12-01
In the absence of an emf the parallel current, j/sub parallel/, in a steady state tokamak will consist of a neoclassical portion plus a wave-driven contribution. Using the drift kinetic equation, the quasilinear (wave-driven) current is computed for high phase speed waves in a torus, and this is combined with the neoclassical term to obtain the general expression for the flux surface average
Quasisymmetric toroidal plasmas with large mean flows
Sugama, H.; Watanabe, T.-H.; Nunami, M.; Nishimura, S.
2011-08-15
Geometric conditions for quasisymmetric toroidal plasmas with large mean flows on the order of the ion thermal speed are investigated. Equilibrium momentum balance equations including the inertia term due to the large flow velocity are used to show that, for rotating quasisymmetric plasmas with no local currents crossing flux surfaces, all components of the metric tensor should be independent of the toroidal angle in the Boozer coordinates, and consequently these systems need to be rigorously axisymmetric. Unless the local radial currents vanish, the Boozer coordinates do not exist and the toroidal flow velocity cannot take any value other than a very limited class of eigenvalues corresponding to very rapid rotation especially for low beta plasmas.
Ferroic nature of magnetic toroidal order.
Zimmermann, Anne S; Meier, Dennis; Fiebig, Manfred
2014-01-01
Electric dipoles and ferroelectricity violate spatial inversion symmetry, and magnetic dipoles and ferromagnetism break time-inversion symmetry. Breaking both symmetries favours magnetoelectric charge-spin coupling effects of enormous interest, such as multiferroics, skyrmions, polar superconductors, topological insulators or dynamic phenomena such as electromagnons. Extending the rationale, a novel type of ferroic order violating space- and time-inversion symmetry with a single order parameter should exist. This existence is fundamental and the inherent magnetoelectric coupling is technologically interesting. A uniform alignment of magnetic vortices, called ferrotoroidicity, was proposed to represent this state. Here we demonstrate that the magnetic vortex pattern identified in LiCoPO4 exhibits the indispensable hallmark of such a ferroic state, namely hysteretic poling of ferrotoroidic domains in the conjugate toroidal field, along with a distinction of toroidal from non-toroidal poling effects. This consolidates ferrotoroidicity as fourth form of ferroic order. PMID:25190207
Toroidal Precession as a Geometric Phase
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Colloquium: Geometry and optimal packing of twisted columns and filaments
NASA Astrophysics Data System (ADS)
Grason, Gregory M.
2015-04-01
This Colloquium presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing nontrivial textures, focusing, in particular, on the common motifs of twisted and toroidal structures. The mathematical framework is presented that relates spacing between linelike, filamentous elements to their backbone orientations, highlighting the explicit connection between the interfilament metric properties and the geometry of non-Euclidean surfaces. The consequences of the hidden connection between packing in twisted filament bundles and packing on positively curved surfaces, like the Thomson problem, are demonstrated for the defect-riddled ground states of physical models of twisted filament bundles. The connection between the "ideal" geometry of fibrations of curved three-dimensional space, including the Hopf fibration, and the non-Euclidean constraints of filament packing in twisted and toroidal bundles is presented, with a focus on the broader dependence of metric geometry on the simultaneous twisting and folding of multifilament bundles.
The effect of sheared toroidal rotation on pressure driven magnetic islands in toroidal plasmas
NASA Astrophysics Data System (ADS)
Hegna, C. C.
2016-05-01
The impact of sheared toroidal rotation on the evolution of pressure driven magnetic islands in tokamak plasmas is investigated using a resistive magnetohydrodynamics model augmented by a neoclassical Ohm's law. Particular attention is paid to the asymptotic matching data as the Mercier indices are altered in the presence of sheared flow. Analysis of the nonlinear island Grad-Shafranov equation shows that sheared flows tend to amplify the stabilizing pressure/curvature contribution to pressure driven islands in toroidal tokamaks relative to the island bootstrap current contribution. As such, sheared toroidal rotation tends to reduce saturated magnetic island widths.
Electromagnetic toroidal excitations in matter and free space
NASA Astrophysics Data System (ADS)
Papasimakis, N.; Fedotov, V. A.; Savinov, V.; Raybould, T. A.; Zheludev, N. I.
2016-03-01
The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information.
Electromagnetic toroidal excitations in matter and free space.
Papasimakis, N; Fedotov, V A; Savinov, V; Raybould, T A; Zheludev, N I
2016-03-01
The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information. PMID:26906961
NASA Astrophysics Data System (ADS)
Dadras, Pouria; Firouzjaee, J. T.; Mansouri, Reza
2012-11-01
We propose a special solution of Einstein equations in the general Vaidya form representing a dynamical black hole having horizon cross-sections with toroidal topology. The concrete model enables us to study for the first time dynamical horizons with toroidal topology, its area law, and the question of matter flux inside the horizon, without using a cut-and-paste technology to construct the solution.
ERIC Educational Resources Information Center
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Toroidal angular momentum transport with non-axisymmetric magnetic fields
NASA Astrophysics Data System (ADS)
Seol, J.; Park, B. H.
2016-05-01
In this study, we calculate the radial transport of the toroidal angular momentum in the presence of non-axisymmetric magnetic fields. It is shown that the radial transport of the toroidal angular momentum, R 2 ∇ ζ . V , is proportional to the first order of gyro-radius. This implies that the neoclassical toroidal viscosity caused by asymmetric magnetic fields can change the toroidal rotation significantly.
Toroidal Alfven eigenmode-induced ripple trapping
White, R.B.; Fredrickson, E.; Darrow, D.; Zarnstorff, M.; Wilson, R.; Zweben, S.; Hill, K.; Chen, Y.; Fu, G.
1995-08-01
Toroidal Alfven eigenmodes are shown to be capable of inducing ripple trapping of high-energy particles in tokamaks, causing intense localized particle loss. The effect has been observed in TFTR [R. Hawryluk, Plasma Phys. Controlled Fusion {bold 33}, 1509 (1991)]. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
PULSAR WIND NEBULAE WITH THICK TOROIDAL STRUCTURE
Chevalier, Roger A.; Reynolds, Stephen P. E-mail: reynolds@ncsu.edu
2011-10-10
We investigate a class of pulsar wind nebulae that show synchrotron emission from a thick toroidal structure. The best studied such object is the small radio and X-ray nebula around the Vela pulsar, which can be interpreted as the result of interaction of a mildly supersonic inward flow with the recent pulsar wind. Such a flow near the center of a supernova remnant can be produced in a transient phase when the reverse shock reaches the center of the remnant. Other nebulae with a thick toroidal structure are G106.6+2.9 and G76.9+1.0. Their structure contrasts with young pulsar nebulae like the Crab Nebula and 3C 38, which show a more chaotic, filamentary structure in the synchrotron emission. In both situations, a torus-jet structure is present where the pulsar wind passes through a termination shock, indicating the flow is initially toroidal. We suggest that the difference is due to the Rayleigh-Taylor instability that operates when the outer boundary of the nebula is accelerating into freely expanding supernova ejecta. The instability gives rise to mixing in the Crab and related objects, but is not present in the nebulae with thick toroidal regions.
Dynamical model for the toroidal sporadic meteors
Pokorný, Petr; Vokrouhlický, David; Nesvorný, David; Campbell-Brown, Margaret; Brown, Peter E-mail: vokrouhl@cesnet.cz E-mail: margaret.campbell@uwo.ca
2014-07-01
More than a decade of radar operations by the Canadian Meteor Orbit Radar have allowed both young and moderately old streams to be distinguished from the dispersed sporadic background component. The latter has been categorized according to broad radiant regions visible to Earth-based observers into three broad classes: the helion and anti-helion source, the north and south apex sources, and the north and south toroidal sources (and a related arc structure). The first two are populated mainly by dust released from Jupiter-family comets and new comets. Proper modeling of the toroidal sources has not to date been accomplished. Here, we develop a steady-state model for the toroidal source of the sporadic meteoroid complex, compare our model with the available radar measurements, and investigate a contribution of dust particles from our model to the whole population of sporadic meteoroids. We find that the long-term stable part of the toroidal particles is mainly fed by dust released by Halley type (long period) comets (HTCs). Our synthetic model reproduces most of the observed features of the toroidal particles, including the most troublesome low-eccentricity component, which is due to a combination of two effects: particles' ability to decouple from Jupiter and circularize by the Poynting-Robertson effect, and large collision probability for orbits similar to that of the Earth. Our calibrated model also allows us to estimate the total mass of the HTC-released dust in space and check the flux necessary to maintain the cloud in a steady state.
On steady poloidal and toroidal flows in tokamak plasmas
McClements, K. G.
2010-08-15
The effects of poloidal and toroidal flows on tokamak plasma equilibria are examined in the magnetohydrodynamic limit. ''Transonic'' poloidal flows of the order of the sound speed multiplied by the ratio of poloidal magnetic field to total field B{sub {theta}/}B can cause the (normally elliptic) Grad-Shafranov (GS) equation to become hyperbolic in part of the solution domain. It is pointed out that the range of poloidal flows for which the GS equation is hyperbolic increases with plasma beta and B{sub {theta}/}B, thereby complicating the problem of determining spherical tokamak plasma equilibria with transonic poloidal flows. It is demonstrated that the calculation of the hyperbolicity criterion can be easily modified when the assumption of isentropic flux surfaces is replaced with the more tokamak-relevant one of isothermal flux surfaces. On the basis of the latter assumption, a simple expression is obtained for the variation of density on a flux surface when poloidal and toroidal flows are simultaneously present. Combined with Thomson scattering measurements of density and temperature, this expression could be used to infer information on poloidal and toroidal flows on the high field side of a tokamak plasma, where direct measurements of flows are not generally possible. It is demonstrated that there are four possible solutions of the Bernoulli relation for the plasma density when the flux surfaces are assumed to be isothermal, corresponding to four distinct poloidal flow regimes. Finally, observations and first principles-based theoretical modeling of poloidal flows in tokamak plasmas are briefly reviewed and it is concluded that there is no clear evidence for the occurrence of supersonic poloidal flows.
Neoclassical Drift of Circulating Orbits Due toToroidal Electric Field in Tokamaks
Hong, Qin; Guan, Xiaoyin; Fisch, Nathaniel J.
2011-07-19
In tokamaks, Ware pinch is a well known neoclassical effect for trapped particles in response to a toroidal electric field. It is generally believed that there exists no similar neoclassical effect for circulating particles without collisions. However, this belief is erroneous, and misses an important effect. We show both analytically and numerically that under the influence of a toroidal electric field parallel to the current, the circulating orbits drift outward toward the outer wall with a characteristic velocity O ({var_epsilon}{sup -1}) larger than the E x B velocity, where {var_epsilon} is the inverse aspect-ratio of a tokamak. During a RF overdrive, the toroidal electric field is anti-parallel to the current. As a consequence, all charged particles, including backward runaway electrons, will drift inward towards the inner wall.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Dobado, A.; Maroto, A. L.
Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space-time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.
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.
Capillary toroid cavity detector for high pressure NMR
Gerald, II, Rex E.; Chen, Michael J.; Klingler, Robert J.; Rathke, Jerome W.; ter Horst, Marc
2007-09-11
A Toroid Cavity Detector (TCD) is provided for implementing nuclear magnetic resonance (NMR) studies of chemical reactions under conditions of high pressures and temperatures. A toroid cavity contains an elongated central conductor extending within the toroid cavity. The toroid cavity and central conductor generate an RF magnetic field for NMR analysis. A flow-through capillary sample container is located within the toroid cavity adjacent to the central conductor to subject a sample material flowing through the capillary to a static magnetic field and to enable NMR spectra to be recorded of the material in the capillary under a temperature and high pressure environment.
Toroidal modeling of penetration of the resonant magnetic perturbation field
Liu Yueqiang; Kirk, A.
2013-04-15
A toroidal, quasi-linear model is proposed to study the penetration dynamics of the resonant magnetic perturbation (RMP) field into the plasma. The model couples the linear, fluid plasma response to a toroidal momentum balance equation, which includes torques induced by both fluid electromagnetic force and by (kinetic) neoclassical toroidal viscous (NTV) force. The numerical results for a test toroidal equilibrium quantify the effects of various physical parameters on the field penetration and on the plasma rotation braking. The neoclassical toroidal viscous torque plays a dominant role in certain region of the plasma, for the RMP penetration problem considered in this work.
Matter in the form of toroidal electromagnetic vortices
NASA Astrophysics Data System (ADS)
Hagen, Wilhelm F.
2015-09-01
The creation of charged elementary particles from neutral photons is explained as a conversion process of electromagnetic (EM) energy from linear to circular motion at the speed of light into two localized, toroidal shaped vortices of trapped EM energy that resist change of motion, perceptible as particles with inertia and hence mass. The photon can be represented as a superposition of left and right circular polarized transverse electric fields of opposite polarity originating from a common zero potential axis, the optical axis of the photon. If these components are separated by interaction with a strong field (nucleon) they would curl up into two electromagnetic vortices (EMV) due to longitudinal magnetic field components forming toroids. These vortices are perceptible as opposite charged elementary particles e+/- . These spinning toroids generate extended oscillating fields that interact with stationary field oscillations. The velocity-dependent frequency differences cause beat signals equivalent to matter waves, leading to interference. The extended fields entangled with every particle explain wave particle duality issues. Spin and magnetic moment are the natural outcome of these gyrating particles. As the energy and hence mass of the electron increases with acceleration so does its size shrink proportional to its reduced wavelength. The artificial weak and strong nuclear forces can be easily explained as different manifestations of the intermediate EM forces. The unstable neutron consists of a proton surrounded by a contracted and captured electron. The associated radial EM forces represent the weak nuclear force. The deuteron consists of two axially separated protons held together by a centrally captured electron. The axial EM forces represent the strong nuclear force, providing stability for "neutrons" only within nucleons. The same principles were applied to determine the geometries of force-balanced nuclei. The alpha-particle emerges as a very compact
Toroidal dipole excitations in metamolecules formed by interacting plasmonic nanorods
NASA Astrophysics Data System (ADS)
Watson, Derek W.; Jenkins, Stewart D.; Ruostekoski, Janne; Fedotov, Vassili A.; Zheludev, Nikolay I.
2016-03-01
We show how the elusive toroidal dipole moment appears as a radiative excitation eigenmode in a metamolecule resonator that is formed by pairs of plasmonic nanorods. We analyze one such nanorod configuration—a toroidal metamolecule. We find that the radiative interactions in the toroidal metamolecule can be qualitatively represented by a theoretical model based on an electric point dipole arrangement. Both a finite-size rod model and the point dipole approximation demonstrate how the toroidal dipole moment is subradiant and difficult to excite by incident light. By means of breaking the geometric symmetry of the metamolecule, the toroidal mode can be excited by linearly polarized light and appears as a Fano resonance dip in the forward scattered light. We provide simple optimization protocols for maximizing the toroidal dipole mode excitation. This opens up possibilities for simplified control and driving of metamaterial arrays consisting of toroidal dipole unit-cell resonators.
Measurement of toroidal vessel eddy current during plasma disruption on J-TEXT
NASA Astrophysics Data System (ADS)
Liu, L. J.; Yu, K. X.; Zhang, M.; Zhuang, G.; Li, X.; Yuan, T.; Rao, B.; Zhao, Q.
2016-01-01
In this paper, we have employed a thin, printed circuit board eddy current array in order to determine the radial distribution of the azimuthal component of the eddy current density at the surface of a steel plate. The eddy current in the steel plate can be calculated by analytical methods under the simplifying assumptions that the steel plate is infinitely large and the exciting current is of uniform distribution. The measurement on the steel plate shows that this method has high spatial resolution. Then, we extended this methodology to a toroidal geometry with the objective of determining the poloidal distribution of the toroidal component of the eddy current density associated with plasma disruption in a fusion reactor called J-TEXT. The preliminary measured result is consistent with the analysis and calculation results on the J-TEXT vacuum vessel.
Measurement of toroidal vessel eddy current during plasma disruption on J-TEXT.
Liu, L J; Yu, K X; Zhang, M; Zhuang, G; Li, X; Yuan, T; Rao, B; Zhao, Q
2016-01-01
In this paper, we have employed a thin, printed circuit board eddy current array in order to determine the radial distribution of the azimuthal component of the eddy current density at the surface of a steel plate. The eddy current in the steel plate can be calculated by analytical methods under the simplifying assumptions that the steel plate is infinitely large and the exciting current is of uniform distribution. The measurement on the steel plate shows that this method has high spatial resolution. Then, we extended this methodology to a toroidal geometry with the objective of determining the poloidal distribution of the toroidal component of the eddy current density associated with plasma disruption in a fusion reactor called J-TEXT. The preliminary measured result is consistent with the analysis and calculation results on the J-TEXT vacuum vessel. PMID:26827315
Transport and dynamics in toroidal fusion systems. Final report, 1992--1995
Schnack, D D
1995-09-15
This document is organized as follows. Discussions are presented on the properties of structured and unstructured meshes, and the data structures useful for describing them. Issues related to the triangulation of an arbitrary set of points in a plane are also discussed. A derivation is made of a finite volume approximation to the resistive MHD equations suitable for use on an unstructured, triangular mesh in toroidal geometry. Boundary conditions are discussed. The specific MHD model, and its implementation on the unstructured mesh, is discussed. A discussion is presented of methods of time integration, and descriptions are given for implementation of semi-implicit and fully implicit algorithms. Examples of the application of the method are given. Included are standard, two- dimensional hydrodynamic and MHD shock problems, as well as applications of the method to the equilibrium and stability of toroidal fusion plasmas in two and three dimensions. The initial results with mesh adaptation are also described.
NASA Astrophysics Data System (ADS)
Almansa, Julio; Salvat-Pujol, Francesc; Díaz-Londoño, Gloria; Carnicer, Artur; Lallena, Antonio M.; Salvat, Francesc
2016-02-01
The Fortran subroutine package PENGEOM provides a complete set of tools to handle quadric geometries in Monte Carlo simulations of radiation transport. The material structure where radiation propagates is assumed to consist of homogeneous bodies limited by quadric surfaces. The PENGEOM subroutines (a subset of the PENELOPE code) track particles through the material structure, independently of the details of the physics models adopted to describe the interactions. Although these subroutines are designed for detailed simulations of photon and electron transport, where all individual interactions are simulated sequentially, they can also be used in mixed (class II) schemes for simulating the transport of high-energy charged particles, where the effect of soft interactions is described by the random-hinge method. The definition of the geometry and the details of the tracking algorithm are tailored to optimize simulation speed. The use of fuzzy quadric surfaces minimizes the impact of round-off errors. The provided software includes a Java graphical user interface for editing and debugging the geometry definition file and for visualizing the material structure. Images of the structure are generated by using the tracking subroutines and, hence, they describe the geometry actually passed to the simulation code.
NASA Astrophysics Data System (ADS)
Ryu, Seungoh
2009-08-01
We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation in the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occurs. We fill this gap by perturbatively incorporating classes of spatially varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity, apply the method to the spherical pore with a simple hemispherical binary distribution of the depletion strength, and obtain bounds for the induced change in the slowest relaxation mode.
REVIEW ARTICLE: Control of non-axisymmetric toroidal plasmas
NASA Astrophysics Data System (ADS)
Boozer, Allen H.
2010-10-01
The control of non-axisymmetric toroidal plasmas, stellarators, has a different character than the control of tokamaks for two reasons. Non-axisymmetric magnetic fields (1) can provide an arbitrarily large fraction of the poloidal magnetic field and (2) can strongly center the plasma in the chamber making it impossible to lose position control. The focus of stellarator design is on plasmas that are stable without feedback, need little or no change in the external magnetic field as the plasma evolves, and require no external power to maintain the desired magnetic configuration. The physics of non-axisymmetric fields is the same whether in a tokamak or a stellarator and whether introduced intentionally or accidentally. Fundamental physics indicates that plasma shape, which is controlled by the distribution of the external magnetic field that is normal to the plasma surface, is the primary control for fusion plasmas. The importance of non-axisymmetric control is set by the importance of toroidal plasma physics. Informed decisions on the development strategy of tokamaks, as well as magnetic fusion in general, require an understanding of the capabilities and difficulties of plasma control at various levels of non-axisymmetric shaping.
Toroidal magnetic confinement of non-neutral plasmas
Yoshida, Zensho; Ogawa, Yuichi; Morikawa, Junji; Himura, Haruhiko; Kondo, Shigeo; Nakashima, Chihiro; Kakuno, Shuichi; Iqbal, Muhamad; Volponi, Francesco; Shibayama, Norihisa; Tahara, Shigeru
1999-12-10
A new method of toroidal non-neutral plasma trap has been developed with applying the chaos-induced radial transport of particles near a magnetic null point. A pure electron plasma is produced by injecting an electron beam. The poloidal gyroradius of an electron at the energy of 1 keV is of order 10 mm, which determines the length scale of the chaotic region. Amongst various applications of toroidal non-neutral plasmas, a possibility of producing very high-{beta} plasma, which is suitable for advanced fusion, has been examined. The self-electric field of a non-neutral plasma can generate a strong shear flow. When the flow velocity is comparable to the Alfven speed (which is smaller than the ion sound speed, if {beta}>1), a high-{beta} equilibrium can be produced in which the plasma pressure is primarily balanced by the dynamic pressure of the flow. This configuration is described by a generalized Bernoulli law.
Toroidal Magnetic Confinement of Non-Neutral Plasmas
Zensho Yoshida; Yuichi Ogawa; Junji Morikawa; Haruhiko Himura; Shigeo Kondo; Chihiro Nakashima; Shuichi Kakuno; Muhamad Iqbal; Francesco Volponi; Norihisa Shibayama; Shigeru Tahara
1999-12-31
A new method of toroidal non-neutral plasma trap has been developed with applying the chaos-induced radial transport of particles near a magnetic null point. A pure electron plasma is produced by injecting an electron beam. The poloidal gyro-radius of an electron at the energy of 1 keV is of order 10 mm, which determines the length scale of the chaotic region. Amongst various applications of toroidal non-neutral plasmas, a possibility of producing very high-{beta} plasma, which is suitable for advanced fusion, has been examined. The self-electric field of a non-neutral plasma can generate a strong shear flow. When the flow velocity is comparable to the Alfven speed (which is smaller than the ion sound speed, if {beta} > 1), a high-{beta} equilibrium can be produced in which the plasma pressure is primarily balanced by the dynamic pressure of the flow. This configuration is described by a generalized Bernoulli law.
Plasmonic Toroidal Metamolecules Assembled by DNA Origami.
Urban, Maximilian J; Dutta, Palash K; Wang, Pengfei; Duan, Xiaoyang; Shen, Xibo; Ding, Baoquan; Ke, Yonggang; Liu, Na
2016-05-01
We show hierarchical assembly of plasmonic toroidal metamolecules that exhibit tailored optical activity in the visible spectral range. Each metamolecule consists of four identical origami-templated helical building blocks. Such toroidal metamolecules show a stronger chiroptical response than monomers and dimers of the helical building blocks. Enantiomers of the plasmonic structures yield opposite circular dichroism spectra. Experimental results agree well with the theoretical simulations. We also show that given the circular symmetry of the structures s distinct chiroptical response along their axial orientation can be uncovered via simple spin-coating of the metamolecules on substrates. Our work provides a new strategy to create plasmonic chiral platforms with sophisticated nanoscale architectures for potential applications such as chiral sensing using chemically based assembly systems. PMID:27082140
Solar Dynamo and Toroidal Field Instabilities
NASA Astrophysics Data System (ADS)
Bonanno, Alfio
2013-10-01
The possibility of non-axisymmetric (kink) instabilities of a toroidal field seated in the tachocline is much discussed in the literature. In this work, the basic properties of kink and quasi-interchange instabilities, produced by mixed toroidal and poloidal configuration, will be briefly reviewed. In particular, it will be shown that the unstable modes are strongly localized near the Equator and not near the Poles as often claimed in the literature. Based on the results of recent numerical simulations, it is argued that a non-zero helicity can already be produced at a non-linear level. A mean-field solar dynamo is then constructed with a positive α-effect in the overshoot layer localized near the Equator, and a meridional circulation with deep return flow. Finally, the possibility that the solar cycle is driven by an αΩ dynamo generated by the negative subsurface shear in the supergranulation layer will also be discussed.
Solar concentrator with a toroidal relay module.
Lin, Jhe-Syuan; Liang, Chao-Wen
2015-10-01
III-V multijunction solar cells require solar concentrators with a high concentration ratio to reduce per watt cost and to increase solar energy transforming efficiency. This paper discusses a novel solar concentrator design that features a high concentration ratio, high transfer efficiency, thin profile design, and a high solar acceptance angle. The optical design of the concentrator utilizes a toroidal relay module, which includes both the off-axis relay lens and field lens design in a single concentric toroidal lens shape. The optical design concept of the concentrator is discussed and the simulation results are shown. The given exemplary design has an aspect ratio of 0.24, a high averaged optical concentration ratio 1230×, a maximum efficiency of 76.8%, and the solar acceptance angle of ±0.9°. PMID:26479646
Defect unbinding on a toroidal nematic shell.
Jesenek, Dalija; Kralj, Samo; Rosso, Riccardo; Virga, Epifanio G
2015-03-28
We study nematic liquid crystal textures exhibiting topological defects (TDs) on a two-dimensional (2D) toroidal shell. For the toroidal topology the total topological charge of TDs is equal to zero. We use a mesoscopic Landau-de Gennes approach which features a 2D nematic order tensor Q. We show that fat tori unbind TDs. If no extrinsic free energy couples Q with the Weingarten tensor of the torus, then defects and antidefects are assembled along the innermost and the outermost circles of the torus, respectively. In this case, we estimate the critical condition for the onset of TDs using an electrostatic analogy. If, on the other hand, an extrinsic free energy is present, then defects are repelled from these regions. PMID:25662487
Magnetohydrodynamic stability of structurally stable toroidal plasmas
NASA Astrophysics Data System (ADS)
Rock, F. C.
1981-11-01
The MHD stability of sharp boundary axisymmetric toroidal plasmas with the poloidal field and 'kidney bean' shape implied by the requirements of structural stability (immunity of the magnetic field topology to small perturbations) is investigated. High values of marginal beta (up to 36 percent for R/a = 2) are found. Results are presented for the four magnetic field topologies on the sharp boundary surface with this shape and as a function of elongation.
Muon dynamics in a toroidal sector magnet
Gallardo, J.C.; Fernow, R.; Palmer, R.B.
1997-09-17
The present scenario for the cooling channel in a high brightness muon collider calls for a quasi-continuous solenoidal focusing channel. The beam line consists of a periodic array of rf cavities and approximately 2 cm long LiH absorbers immersed in a solenoid with alternating focusing field (FOFO). The authors present a Hamiltonian formulation of muon dynamics in toroidal sector solenoids (bent solenoid).
Neoclassical transport in enhanced confinement toroidal plasmas
Lin, Z.; Tang, W.M.; Lee, W.W.
1996-11-01
It has recently been reported that ion thermal transport levels in enhanced confinement tokamak plasmas have been observed to fall below the irreducible minimum level predicted by standard neoclassical theory. This apparent contradiction is resolved in the present analysis by relaxing the basic neoclassical assumption that the ions orbital excursions are much smaller than the local toroidal minor radius and the equilibrium scale lengths of the system.
Toroidal Dipole Moment of a Massless Neutrino
Cabral-Rosetti, L. G.; Mondragon, M.; Perez, E. Reyes
2009-04-20
We obtain the toroidal dipole moment of a massless neutrino {tau}{sub v{sub I}}{sup M} using the results for the anapole moment of a massless Dirac neutrino a{sub v{sub I}}{sup D}, which was obtained in the context of the Standard Model of the electroweak interactions (SM)SU(2){sub L} x U(1){sub Y}.
NASA Astrophysics Data System (ADS)
Gilman, P. A.; Fox, P.
1997-05-01
At the 1996 AAS/SPD meeting in Madison we reported first results for the joint instability of differential rotation and toroidal magnetic fields to 2D disturbances (see also Gilman and Fox, Paper I, July 20 1997 issue of ApJ). This analysis was for the toroidal field profile B=a*sin(LAT)cos(LAT). This paper reports results for the profile B=(a*sin(LAT)+b*(sin(LAT))(3) ))cos(LAT), which, with b<-a<0, allows for a node in the toroidal field at latitude arcsin (-a/b). This generalization is of interest because we should expect such a node to appear and migrate equatorward as the sun proceeds from one sunspot cycle to the next. As with the simpler profile, instability occurs for virtually all differential rotation amplitudes, and all toroidal field amplitudes and shapes, and remains confined to disturbances with longitudinal wave number m=1. For a, b>0, the instability is enhanced for the same a compared to the b=0 case, particularly in high latitudes. For 0>b>-a (so no node is present) the instability is similar to the b=0 case but with diminished growth rates, due to the reduction of toroidal fields at high latitudes. At b=-a, the symmetric mode of instability vanishes, but the antisymmetric mode remains. For b<-a<0, both symmetric and antisymmetric modes are unstable, but with disturbances confined largely to the domain poleward of the node, unless the toroidal field energy greatly exceeds the kinetic energy of differential rotation. Unstable disturbances spread and migrate toward the equator as the field strength is increased and as the node is moved equatorward. Thus, the instability may still contribute to the existence of the solar butterfly diagram, and to other solar dynamo presses.
Finite toroidal flow generated by unstable tearing mode in a toroidal plasma
Hao, G. Z. Wang, A. K.; Xu, Y. H.; He, H. D.; Xu, M.; Qu, H. P.; Peng, X. D.; Xu, J. Q.; Qiu, X. M.; Liu, Y. Q.; Sun, Y.; Cui, S. Y.
2014-12-15
The neoclassical toroidal plasma viscosity torque and electromagnetic torque, generated by tearing mode (TM) in a toroidal plasma, are numerically investigated using the MARS-Q code [Liu et al., Phys. Plasmas 20, 042503 (2013)]. It is found that an initially unstable tearing mode can intrinsically drive a toroidal plasma flow resulting in a steady state solution, in the absence of the external momentum input and external magnetic field perturbation. The saturated flow is in the order of 0.5%ω{sub A} at the q=2 rational surface in the considered case, with q and ω{sub A} being the safety factor and the Alfven frequency at the magnetic axis, respectively. The generation of the toroidal flow is robust, being insensitive to the given amplitude of the perturbation at initial state. On the other hand, the flow amplitude increases with increasing the plasma resistivity. Furthermore, the initially unstable tearing mode is fully stabilized by non-linear interaction with the self-generated toroidal flow.
Superconducting magnets for toroidal fusion reactors
Haubenreich, P.N.
1980-01-01
Fusion reactors will soon be employing superconducting magnets to confine plasma in which deuterium and tritium (D-T) are fused to produce usable energy. At present there is one small confinement experiment with superconducting toroidal field (TF) coils: Tokamak 7 (T-7), in the USSR, which operates at 4 T. By 1983, six different 2.5 x 3.5-m D-shaped coils from six manufacturers in four countries will be assembled in a toroidal array in the Large Coil Test Facility (LCTF) at Oak Ridge National Laboratory (ORNL) for testing at fields up to 8 T. Soon afterwards ELMO Bumpy Torus (EBT-P) will begin operation at Oak Ridge with superconducting TF coils. At the same time there will be tokamaks with superconducting TF coils 2 to 3 m in diameter in the USSR and France. Toroidal field strength in these machines will range from 6 to 9 T. NbTi and Nb/sub 3/Sn, bath cooling and forced flow, cryostable and metastable - various designs are being tried in this period when this new application of superconductivity is growing and maturing.
Information geometry of Bayesian statistics
NASA Astrophysics Data System (ADS)
Matsuzoe, Hiroshi
2015-01-01
A survey of geometry of Bayesian statistics is given. From the viewpoint of differential geometry, a prior distribution in Bayesian statistics is regarded as a volume element on a statistical model. In this paper, properties of Bayesian estimators are studied by applying equiaffine structures of statistical manifolds. In addition, geometry of anomalous statistics is also studied. Deformed expectations and deformed independeces are important in anomalous statistics. After summarizing geometry of such deformed structues, a generalization of maximum likelihood method is given. A suitable weight on a parameter space is important in Bayesian statistics, whereas a suitable weight on a sample space is important in anomalous statistics.
Toroidal rotation and halo current produced by disruptions
NASA Astrophysics Data System (ADS)
Strauss, Henry; Sugiyama, Linda; Paccagnella, Roberto; Breslau, Joshua; Jardin, Stephen
2013-10-01
In several experiments including JET, it was observed that disruptions were accompanied by toroidal rotation. There is a concern that there may be a resonance between rotating toroidal perturbations and the resonant frequencies of the ITER vacuum vessel, causing enhanced damage. MHD simulations with M3D demonstrate that disruptions produce toroidal rotation. The toroidal velocity can produce several rotations of the sideways force during a disruption. Edge localized modes (ELMs) also produce poloidal and toroidal rotation. A theory of rotation produced by MHD activity will be presented. In the case of ELMs, the theory gives toroidal rotation Alfven Mach number, Mϕ ~10-2βN . This is consistent with a scaling for intrinsic toroidal rotation in H mode tokamaks. It was also discovered on JET that disruptions were accompanied by toroidal variation of the plasma current Iϕ. From ∇ . j = 0 , the toroidal current variation ΔIϕ is proportional to the 3D halo current, ∮Jn Rdl , where Jn is the normal current density at the wall. The 3D halo current is calculated analytically and computationally. A bound on ΔIϕ /Iϕ is found, proportional to the halo current fraction and toroidal peaking factor. Supported by USDOE and ITER.
Toroid cavity/coil NMR multi-detector
Gerald, II, Rex E.; Meadows, Alexander D.; Gregar, Joseph S.; Rathke, Jerome W.
2007-09-18
An analytical device for rapid, non-invasive nuclear magnetic resonance (NMR) spectroscopy of multiple samples using a single spectrometer is provided. A modified toroid cavity/coil detector (TCD), and methods for conducting the simultaneous acquisition of NMR data for multiple samples including a protocol for testing NMR multi-detectors are provided. One embodiment includes a plurality of LC resonant circuits including spatially separated toroid coil inductors, each toroid coil inductor enveloping its corresponding sample volume, and tuned to resonate at a predefined frequency using a variable capacitor. The toroid coil is formed into a loop, where both ends of the toroid coil are brought into coincidence. Another embodiment includes multiple micro Helmholtz coils arranged on a circular perimeter concentric with a central conductor of the toroid cavity.
NASA Technical Reports Server (NTRS)
Jordan, T. M.
1970-01-01
The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.
NASA Technical Reports Server (NTRS)
Jordan, T. M.
1970-01-01
A description of the FASTER-III program for Monte Carlo Carlo calculation of photon and neutron transport in complex geometries is presented. Major revisions include the capability of calculating minimum weight shield configurations for primary and secondary radiation and optimal importance sampling parameters. The program description includes a users manual describing the preparation of input data cards, the printout from a sample problem including the data card images, definitions of Fortran variables, the program logic, and the control cards required to run on the IBM 7094, IBM 360, UNIVAC 1108 and CDC 6600 computers.
Landau damping of geodesic acoustic mode in toroidally rotating tokamaks
Ren, Haijun; Cao, Jintao
2015-06-15
Geodesic acoustic mode (GAM) is analyzed by using modified gyro-kinetic (MGK) equation applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Dispersion relation of GAM in the presence of arbitrary toroidal Mach number is analytically derived. The effects of toroidal rotation on the GAM frequency and damping rate do not depend on the orientation of equilibrium flow. It is shown that the toroidal Mach number M increases the GAM frequency and dramatically decreases the Landau damping rate.
Transport of Parallel Momentum by Toroidal Ion Temperature Gradient Instability near Marginality
E.S. Yoon and T.S. Hahm
2009-10-20
The turbulent angular momentum flux carried by ions resonant with toroidal ion temperature gradient(ITG) instability is calculated via quasilinear calculation using the phase-space conserving gyrokinetic equation in the laboratory frame. The results near ITG marginality indicate that the inward turbulent equipartition (TEP) momentum pinch [Hahm T.S. et al 2007 Phys. Plasmas 14 072302] remains as the most robust part of pinch. In addition, ion temperature gradient driven momentum flux is inward for typical parameters, while density gradient driven momentum flux is outward as in the previous kinetic result in slab geometry [Diamond P.H. et al 2008 Phys. Plasmas 15 012303].
Toroidal magnetic detector for high resolution measurement of muon momenta
Bonanos, Peter
1992-01-01
A muon detector system including central and end air-core superconducting toroids and muon detectors enclosing a central calorimeter/detector. Muon detectors are positioned outside of toroids and all muon trajectory measurements are made in a nonmagnetic environment. Internal support for each magnet structure is provided by sheets, located at frequent and regularly spaced azimuthal planes, which interconnect the structural walls of the toroidal magnets. In a preferred embodiment, the shape of the toroidal magnet volume is adjusted to provide constant resolution over a wide range of rapidity.
Toroidal magnetic detector for high resolution measurement of muon momenta
Bonanos, P.
1992-01-07
A muon detector system including central and end air-core superconducting toroids and muon detectors enclosing a central calorimeter/detector. Muon detectors are positioned outside of toroids and all muon trajectory measurements are made in a nonmagnetic environment. Internal support for each magnet structure is provided by sheets, located at frequent and regularly spaced azimuthal planes, which interconnect the structural walls of the toroidal magnets. In a preferred embodiment, the shape of the toroidal magnet volume is adjusted to provide constant resolution over a wide range of rapidity. 4 figs.
Berry phases and zero-modes in toroidal topological insulator
NASA Astrophysics Data System (ADS)
Fonseca, Jakson M.; Carvalho-Santos, Vagson L.; Moura-Melo, Winder A.; Pereira, Afranio R.
2016-06-01
An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology.
Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows
Garcia de Andrade, L.C.
2006-02-15
Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation of the almost helical plasma flow contributes to the twist of the magnetic flux tube through the total Frenet torsion along the tube.
Edge ambipolar potential in toroidal fusion plasmasa)
NASA Astrophysics Data System (ADS)
Spizzo, G.; Vianello, N.; White, R. B.; Abdullaev, S. S.; Agostini, M.; Cavazzana, R.; Ciaccio, G.; Puiatti, M. E.; Scarin, P.; Schmitz, O.; Spolaore, M.; Terranova, D.
2014-05-01
A series of issues with toroidally confined fusion plasmas are related to the generation of 3D flow patterns by means of edge magnetic islands, embedded in a chaotic field and interacting with the wall. These issues include the Greenwald limit in Tokamaks and reversed-field pinches, the collisionality window for ELM mitigation with the resonant magnetic perturbations (RMPs) in Tokamaks, and edge islands interacting with the bootstrap current in stellarators. Measurements of the 2D map of the edge electric field Er(r =a,θ,ϕ) in the RFX reversed-field pinch show that Er has the same helicity of the magnetic islands generated by a m/n perturbation: in fact, defining the helical angle u =mθ-nϕ+ωt, maps show a sinusoidal dependence as a function of u, Er=E ˜rsin u. The associated E × B flow displays a huge convective cell with v(a)≠0 which, in RFX and near the Greenwald limit, determines a stagnation point for density and a reversal of the sign of Er. From a theoretical point of view, the question is how a perturbed toroidal flux of symmetry m/n gives rise to an ambipolar potential Φ =Φ˜sin u. On the basis of a model developed with the guiding center code Orbit and applied to RFX and the TEXTOR tokamak, we will show that the presence of an m/n perturbation in any kind of device breaks the toroidal symmetry with a drift proportional to the gyroradius ρ, thus larger for ions (ρi ≫ ρe). Immediately, an ambipolar potential arises to balance the drifts, with the same symmetry as the original perturbation.
Edge ambipolar potential in toroidal fusion plasmas
Spizzo, G. Vianello, N.; Agostini, M.; Puiatti, M. E.; Scarin, P.; Spolaore, M.; Terranova, D.; White, R. B.; Abdullaev, S. S.; Schmitz, O.; Cavazzana, R.; Ciaccio, G.
2014-05-15
A series of issues with toroidally confined fusion plasmas are related to the generation of 3D flow patterns by means of edge magnetic islands, embedded in a chaotic field and interacting with the wall. These issues include the Greenwald limit in Tokamaks and reversed-field pinches, the collisionality window for ELM mitigation with the resonant magnetic perturbations (RMPs) in Tokamaks, and edge islands interacting with the bootstrap current in stellarators. Measurements of the 2D map of the edge electric field E{sup r}(r=a,θ,ϕ) in the RFX reversed-field pinch show that E{sup r} has the same helicity of the magnetic islands generated by a m/n perturbation: in fact, defining the helical angle u=mθ−nϕ+ωt, maps show a sinusoidal dependence as a function of u, E{sup r}=E{sup ~r}sin u. The associated E × B flow displays a huge convective cell with v(a)≠0 which, in RFX and near the Greenwald limit, determines a stagnation point for density and a reversal of the sign of E{sup r}. From a theoretical point of view, the question is how a perturbed toroidal flux of symmetry m/n gives rise to an ambipolar potential Φ=Φ{sup ~}sin u. On the basis of a model developed with the guiding center code ORBIT and applied to RFX and the TEXTOR tokamak, we will show that the presence of an m/n perturbation in any kind of device breaks the toroidal symmetry with a drift proportional to the gyroradius ρ, thus larger for ions (ρ{sub i} ≫ ρ{sub e}). Immediately, an ambipolar potential arises to balance the drifts, with the same symmetry as the original perturbation.
NASA Astrophysics Data System (ADS)
Sontag, A. C.; Garstka, G. D.; Fonck, R. J.; Schooff, R. J.; Thorson, T. A.; Tritz, K. L.
2001-01-01
Magnetic equilibrium reconstruction on the PEGASUS toroidal experiment is a crucial tool to determine macroscopic plasma parameters, such as geometry, li, βt, and qψ. These parameters are tightly coupled to the plasma shape due to the very high toroidicity in PEGASUS where A≈1.1-1.3. A systematic scan of model plasma parameters in a magnetic equilibrium code has been employed to determine an acceptable array of magnetic diagnostics for accurately characterizing the plasma equilibrium. The magnetic diagnostics used include a poloidal array of magnetic pickup coils and flux loops along with a Rogowski loop for the toroidal plasma current. A 270 GHz μ wave interferometer for line averaged density in conjunction with spectroscopic temperature estimates provide a central pressure constraint. Visible images of the plasma provide constraints on the plasma size and location. A one-dimensional SXR camera is being developed to provide a measurement of the magnetic axis location. A time evolving current filament model and wall flux loops are used to determine the induced currents flowing in the continuous, resistive vacuum vessel wall. The ability of the equilibrium reconstruction code to reproduce model equilibria using this diagnostic set provides a quantitative measure of the accuracy of these equilibrium reconstructions. A Monte Carlo analysis with Gaussian noise added to the model data tests the robustness of this technique. A comparison of the model equilibria with the reconstructions obtained using noisy data is shown.
Mechanical design aspects of the Advanced Toroidal Facility Thomson scattering diagnostic
Shipley, W.D.; Kindsfather, R.R.; Rasmussen, D.A.
1987-01-01
A two-dimensional Thomson scattering system has been designed for the Advanced Toroidal Facility (ATF), a torsatron experiment at the Oak Ridge National Laboratory (ORNL). The system is a modification of the Thomson scattering system used on the Impurity Study Experiment (ISX-B) tokamak. It will provide measurements of electron temperature (T/sub e/) and density (n/sub e/) at 15 points along a vertical chord. With multiple shots, a T/sub e/ and n/sub e/ map of a toroidal cross section of ATF can be obtained. The horizontal Thomson scattering viewing port is offset by 15/sup 0/ toroidally from the ports through which the vertical laser beam passes. The modifications to the ISX-B Thomson scattering system are either changes required to adapt the system to the ATF device geometry or changes that result in improvements to the original system. This paper deals with the mechanical design aspects of the laser light baffle plates that reduce the amount of extraneous light entering the plasma, the upper and lower vacuum extensions that contain the baffles and attach to the ATF vacuum vessel, the entrance window assembly, the laser dump assembly, the viewing window and shutter assembly, and the alignment target mechanism and drive used to determine the ampping of data points in the plasma cross section.
New capabilities of TOPICA code: lower hybrid antennas and full toroidal plasmas
NASA Astrophysics Data System (ADS)
Lancellotti, V.; Wright, J. C.
2005-10-01
TOPICA (TOrino Polytechnic Ion Cyclotron Antenna) code is a numerical suite aimed at the performance prediction and analysis of plasma-facing antennas. It is capable of handling real-life 3D antenna geometries (with housing, Faraday screen, etc.) as well as a realistic plasma model, including measured density and temperature profiles. Thanks to the approach underlying the code (i.e. the formal splitting of the problem into two parts: the vacuum region around the antenna and the plasma region inside the toroidal chamber), TOPICA can be extended to deal with lower hybrid (waveguide grill) antennas, as well as toroidal plasma. TOPICA has been upgraded to simulate and design lower hybrid (waveguide grill) antennas. On the other hand, to include plasma curvature effects, TOPICA can adopt the plasma impedance matrix computed independently via the fully toroidal TORIC plasma code. This way TOPICA both provides more accurate antenna parameters and yields the proper input (i.e. the electric field in front of the Faraday shield) to self-consistently run TORIC in a subsequent plasma analysis. In this work an account for the new capabilities of TOPICA will be presented.
Sontag, A. C.; Garstka, G. D.; Fonck, R. J.; Schooff, R. J.; Thorson, T. A.; Tritz, K. L.
2001-01-01
Magnetic equilibrium reconstruction on the PEGASUS toroidal experiment is a crucial tool to determine macroscopic plasma parameters, such as geometry, l{sub i}, {beta}{sub t}, and q{sub {psi}}. These parameters are tightly coupled to the plasma shape due to the very high toroidicity in PEGASUS where A{approx}1.1--1.3. A systematic scan of model plasma parameters in a magnetic equilibrium code has been employed to determine an acceptable array of magnetic diagnostics for accurately characterizing the plasma equilibrium. The magnetic diagnostics used include a poloidal array of magnetic pickup coils and flux loops along with a Rogowski loop for the toroidal plasma current. A 270 GHz {mu} wave interferometer for line averaged density in conjunction with spectroscopic temperature estimates provide a central pressure constraint. Visible images of the plasma provide constraints on the plasma size and location. A one-dimensional SXR camera is being developed to provide a measurement of the magnetic axis location. A time evolving current filament model and wall flux loops are used to determine the induced currents flowing in the continuous, resistive vacuum vessel wall. The ability of the equilibrium reconstruction code to reproduce model equilibria using this diagnostic set provides a quantitative measure of the accuracy of these equilibrium reconstructions. A Monte Carlo analysis with Gaussian noise added to the model data tests the robustness of this technique. A comparison of the model equilibria with the reconstructions obtained using noisy data is shown.
Toroidal membrane vesicles in spherical confinement.
Bouzar, Lila; Menas, Ferhat; Müller, Martin Michael
2015-09-01
We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically. PMID:26465512
Polar interface phonons in ionic toroidal systems
NASA Astrophysics Data System (ADS)
Nguyen, N. D.; Evrard, R.; Stroscio, Michael A.
2016-09-01
We use the dielectric continuum model to obtain the polar (Fuchs–Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus.
Continuum damping of ideal toroidal Alfven eigenmodes
Zhang, X.D.; Zhang, Y.Z.; Mahajan, S.M.
1993-08-01
A perturbation theory based on the two dimensional (2D) ballooning transform is systematically developed for ideal toroidal Alfven eigenmodes (TAEs). A formula, similar to the Fermi golden rule for decaying systems in quantum mechanics, is derived for the continuum damping rate of the TAE; the decay (damping) rate is expressed explicitly in terms of the coupling of the TAE to the continuum spectrum. Numerical results are compared with previous calculations. It is found that in some narrow intervals of the parameter m{cflx {epsilon}} the damping rate varies very rapidly. These regions correspond precisely to the root missing intervals of the numerical solution by Rosenbluth et al.
Plasma current resonance in asymmetric toroidal systems
Hazeltine, R. D.; Catto, Peter J.
2015-09-15
The well-known singularity in the magnetic differential equation for plasma current in an asymmetric toroidal confinement system is resolved by including in the pressure tensor corrections stemming from finite Larmor radius. The result provides an estimate of the amplitude of spikes in the parallel current that occur on rational magnetic surfaces. Resolution of the singularity is shown to depend on both the ambipolarity condition—the requirement of zero surface-averaged radial current—and the form of the magnetic differential equation near the rational surface.
Design of toroidal transformers for maximum efficiency
NASA Technical Reports Server (NTRS)
Dayton, J. A., Jr.
1972-01-01
The design of the most efficient toroidal transformer that can be built given the frequency, volt-ampere rating, magnetic flux density, window fill factor, and materials is described. With the above all held constant and only the dimensions of the magnetic core varied, the most efficient design occurs when the copper losses equal 60 percent of the iron losses. When this criterion is followed, efficiency is only slightly dependent on design frequency and fill factor. The ratios of inside diameter to outside diameter and height to build of the magnetic core that result in transformers of maximum efficiency are computed.
Polar interface phonons in ionic toroidal systems.
Nguyen, N D; Evrard, R; Stroscio, Michael A
2016-09-01
We use the dielectric continuum model to obtain the polar (Fuchs-Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus. PMID:27357246
Proposal to produce large compact toroids
Phillips, J.A.
1981-03-01
Relatively large, hot compact toroids might be produced in the annular space between two concentric one-turn coils. With currents in the two coils flowing in the same direction, the magnetic fields on each side of the plasma are in opposite directions. As the fields are raised, the plasma ring is heated and compressed radially towards the center of the annular space. By the addition of two sets of auxiliary coils, the plasma ring can be ejected out one end of the two-coil system into a long axial magnetic field.
Microwave produced plasma in a Toroidal Device
NASA Astrophysics Data System (ADS)
Singh, A. K.; Edwards, W. F.; Held, E. D.
2010-11-01
A currentless toroidal plasma device exhibits a large range of interesting basic plasma physics phenomena. Such a device is not in equilibrium in a strict magneto hydrodynamic sense. There are many sources of free energy in the form of gradients in plasma density, temperature, the background magnetic field and the curvature of the magnetic field. These free energy sources excite waves and instabilities which have been the focus of studies in several devices in last two decades. A full understanding of these simple plasmas is far from complete. At Utah State University we have recently designed and installed a microwave plasma generation system on a small tokamak borrowed from the University of Saskatchewan, Saskatoon, Canada. Microwaves are generated at 2.45 GHz in a pulsed dc mode using a magnetron from a commercial kitchen microwave oven. The device is equipped with horizontal and vertical magnetic fields and a transformer to impose a toroidal electric field for current drive. Plasmas can be obtained over a wide range of pressure with and without magnetic fields. We present some preliminary measurements of plasma density and potential profiles. Measurements of plasma temperature at different operating conditions are also presented.
Future Directions for the PEGASUS Toroidal Experiment
NASA Astrophysics Data System (ADS)
Fonck, R.; Pegasus Team
1999-11-01
The PEGASUS Toroidal Experiment is uniquely poised to explore the tokamak/spheromak transition regime in the near future. To this end, a new low-inductance toroidal field coil set will allow transient exploration of the Ip/ITF > 3 regime and associated plasma relaxation phenomena. The addition of a transformer and inline inductor to the ohmic power supply will increase the pulse length to 0.03-0.05 s and will couple 5-10x the present power to the plasma. The High Harmonic Fast Wave (HHFW) antenna is complete and installation is planned for Fall 1999. The power supplies for the HHFW system have been tested up to 0.7 MW into dummy loads with future upgrades to 2 MW. Poloidal current injection via plasma guns is being tested for generating non-inductive target plasmas, thus reducing startup volt second consumption. If successful, a coaxial array of plasma guns will be used to initiate and drive the startup plasma, achieving non-inductive plasma currents 0.1-0.2 MA. Investigation of the viability of Electron Bernstein Wave heating in overdense ST plasmas is also planned, and may lead to an alternative method of non-inductive current ramp and sustainment.
Propulsion using the electron spiral toroid
Seward, Clint
1998-01-15
A new propulsion method is proposed which could potentially reduce propellant needed for space travel by three orders of magnitude. It uses the newly patented electron spiral toroid (EST), which stores energy as magnetic field energy. The EST is a hollow toroid of electrons, all spiraling in parallel paths in a thin outer shell. The electrons satisfy the coupling condition, forming an electron matrix. Stability is assured as long as the coupling condition is satisfied. The EST is held in place with a small external electric field; without an external magnetic field. The EST system is contained in a vacuum chamber. The EST can be thought of as an energetic entity, with electrons at 10,000 electron volts. Propulsion would not use combustion, but would heat propellant through elastic collisions with the EST surface and eject them for thrust. Chemical rocket combustion heats propellant to 4000 deg. C; an EST will potentially heat the propellant 29,000 times as much, reducing propellant needs accordingly. The thrust can be turned ON and OFF. The EST can be recharged as needed.
NASA Astrophysics Data System (ADS)
Smania, Daniel
2007-07-01
We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admit a topological conjugacy, quasiconformal outside the filled-in Julia set, are indeed quasiconformally conjugate. The proof uses a new abstract removability-type result for quasiconformal maps, following ideas of Heinonen and Koskela and of Kallunki and Koskela, optimized for applications in complex dynamics. We prove, as the first application of this new method, that, for even criticalities distinct from two, the period two cycle of the Fibonacci renormalization operator is hyperbolic with 1 -dimensional unstable manifold.
NASA Astrophysics Data System (ADS)
Prástaro, Agostino
2008-02-01
Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.
2-D skin-current toroidal-MHD-equilibrium code
Feinberg, B.; Niland, R.A.; Coonrod, J.; Levine, M.A.
1982-09-01
A two-dimensional, toroidal, ideal MHD skin-current equilibrium computer code is described. The code is suitable for interactive implementation on a minicomptuer. Some examples of the use of the code for design and interpretation of toroidal cusp experiments are presented.
Variable control of neutron albedo in toroidal fusion devices
Jassby, D.L.; Micklich, B.J.
1983-06-01
This invention pertains to methods of controlling in the steady state, neutron albedo in toroidal fusion devices, and in particular, to methods of controlling the flux and energy distribution of collided neutrons which are incident on an outboard wall of a toroidal fusion device.
NASA Astrophysics Data System (ADS)
Xu, Y.; Wang, S.; Zhang, D.
2016-04-01
A new mechanism of ion cyclotron range of frequency (ICRF)-induced rotation is proposed to explain the toroidal rotation with minority ICRF heating without net momentum injection. For ICRF waves launched with the symmetric spectrum, a nonlinear toroidal force can be generated through the asymmetric absorption of the toroidal wave momentum, which is due to the finite toroidal rotation of minority ions. This ICRF-induced toroidal force can drive a significant toroidal rotation of bulk ions.
Magnetic geometry, plasma profiles, and stability
Connor, J. W.
2006-07-15
The history of the stability of short wavelength modes, such as MHD instabilities and drift waves, has been a long and tortuous one as increasingly realistic representations of the equilibrium magnetic geometry have been introduced. Early work began with simple slab or cylindrical models where plasma profiles and magnetic shear were seen to play key roles. Then the effects of toroidal geometry, in particular the constraints imposed by periodicity in the presence of magnetic shear, provided a challenge for theory, which was met by the ballooning transformation. More recently the limitations on the conventional ballooning theory arising from effects such as toroidal rotation shear, low magnetic shear, and the presence of the plasma edge have been recognized. These have led in turn to modifications and extensions of this theory. These developments have produced a continuously changing view of the stability of the 'universal' drift wave, for example. After a survey of this background, we describe more recent work of relevance to currently important topics, such as transport barriers characterized by the presence of strong rotation shear and low magnetic shear and the edge localized modes that occur in H-mode.
Conventionalism and integrable Weyl geometry
NASA Astrophysics Data System (ADS)
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Segmented saddle-shaped passive stabilization conductors for toroidal plasmas
Leuer, James A.
1990-05-01
A large toroidal vacuum chamber for plasma generation and confinement is lined with a toroidal blanket for shielding using modules segmented in the toroidal direction. To provide passive stabilization in the same manner as a conductive vacuum chamber wall, saddle-shaped conductor loops are provided on blanket modules centered on a midplane of the toroidal chamber with horizontal conductive bars above and below the midplane, and vertical conductive legs on opposite sides of each module to provide return current paths between the upper and lower horizontal conductive bars. The close proximity of the vertical legs provided on adjacent modules without making physical contact cancel the electromagnetic field of adjacent vertical legs. The conductive bars spaced equally above and below the midplane simulate toroidal conductive loops or hoops that are continuous, for vertical stabilization of the plasma even though they are actually segmented.
Formation of a compact toroid for enhanced efficiency
Mozgovoy, A. G.; Romadanov, I. V.; Ryzhkov, S. V.
2014-02-15
We report here our results on the formation of a plasma configuration with the generic name of compact toroid (CT). A method of compact toroid formation to confine, heat and compress a plasma is investigated. Formation of a compact torus using an additional toroidal magnetic field helps to increase the plasma current to a maintainable level of the original magnetic field. We design the Compact Toroid Challenge (CTC) experiment in order to improve the magnetic flux trapping during field reversal in the formation of a compact toroid. The level of the magnetic field immersed in the plasma about 70% of the primary field is achieved. The CTC device and scheme of high level capturing of magnetic flux are presented.
Formation of a compact toroid for enhanced efficiency
NASA Astrophysics Data System (ADS)
Mozgovoy, A. G.; Romadanov, I. V.; Ryzhkov, S. V.
2014-02-01
We report here our results on the formation of a plasma configuration with the generic name of compact toroid (CT). A method of compact toroid formation to confine, heat and compress a plasma is investigated. Formation of a compact torus using an additional toroidal magnetic field helps to increase the plasma current to a maintainable level of the original magnetic field. We design the Compact Toroid Challenge (CTC) experiment in order to improve the magnetic flux trapping during field reversal in the formation of a compact toroid. The level of the magnetic field immersed in the plasma about 70% of the primary field is achieved. The CTC device and scheme of high level capturing of magnetic flux are presented.
Plasmonic Toroidal Dipolar Response under Radially Polarized Excitation.
Bao, Yanjun; Zhu, Xing; Fang, Zheyu
2015-01-01
Plasmonic toroidal resonance has attracted growing interests because of its low loss electromagnetic properties and potential high sensitive nanophotonic applications. However, the realization in a metamaterial requires three-dimensional complicated structural design so far. In this paper, we design a simple metal-dielectric-metal (MIM) sandwich nanostructure, which exhibits a strong toroidal dipolar resonance under radially polarized excitation. The toroidal dipole moment as the dominant contribution for the scattering is demonstrated by the mirror-image method and further analyzed by Lagrangian hybridization model. The proposed toroidal configuration also shows a highly tolerant for misalignment between the structure center and the incident light focus. Our study proves the way for the toroidal plasmonic application with the cylindrical vector beams. PMID:26114966
Segmented saddle-shaped passive stabilization conductors for toroidal plasmas
Leuer, J.A.
1990-05-01
A large toroidal vacuum chamber for plasma generation and confinement is lined with a toroidal blanket for shielding using modules segmented in the toroidal direction. To provide passive stabilization in the same manner as a conductive vacuum chamber wall, saddle-shaped conductor loops are provided on blanket modules centered on a midplane of the toroidal chamber with horizontal conductive bars above and below the midplane, and vertical conductive legs on opposite sides of each module to provide return current paths between the upper and lower horizontal conductive bars. The close proximity of the vertical legs provided on adjacent modules without making physical contact cancel the electromagnetic field of adjacent vertical legs. The conductive bars spaced equally above and below the midplane simulate toroidal conductive loops or hoops that are continuous, for vertical stabilization of the plasma even though they are actually segmented. 5 figs.
Plasmonic Toroidal Dipolar Response under Radially Polarized Excitation
Bao, Yanjun; Zhu, Xing; Fang, Zheyu
2015-01-01
Plasmonic toroidal resonance has attracted growing interests because of its low loss electromagnetic properties and potential high sensitive nanophotonic applications. However, the realization in a metamaterial requires three-dimensional complicated structural design so far. In this paper, we design a simple metal-dielectric-metal (MIM) sandwich nanostructure, which exhibits a strong toroidal dipolar resonance under radially polarized excitation. The toroidal dipole moment as the dominant contribution for the scattering is demonstrated by the mirror-image method and further analyzed by Lagrangian hybridization model. The proposed toroidal configuration also shows a highly tolerant for misalignment between the structure center and the incident light focus. Our study proves the way for the toroidal plasmonic application with the cylindrical vector beams. PMID:26114966
Compact toroids generated by a magnetized coaxial source in the CTX experiment
Sherwood, A.R.; Henins, I.; Hoida, H.W.; Jarboe, T.R.; McKenna, K.F.; Linford, R.K.; Marshall, J.; Platts, D.A.
1981-01-01
Compact toroids containing both toroidal and poloidal magnetic field (Spheromak-type) have been generated in CTX using a magnetized coaxial plasma gun. These CTs tear loose from the gun by magnetic field line reconnection, and they are trapped in flux conservers having various geometries. In a straight cylindrical flux conserver the CTs are observed to be unstable to a gross tilting mode. Stability to the tilting mode has been demonstrated in flux conservers having an oblate trapping region; however, the geometry of the entrance region leading to the trapping volume can also have important effects. Lifetimes of about 150 ..mu..s for the CTs are typically observed. Interferometric measurements give a value of about 2 x 10/sup 14/ cm/sup -3/ for the initial plasma density. The plasma temperature measured at a single spot near the minor magnetic axis decreases to around 10 eV by the time the magnetic reconnection is complete. Spectrographic measurements and pressure probe results are in agreement with this temperature. A snipper coil has been installed to induce the CT to tear loose from the gun sooner. The use of this coil is observed to speed up the magnetic field reconnection process by about a factor of 2.
Epithelial Proliferation on Curved Toroidal Surfaces
NASA Astrophysics Data System (ADS)
Chang, Ya-Wen; Cruz, Ricardo; Fragkopoulos, Alexandros; Marquez, Samantha; Garcia, Andres; Fernandez-Nieves, Alberto
Cellular environment influences a multitude of cellular functions by providing chemical and physical signals that modulate cell behavior, dynamics, development, and eventually survival. In strongly interacting epithelial cells, cells coordinate their behavior to respond to mechanical constraints in 2D. Local differences in tissue tension has also been shown to impact cell reproduction within an epithelial-cell sheet. Much less is known about how cells respond to out-of-plane curvatures. Here, we describe the proliferation of MDCK on toroidal hydrogel substrates, which unlike spheres or planes, have regions of both positive and negative Gaussian curvature. Additionally, the range of curvatures can be controlled by varying the size and aspect ratio of the torus, allowing us to quantify the relation between substrate curvature and cell proliferation.
Isomorphic routing on a toroidal mesh
NASA Technical Reports Server (NTRS)
Mao, Weizhen; Nicol, David M.
1993-01-01
We study a routing problem that arises on SIMD parallel architectures whose communication network forms a toroidal mesh. We assume there exists a set of k message descriptors (xi, yi), where (xi, yi) indicates that the ith message's recipient is offset from its sender by xi hops in one mesh dimension, and yi hops in the other. Every processor has k messages to send, and all processors use the same set of message routing descriptors. The SIMD constraint implies that at any routing step, every processor is actively routing messages with the same descriptors as any other processor. We call this isomorphic routing. Our objective is to find the isomorphic routing schedule with least makespan. We consider a number of variations on the problem, yielding complexity results from O(k) to NP-complete. Most of our results follow after we transform the problem into a scheduling problem, where it is related to other well-known scheduling problems.
Nonideal magnetohydrodynamic instabilities and toroidal magnetic confinement
Furth, H.P.
1985-05-01
The marked divergence of experimentally observed plasma instability phenomena from the predictions of ideal magnetohydrodynamics led in the early 1960s to the formulations of finite-resistivity stability theory. Beginning in the 1970s, advanced plasma diagnostics have served to establish a detailed correspondence between the predictions of the finite-resistivity theory and experimental plasma behavior - particularly in the case of the resistive kink mode and the tokamak plasma. Nonlinear resistive-kink phenomena have been found to govern the transport of magnetic flux and plasma energy in the reversed-field pinch. The other predicted finite-resistivity instability modes have been more difficult to identify directly and their implications for toroidal magnetic confinement are still unresolved.
Toroidal microinstability studies of high temperature tokamaks
Rewoldt, G.; Tang, W.M.
1989-07-01
Results from comprehensive kinetic microinstability calculations are presented showing the effects of toroidicity on the ion temperature gradient mode and its relationship to the trapped-electron mode in high-temperature tokamak plasmas. The corresponding particle and energy fluxes have also been computed. It is found that, although drift-type microinstabilities persist over a wide range of values of the ion temperature gradient parameter /eta//sub i/ /equivalent to/ (dlnT/sub i//dr)/(dlnn/sub i//dr), the characteristic features of the dominant mode are those of the /eta//sub i/-type instability when /eta//sub i/ > /eta//sub ic/ /approximately/1.2 to 1.4 and of the trapped-electron mode when /eta//sub i/ < /eta//sub ic/. 16 refs., 7 figs.
Fluid interaction with spinning toroidal tanks
NASA Technical Reports Server (NTRS)
Fester, D. A.; Anderson, J. E.
1977-01-01
An experimental study was conducted to evaluate propellant behavior in spinning torroidal tanks that could be used in a retropropulsion system of an advanced outer-planet Pioneer orbiter. Information on propellant slosh and settling and on ullage orientation and stability was obtained. The effects of axial acceleration, spin rate, spin-rate change, and spacecraft wobble, both singly and in combination, were evaluated using a one-eighth scale transparent tank in one-g and low-g environments. Liquid loadings ranged from 5% to 96% full. The impact of a surface tension acquisition device was assessed by comparison with bare-tank results. The testing simulated the behavior of the fluorine/hydrazine and nitrogen textroxide/monomethylhydrazine propellants. Results are presented that indicate that no major fluid behavior problems would be encountered with any of the four propellants in the toroidal tanks of a spin-stabilized orbiter spacecraft.
Toroid Joining Gun For Fittings And Couplings
NASA Technical Reports Server (NTRS)
Fox, Robert L.; Swaim, Robert J.; Johnson, Samuel D.; Buckley, John D.; Copeland, Carl E.; Coultrip, Robert H.; Johnston, David F.; Phillips, William M.
1992-01-01
Hand-held gun used to join metal heat-to-shrink couplings. Uses magnetic induction (eddy currents) to produce heat in metal coupling, and thermocouple to measure temperature and signals end of process. Gun, called "toroid joining gun" concentrates high levels of heat in localized areas. Reconfigured for use on metal heat-to-shrink fitting and coupling applications. Provides rapid heating, operates on low power, lightweight and portable. Safe for use around aircraft fuel and has no detrimental effects on surrounding surfaces or objects. Reliable in any environment and under all weather conditions. Gun logical device for taking full advantage of capabilities of new metal heat-to-shrink couplings and fittings.
Helicity of a toroidal vortex with swirl
NASA Astrophysics Data System (ADS)
Bannikova, E. Yu.; Kontorovich, V. M.; Poslavsky, S. A.
2016-04-01
Based on the solutions of the Bragg-Hawthorne equation, we discuss the helicity of a thin toroidal vortex in the presence of swirl, orbital motion along the torus directrix. The relation between the helicity and circulations along the small and large linked circumferences (the torus directrix and generatrix) is shown to depend on the azimuthal velocity distribution in the core of the swirling ring vortex. In the case of nonuniform swirl, this relation differs from the well-known Moffat relation, viz., twice the product of such circulations multiplied by the number of linkages. The results can find applications in investigating the vortices in planetary atmospheres and the motions in the vicinity of active galactic nuclei.
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.
NASA Astrophysics Data System (ADS)
Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan; Taylor, Washington
2015-11-01
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.
Rodrigues, Paulo; Bizarro, Joao P. S.
2013-04-15
The axisymmetry condition and two of Maxwell's equations are used to show that, in general, there are no nested magnetic surfaces around a poloidal-magnetic-field null for a sufficiently small value of the toroidal current density flowing there. Hence, the toroidal current density at the axis of a magnetic configuration with extreme shear reversal cannot continuously approach zero unless nested surfaces are first broken or particular values are assigned to boundary conditions and other plasma parameters. The threshold of the toroidal current-density at which the topology changes is shown to be set by such parameters, and some examples of the predicted topology transition are presented using analytical solutions of the Grad-Shafranov equation.
Nuclear resonance tomography with a toroid cavity detector
Woelk, K.; Rathke, J.W.; Klingler, R.J.
1996-11-12
A toroid cavity detection system is described for determining the spectral properties and distance from a fixed point for a sample using Nuclear Magnetic Resonance. The detection system consists of a toroid with a central conductor oriented along the main axis of the toroidal cylinder and perpendicular to a static uniform magnetic field oriented along the main axis of the toroid. An rf signal is input to the central conductor to produce a magnetic field perpendicular to the central axis of the toroid and whose field strength varies as the inverse of the radius of the toroid. The toroid cavity detection system can be used to encapsulate a sample, or the detection system can be perforated to allow a sample to flow into the detection device or to place the samples in specified sample tubes. The central conductor can also be coated to determine the spectral property of the coating and the coating thickness. The sample is then subjected to the respective magnetic fields and the responses measured to determine the desired properties. 4 figs.
Nuclear resonance tomography with a toroid cavity detector
Woelk, Klaus; Rathke, Jerome W.; Klingler, Robert J.
1996-01-01
A toroid cavity detection system for determining the spectral properties and distance from a fixed point for a sample using Nuclear Magnetic Resonance. The detection system consists of a toroid with a central conductor oriented along the main axis of the toroidal cylinder and perpendicular to a static uniform magnetic field oriented along the main axis of the toroid. An rf signal is inputted to the central conductor to produce a magnetic field perpendicular to the central axis of the toroid and whose field strength varies as the inverse of the radius of the toroid. The toroid cavity detection system can be used to encapsulate a sample, or the detection system can be perforated to allow a sample to flow into the detection device or to place the samples in specified sample tubes. The central conductor can also be coated to determine the spectral property of the coating and the coating thickness. The sample is then subjected to the respective magnetic fields and the responses measured to determine the desired properties.
Analysis of vortical flow with axial swirl and toroidal circulation
NASA Astrophysics Data System (ADS)
Bhattacharya, Sukalyan
2006-11-01
Vortical flows with an axial swirl and a toroidal circulation can be observed in a wide range of fluid mechanical phenomena such as flow around rotary machines or natural vortices like tornadoes and hurricanes. These flows can be described by a general scalar equation if incompressible fluid and negligible viscous dissipation are assumed. We consider one of the simpler cases of this general formulation where the involved equation has a resemblance with the governing equation of the hydrogen problem. As a result, we obtain a quantization relation similar to the expression of quantized energies in an hydrogen atom. We solve the equation for two systems. First, we consider three- dimensional vortices confined between two parallel walls. Our examples include flows between two infinite plates, inside and outside of a vertical cylinder bounded at the ends by walls, and in an axially confined annular region. Then we also use our formulation to compute highly chaotic velocity fields with three-dimensional vortical structures which qualitatively mimic the features of physical flows. Hence, these solutions may be used in modeling of complicated flow systems.
The residual zonal flow in tokamak plasmas toroidally rotating at arbitrary velocity
Zhou, Deng
2014-08-15
Zonal flows, initially driven by ion-temperature-gradient turbulence, may evolve due to the neoclassic polarization in a collisionless tokamak plasma. In our previous work [D. Zhou, Nucl. Fusion 54, 042002 (2014)], the residual zonal flow in a tokamak plasma rotating toroidally at sonic speed is found to have the same form as that of a static plasma. In the present work, the form of the residual zonal flow is presented for tokamak plasmas rotating toroidally at arbitrary velocity. The gyro-kinetic equation is analytically solved for low speed rotation to give the expression of residual zonal flows, and the expression is then generalized for cases with arbitrary rotating velocity through interpolation. The zonal flow level decreases as the rotating velocity increases. The numerical evaluation is in good agreement with the former simulation result for high aspect ratio tokamaks.
The development of an aluminum toroidal shell-type impact limiter
Mello, R.M.; Wilson, W.K.; Nair, B.R.
1989-01-01
The impact limiters on a Type B transportation cask are designed to absorb the impact energy for the 9-meter (30 foot) drop accident conditions without bottoming out in order to limit deceleration loadings on the cask. Toroidal shell-type impact limiters made from stainless steel have been investigated in the past for transportation cask service in Japan (Y. Sugita and S. Mochizuki) and by the General Electric Company (R.J. Pomares, et al.). These designs were relatively heavy and quite rigid causing high deceleration loads on the cask. This paper presents the results of an investigation to determine the feasibility of an aluminum Alloy 6061-T6 toroidal shell impact limiter for a Legal Weight Truck (LWT) cask being developed by the Westinghouse Corporation for the United States Department of Energy. The incentives for the study were the potential advantages such as a compact configuration, lightweight, durability, and essentially maintenance-free operation. 4 refs., 10 figs.
Tracking formulas and strategies for a receiver oriented dual-axis tracking toroidal heliostat
Guo, Minghuan; Wang, Zhifeng; Liang, Wenfeng; Zhang, Xiliang; Zang, Chuncheng; Lu, Zhenwu; Wei, Xiudong
2010-06-15
A 4 m x 4 m toroidal heliostat with receiver oriented dual-axis tracking, also called spinning-elevation tracking, was developed as an auxiliary heat source for a hydrogen production system. A series of spinning-elevation tracking formulas have been derived for this heliostat. This included basic tracking formulas, a formula for the elevation angle for heliostat with a mirror-pivot offset, and a more general formula for the biased elevation angle. This paper presents the new tracking formulas in detail and analyzes the accuracy of applying a simplifying approximation. The numerical results show these receiver oriented dual-axis tracking formula approximations are accurate to within 2.5 x 10{sup -6} m in image plane. Some practical tracking strategies are discussed briefly. Solar images from the toroidal heliostat at selected times are also presented. (author)
Toroidal Single Wall Carbon Nanotubes in Fullerene Crop Circles
NASA Technical Reports Server (NTRS)
Han, Jie; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
We investigate energetics and structure of circular and polygonal single wall carbon nanotubes (SWNTs) using large scale molecular simulations on NAS SP2, motivated by their unusual electronic and magnetic properties. The circular tori are formed by bending tube (no net whereas the polygonal tori are constructed by turning the joint of two tubes of (n, n), (n+1, n-1) and (n+2, n-2) with topological pentagon-heptagon defect, in which n =5, 8 and 10. The strain energy of circular tori relative to straight tube decreases by I/D(sup 2) where D is torus diameter. As D increases, these tori change from buckling to an energetically stable state. The stable tori are perfect circular in both toroidal and tubular geometry with strain less than 0. 03 eV/atom when D greater than 10, 20 and 40 nm for torus (5,5), (8,8) and (10, 10). Polygonal tori, whose strain is proportional to the number of defects and I/D are energetically stable even for D less than 10 nm. However, their strain is higher than that of perfect circular tori. In addition, the local maximum strain of polygonal tori is much higher than that of perfect circular tori. It is approx. 0.03 eV/atom or less for perfect circular torus (5,5), but 0.13 and 0.21 eV/atom for polygonal tori (6,4)/(5,5) and (7,3)/(5,5). Therefore, we conclude that the circular tori with no topological defects are more energetically stable and kinetically accessible than the polygonal tori containing the pentagon-heptagon defects for the laser-grown SWNTs and Fullerene crop circles.
Kinetic effect of toroidal rotation on the geodesic acoustic mode
Guo, W. Ye, L.; Zhou, D.; Xiao, X.; Wang, S.
2015-01-15
Kinetic effects of the toroidal rotation on the geodesic acoustic mode are theoretically investigated. It is found that when the toroidal rotation increases, the damping rate increases in the weak rotation regime due to the rotation enhancement of wave-particle interaction, and it decreases in the strong rotation regime due to the reduction of the number of resonant particles. Theoretical results are consistent with the behaviors of the geodesic acoustic mode recently observed in DIII-D and ASDEX-Upgrade. The kinetic damping effect of the rotation on the geodesic acoustic mode may shed light on the regulation of turbulence through the controlling the toroidal rotation.
Kinetic energy principle and neoclassical toroidal torque in tokamaks
Park, Jong-Kyu
2011-11-15
It is shown that when tokamaks are perturbed, the kinetic energy principle is closely related to the neoclassical toroidal torque by the action invariance of particles. Especially when tokamaks are perturbed from scalar pressure equilibria, the imaginary part of the potential energy in the kinetic energy principle is equivalent to the toroidal torque by the neoclassical toroidal viscosity. A unified description therefore should be made for both physics. It is also shown in this case that the potential energy operator can be self-adjoint and thus the stability calculation can be simplified by minimizing the potential energy.
Kinetic Energy Principle And Neoclassical Toroidal Torque In Tokamaks
Jong-Kyu Park
2011-11-07
It is shown that when tokamaks are perturbed the kinetic energy principle is closely related to the neoclassical toroidal torque by the action invariance of particles. Especially when tokamaks are perturbed from scalar pressure equilibria, the imaginary part of the potential energy in the kinetic energy principle is equivalent to the toroidal torque by the Neoclassical Toroidal Viscosity (NTV). A unified description therefore should be made for both physics. It is also shown in this case that the potential energy operator can be self-adjoint and thus the stability calculation can be simplified by minimizing the potential energy
Toroidal transducer with two large focal zones for increasing the coagulated volume
NASA Astrophysics Data System (ADS)
Vincenot, J.; Melodelima, D.; Kocot, A.; Chavrier, F.; Chapelon, J. Y.
2012-11-01
Toroidal HIFU transducers have been shown to generate large conical ablations (7 cm3 in 40 seconds). The focal zone is composed of a first ring-shaped focal zone and an overlap of ultrasound beams behind this first focus. A HIFU device has been developed on this principle to treat liver metastases during an open procedure. Although these large lesions contribute to reduce treatment time, it is still needed to juxtapose 4 to 9 single HIFU lesions to treat liver metastasis (2 cm in diameter) with safety margins. In this work, a different toroidal geometry was used. With this transducer, the overlap area is located between the probe and the focal ring. The objective was to use this transducer with electronic focusing in order to create a spherical shape lesion with sufficient volume for the destruction of a metastasis of 2 cm in diameter without any mechanical displacement. The operating frequency of the toroidal transducer was 2.5 MHz. The radius of curvature was 70 mm with a diameter of 67 mm. The focal ring had a radius of 15 mm. The overlap zone extent between 35 to 55 mm from the emitting surface. An ultrasound-imaging probe (working at 7.5 MHz) was placed in a central circular opening of 26 mm in the HIFU transducer and was aligned with the focal plane. The transducer was divided into 32 rings of 78 mm2. Using a 32 channels amplifier with a phase resolution of 1.4 degrees, it was possible to change the diameter (0 to 15 mm) and depth (45 to 85 mm) of the focus circle to maximize dimensions of the lesion. Tests were conducted in vitro, in bovine liver samples. This toroidal geometry and the use of electronic beam steering allow the creation of roughly spherical lesions (diameter of 47 mm, depth of 35 mm). This treatment was obtained in 6 minutes and 10 seconds without any mechanical displacement of the transducer. The lesions obtained were homogeneous and no untreated area was observed. In conclusion, these results indicate that the treatment of a liver
On the use of a toroidal mirror to focus neutrons at the ILL neutron spin echo spectrometer IN15
Hayes, C.; Alefeld, B.; Copley, J.R.D.
1997-09-01
The IN15 neutron spin echo spectrometer at the Institut Laue-Langevin (Grenoble) has been designed to accomodate a toroidal focusing mirror. This mirror will be used to increase the intensity at the sample position for measurements at long neutron wavelengths and to perform measurements in the low q-range (10{sup -3} {angstrom}{sup -1}). This paper summarizes the results of ray-tracing simulations for the toroidal mirror system. These calculations were performed in order to assess the effects of the neutron wavelength, gravitational fall, wavelength resolution and spherical aberrations on the quality of the focused beam. The gain in flux that can be expected from the focusing geometry is estimated. The recent installation and characterisation of the mirror is also briefly described.
NASA Technical Reports Server (NTRS)
Mcdonough, T. R.
1974-01-01
The trapping of Titan's escaping atmosphere in the Saturnian system by a toroidal ring is discussed. The radius of the toroid is comparable to Titan's orbit, or about ten times larger than the visible rings. Theoretical atmospheric models are formulated that consider Saturn's gravitational attraction and magnetospheric properties in forming this toroid and in protecting toroid particles from direct ionization by solar wind particles.
Kim, Jin Young; Noh, Jun Hong; Zhu, Kai; Halverson, Adam F; Neale, Nathan R; Park, Sangbaek; Hong, Kug Sun; Frank, Arthur J
2011-04-26
We report on the preparation of transparent oriented titania nanotube (NT) photoelectrodes and the effect of illumination direction on light harvesting, electron transport, and recombination in dye-sensitized solar cells (DSSCs) incorporating these electrodes. High solar conversion efficiency requires that the incident light enters the cell from the photoelectrode side. However, it has been synthetically challenging to prepare transparent TiO(2) NT electrodes by directly anodizing Ti metal films on transparent conducting oxide (TCO) substrates because of the difficulties of controlling the synthetic conditions. We describe a general synthetic strategy for fabricating transparent TiO(2) NT films on TCO substrates. With the aid of a conducting Nb-doped TiO(2) (NTO) layer between the Ti film and TCO substrate, the Ti film was anodized completely without degrading the TCO. The NTO layer was found to protect the TCO from degradation through a self-terminating mechanism by arresting the electric field-assisted dissolution process at the NT-NTO interface. The illumination direction and wavelength of the light incident on the DSSCs were shown to strongly influence the incident photon-to-current conversion efficiency, light-harvesting, and charge-collection properties, which, in turn, affect the photocurrent density, photovoltage, and solar energy conversion efficiency. Effects of NT film thickness on the properties and performance of DSSCs were also examined. Illuminating the cell from the photoelectrode substantially increased the conversion efficiency compared with illuminating it from the counter-electrode side. PMID:21395234
ERIC Educational Resources Information Center
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
ERIC Educational Resources Information Center
Kuntz, Gilles
The first section of this paper on World Wide Web applications related to dynamic geometry addresses dynamic geometry and teaching, including the relationship between dynamic geometry and direct manipulation, key features of dynamic geometry environments, the importance of direct engagement of the learner using construction software for…
System and method of operating toroidal magnetic confinement devices
Chance, M.S.; Jardin, S.C.; Stix, T.H.; Grimm, R.C.; Manickam, J.; Okabayashi, M.
1984-08-30
This invention pertains to methods and arrangements for attaining high beta values in plasma confinement devices. More specifically, this invention pertains to methods for accessing the second stability region of operation in toroidal magnetic confinement devices.
Toroidal band limiter for a plasma containment device
Kelley, George G.
1978-01-01
This invention relates to a toroidal plasma confinement device having poloidal and toroidal magnetic fields for confining a toroidal plasma column with a plasma current induced therein along an endless, circular equilibrium axis in a torus vacuum cavity wherein the improvement comprises the use of a toroidal plasma band limiter mounted within the vacuum cavity in such a manner as to ensure that the plasma energy is distributed more uniformly over the limiter surface thereby avoiding intense local heating of the limiter while at the same time substantially preventing damage to the plasma containment wall of the cavity by the energetic particles diffusing out from the confined plasma. A plurality of poloidal plasma ring limiters are also utilized for containment wall protection during any disruptive instability that might occur during operation of the device.
Equilibrium analysis of tokamak discharges with toroidal variation
Zwingmann, W.; Becoulet, M.; Moreau, Ph.; Nardon, E.
2006-11-30
Tokamaks provide a field structure that is almost axisymmetric around the torus axis. There are however always small toroidal variations due to the limited number of toroidal field coils, the magnetic field ripple. On the other hand, non-axisymmetric external fields are applied on purpose to ergodise the field structure close to the separatrix, to control the heat and particle transport across the plasma boundary. We present a perturbation method to calculate the magnetic field of tokamak discharges with with weak toroidal variation. The method is applied for the equilibrium reconstruction of Tore Supra discharges with toroidal ripple. The perturbation method does not rely on a flux surface representation and can therefore be applied to structures with magnetic islands. We obtain the plasma response to the field of ergodising external coils, as proposed for the ITER device.
High-frequency electric field measurement using a toroidal antenna
Lee, Ki Ha
2002-01-01
A simple and compact method and apparatus for detecting high frequency electric fields, particularly in the frequency range of 1 MHz to 100 MHz, uses a compact toroidal antenna. For typical geophysical applications the sensor will be used to detect electric fields for a wide range of spectrum starting from about 1 MHz, in particular in the frequency range between 1 to 100 MHz, to detect small objects in the upper few meters of the ground. Time-varying magnetic fields associated with time-varying electric fields induce an emf (voltage) in a toroidal coil. The electric field at the center of (and perpendicular to the plane of) the toroid is shown to be linearly related to this induced voltage. By measuring the voltage across a toroidal coil one can easily and accurately determine the electric field.
Melodelima, D.; N'Djin, W. A.; Parmentier, H.; Chapelon, J. Y.; Rivoire, M.
2009-04-14
A new geometry of HIFU transducer is described to enlarge the coagulated volume. The geometry of the transducer was not spherical. The surface of the transducer was built based on a toroid geometry. The transducer was generated by the revolution of a circle about an axis lying in its plane. Eight emitters operating at a frequency of 3 MHz were diced out of a single toroid piezocomposite element. Each of the eight emitters was divided into 32 transducers. The focal zone is conical and located at 70 mm from the transducer. A 7.5 MHz ultrasound imaging probe is placed in the centre of the device for guiding the treatment. Our long-term objective is to develop a device that can be used during surgery. In vivo trials have been performed on 13 pigs to demonstrate this new principle and to evaluate the vascular tolerance of the treatment. This new geometry combined with consecutive activation of the eight emitters around the toroid allows achieving a mean thermal ablation of 7.0{+-}2.5 cm3 in 40 seconds. All lesions were visible with high contrast on sonograms. The correlation between the size of lesions observed on sonograms and during gross examination was 92%. This allows the user to easily enlarge the coagulated volume by juxtaposing single lesions. The pigs tolerate the treatment well over the experimental period even when coagulation was produced through portal and/or hepatic veins.
Theoretical modelling of the feedback stabilization of external MHD modes in toroidal geometry
NASA Astrophysics Data System (ADS)
Chance, M. S.; Chu, M. S.; Okabayashi, M.; Turnbull, A. D.
2002-03-01
A theoretical framework for understanding the feedback mechanism for stabilization of external MHD modes has been formulated. Efficient computational tools - the GATO stability code coupled with a substantially modified VACUUM code - have been developed to effectively design viable feedback systems against these modes. The analysis assumed a thin resistive shell and a feedback coil structure accurately modelled in θ and phi, albeit with only a single harmonic variation in phi. Time constants and induced currents in the enclosing resistive shell are calculated. An optimized configuration based on an idealized model has been computed for the DIII-D device. Up to 90% of the effectiveness of an ideal wall can be achieved.
Analysis of scrape-off layer in toroidal helical systems
NASA Astrophysics Data System (ADS)
Nagasaki, Kazunobu; Itoh, Kimitaka; Itoh, Sanae-I.; Fukuyama, Atsushi
1990-03-01
Magnetic field structure of the scrape-off layer region in toroidal helical systems is analyzed by using toroidal harmonic functions. The connection length of the field line to the wall is calculated for various configurations. It is found that L has a logarythmic dependence on the distance from the outermost magnetic surface or from the residual magnetic islands. The effect of the axisymmetric fields on the stress structure is also discussed.
The role of stellarators in the advanced toroidal program
Sheffield, J.
1987-01-01
The goals of this Program as discussed in the DOE-Magnetic Fusion Program Plan and in the Technical Program Activity, have two parts: development of a better understanding of the underlying physics of toroidal devices and the development of the stellarator as a candidate reactor, and as a source of building blocks for other toroidal reactors, such as the tokamak-stellarator hybrid. This paper briefly discusses these concepts. 3 refs.
Chaos in toroidal ion-temperature-gradient-driven modes in dust-contaminated magnetoplasma
NASA Astrophysics Data System (ADS)
Qamar, Anisa; Yaqub Khan, M.; Atta-Ullah-Shah; Mirza, Arshad M.; Ayub, M.
2011-06-01
A new set of nonlinear equations for toroidal ion-temperature-gradient-driven (ITGD) drift-dissipative waves is derived by using Braginskii's transport model of the ion dynamics and the Boltzmann distribution of electrons in the presence of negatively charged dust grains. The temporal behaviour of the nonlinear ITGD mode is found to be governed by three nonlinear equations for the amplitudes, which is a generalization of Lorenz- and Stenflo-type equations admitting chaotic trajectories. The linear stability analysis has been presented and stationary points for our generalized mode coupling equations are also derived.
Plasma Behavior in the PEGASUS Toroidal Experiment
NASA Astrophysics Data System (ADS)
Thorson, T.; Pegasus Team
1999-11-01
Initial operations on PEGASUS are focussed on exploring the extremely low aspect ratio regime of operation (A < 1.2) at low toroidal field with ohmic heating. A magnetic null region is achieved for breakdown using the internal poloidal field coils. With a short-pulse ohmic power supply, Ip 0.1 MA has been achieved with A = 1.1 - 1.4 at Bt = 0.07 T. High loop voltage gives a high current ramp, 30-200 MA/sec, and correspondingly highly elongated plasmas (> 3). The plasmas stretch vertically until contact is made with the upper and lower limiters; this is often followed by an influx of impurities and abrupt decrease in the current ramp rate. Strong radial compression results in termination through an n = 0 instability. Low voltage operation with the longer-pulse ohmic power supply should reduce the plasma elongation and control limiter interactions during current channel growth. Completion of the power systems, plus upgrades to the limiters and wall conditioning will allow operation at full pulse length ( ~ 0.05 sec) and plasma current ( ~ 0.3 MA), and thus provide a target plasma for the higher harmonic fast wave heating system.
Toroidal nanotraps for cold polar molecules
Salhi, Marouane; Passian, Ali; Siopsis, George
2015-09-14
Electronic excitations in metallic nanoparticles in the optical regime that have been of great importance in surface-enhanced spectroscopy and emerging applications of molecular plasmonics, due to control and confinement of electromagnetic energy, may also be of potential to control the motion of nanoparticles and molecules. Here, we propose a concept for trapping polarizable particles and molecules using toroidal metallic nanoparticles. Specifically, gold nanorings are investigated for their scattering properties and field distribution to computationally show that the response of these optically resonant particles to incident photons permit the formation of a nanoscale trap when proper aspect ratio, photon wavelength, andmore » polarization are considered. However, interestingly the resonant plasmonic response of the nanoring is shown to be detrimental to the trap formation. The results are in good agreement with analytic calculations in the quasistatic limit within the first-order perturbation of the scalar electric potential. The possibility of extending the single nanoring trapping properties to two-dimensional arrays of nanorings is suggested by obtaining the field distribution of nanoring dimers and trimers.« less
Efficient magnetic fields for supporting toroidal plasmas
NASA Astrophysics Data System (ADS)
Landreman, Matt; Boozer, Allen H.
2016-03-01
The magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However, the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region, so plasma configurations should be chosen that can be supported as efficiently as possible by distant coils. The efficiency of an externally generated magnetic field is a measure of the field's shaping component magnitude at the plasma compared to the magnitude near the coils; the efficiency of a plasma equilibrium can be measured using the efficiency of the required external shaping field. Counterintuitively, plasma shapes with low curvature and spectral width may have low efficiency, whereas plasma shapes with sharp edges may have high efficiency. Two precise measures of magnetic field efficiency, which correctly identify such differences in difficulty, will be examined. These measures, which can be expressed as matrices, relate the externally produced normal magnetic field on the plasma surface to the either the normal field or current on a distant control surface. A singular value decomposition (SVD) of either matrix yields an efficiency ordered basis for the magnetic field distributions. Calculations are carried out for both tokamak and stellarator cases. For axisymmetric surfaces with circular cross-section, the SVD is calculated analytically, and the range of poloidal and toroidal mode numbers that can be controlled to a given desired level is determined. If formulated properly, these efficiency measures are independent of the coordinates used to parameterize the surfaces.
Compact toroid injection into C-2U
NASA Astrophysics Data System (ADS)
Roche, Thomas; Gota, H.; Garate, E.; Asai, T.; Matsumoto, T.; Sekiguchi, J.; Putvinski, S.; Allfrey, I.; Beall, M.; Cordero, M.; Granstedt, E.; Kinley, J.; Morehouse, M.; Sheftman, D.; Valentine, T.; Waggoner, W.; the TAE Team
2015-11-01
Sustainment of an advanced neutral beam-driven FRC for a period in excess of 5 ms is the primary goal of the C-2U machine at Tri Alpha Energy. In addition, a criteria for long-term global sustainment of any magnetically confined fusion reactor is particle refueling. To this end, a magnetized coaxial plasma-gun has been developed. Compact toroids (CT) are to be injected perpendicular to the axial magnetic field of C-2U. To simulate this environment, an experimental test-stand has been constructed. A transverse magnetic field of B ~ 1 kG is established (comparable to the C-2U axial field) and CTs are fired across it. As a minimal requirement, the CT must have energy density greater than that of the magnetic field it is to penetrate, i.e., 1/2 ρv2 >=B2 / 2μ0 . This criteria is easily met and indeed the CTs traverse the test-stand field. A preliminary experiment on C-2U shows the CT also capable of penetrating into FRC plasmas and refueling is observed resulting in a 20 - 30% increase in total particle number per single-pulsed CT injection. Results from test-stand and C-2U experiments will be presented.
Toroidal nanotraps for cold polar molecules
NASA Astrophysics Data System (ADS)
Salhi, Marouane; Passian, Ali; Siopsis, George
2015-09-01
Electronic excitations in metallic nanoparticles in the optical regime that have been of great importance in surface-enhanced spectroscopy and emerging applications of molecular plasmonics, due to control and confinement of electromagnetic energy, may also be of potential to control the motion of nanoparticles and molecules. Here, we propose a concept for trapping polarizable particles and molecules using toroidal metallic nanoparticles. Specifically, gold nanorings are investigated for their scattering properties and field distribution to computationally show that the response of these optically resonant particles to incident photons permit the formation of a nanoscale trap when proper aspect ratio, photon wavelength, and polarization are considered. However, interestingly the resonant plasmonic response of the nanoring is shown to be detrimental to the trap formation. The results are in good agreement with analytic calculations in the quasistatic limit within the first-order perturbation of the scalar electric potential. The possibility of extending the single nanoring trapping properties to two-dimensional arrays of nanorings is suggested by obtaining the field distribution of nanoring dimers and trimers.
RF plasma heating in toroidal fusion devices
Golant, V.E.; Fedorov, V.I. )
1989-01-01
The purpose of the present book is to provide, in seven chapters, a unified overview of the methods for rf heating of plasmas in toroidal fusion experiments. In Chapter 1 the problem of plasma heating in tokamaks and stellarators is formulated and the requirements for auxiliary heating techniques are described. This chapter also contains a brief review of the results of research on tokamaks and stellarators. Chapter 2 is devoted to a theoretical description of the principal physical effects involved in the rf heating of plasmas, especially the characteristics of wave propagation, of the mechanisms by which waves are absorbed and plasma heating takes place, and of the nonlinear effects that accompany heating. The primary emphasis is on a qualitative physical picture of these effects. Chapters 3-6, in turn, deal with the major rf heating techniques currently under investigation, electron cyclotron (ECH), ion cyclotron (ICH), lower hybrid (LHH), and Alfven wave heating. In each of these chapters the main schemes for heating are described, the results of theoretical analyses and numerical simulations are discussed, the technology of the heating systems is briefly described, and experimental work published through the end of 1984 is reviewed. Finally, in Chapter 7 the different rf heating techniques are compared; they are contrasted with neutral beam injection, and the feasibility of adiabatic compression as a means of heating plasmas is examined. Separate abstracts were prepared for each chapter of this book. 246 refs.
Toroidal nanotraps for cold polar molecules
Salhi, Marouane; Passian, Ali; Siopsis, George
2015-09-14
Electronic excitations in metallic nanoparticles in the optical regime that have been of great importance in surface-enhanced spectroscopy and emerging applications of molecular plasmonics, due to control and confinement of electromagnetic energy, may also be of potential to control the motion of nanoparticles and molecules. Here, we propose a concept for trapping polarizable particles and molecules using toroidal metallic nanoparticles. Specifically, gold nanorings are investigated for their scattering properties and field distribution to computationally show that the response of these optically resonant particles to incident photons permit the formation of a nanoscale trap when proper aspect ratio, photon wavelength, and polarization are considered. However, interestingly the resonant plasmonic response of the nanoring is shown to be detrimental to the trap formation. The results are in good agreement with analytic calculations in the quasistatic limit within the first-order perturbation of the scalar electric potential. The possibility of extending the single nanoring trapping properties to two-dimensional arrays of nanorings is suggested by obtaining the field distribution of nanoring dimers and trimers.
Sawtooth Instability in the Compact Toroidal Hybrid
NASA Astrophysics Data System (ADS)
Herfindal, J. L.; Maurer, D. A.; Hartwell, G. J.; Ennis, D. A.; Knowlton, S. F.
2015-11-01
Sawtooth instabilities have been observed in the Compact Toroidal Hybrid (CTH), a current-carrying stellarator/tokamak hybrid device. The sawtooth instability is driven by ohmic heating of the core plasma until the safety factor drops below unity resulting in the growth of an m = 1 kink-tearing mode. Experiments varying the vacuum rotational transform from 0.02 to 0.13 are being conducted to study sawtooth property dependance on vacuum flux surface structure. The frequency of the sawtooth oscillations increase from 2 kHz to 2.8 kHz solely due the decrease in rise time of the oscillation, the crash time is unchanged. CTH has three two-color SXR cameras, a three-channel 1mm interferometer, and a new bolometer system capable of detecting the signatures of sawtooth instabilities. The new bolometer system consists of two cameras, each containing a pair of diode arrays viewing the plasma directly or through a beryllium filter. Electron temperature measurements are found with the two-color SXR cameras through a ratio of the SXR intensities. Impurity radiation can drastically affect the electron temperature measurement, therefore new filters consisting of aluminum and carbon were selected to avoid problematic line radiation while maximizing the signal for a 100 eV plasma. This work is supported by U.S. Department of Energy Grant No. DE-FG02-00ER54610.
Tearing Mode Stability of Evolving Toroidal Equilibria
NASA Astrophysics Data System (ADS)
Pletzer, A.; McCune, D.; Manickam, J.; Jardin, S. C.
2000-10-01
There are a number of toroidal equilibrium (such as JSOLVER, ESC, EFIT, and VMEC) and transport codes (such as TRANSP, BALDUR, and TSC) in our community that utilize differing equilibrium representations. There are also many heating and current drive (LSC and TORRAY), and stability (PEST1-3, GATO, NOVA, MARS, DCON, M3D) codes that require this equilibrium information. In an effort to provide seamless compatibility between the codes that produce and need these equilibria, we have developed two Fortran 90 modules, MEQ and XPLASMA, that serve as common interfaces between these two classes of codes. XPLASMA provides a common equilibrium representation for the heating and current drive applications while MEQ provides common equilibrium and associated metric information needed by MHD stability codes. We illustrate the utility of this approach by presenting results of PEST-3 tearing stability calculations of an NSTX discharge performed on profiles provided by the TRANSP code. Using the MEQ module, the TRANSP equilibrium data are stored in a Fortran 90 derived type and passed to PEST3 as a subroutine argument. All calculations are performed on the fly, as the profiles evolve.
Spontaneous toroidal flow generation due to negative effective momentum diffusivity
McMillan, Ben F.
2015-02-15
Spontaneous structure formation, and in particular, zonal flows, is observed in a broad range of natural and engineered systems, often arising dynamically as the saturated state of a linear instability. Flows in tokamaks are known to self-organise on small scales, but large scale toroidal flows also arise even when externally applied torques are zero. This has previously been interpreted as the result of small externally imposed breaking of a symmetry. However, we show that for large enough field line pitch, a robust spontaneous symmetry breaking occurs, leading to the generation of strong toroidal flow structures; parameters are typical of Spherical Tokamak discharges with reversed shear profiles. The short wavelength dynamics are qualitatively similar to the growth of poloidal flow structures, and toroidal flow gradients nonlinearly saturate at levels where the shearing rate is comparable to linear growth rate. On long wavelengths, we measure Prandtl numbers of around zero for these systems, in conjunction with the formation of structured toroidal flows, and we show that this is consistent with a model of momentum transport where fluxes act to reinforce small flow gradients: the effective momentum diffusivity is negative. Toroidal flow structures are largely unaffected by collisional damping, so this may allow toroidal bulk flows of order the ion thermal velocity to be maintained with zero momentum input. This phenomenon also provides a mechanism for the generation of localised meso-scale structures like transport barriers.
Ambipolar magnetic fluctuation-induced heat transport in toroidal devices
Terry, P.W.; Fiksel, G.; Ji, H.; Almagri, A.F.; Cekic, M.; Den Hartog, D.J.; Diamond, P.H.; Prager, S.C.; Sarff, J.S.; Shen, W.; Stoneking, M.; Ware, A.S.
1996-05-01
The total magnetic fluctuation-induced electron thermal flux has been determined in the Madison Symmetric Torus (MST) reversed-field pinch [Fusion Technol. {bold 19}, 131 (1991)] from the measured correlation of the heat flux along perturbed fields with the radial component of the perturbed field. In the edge region the total flux is convective and intrinsically ambipolar constrained, as evidenced by the magnitude of the thermal diffusivity, which is well approximated by the product of ion thermal velocity and the magnetic diffusivity. A self-consistent theory is formulated and shown to reproduce the experimental results, provided nonlinear charge aggregation in streaming electrons is accounted for in the theory. For general toroidal configurations, it is shown that ambipolar constrained transport applies when remote magnetic fluctuations (i.e., global modes resonant at distant rational surfaces) dominate the flux. Near locations where the dominant modes are resonant, the transport is nonambipolar. This agrees with the radial variation of diffusivity in MST. Expectations for the tokamak are also discussed. {copyright} {ital 1996 American Institute of Physics.}
New picture of the 1/1 internal kink and sawtooth in compressible toroidal plasmas
NASA Astrophysics Data System (ADS)
Sugiyama, Linda
2013-10-01
The m = 1 , n = 1 internal kink mode and the sawtooth crash have been analyzed extensively in magnetically confined toroidal plasmas. Nevertheless, many questions remain. A new analysis, with the aid of numerical simulation, shows that small parameter expansions such as large aspect ratio break down in general for the MHD compressible toroidal 1/1 instability with realistically small growth rates. The perpendicular momentum rate of change ρ ∂v⊥ / ∂ t must be very small compared to the individual terms in - ρ (v . ∇) v |⊥ + J × B |⊥ -∇⊥ p . The lowest order mode still has the standard 1/1 internal kink form, but the v⊥ magnitude and growth rate are determined by the higher order terms. Terms containing B~ϕ , nominally associated with the compressional Alfvén wave are important. One corollary is that reduced MHD (RMHD) fails completely and Sweet-Parker-type reconnection never develops. At a critical nonlinear amplitude, associated with the growth of the higher toroidal harmonics, a fast, explosive crash begins with rapidly accelerating velocity growth that matches observations. Other transverse MHD instabilities experience analogous effects. Work supported by the U.S. Department of Energy.
Kimin Kim, et al
2013-04-23
Accurate calculation of perturbed distribution function δf and perturbed magnetic fi eld δB is essential to achieve prediction of non-ambipolar transport and neoclassical toroidal viscosity (NTV) in perturbed tokamaks. This paper reports a study of the NTV with a δf particle code (POCA) and improved understanding of magnetic braking in tokamak experiments. POCA calculates the NTV by computing f with guiding-center orbit motion and using B from the ideal perturbed equilibrium code (IPEC). POCA simulations are compared with experimental estimations for NTV, which are measured from angular momentum balance (DIII-D) and toroidal rotational damping rate (NSTX). The calculation shows good agreement in total NTV torque for the DIII-D discharge, where an analytic neoclassical theory also gives a consistent result thanks to relatively large aspect-ratio and slow toroidal rotations. In NSTX discharges, where the aspect-ratio is small and the rotation is fast, the theory only gives a qualitative guide for predicting NTV. However, the POCA simulation largely improves the quantitative NTV prediction for NSTX. It is discussed that a self- consistent calculation of δ B using general perturbed equilibria is eventually necessary since a non-ideal plasma response can change the perturbed eld and thereby the NTV torque.
Peeters, A. G.; Angioni, C.; Strintzi, D.
2007-06-29
In this Letter, the influence of the ''Coriolis drift'' on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiment000.
Learning Geometry through Dynamic Geometry Software
ERIC Educational Resources Information Center
Forsythe, Sue
2007-01-01
In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…
Dipolar condensates confined in a toroidal trap: Ground state and vortices
NASA Astrophysics Data System (ADS)
Abad, M.; Guilleumas, M.; Mayol, R.; Pi, M.; Jezek, D. M.
2010-04-01
We study a Bose-Einstein condensate of Cr52 atoms confined in a toroidal trap with a variable strength of s-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system from a pancake-shaped condensate when it is large to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity fields, finding that these also show a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the z direction provides a qualitative measure of the difference between the velocity in the different density peaks.
Advancing High Current Startup via Localized Helicity Injection in the PEGASUS Toroidal Experiment
NASA Astrophysics Data System (ADS)
Hinson, E. T.; Barr, J. L.; Bongard, M. W.; Burke, M. G.; Fonck, R. J.; Perry, J. M.; Redd, A. J.; Schlossberg, D. J.
2013-10-01
Non-solenoidal startup via local helicity injection (LHI) and poloidal field induction is used to produce Ip = 0 . 17 MA tokamak discharges. Impurity contamination has been reduced to negligible levels by use of conical frustum cathode geometry and local scraper limiters. Attainable currents are governed by global limits of helicity and energy balance, and Taylor relaxation. A simple lumped parameter model based on these limits is used to project discharge evolution, and indicates that attaining 1 MA in NSTX-U will require LHI-driven effective loop voltages to dominate contributions from dLp / dt . This regime contrasts with results to date and will be tested at 0.3 MA in PEGASUS with a new integrated multi-injector array. Injector impedance characteristics are consistent with magnetically-limited regimes observed in higher-power foilless diodes. Bursts of MHD are measured on time scales of order ~ 100 μ s, and correlate with rapid equilibrium changes, discrete rises in Ip, redistribution of the toroidal current, ion heating (Ti ~ 1 keV), transient drops in injector voltage, and apparent n = 1 line-tied kink activity at the injector. NIMROD simulations of high-field-side HI discharges in PEGASUS are in qualitative agreement, suggesting Ip buildup results from inward propagating toroidal current loops created by intermittent reconnection of injected current streams. Work supported by US DOE Grant DE-FG02-96ER54375.
Toroidal dust motion in magnetized plasmas
Reichstein, Torben; Pilch, Iris; Piel, Alexander
2010-09-15
In a magnetized anodic plasma, dust particles can be confined in a torus-shaped cloud with a distinct dust-free region (void) in its center. The formation of these clouds and their dynamical behavior are experimentally studied with a new observation geometry. The particles rotate about the major axis of the torus. A refined model for the description of the particle dynamics is presented that accounts for inertia and many-body effects.
Control of toroidal-like asymmetries in a heliac
NASA Astrophysics Data System (ADS)
Spanjers, G. G.; Nelson, B. A.; Ribe, F. L.; Jarboe, T. R.; Barnes, D. C.
1993-05-01
A simple modification to the heliac coil configuration [A. H. Boozer et al., Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1966), Vol. 1, p. 103] is described that reduces the toroidal perturbation to the magnetic field structure and significantly restores the helical symmetry. This is accomplished by shifting the internal current-carrying conductor (hardcore) of the heliac radially inward from its normal position at the geometric center of the external l=1 coils. It is shown by computations that a large-aspect-ratio toroidal heliac is similar to a helically symmetric linear heliac in which the hardcore has been shifted. This similarity is seen in the analytic form of the magnetic potential, the flux surface shape, and in the harmonic spectra of the field lines. It is then shown that the toroidicity perturbations can be reduced in a toroidal heliac by combining these effects—using a radially inward hardcore shift in the toroidal configuration. In the experiments reported here the toroidal-like effects are created in the linear High Beta Q Machine (HBQM) heliac [C. M. Greenfield et al., Phys. Fluids B 2, 133 (1990)] by shifting the hardcore off the geometric center of the l=1 coils. The induced toroidal-like effects are seen from an asymmetry in the axial excluded flux; however, no decrease in global beta is seen as compared to the unshifted symmetric case (G. G. Spanjers, Ph.D. dissertation, University of Washington, 1992) indicating the absence of large-scale magnetohydrodynamic instabilities at high beta.
General very special relativity is Finsler geometry
Gibbons, G. W.; Gomis, Joaquim; Pope, C. N.
2007-10-15
We ask whether Cohen and Glashow's very special relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved space-time with a cosmological constant. We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to noncommutative translations analogous to those of the de Sitter deformation of the Poincare group: space-time remains flat. Only a 1-parameter family DISIM{sub b}(2) of deformations of SIM(2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point-particle action invariant under DISIM{sub b}(2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIM{sub b}(2)-invariant wave equations for particles of spins 0, (1/2), and 1. The experimental bound, |b|<10{sup -26}, raises the question 'Why is the dimensionless constant b so small in very special relativity?'.
Combinatorial Geometry Printer Plotting.
Energy Science and Technology Software Center (ESTSC)
1987-01-05
Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.
Geometry of area without length
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming; Inami, Takeo
2016-01-01
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.
A volume H/sup /minus// ion source with a toroidal discharge chamber
Prelec, K.
1989-01-01
A new volume H/sup /minus// ion source has been designed with the objective to reach a current of 50 mA in 1 ms pulses, to be eventually used on the new RFQ preinjector at BNL's Alternating Gradient Synchrotron. Its main feature is a full rotational symmetry, with a toroidal discharge chamber separated from the central extraction region by a conically shaped dipole field. Preliminary studies consisted of measurements of the H/sup /minus// yield and the accompanying electron component as a function of the discharge current, discharge voltage, pressure, and extraction voltage for several geometries of the conical field; effects of the filament heating current were also studied, both for dc and ac cases. So far, it was possible to extract an H/sup /minus// current of 30 mA through an aperture of 1 cm/sup 2/, with an electron component of about 750 mA. 4 refs., 6 figs.
Calculation of the vacuum Green's function valid for high toroidal mode number in tokamaks.
NASA Astrophysics Data System (ADS)
Chance, Morrell; Turnbull, Alan
2005-10-01
The present evaluation of the Green's function used for the magmetic scalar potential in vacuum calculations for axisymmetric geometry in the vacuum segments of gato, pest and other mhd stability codes has been found to be deficient for moderately high toroidal mode numbers. This was due to the loss of numerical precision arising from the upward recursion relation used for generating the functions to high mode numbers. The recursion is initiated from the complete elliptic integrals of the first and second kinds. To ameliorate this, a direct integration of the integral representation of the function was crafted to achieve the necessary high accuracy for moderately high mode numbers. At very high mode numbers the loss of numerical precision due to the oscillatory behavior of the integrand is further avoided by judiciously deforming the integration contour in the complex plane. Machine precision, roughly 14 -- 16 digits, accuracy can be achieved by using a combination of both these techniques.
ERIC Educational Resources Information Center
McDonald, Nathaniel J.
2001-01-01
Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…
Theory for neoclassical toroidal plasma viscosity in tokamaks
NASA Astrophysics Data System (ADS)
Shaing, K. C.; Chu, M. S.; Hsu, C. T.; Sabbagh, S. A.; Seol, Jae Chun; Sun, Y.
2012-12-01
Error fields and magnetohydrodynamic modes break toroidal symmetry in tokamaks. The broken symmetry enhances the toroidal plasma viscosity, which results in a steady-state toroidal plasma flow. A theory for neoclassical toroidal plasma viscosity in the low-collisionality regimes is developed. It extends stellarator transport theory to include multiple modes and to allow for |m - nq| ˜ 1. Here, m is the poloidal mode number, n is the toroidal mode number and q is the safety factor. The bounce averaged drift kinetic equation is solved in several asymptotic limits to obtain transport fluxes. These fluxes depend non-linearly on the radial electric field except for those in the 1/ν regime. Here, ν is the collision frequency. The theory is refined to include the effects of the superbanana plateau resonance at the phase space boundary and the finite ∇B drift on the collisional boundary layer fluxes. Analytical expressions that connect all asymptotic limits are constructed and are in good agreement with the numerical results. The flux-force relations that relate transport fluxes to forces are used to illustrate the roles of transport fluxes in the momentum equation. It is shown that the ambipolar state is reached when the momentum equation is relaxed. It is also shown that the origin of the momentum for plasma flow generated without momentum sources is the local unbalance of particles' momenta and is diamagnetic in nature regardless of the details of the theory.
Toroidal Plasma Thruster for Interplanetary and Interstellar Space Flights
N.N. Gorelenkov; L.E. Zakharov; and M.V. Gorelenkova
2001-07-11
This work involves a conceptual assessment for using the toroidal fusion reactor for deep space interplanetary and interstellar missions. Toroidal thermonuclear fusion reactors, such as tokamaks and stellarators, are unique for space propulsion, allowing for a design with the magnetic configuration localized inside toroidal magnetic field coils. Plasma energetic ions, including charged fusion products, can escape such a closed configuration at certain conditions, a result of the vertical drift in toroidal rippled magnetic field. Escaping particles can be used for direct propulsion (since toroidal drift is directed one way vertically) or to create and heat externally confined plasma, so that the latter can be used for propulsion. Deuterium-tritium fusion neutrons with an energy of 14.1 MeV also can be used for direct propulsion. A special design allows neutrons to escape the shield and the blanket of the tokamak. This provides a direct (partial) conversion of the fusion energy into the directed motion of the propellant. In contrast to other fusion concepts proposed for space propulsion, this concept utilizes the natural drift motion of charged particles out of the closed magnetic field configuration.
Non-solenoidal Plasma Startup in the Pegasus Toroidal Experiment
NASA Astrophysics Data System (ADS)
Sontag, Aaron
2008-11-01
Non-solenoidal (NS) startup will simplify the design of future tokamaks by eliminating need for a central solenoid and is required for an ST based CTF. In Pegasus, washer-stack current sources (plasma guns) are used to initiate NS discharges via point-source DC helicity injection. Current injected parallel to the helical vacuum field can relax into a tokamak-like configuration with toroidally-averaged closed flux and tokamak-like confinement. This requires no modification of the vacuum vessel and is scalable to fusion grade systems with proper geometry. Guns in the divertor region create discharges with Ip up to 50 kA, 3 times the vacuum windup. Nonlinear 3D simulation with NIMROD shows excitation of a line-tied kink, producing poloidal flux amplification. Evidence of flux amplification includes: reversal of edge poloidal magnetic flux; Ip increase over vacuum geometric windup; plasma position subject to radial force balance; and persistence of Ip after gun shut-off. Equilibria show high edge current (li = 0.2) and elevated q (qmin> 6), allowing access to high IN (IN> 12). Guns at the outboard midplane produce Ip up to 7 times the vacuum windup with large n=1 activity when edge q passes through rational surfaces. Line averaged density up to 2x10^19 m-3 after relaxation shows an increase in particle confinement over non-relaxed cases. Maximum Ip is determined by helicity and radial force balance, tokamak stability, and Taylor relaxation. Coupling midplane gun discharges to other CD is straightforward due to Ip decay times >3 ms. Poloidal field induction has been used to create NS discharges up to 80 kA and gun plasmas with Ip of 60 kA have been ramped to over 100 kA by including OH drive. Present research is aimed at understanding the physics of this technique in order to form NS targets in excess of 200 kA and design NS startup systems for larger devices.
Comparison of Microinstability Properties for Stellarator Magnetic Geometries
G. Rewoldt; L.-P. Ku; W.M. Tang
2005-06-16
The microinstability properties of seven distinct magnetic geometries corresponding to different operating and planned stellarators with differing symmetry properties are compared. Specifically, the kinetic stability properties (linear growth rates and real frequencies) of toroidal microinstabilities (driven by ion temperature gradients and trapped-electron dynamics) are compared, as parameters are varied. The familiar ballooning representation is used to enable efficient treatment of the spatial variations along the equilibrium magnetic field lines. These studies provide useful insights for understanding the differences in the relative strengths of the instabilities caused by the differing localizations of good and bad magnetic curvature and of the presence of trapped particles. The associated differences in growth rates due to magnetic geometry are large for small values of the temperature gradient parameter n identical to d ln T/d ln n, whereas for large values of n, the mode is strongly unstable for all of the different magnetic geometries.
NASA Astrophysics Data System (ADS)
Doares, A. R.; Wang, K.; Patterson, A. S.; Stoneking, M. R.
2014-10-01
Electron plasma is confined with a purely toroidal magnetic field in the Lawrence Non-Neutral Torus II (R0 = 18 cm, a ~ 2 cm), for times (~1 s) that are much longer than any of the dynamical timescales of the system. The experiment can be operated as a variable-length partial torus or a full torus trap. The damping rate for the m = 1 diocotron mode in a partial torus trap is found to depend on the equilibrium position (major radius) and on magnetic field (150 G--550 G). We report on efforts to explain these results in terms of rotational and magnetic pumping effects using 3D (Poisson-Boltzmann) equilibria calculations. Novel full torus asymmetry modes are examined with multiple separatrices and a new charge tomography is developed to infer charge density from image charge measurements on the conducting boundary. This work is supported by National Science Foundation Award No. 1202540.
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
NASA Astrophysics Data System (ADS)
Throumoulopoulos, George; Kuiroukidis, Apostolos; Tasso, Henri
2015-11-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis. This work has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018 under grant agreement No 633053.
Toroidal Superheavy Nuclei in Skyrme-Hartree-Fock Approach
Staszczak, A.; Wong, Cheuk-Yin
2009-01-01
Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of superheavy elements. For nuclei with a sufficient oblate deformation (Q_{20} < -200 b), it becomes energetically favorable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state energy is strongly dependent both on the atomic number Z and the mass number A. We discuss the region of Z and A where the toroidal SHF+BCS total energy begins to be a global minimum.
Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure
Kuiroukidis, Ap; Throumoulopoulos, G. N.; Tasso, H.
2015-08-15
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Novel Design for Centrifugal Countercurrent Chromatography: I. Zigzag Toroidal Column.
Yang, Yi; Aisa, Haji Akber; Ito, Yoichiro
2009-01-01
The toroidal coil using an equilateral triangular core has improved both retention of the stationary phase and peak resolution of the conventional toroidal coil in centrifugal countercurrent chromatography. To further improve the retention of stationary phase and peak resolution, a novel zigzag toroidal coil was designed and the performance of the system was evaluated at various flow rates. The results indicated that both retention of stationary phase and peak resolution were improved as the flow rate was decreased. Modification of the tubing by pressing at given intervals with a pair of pliers improved the peak resolution without increasing the column pressure. All these separations were performed under low column pressure indicating the separation can be further improved by increasing the column length and/or revolution speed without damaging the separation column. PMID:20046954
Profiling compact toroid plasma density on CTIX with laser deflection
NASA Astrophysics Data System (ADS)
Brockington, Samuel Joseph Erwin
A laser deflectometer measures line-integrated plasma density gradient using laser diodes and amplified point detectors. A laser passing through an optically thin plasma is refracted by an amount proportional to the line-integrated electron density gradient. I have designed, installed, and operated a deflection diagnostic for the Compact Toroid Injection Experiment (CTIX), a plasma rail gun which can create compact toroid (CT) plasmas of controllable density and velocity. The diagnostic design and motivation are discussed, as well as three experiments performed with deflectometry. Thus, my thesis consists of the design of the deflectometer diagnostic, a comparison of its accuracy to interferometer density measurements, and finally a survey of compact toroid density profiles in two dimensions conducted with an array of detectors.
Bi-2223 HTS winding in toroidal configuration for SMES coil
NASA Astrophysics Data System (ADS)
Kondratowicz-Kucewicz, B.; Janowski, T.; Kozak, S.; Kozak, J.; Wojtasiewicz, G.; Majka, M.
2010-06-01
Energy can be stored in the magnetic field of a coil. Superconducting Magnetic Energy Storage (SMES) is very promising as a power storage system for load levelling or power stabilizer. However, the strong electromagnetic force caused by high magnetic field and large coil current is a problem in SMES systems. A toroidal configuration would have a much less extensive external magnetic field and electromagnetic forces in winding. The paper describes the design of HTS winding for SMES coil in modular toroid configuration consist of seven Bi-2223 double-pancakes as well as numerical analysis of SMES magnet model using FLUX 3D package. As the results of analysis the paper presents the optimal coil configuration and the parameters such as radius of toroidal magnet, energy stored in magnet and magnetic field distribution.
Propagations of drift waves in toroidal plasma systems
Yoshikawa, S.; Cheng, C.Z.
1990-05-01
Drift wave patterns in toroidal plasmas are studied. The dispersion relation was simplified to retain both the shear and the toroidal coupling effects. Since the dispersion relation does not depend on the toroidal angle, {phi}, the dispersion is solved in the two- dimensional space made up with minor radius and poloidal angle. The dispersion relation can be reduced into second-order, partial differential equations of a hyperbolic type. The one-dimensional convective mode analysis, which was originated in the 1960's, was extended into the two-dimensional analysis. Depending on the strength of the magnetic shear, one can obtain either the convective or the localized solutions. The results show that the plasma is expected to be unstable for large azimuthal mode number and that the plasma instability tends to be more stabilized for large mass ions. 8 refs., 3 figs., 1 tab.
Polymer- and salt-induced toroids of hexagonal DNA.
Ubbink, J; Odijk, T
1995-01-01
A model is proposed for polymer- and salt-induced toroidal condensates of DNA, based on a recent theory of the undulation enhancement of the electrostatic interaction in the bulk hexagonal phase of semiflexible polyions. In a continuum approximation, the thermodynamic potential of a monomolecular toroid may be split up in bulk, surface, and curvature contributions. With the help of an approximate analytical minimization procedure, the optimal torus dimensions are calculated as a function of the concentrations of inert polymer and added salt. The stability of the torus is analyzed in terms of its surface tension and a bulk melting criterion. The theory should be applicable to psi-toroids that are not too thick. PMID:7711268
High-Q toroidal cavities for high frequency klystrons.
NASA Technical Reports Server (NTRS)
Branch, G. M.
1972-01-01
A toroidal cavity developed for a 4-KW 12 GHz satellite-borne television transmitter klystron is described. The cavity has an internal Q 40% higher than that of a conventional cylindrical doubly reentrant cavity, thus yielding higher circuit efficiency and conserving energy which cannot be recovered in multistage depressed potential beam collectors. As a result of optimization studies with a digital computer program for obtaining cavity field distributions by a relaxation method and for computing the intrinsic cavity parameters, a particular cavity configuration with conical reentrant tunnel tips and toroidal walls is shown to provide good thermal characteristics and mechanical rigidity as well as low internal losses.
Dynamically controlled toroidal and ring-shaped magnetic traps
Fernholz, T.; Gerritsma, R.; Spreeuw, R. J. C.; Krueger, P.
2007-06-15
We present traps with toroidal (T{sup 2}) and ring-shaped topologies based on adiabatic potentials for radio-frequency-dressed Zeeman states in a ring-shaped magnetic quadrupole field. Simple adjustment of the radio-frequency fields provides versatile possibilities for dynamical parameter tuning, topology change, and controlled potential perturbation. We show how to induce toroidal and poloidal rotations, and demonstrate the feasibility of preparing degenerate quantum gases with reduced dimensionality and periodic boundary conditions. The great level of dynamical and even state-dependent control is useful for atom interferometry.
On the longitudinal coupling impedance of a toroidal beam tube
Hahn, H.; Tepikian, S.
1990-01-01
In this paper, the longitudinal coupling impedance of a smooth toroidal beam tube is derived. By treating the torus as a slow-wave structure, the well-known method of describing the impedance in terms of cavity resonances can be used. A simple analytical expression for the coupling impedance of a toroidal beam tube with square cross section valid in the low-frequency limit is obtained. The results from the present study are compared with previously published solutions and qualitative differences are pointed out. 16 refs., 3 figs., 1 tab.
On the vector Helmholtz equation in toroidal waveguides
Biro, Thomas
2005-02-15
A wave splitting method is proposed to solve the problem of propagation of microwaves in a circular waveguide bend of circular cross section. The splitting method, applied to the vector Helmholtz equation, gives a stable solution in terms of waves propagating to the right and to the left in the bend. The formulation is particularly transparent for analyzing the scattering properties of toroidal bends. The basis for the transparency of the method is that the wave splitting is formally exact as the exponential of the square root of a differential operator. The modal functions of the straight cylindrical waveguide are chosen as basis functions in the transverse quasi-toroidal variables.
The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
NASA Astrophysics Data System (ADS)
Glasser, A. H.
2016-07-01
A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for fixed-boundary modes in a cylindrical plasma. For toroidal mode number n ≠ 0 , the stability problem is reduced to the numerical integration of a high-order complex system of ordinary differential equations, the Euler-Lagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straight-fieldline flux coordinate system. Unlike the cylindrical case, different poloidal harmonics couple to each other, which introduces coupling between adjacent singular intervals. A boundary condition is used at each singular surface, where m = nq and q ( ψ ) is the safety factor, to cross the singular surface and continue the solutions beyond it. Fixed-boundary instability is indicated by the vanishing of a real determinant of a Hermitian complex matrix constructed from the fundamental matrix of solutions, the generalization of Newcomb's crossing criterion. In the absence of fixed-boundary instabilities, an M × M plasma response matrix W P , with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum boundary. This is added to a vacuum response matrix W V to form a total response matrix W T . The existence of negative eigenvalues of W T indicates the presence of free-boundary instabilities. The method is implemented in the fast and accurate DCON code.
Podesta, M; Fredrickson, E D; Gorelenkov, N N; LeBlanc, B P; Heidbrink, W W; Crocker, N A; Kubota, S
2010-08-19
The effects of a sheared toroidal rotation on the dynamics of bursting Toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40 557 (2000)]. The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of increased damping is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes.
Podesta, M.; Bell, R. E.; Fredrickson, E. D.; Gorelenkov, N. N.; LeBlanc, B. P.; Heidbrink, W. W.; Crocker, N. A.; Kubota, S.; Yuh, H.
2010-12-15
The effects of a sheared toroidal rotation on the dynamics of bursting toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)]. The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of decorrelation of the modes by the sheared rotation is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes on NSTX.
Computational Knowledge for Toroidal Confinement Physics: Part I
Chang, C. S.
2009-02-19
Basic high level computational knowledge for studying the toroidal confinement physics is discussed. Topics include the primacy hierarchy of simulation quantities in statistical plasma physics, importance of the nonlinear-multiscale self-organization phenomena in a computational study, different types of codes for different applications, and different types of computer architectures for different types of codes.
Development of a high capacity toroidal Ni/Cd cell
NASA Technical Reports Server (NTRS)
Holleck, G. L.; Foos, J. S.; Avery, J. W.; Feiman, V.
1981-01-01
A nickel cadmium battery design which can offer better thermal management, higher energy density and much lower cost than the state-of-the-art is emphasized. A toroidal Ni/Cd cell concept is described. It was critically reviewed and used to develop two cell designs for practical implementation. One is a double swaged and the other a swaged welded configuration.
Flat-band assembly for toroidal transformer cores
NASA Technical Reports Server (NTRS)
Mclyman, W. T.
1973-01-01
Toroidal transformer cores are often banded together by means of strap. Spot welds secure strap. Proper tension is obtained by use of special fixture in conjunction with winding of wire which is placed temporarily on core; winding is excited by dc current to hold core halves together magnetically during alignment.
Plasma Properties of Microwave Produced Plasma in a Toroidal Device
NASA Astrophysics Data System (ADS)
Singh, Ajay; Edwards, W. F.; Held, Eric
2011-10-01
We have modified a small tokamak, STOR-1M, on loan from University of Saskatchewan, to operate as a low-temperature (~5 eV) toroidal plasma machine with externally induced toroidal magnetic fields ranging from zero to ~50 G. The plasma is produced using microwave discharges at relatively high pressures. Microwaves are produced by a kitchen microwave-oven magnetron operating at 2.45 GHz in continuous operating mode, resulting in pulses ~0.5 s in duration. Initial measurements of plasma formation in this device with and without applied magnetic fields are presented. Plasma density and temperature profiles have been measured using Langmuir probes and the magnetic field profile inside the plasma has been obtained using Hall probes. When the discharge is created with no applied toroidal magnetic field, the plasma does not fill the entire torus due to high background pressure. However, when a toroidal magnetic field is applied, the plasma flows along the applied field, filling the torus. Increasing the applied magnetic field seems to aid plasma formation - the peak density increases and the density gradient becomes steeper. Above a threshold magnetic field, the plasma develops low-frequency density oscillations due to probable excitation of flute modes in the plasma.
The ATF (Advanced Toroidal Facility) Status and Control System
Baylor, L.R.; Devan, W.R.; Sumner, J.N.; Alban, A.M.
1987-01-01
The Advanced Toroidal Facility (ATF) Status and Control System (SCS) is a programmable controller-based state monitoring and supervisory control system. This paper describes the SCS implementation and its use of a host computer to run a commercially available software package that provides color graphic interactive displays, alarm logging, and archiving of state data.
Collisional damping of the geodesic acoustic mode with toroidal rotation. I. Viscous damping
NASA Astrophysics Data System (ADS)
Gong, Xueyu; Xie, Baoyi; Guo, Wenfeng; Chen, You; Yu, Jiangmei; Yu, Jun
2016-03-01
With the dispersion relation derived for the geodesic acoustic mode in toroidally rotating tokamak plasmas using the fluid model, the effect of the toroidal rotation on the collisional viscous damping of the geodesic acoustic mode is investigated. It is found that the collisional viscous damping of the geodesic acoustic mode has weak increase with respect to the toroidal Mach number.
Resistivity and sheared rotation effects on the toroidal external kink mode
NASA Astrophysics Data System (ADS)
Cole, A. J.; Brennan, D. P.; Finn, J. M.
2014-10-01
We present PEST-III analysis of the toroidal external kink with plasma resistivity and sheared rotation for a range of equilibria varying elongation, driven unstable by increasing β. The results show that the typical ordering for marginally stable β values is βrp,rw <βrp,iw <βip,rw <βip,iw , where rp,ip signify resistive or ideal plasma, and iw,rw indicate ideal wall or resistive wall (no-wall). The two resistive plasma β limits are significantly lower than the two ideal plasma values. We vary aspects of the tearing layer physics by means of a variational principle with Padé approximants, and compare with a general computational solution for the layers to gain insight. We also include pressure gradient and local velocity shear within the layers. Global rotation shear Ω' is included in the form of a relative rotation of the q = 2 , 3 , ... surfaces and we investigate the resultant effect on the poloidal mode number spectrum. We then present a model for active feedback control, which is the toroidal generalization building on recent results in cylindrical mode control theory [D. P. Brennan and J. M. Finn, submitted to Phys. Plasmas (2014)].
Entropy production and Onsager symmetry in neoclassical transport processes of toroidal plasmas
Sugama, H.; Horton, W.
1996-01-01
Entropy production and Onsager symmetry in neoclassical transport processes of magnetically confined plasmas are studied in detail for general toroidal systems, including nonaxisymmetric configurations. It is found that the flux surface average of the entropy production defined from the linearized collision operator and the gyroangle-averaged distribution function coincides with the sum of the inner products of the thermodynamic forces and the conjugate fluxes consisting of the Pfirsch-Schlueter, banana-plateau, nonaxisymmetric parts of the neoclassical radial fluxes and the parallel current. It is proved from the self-adjointness of the linearized collision operator that the Onsager symmetry is robustly valid for the neoclassical transport equations in the cases of general toroidal plasmas consisting of electrons and multi-species ions with arbitrary collision frequencies. It is shown that the Onsager symmetry holds whether or not the ambipolarity condition is used to reduce the number of the conjugate pairs of the transport fluxes and the thermodynamic forces. The full transport coefficients for the banana-plateau and nonaxisymmetric parts are separately derived, and their symmetry properties are investigated. The nonaxisymmetric transport equations are obtained for arbitrary collision frequencies in the Pfirsch{endash}Schlueter and plateau regimes, and it is directly confirmed that the total banana-plateau and nonaxisymmetric transport equations satisfy the Onsager symmetry. {copyright} {ital 1996 American Institute of Physics.}
An analytic model of toroidal half-wave oscillations: Implication on plasma density estimates
NASA Astrophysics Data System (ADS)
Bulusu, Jayashree; Sinha, A. K.; Vichare, Geeta
2015-06-01
The developed analytic model for toroidal oscillations under infinitely conducting ionosphere ("Rigid-end") has been extended to "Free-end" case when the conjugate ionospheres are infinitely resistive. The present direct analytic model (DAM) is the only analytic model that provides the field line structures of electric and magnetic field oscillations associated with the "Free-end" toroidal wave for generalized plasma distribution characterized by the power law ρ = ρo(ro/r)m, where m is the density index and r is the geocentric distance to the position of interest on the field line. This is important because different regions in the magnetosphere are characterized by different m. Significant improvement over standard WKB solution and an excellent agreement with the numerical exact solution (NES) affirms validity and advancement of DAM. In addition, we estimate the equatorial ion number density (assuming H+ atom as the only species) using DAM, NES, and standard WKB for Rigid-end as well as Free-end case and illustrate their respective implications in computing ion number density. It is seen that WKB method overestimates the equatorial ion density under Rigid-end condition and underestimates the same under Free-end condition. The density estimates through DAM are far more accurate than those computed through WKB. The earlier analytic estimates of ion number density were restricted to m = 6, whereas DAM can account for generalized m while reproducing the density for m = 6 as envisaged by earlier models.
NASA Astrophysics Data System (ADS)
Lee, S. Y.; Kwak, S. Y.; Seo, J. H.; Lee, S. Y.; Park, S. H.; Kim, W. S.; Lee, J. K.; Bae, J. H.; Kim, S. H.; Sim, K. D.; Seong, K. C.; Jung, H. K.; Choi, K.; Hahn, S.
2009-10-01
Superconducting magnetic energy storage (SMES) is one of the promising power system applications of superconducting technology and has been actively researched and developed worldwide. Generally, there are three types of SMES-solenoid, multiple solenoid, and toroid. Among these types, toroid type seems to require more wires than solenoid type and multiple solenoid type at the same operating current. However toroid type reduces normal field in the wire and stray field dramatically because magnetic field is confined inside the coil. So, the total length of wire in the toroid type can be reduced in comparison with that in the solenoid type by increasing operating current. In this paper, a 2.5 MJ class SMES with HTS magnets of single solenoid, multiple solenoid and modular toroid type were optimized using a recently developed multi-modal optimization technique named multi-grouped particle swarm optimization (MGPSO). The objective of the optimization was to minimize the total length of HTS superconductor wires satisfying some equality and inequality constraints. The stored energy and constraints were calculated using 3D magnetic field analysis techniques and an automatic tetrahedral mesh generator. Optimized results were verified by 3D finite element method (FEM).
High-frequency electric field measurement using a toroidal antenna
Lee, K.H.
1997-01-01
In this paper the author describes an innovative method of measuring high-frequency electric fields using a toroid. For typical geophysical applications the new sensor will detect electric fields for a wide range of spectrum starting from 1.0 MHz. This window, in particular the lower frequency range between 1.0 to 100 MHz, has not been used for existing electromagnetic or radar systems to detect small objects in the upper few meters of the ground. Ground penetrating radar (GPR) can be used successfully in this depth range if the ground is resistive but most soils are, in fact, conductive (0.01 to 1.0 S/m) rendering GPR inefficient. Other factors controlling the resolution of GPR system for small objects is the spatial averaging inherent in the electric dipole antenna and the scattering caused by soil inhomogeneities of dimensions comparable to the wavelength (and antenna size). For maximum resolution it is desirable to use the highest frequencies but the scattering is large and target identification is poor. Time-varying magnetic fields induce an emf (voltage) in a toroid. The electric field at the center of the toroid is shown to be linearly related to this induced voltage. By measuring the voltage across a toroid one can easily and accurately determine the electric field. The new sensor will greatly simplify the cumbersome procedure involved with GPR measurements with its center frequency less than 100 MHz. The overall size of the toroidal sensor can be as small as a few inches. It is this size advantage that will not only allow easy fabrication and deployment of multi-component devices either on the surface or in a borehole, but it will render greatly improved resolution over conventional systems.
ERIC Educational Resources Information Center
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Geometry of multihadron production
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
ERIC Educational Resources Information Center
Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem
2009-01-01
Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…
Euclidean Geometry via Programming.
ERIC Educational Resources Information Center
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
ERIC Educational Resources Information Center
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
Planetary Image Geometry Library
NASA Technical Reports Server (NTRS)
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
NASA Astrophysics Data System (ADS)
Mastrano, A.; Suvorov, A. G.; Melatos, A.
2015-03-01
A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic field aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalizes previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g. spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin-downs, and are not purely dipolar.
Pahari, Sambaran; Lachhvani, Lavkesh; Bajpai, Manu; Rathod, Karan; Yeole, Yogesh; Chattopadhyay, P K
2015-08-01
A suitable charge-collector has been designed and developed to estimate charge-content of electron plasmas in a Small Aspect Ratio Toroidal Experiment in a C-shaped trap (SMARTEX-C). The electrons are periodically injected and held in the trap with the aid of electrostatic end-fields and a toroidal magnetic field. After a preset "hold" time, the trapped charges are dumped onto a grounded collector (by gating it). As the charges flow along the magnetic field lines onto the collector, the integrated current gives the charge-content of the plasma at the instant of dump. In designing such a charge collector, several challenges peculiar to the geometry of the trap and the nature of the plasma had to be addressed. Instantaneous charge measurements synchronised with the E × B drift of the plasma, along with fast transit times of electrons to the collector (few 100 ns or less) (due to the low aspect ratio of the trap) essentially require fast gating of the collector. The resulting large capacitive transients alongside low charge content (few nC) of such plasmas further lead to increasing demands on response and sensitivity of the collector. Complete cancellation of such transients is shown to be possible, in principle, by including the return path in our measurement circuit but the "non-neutrality" of the plasma acts as a further impediment. Ultimately, appropriate shielding and measurement circuits allow us to (re)distribute the capacitance and delineate the paths of these currents, leading to effective cancellation of transients and marked improvement in sensitivity. Improved charge-collector has thus been used to successfully estimate the time evolution of total charge of the confined electron plasma in SMARTEX-C. PMID:26329189
NASA Astrophysics Data System (ADS)
Pahari, Sambaran; Lachhvani, Lavkesh; Bajpai, Manu; Rathod, Karan; Yeole, Yogesh; Chattopadhyay, P. K.
2015-08-01
A suitable charge-collector has been designed and developed to estimate charge-content of electron plasmas in a Small Aspect Ratio Toroidal Experiment in a C-shaped trap (SMARTEX-C). The electrons are periodically injected and held in the trap with the aid of electrostatic end-fields and a toroidal magnetic field. After a preset "hold" time, the trapped charges are dumped onto a grounded collector (by gating it). As the charges flow along the magnetic field lines onto the collector, the integrated current gives the charge-content of the plasma at the instant of dump. In designing such a charge collector, several challenges peculiar to the geometry of the trap and the nature of the plasma had to be addressed. Instantaneous charge measurements synchronised with the E × B drift of the plasma, along with fast transit times of electrons to the collector (few 100 ns or less) (due to the low aspect ratio of the trap) essentially require fast gating of the collector. The resulting large capacitive transients alongside low charge content (few nC) of such plasmas further lead to increasing demands on response and sensitivity of the collector. Complete cancellation of such transients is shown to be possible, in principle, by including the return path in our measurement circuit but the "non-neutrality" of the plasma acts as a further impediment. Ultimately, appropriate shielding and measurement circuits allow us to (re)distribute the capacitance and delineate the paths of these currents, leading to effective cancellation of transients and marked improvement in sensitivity. Improved charge-collector has thus been used to successfully estimate the time evolution of total charge of the confined electron plasma in SMARTEX-C.
Pahari, Sambaran; Lachhvani, Lavkesh Bajpai, Manu; Rathod, Karan; Yeole, Yogesh; Chattopadhyay, P. K.
2015-08-15
A suitable charge-collector has been designed and developed to estimate charge-content of electron plasmas in a Small Aspect Ratio Toroidal Experiment in a C-shaped trap (SMARTEX-C). The electrons are periodically injected and held in the trap with the aid of electrostatic end-fields and a toroidal magnetic field. After a preset “hold” time, the trapped charges are dumped onto a grounded collector (by gating it). As the charges flow along the magnetic field lines onto the collector, the integrated current gives the charge-content of the plasma at the instant of dump. In designing such a charge collector, several challenges peculiar to the geometry of the trap and the nature of the plasma had to be addressed. Instantaneous charge measurements synchronised with the E × B drift of the plasma, along with fast transit times of electrons to the collector (few 100 ns or less) (due to the low aspect ratio of the trap) essentially require fast gating of the collector. The resulting large capacitive transients alongside low charge content (few nC) of such plasmas further lead to increasing demands on response and sensitivity of the collector. Complete cancellation of such transients is shown to be possible, in principle, by including the return path in our measurement circuit but the “non-neutrality” of the plasma acts as a further impediment. Ultimately, appropriate shielding and measurement circuits allow us to (re)distribute the capacitance and delineate the paths of these currents, leading to effective cancellation of transients and marked improvement in sensitivity. Improved charge-collector has thus been used to successfully estimate the time evolution of total charge of the confined electron plasma in SMARTEX-C.
Summary of US-Japan Exchange 2004 New Directions and Physics for Compact Toroids
Intrator, T; Nagata, M; Hoffman, A; Guo, H; Steinhauer, L; Ryutov, D; Miller, R; Okada, S
2005-08-15
relaxation. A variety of key themes surrounding the physics of CT's were found to recur during this conference. These included questions and answers touching upon magnetic flux build up in CT's, generalized relaxation processes that extend beyond the Taylor picture, the importance of plasma flows, toroidal magnetic fields in FRC's, and CT power plant considerations. This document briefly outlines the tenor of these discussions.
Podestà, M.; Gorelenkov, N. N.; White, R. B.; Fredrickson, E. D.; Gerhardt, S. P.; Kramer, G. J.
2013-08-15
A second Neutral Beam (NB) injection line is being installed on the NSTX Upgrade device, resulting in six NB sources with different tangency radii that will be available for heating and current drive. This work explores the properties of instabilities in the frequency range of the Toroidal Alfvén Eigenmode (TAE) for NSTX-U scenarios with various NB injection geometries, from more perpendicular to more tangential, and with increased toroidal magnetic field with respect to previous NSTX scenarios. Predictions are based on analysis through the ideal MHD code NOVA-K. For the scenarios considered in this work, modifications of the Alfvén continuum result in a frequency up-shift and a broadening of the radial mode structure. The latter effect may have consequences for fast ion transport and loss. Preliminary stability considerations indicate that TAEs are potentially unstable with ion Landau damping representing the dominant damping mechanism.
Toroidal Alfv{acute e}n eigenmodes in TFTR deuterium{endash}tritium plasmas
Nazikian, R.; Fu, G.Y.; Chang, Z.; Batha, S.H.; Berk, H.; Budny, R.V.; Chen, Y.; Cheng, C.Z.; Darrow, D.S.; Gorelenkov, N.N.; Levinton, F.M.; Medley, S.; Petrov, M.P.; Redi, M.; Ruskov, E.; Spong, D.A.; White, R.B.; Zweben, S.J.
1998-05-01
Purely alpha-particle-driven toroidal Alfv{acute e}n eigenmodes (TAEs) with toroidal mode numbers n=1{endash}6 have been observed in deuterium{endash}tritium (D{endash}T) plasmas on the tokamak fusion test reactor [D. J. Grove and D. M. Meade, Nucl. Fusion {bold 25}, 1167 (1985)]. The appearance of mode activity following termination of neutral beam injection in plasmas with q(0){gt}1 is generally consistent with theoretical predictions of TAE stability [G. Y. Fu {ital et al.} Phys. Plasmas {bold 3}, 4036 (1996)]. Internal reflectometer measurements of TAE activity is compared with theoretical calculations of the radial mode structure. Core localization of the modes to the region of reduced central magnetic shear is confirmed, however the mode structure can deviate significantly from theoretical estimates. The peak measured TAE amplitude of {delta}n/n{approximately}10{sup {minus}4} at r/a{approximately}0.3{minus}0.4 corresponds to {delta}B/B{approximately}10{sup {minus}5}, while {delta}B/B{approximately}10{sup {minus}8} is measured at the plasma edge. Enhanced alpha particle loss associated with TAE activity has not been observed. {copyright} {ital 1998 American Institute of Physics.}
Toroidal Alfvén Eigenmodes in TFTR Deuterium-Tritium Plasmas
G.Y. Fu; H. Berk; R. Nazikian; S.H. Batha; Z. Chang; et al
1998-01-01
Purely alpha-particle-driven Toroidal Alfvén Eigenmodes (TAEs) with toroidal mode numbers n=1-6 have been observed in Deuterium-Tritium (D-T) plasmas on the Tokamak Fusion Test Reactor [D.J. Grove and D.M. Meade, Nucl. Fusion 25, 1167 (1985)]. The appearance of mode activity following termination of neutral beam injection in plasmas with q(0)>1 is generally consistent with theoretical predictions of TAE stability [G.Y. Fu et al., Phys. Plasmas 3, 4036 (1996]. Internal reflectometer measurements of TAE activity is compared with theoretical calculations of the radial mode structure. Core localization of the modes to the region of reduced central magnetic shear is confirmed, however the mode structure can deviate significantly from theoretical estimates. The peak measured TAE amplitude of delta n/n~10(superscript -4) at r/a~0.3-0.4 corresponds to delta B/B~10-5, while dB/B~10(superscript -8) is measured at the plasma edge. Enhanced alpha particle loss associated with TAE activity has not been observed.
Observation of the Early Transition from Slab to mixed Slab-Toroidal ETG Turbulence
NASA Astrophysics Data System (ADS)
Balbaky, Abed; Sokolov, Vladimir; Sen, Amiya K.
2014-10-01
Parametric studies of the transition between the slab branch of electron temperature gradient (ETG) mode and the mixed slab-toroidal branch of the ETG mode in CLM are reported. CLM was operated in a mirror machine configuration with a cell length of 50--100 cm, and a mirror ratio of 1--2. For typical CLM parameters and a mode localized at r = 2 cm this provides a range for inverse radius of curvature Rc - 1 between 0 and .006 cm-1. Under normal conditions theory predicts transition between slab and toroidal modes would occur when the parameter k| |Rc / 2k⊥ ρ ~ 1. Recent experiments have obtained an experimental scaling of mode amplitude and frequency as a function of Rc - 1. They indicate that even for much more modest levels of k| |Rc / 2k⊥ ρ ~ . 1 , there are substantial increases in saturated mode, up to 5 times larger than the pure slab mode. Changes in real frequency in the mode are generally small, on the order of <5%. This research was supported by the Department of Electrical Engineering of Columbia University.
SV40 late protein VP4 forms toroidal pores to disrupt membranes for viral release.
Raghava, Smita; Giorda, Kristina M; Romano, Fabian B; Heuck, Alejandro P; Hebert, Daniel N
2013-06-01
Nonenveloped viruses are generally released from the cell by the timely lysis of host cell membranes. SV40 has been used as a model virus for the study of the lytic nonenveloped virus life cycle. The expression of SV40 VP4 at later times during infection is concomitant with cell lysis. To investigate the role of VP4 in viral release and its mechanism of action, VP4 was expressed and purified from bacteria as a fusion protein for use in membrane disruption assays. Purified VP4 perforated membranes as demonstrated by the release of fluorescent markers encapsulated within large unilamellar vesicles or liposomes. Dynamic light scattering results revealed that VP4 treatment did not cause membrane lysis or change the size of the liposomes. Liposomes encapsulated with 4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-3-indacene-labeled streptavidin were used to show that VP4 formed stable pores in membranes. These VP4 pores had an inner diameter of 1-5 nm. Asymmetrical liposomes containing pyrene-labeled lipids in the outer monolayer were employed to monitor transbilayer lipid diffusion. Consistent with VP4 forming toroidal pore structures in membranes, VP4 induced transbilayer lipid diffusion or lipid flip-flop. Altogether, these studies support a central role for VP4 acting as a viroporin in the disruption of cellular membranes to trigger SV40 viral release by forming toroidal pores that unite the outer and inner leaflets of membrane bilayers. PMID:23651212
Geometry of Thin Nematic Elastomer Sheets
NASA Astrophysics Data System (ADS)
Aharoni, Hillel; Sharon, Eran; Kupferman, Raz
A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods.
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
Geometry-induced modification of fluctuation spectrum in quasi-two-dimensional condensates
NASA Astrophysics Data System (ADS)
Roy, Arko; Angom, D.
2016-08-01
We report the structural transformation of the low-lying spectral modes, especially the Kohn mode, from radial to circular topology as harmonic confining potential is modified to a toroidal one, and this corresponds to a transition from simply to multiply connected geometry. For this we employ the Hartree–Fock–Bogoliubov theory to examine the evolution of low energy quasiparticles. We, then, use the Hartree–Fock–Bogoliubov theory with the Popov approximation to demonstrate the two striking features of quantum and thermal fluctuations. At T = 0, the non-condensate density due to interaction induced quantum fluctuations increases with the transformation from pancake to toroidal geometry. The other feature is, there is a marked change in the density profile of the non-condensate density at finite temperatures with the modification of trapping potential. In particular, the condensate and non-condensate density distributions have overlapping maxima in the toroidal condensate, which is in stark contrast to the case of pancake geometry. The genesis of this difference lies in the nature of the thermal fluctuations.
The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code
NASA Astrophysics Data System (ADS)
Jiang, Peng; Lin, Zhihong; Ihor, Holod; Xiao, Chijie
2016-02-01
The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code (GTC). The ion and electron density profiles become partially flattened inside the islands. The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side, which do not move along the perturbed magnetic field lines. When the fraction of trapped particles decreases, the density profile at the low field becomes more flattened. supported by National Special Research Program of China for ITER (Nos. 2013GB111000 and 2014GB107004), China Scholarship Council (No. 2011601098), U.S. DOE Grants DE-SC0010416 and DE-FG02-07ER54916
Neoclassical electron and ion transport in toroidally rotating plasmas
Sugama, H.; Horton, W.
1997-06-01
Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch{endash}Schl{umlt u}ter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the radial thermodynamic forces conjugate to the inward fluxes, respectively. {copyright} {ital 1997 American Institute of Physics.}
The toroidal field coil design for ARIES-ST
Reiersen, W.; Dahlgren, F.; Fan, H.M.; Neumeyer, C.; Zatz, I.
2000-01-21
An evolutionary process was used to develop the toroidal field (TF) coil design for the ARIES-ST (Spherical Tokamak). Design considerations included fabricability, assembly, maintenance, energy efficiency, and structural robustness. The design addresses a number of the concerns (complexity) and criticisms (high cost, high recirculating power) of fusion. It does this by: (1) Applying advanced, but available laser forming and spray casting techniques for manufacturing the TF coil system; (2) Adopting a simple single toroidal field coil system to make assembly and maintenance much easier, the single turn design avoids the necessity of using the insulation as a structural component of the TF coils, and hence is much more robust than multi-turn designs; and (3) Using a high conductivity copper alloy and modest current densities to keep the recirculating power modest.
Nuclear magnetic resonance tomography with a toroid cavity detector
Woelk, K.; Rathke, J.W.; Klingler, R.J.
1995-02-01
A new type of nuclear magnetic resonance (NMR) tomography has been developed at Argonne National Laboratory. The method uses the strong radio frequency field gradient within a cylindrical toroid cavity to provide high-resolution NMR spectral information while simultaneously resolving distances on the micron scale. The toroid cavity imaging technique differs from conventional magnetic resonance imaging (MRI) in that NMR structural information is not lost during signal processing. The new technique could find a wide range of applications in the characterization of surface layers and in the production of advanced materials. Potential areas of application include in situ monitoring of growth sites during ceramic formation processes, analysis of the oxygen annealing step for wires coated with high-temperature superconducting films, and investigation of the reaction chemistry as a function of distance within the diffusion layer for electrochemical processes.
Stabilization of ballooning modes with sheared toroidal rotation
Miller, R.L.; Waelbroeck, F.W.; Lao, L.L.; Taylor, T.S.
1994-11-01
A new code demonstrates the stabilization of MHD ballooning modes by sheared toroidal rotation. A shifted-circle model is used to elucidate the physics and numerically reconstructed equilibria are used to analyze DIII-D discharges. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (d{Omega}/dq where {Omega} is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and, in the shifted circle model, direct stable access to the second stability regime occurs when this frequency is a fraction of the Alfven frequency {omega}{sub A} = V{sub A}/qR. Shear stabilization is also demonstrated for an equilibrium reconstruction of a DIII-D VH-mode.
Experimental studies of compact toroids. Progress report, 1990--1991
Not Available
1991-12-01
The Berkeley Compact Toroid Experiment (BCTX) device is a plasma device with a Marshall-gun generated, low aspect ratio toroidal plasma. The device is capable of producing spheromak-type discharges and may, with some modification, produce low-aspect ratio tokamak configurations. A unique aspect of this experimenal devie is its large lower hybrid (LH) heating system, which consists of two 450MHz klystron tubes generating 20 megawatts each into a brambilla-type launching structure. Successful operation with one klystron at virtually full power (18 MW) has been accomplished with 110 {mu}s pulse length. A second klystron is currently installed in its socket and magnet but has not been added to the RF drive system. This report describes current activities and accomplishments and describes the anticipated results of next year`s activity.
Energy Science and Technology Software Center (ESTSC)
2005-01-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less
NASA Astrophysics Data System (ADS)
Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.
2014-06-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Evolution of the alpha particle driven toroidicity induced Alfven mode
Wu, Y.; White, R.B.; Cheng, C.Z.
1994-04-01
The interaction of alpha particles with a toroidicity induced Alfven eigenmode is investigated self-consistently by using a kinetic dispersion relation. All important poloidal harmonics and their radial mode profiles are included. A Hamiltonian guiding center code is used to simulate the alpha particle motion. The simulations include particle orbit width, nonlinear particle dynamics and the effects of the modes on the particles. Modification of the particle distribution leading to mode saturation is observed. There is no significant alpha particle loss.
Dual Telecentric Lens System For Projection Onto Tilted Toroidal Screen
NASA Technical Reports Server (NTRS)
Gold, Ronald S.; Hudyma, Russell M.
1995-01-01
System of two optical assemblies for projecting image onto tilted toroidal screen. One projection lens optimized for red and green spectral region; other for blue. Dual-channel approach offers several advantages which include: simplified color filtering, simplified chromatic aberration corrections, less complex polarizing prism arrangement, and increased throughput of blue light energy. Used in conjunction with any source of imagery, designed especially to project images formed by reflection of light from liquid-crystal light valve (LCLV).
Toroidal qubits: naturally-decoupled quiet artificial atoms
Zagoskin, Alexandre M.; Chipouline, Arkadi; Il’ichev, Evgeni; Johansson, J. Robert; Nori, Franco
2015-01-01
The requirements of quantum computations impose high demands on the level of qubit protection from perturbations; in particular, from those produced by the environment. Here we propose a superconducting flux qubit design that is naturally protected from ambient noise. This decoupling is due to the qubit interacting with the electromagnetic field only through its toroidal moment, which provides an unusual qubit-field interaction, which is suppressed at low frequencies. PMID:26607667
Toroidal constant-tension superconducting magnetic energy storage units
Herring, J. Stephen
1992-01-01
A superconducting magnetic energy storage unit is provided in which the magnet is wound in a toroidal fashion such that the magnetic field produced is contained only within the bore of the magnet, and thus producing a very low external field. The superconducting magnet includes a coolant channel disposed through the wire. The bore of the magnet comprises a storage volume in which cryogenic coolant is stored, and this volume supplies the coolant to be delivered to the coolant channel in the magnet.
Observations of high-beta toroidal plasmas
NASA Astrophysics Data System (ADS)
Halle, J. H.; Kellman, A. G.; Post, R. S.; Prager, S. C.; Strait, E. J.; Zarnstorff, M. C.
1981-05-01
A range of MHD stable high-beta plasmas is attained both in the kinetic regime with beta equal to 33% (nine times the fluid ballooning limit) and near the single-fluid regime with beta equal to 8% (twice the theoretical limit). It is found that MHD theory is inadequate and that kinetic effects are apparently more powerful than is generally assumed. It is pointed out that since a reactor (with trapped particles, large-gyroradii ions from neutral beams) may be no more fluid-like than the octupole experiments, their designs should perhaps not necessarily be constrained by the MHD ballooning instability beta limit. Diamagnetic current measurements are found to agree roughly with single-fluid results in the fluid-like case but to depart sharply in the kinetic regime.
Nanospheres, nanotubes, toroids, and gels with controlled macroscopic chirality.
Arias, Sandra; Freire, Félix; Quiñoá, Emilio; Riguera, Ricardo
2014-12-01
The interaction of a highly dynamic poly(aryl acetylene) (poly-1) with Li(+), Na(+), and Ag(+) leads to macroscopically chiral supramolecular nanospheres, nanotubes, toroids, and gels. With Ag(+), nanospheres with M helicity and tunable sizes are generated, which complement those obtained from the same polymer with divalent cations. With Li(+) or Na(+), poly-1 yields chiral nanotubes, gels, or toroids with encapsulating properties and M helicity. Right-handed supramolecular structures can be obtained by using the enantiomeric polymer. The interaction of poly-1 with Na(+) produces nanostructures whose helicity is highly dependent on the solvation state of the cation. Therefore, structures with either of the two helicities can be prepared from the same polymer by manipulation of the cosolvent. Such chiral nanotubes, toroids, and gels have previously not been obtained from helical polymer-metal complexes. Chiral nanospheres made of poly(aryl acetylene) that were previously assembled with metal(II) species can now be obtained with metal(I) species. PMID:25209219
Expansions of non-symmetric toroidal magnetohydrodynamic equilibria
NASA Astrophysics Data System (ADS)
Weitzner, Harold
2016-06-01
Expansions of non-symmetric toroidal ideal magnetohydrodynamic equilibria with nested flux surfaces are carried out for two cases. The first expansion is in a topological torus in three dimensions, in which physical quantities are periodic of period 2 π in y and z. Data is given on the flux surface x = 0. Despite the possibility of magnetic resonances the power series expansion can be carried to all orders in a parameter which measures the flux between x = 0 and the surface in question. Resonances are resolved by appropriate addition resonant fields, as by Weitzner, [Phys. Plasmas 21, 022515 (2014)]. The second expansion is about a circular magnetic axis in a true torus. It is also assumed that the cross section of a flux surface at constant toroidal angle is approximately circular. The expansion is in an analogous flux coordinate, and despite potential resonance singularities, may be carried to all orders. Non-analytic behavior occurs near the magnetic axis. Physical quantities have a finite number of derivatives there. The results, even though no convergence proofs are given, support the possibility of smooth, well-behaved non-symmetric toroidal equilibria.
Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks
NASA Astrophysics Data System (ADS)
Lazzaro, E.
2016-05-01
In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co- I p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.
Modeling and analysis of silicon-embedded MEMS toroidal inductors
NASA Astrophysics Data System (ADS)
Araghchini, M.; Lang, J. H.
2013-12-01
This paper presents the modeling and analysis of three-dimensional silicon-embedded toroidal inductors designed for power converter applications. Special attention is given to modeling phenomena associated with the presence of silicon, namely an increase in loss and parasitic capacitance. Silicon-embedded inductors can be fabricated with silicon inside the donut-shaped toroidal core and inside the donut hole, as well as with silicon above, below and outside the inductor. It is argued here that, with the exception of the losses in the core at high doping densities, the losses in the silicon can be tolerated in many power applications, making fully-integrated silicon-embedded air-core inductors viable for power applications. An equivalent circuit model is presented for such inductors which captures the stored magnetic energy, the parasitic electric energy stored between the windings and the silicon, the loss in the toroidal windings, and the electrically- and magnetically-driven losses inside the silicon. The model developed here is verified against experimental data, and the comparison shows a good match over the frequency range of interest to power electronics applications.
3D toroidal physics: Testing the boundaries of symmetry breakinga)
NASA Astrophysics Data System (ADS)
Spong, Donald A.
2015-05-01
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.
3D toroidal physics: Testing the boundaries of symmetry breaking
Spong, Donald A.
2015-05-15
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.
Connection formula for banana-drift neoclassical toroidal viscosity
NASA Astrophysics Data System (ADS)
Cole, A. J.; Hegna, C. C.; Callen, J. D.
2010-11-01
Non-resonant magnetic perturbations can affect plasma rotation in toroidally confined plasmas through their modification to |B|. Variations along a field line induce nonambipolar radial transport and produce a global neoclassical toroidal viscous force [NTV]. In this work, a previously calculated WKB-type solution smoothly connecting the low-collisionality ``1/ν'' and ``ν-√ν'' regimes is extended to include the superbanana plateau [sbp] regime [1]. The sbp effect occurs for particles whose toroidal ExB precessional drift vanishes. In this case, the relevant drift kinetic equation exhibits a ``turning point'' and the WKB method fails. We employ the connection formula method of Langer [2] which continuously varies between the previous WKB result and the superbanana regime without difficultly at the turning point. The resultant smoothed NTV is presented in terms of flows along flux surfaces. [4pt] [1] K. C. Shaing, S. A. Sabbagh, and M. S. Chu, PPCF 51, 035009 (2009), and refs. cited therein. [0pt] [2] R. E. Langer, Phys. Rev. 51, 669 (1937).
Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity.
Kartashov, Yaroslav V; Malomed, Boris A; Shnir, Yasha; Torner, Lluis
2014-12-31
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis (m), appear in many fields, including field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multicomponent systems, or as trapped quasilinear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0, 1, 2 are produced. They are stable for m≤1, and do not exist for s>1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented in a Bose-Einstein condensate (BEC) by means of the Feshbach resonance controlled by inhomogeneous magnetic fields. PMID:25615341
Aetukuri, Nagaphani B; McCloskey, Bryan D; García, Jeannette M; Krupp, Leslie E; Viswanathan, Venkatasubramanian; Luntz, Alan C
2015-01-01
Given their high theoretical specific energy, lithium-oxygen batteries have received enormous attention as possible alternatives to current state-of-the-art rechargeable Li-ion batteries. However, the maximum discharge capacity in non-aqueous lithium-oxygen batteries is limited to a small fraction of its theoretical value due to the build-up of insulating lithium peroxide (Li₂O₂), the battery's primary discharge product. The discharge capacity can be increased if Li₂O₂ forms as large toroidal particles rather than as a thin conformal layer. Here, we show that trace amounts of electrolyte additives, such as H₂O, enhance the formation of Li₂O₂ toroids and result in significant improvements in capacity. Our experimental observations and a growth model show that the solvating properties of the additives prompt a solution-based mechanism that is responsible for the growth of Li₂O₂ toroids. We present a general formalism describing an additive's tendency to trigger the solution process, providing a rational design route for electrolytes that afford larger lithium-oxygen battery capacities. PMID:25515890
NASA Astrophysics Data System (ADS)
Aetukuri, Nagaphani B.; McCloskey, Bryan D.; García, Jeannette M.; Krupp, Leslie E.; Viswanathan, Venkatasubramanian; Luntz, Alan C.
2015-01-01
Given their high theoretical specific energy, lithium-oxygen batteries have received enormous attention as possible alternatives to current state-of-the-art rechargeable Li-ion batteries. However, the maximum discharge capacity in non-aqueous lithium-oxygen batteries is limited to a small fraction of its theoretical value due to the build-up of insulating lithium peroxide (Li2O2), the battery’s primary discharge product. The discharge capacity can be increased if Li2O2 forms as large toroidal particles rather than as a thin conformal layer. Here, we show that trace amounts of electrolyte additives, such as H2O, enhance the formation of Li2O2 toroids and result in significant improvements in capacity. Our experimental observations and a growth model show that the solvating properties of the additives prompt a solution-based mechanism that is responsible for the growth of Li2O2 toroids. We present a general formalism describing an additive’s tendency to trigger the solution process, providing a rational design route for electrolytes that afford larger lithium-oxygen battery capacities.
Impact of plasma poloidal rotation on resistive wall mode instability in toroidally rotating plasmas
Aiba, N.; Shiraishi, J.; Tokuda, S.
2011-02-15
Stability of resistive wall mode (RWM) is investigated in a cylindrical plasma and an axisymmetric toroidal plasma by taking into account not only toroidal rotation but also poloidal rotation. Since the Doppler shifted frequency is responsible for the RWM stability, the modification of this Doppler shifted frequency by poloidal rotation affects the rotation effect on RWM. When a poloidal rotation frequency is not so large, the effect of poloidal rotation on the RWM stability can be approximately treated with the modified toroidal rotation frequency. In a toroidal plasma, this modified frequency is determined by subtracting a toroidal component of the rotation parallel to the magnetic field from the toroidal rotation frequency. The poloidal rotation that counteracts the effect of the Doppler shift strongly reduces the stabilizing effect of toroidal rotation, but by changing the rotational direction, the poloidal rotation enhances this stabilizing effect. This trend is confirmed in not only a cylindrical plasma but also a toroidal plasma. This result indicates that poloidal rotation produces the dependence of the critical toroidal rotation frequency for stabilizing RWM on the rotational direction of toroidal rotation in the same magnetic configuration.
Heuristic Approach to the Schwarzschild Geometry
NASA Astrophysics Data System (ADS)
Visser, Matt
In this article I present a simple Newtonian heuristic for motivating a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames (the Einstein equivalence principle), plus the use of Galilean coordinate transformations to connect the freely falling local inertial frames back to the "fixed stars." Because of the heuristic and quasi-Newtonian manner in which the specific choice of spacetime geometry is motivated, we are at best justified in expecting it to be a weak-field approximation to the true spacetime geometry. However, in the case of a spherically symmetric point mass the result is coincidentally an exact solution of the full vacuum Einstein field equations — it is the Schwarzschild geometry in Painlevé-Gullstrand coordinates. This result is much stronger than the well-known result of Michell and Laplace whereby a Newtonian argument correctly estimates the value of the Schwarzschild radius — using the heuristic presented in this article one obtains the entire Schwarzschild geometry. The heuristic also gives sensible results — a Riemann flat geometry — when applied to a constant gravitational field. Furthermore, a subtle extension of the heuristic correctly reproduces the Reissner-Nordström geometry and even the de Sitter geometry. Unfortunately the heuristic construction is not truly generic. For instance, it is incapable of generating the Kerr geometry or anti-de Sitter space. Despite this limitation, the heuristic does have useful pedagogical value in that it provides a simple and direct plausibility argument (not a derivation) for the Schwarzschild geometry — suitable for classroom use in situations where the full power and technical machinery of general relativity might be inappropriate. The extended heuristic provides more challenging problems — suitable for use at the graduate level.
Density Limits in Toroidal Magnetic Confinement Experiments
NASA Astrophysics Data System (ADS)
Greenwald, Martin
2001-10-01
The density limit represents one of the fundamental operating boundaries for magnetic confinement devices - one with practical importance to the goal of fusion power. With fusion reactivity maximized at a plasma temperature on the order of 10 keV and a reaction rate scaling as n^2, an optimum density can be calculated which is not guaranteed to be achievable in any given device. Unlike operational limits for plasma current or pressure, the density limit cannot be explained by magneto-hydrodynamics alone. There is general agreement that the proximate cause for the disruptive limit in the tokamak is cooling of the plasma edge and subsequent current profile shrinkage. The edge cooling may be dominated by atomic physics processes or as suggested in recent experiments, by anomalous transport. A similar picture is emerging for the reversed field pinch (RFP), while the limit in stellarators is apparently due to loss of thermal equilibrium from radiation. Empirical scaling laws in which the maximum plasma density is proportional to the average current density have been fairly successful in predicting the limit for subsequent experiments. Surprisingly, the density limits found in tokamaks and RFPs are virtually identical. Currentless stellarators reach similar density limits, though the expression needs to be recast in terms of the rotational transform. While scaling laws have done a reasonable job in describing data from many recent experiments, they can only give hints at the underlying physics. Understanding the mechanism for the density limit is crucial for extrapolating machine performance into untested regimes and so far, a completely satisfactory theory has not emerged. It seems likely that robust, reliable predictions will only come from the development of a first-principles theory backed up by detailed experimental observations. The extensive work already accomplished and reviewed here should provide a solid basis for such development.
Fluid Motion and the Toroidal Magnetic Field Near the Top of Earth's Liquid Outer Core.
NASA Astrophysics Data System (ADS)
Celaya, Michael Augustine
field (B_{T }) near the top of the corp. The flow, obtained as a solution to (1), is treated as a known quantity, as is the poloidal field. Solutions are sought which minimize the difference between observed and predicted poloidal main field at Earth's surface. As in problem (1), aliasing in space and time stand as potential impediments to good resolution of the toroidal field. Steady degree 10 models of B_{T} are obtained which display convergence in space and time without damping. Poloidal field noise, as well as sensitivity to the flow model used in the inversions, limit resolution of toroidal field geometry. Nevertheless, estimates indicate the magnitude of B_{T } does not exceed 8times 10^ {-5}T, or about half that of the poloidal field near the core surface. Such a low value favors weak -field dynamo models but does not necessarily endorse a geostrophic force balance just beneath the mantle because partial_{r}B _{T} may be large enough to violate conditions required by geostrophy.
MHD Modeling in Complex 3D Geometries: Towards Predictive Simulation of SIHI Current Drive
NASA Astrophysics Data System (ADS)
Hansen, Christopher James
The HIT-SI experiment studies Steady Inductive Helicity Injection (SIHI) for the purpose of forming and sustaining a spheromak plasma. A spheromak is formed in a nearly axisymmetric flux conserver, with a bow tie cross section, by means of two semi-toroidal injectors. The plasma-facing surfaces of the device, which are made of copper for its low resistivity, are covered in an insulating coating in order to operate in a purely inductive manner. Following formation, the spheromak flux and current are increased during a quiescent period marked by a decrease in the global mode activity. A proposed mechanism, Imposed Dynamo Current Drive (IDCD), is expected to be responsible for this phase of quiescent current drive. Due to the geometric complexity of the experiment, previous numerical modeling efforts have used a simplified geometry that excludes the injector volumes from the simulated domain. The effect of helicity injection is then modeled by boundary conditions on this reduced plasma volume. The work presented here has explored and developed more complete computational models of the HIT-SI device. This work is separated into 3 distinct but complementary areas: 1) Development of a 3D MHD equilibrium code that can incorporate the non-axisymmetric injector fields present in HIT-SI and investigation of equilibria of interest during spheromak sustainment. 2) A 2D axisymmetric MHD equilibrium code that was used to explore reduced order models for mean-field evolution using equations derived from IDCD theory including coupling to 3D equilibria. 3) A 3D time-dependent non-linear MHD code that is capable of modeling the entire plasma volume including dynamics within the injectors. Although HIT-SI was the motivation for, and experiment studied in this research, the tools and methods developed are general --- allowing their application to a broad range of magnetic confinement experiments. These tools constitute a significant advance for modeling plasma dynamics in devices with
NASA Astrophysics Data System (ADS)
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Asymptotics of Height Change on Toroidal Temperleyan Dimer Models
NASA Astrophysics Data System (ADS)
Dubédat, Julien; Gheissari, Reza
2015-04-01
The dimer model is an exactly solvable model of planar statistical mechanics. In its critical phase, various aspects of its scaling limit are known to be described by the Gaussian free field. For periodic graphs, criticality is an algebraic condition on the spectral curve of the model, determined by the edge weights (Kenyon et al. in Ann Math (2) 163(3):1019-1056, 2006); isoradial graphs provide another class of critical dimer models, in which the edge weights are determined by the local geometry. In the present article, we consider another class of graphs: general Temperleyan graphs, i.e. graphs arising in the (generalized) Temperley bijection between spanning trees and dimer models. Building in particular on Forman's formula and representations of Laplacian determinants in terms of Poisson operators, and under a minimal assumption—viz. that the underlying random walk converges to Brownian motion—we show that the natural topological observable on macroscopic tori converges in law to its universal limit, i.e. the law of the periods of the dimer height function converges to that of the periods of a compactified free field.
Students Discovering Spherical Geometry Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Toroidal cell and battery. [storage battery for high amp-hour load applications
NASA Technical Reports Server (NTRS)
Nagle, W. J. (Inventor)
1981-01-01
A toroidal storage battery designed to handle relatively high amp-hour loads is described. The cell includes a wound core disposed within a pair of toroidal channel shaped electrodes spaced apart by nylon insulator. The shape of the case electrodes of this toroidal cell allows a first planar doughnut shaped surface and the inner cylindrical case wall to be used as a first electrode and a second planar doughnut shaped surface and the outer cylindrical case wall to be used as a second electrode. Connectors may be used to stack two or more toroidal cells together by connecting substantially the entire surface area of the first electrode of a first cell to substantially the entire surface area of the second electrode of a second cell. The central cavity of each toroidal cell may be used as a conduit for pumping a fluid through the toroidal cell to thereby cool the cell.
First-principles approach to investigate toroidal property of magnetoelectric multiferroic GaFeO3
NASA Astrophysics Data System (ADS)
Nie, Yung-mau
2016-01-01
A first-principles approach incorporating the concept of toroidal moments as a measure of the spin vortex is proposed and applied to simulate the toroidization of magnetoelectric multiferroic GaFeO3. The nature of space-inversion and time-reversal violations of ferrotoroidics is reproduced in the simulated magnetic structure of GaFeO3. For undoped GaFeO3, a toroidal moment of -22.38 μB Å per unit cell was obtained, which is the best theoretical estimate till date. Guided by the spin vortex free-energy minimization perturbed by an externally applied field, it was discovered that the minority spin markedly biases the whole toroidization. In summary, this approach not only calculates the toroidal moment but provides a way to understand the toroidal nature of magnetoelectric multiferroics.
Electrical and mechanical design report of the muon toroids for the beamline to the muon laboratory
Visser, A.; Western, J.; Skraboly, A.
1987-03-01
This report describes two large steel toroids used to remove beam halo for experiment 665. One toroid is 88 inch diameter and 30 feet long. The other is 120 inch diameter and 20 feet long. Both have a 7 inch diameter center hole for passage of the beam and the excitation windings. The assembled hybrid coil has water-cooled conductors in the center hole and cables on the outside. This permits the use of one piece steel plates through which the center core is inserted after assembly of the toroid steel. These toroids have advantages over conventional toroids in many aspects. The main ones being its reduced power consumption, simplicity of machining and assembly, and lower coil costs. Estimates of the induction and a simple method to buck the remnant magnetic field are included. The bucking method does not completely degauss all the toroid steel.
Dynamic spin-flip shot noise of mesoscopic transport through a toroidal carbon nanotube
NASA Astrophysics Data System (ADS)
Zhao, H. K.; Zhang, J.; Wang, J.
2015-01-01
The shot noise in a toroidal carbon nanotube (TCN) interferometer under the perturbation of a rotating magnetic field (RMF) has been investigated. A general shot noise formula has been derived by calculating the current correlation. It was found that photon absorption and emission induce novel features of dynamic shot noise. The oscillatory behavior of shot noise and Fano factor vary with the Aharonov-Bohm (AB) magnetic flux, and they are sensitively dependent on the Zeeman energy, frequency of RMF, and source-drain bias. By adjusting the Zeeman energy, the AB oscillation structures of shot noise and Fano factor show valley-to-peak transformation. The shot noise increases nonlinearly with increasing the Zeeman energy and photon energy. The enhancement and asymmetry of shot noise can be attributed to the spin-flip effect.
Wall thickness effect on the resistive wall mode stability in toroidal plasmas
Zheng, L.-J.; Kotschenreuther, M.T.
2005-07-15
The effect of finite wall thickness on the stability of n=1 resistive wall modes in toroidal plasmas is investigated. A fusion reactor-relevant configuration is examined. The investigation employs a novel ideal-magnetohydrodynamics adaptive shooting code for axisymmetric plasmas, extended to take into account the wall thickness. Although finite wall thickness generally reduces the growth rate of the resistive wall modes, no contribution to stabilization is found to be made by the portion of the wall that is located beyond the critical position for perfectly conducting wall stabilization. Thus, when the inner side of the wall lies near the critical wall position, the scaling of the growth rate versus wall thickness in the realistic thick-wall calculation is significantly different from that of the usual thin-wall theory. The thin-wall estimate is relevant only when the wall is brought very close to the plasma and is not too thick.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Network geometry with flavor: From complexity to quantum geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
The vector potential of a circular cylindrical antenna in terms of a toroidal harmonic expansion
NASA Astrophysics Data System (ADS)
Selvaggi, Jerry; Salon, Sheppard; Chari, M. V. K.
2008-08-01
A toroidal harmonic expansion is developed which is used to represent the vector potential due to a circular cylindrical antenna with a rectangular cross section at any arbitrary point in space. The singular part of the antenna kernel is represented by an associated toroidal harmonic expansion and the analytic part of the kernel is represented by a binomial expansion. A simple example is given to illustrate the application of the toroidal expansion.
Toroidal spiral Nambu-Goto strings around higher-dimensional black holes
Igata, Takahisa; Ishihara, Hideki
2010-08-15
We present solutions of the Nambu-Goto equation for test strings in a shape of toroidal spiral in five-dimensional spacetimes. In particular, we show that stationary toroidal spirals exist around the five-dimensional Myers-Perry black holes. We also show the existence of innermost stationary toroidal spirals around the five-dimensional black holes like geodesic particles orbiting around four-dimensional black holes.
ERIC Educational Resources Information Center
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061
ERIC Educational Resources Information Center
KLIER, KATHERINE M.
PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…
Geometry of spinor regularization
NASA Technical Reports Server (NTRS)
Hestenes, D.; Lounesto, P.
1983-01-01
The Kustaanheimo theory of spinor regularization is given a new formulation in terms of geometric algebra. The Kustaanheimo-Stiefel matrix and its subsidiary condition are put in a spinor form directly related to the geometry of the orbit in physical space. A physically significant alternative to the KS subsidiary condition is discussed. Derivations are carried out without using coordinates.
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
NASA Technical Reports Server (NTRS)
Huber, Martin C. E.; Timothy, J. G.; Morgan, Jeffrey S.; Lemaitre, Gerard; Tondello, Giuseppe; Naletto, Giampiero
1991-01-01
A technique has been developed which permits toroidal, and coma-corrected toroidal, diffraction gratings to be replicated from spherical master gratings by the use of elastically-deformable substrates. Toroidal gratings correct for astigmatism and, thus, make it possible to construct stigmatic spectrometers that employ a single reflective diffraction grating. These spectrometers are particularly useful for the extreme-ultraviolet (EUV) wavelength range, where reflection coefficients are low, since the single optical surface provides for dispersion, focusing, and astigmatism correction. The fabrication procedures for the pure toroidal, and coma-corrected toroidal, gratings are described, and initial test results are presented. The use of the toroidal gratings in a high-resolution sounding-rocket EUV spectroheliometer, and in both the coronal diagnostics spectrometer and the ultraviolet coronagraph spectrometer on the ESA/NASA solar and heliospheric observatory mission, is described briefly, and the use of this technique for the fabrication of a coma-corrected toroidal grating for the prime Rowland spectrograph of the FUSE/Lyman mission is briefly discussed.
NASA Astrophysics Data System (ADS)
Sontag, Aaron Christopher
2002-01-01
Tools have been developed to perform MHD equilibrium reconstruction of low-A ST discharges in the Pegasus Toroidal Experiment, including hardware to measure discharge properties and software to calculate the equilibrium state. Diagnostics to constrain the equilibrium fits include magnetic flux loops, magnetic field pickup coils, a diamagnetic loop, and a plasma Rogowski. A locally developed code which couples a Grad-Shafranov solver to a Levenberg-Marquardt least squares fitting routine is used to perform the reconstructions. These tools are sufficient to determine the global plasma parameters including the plasma geometry and plasma current to within a few percent. ℓi is determined to 9% and q95 is determined to within 6%. The values of betap and betat are determined to within 15% while q0 is constrained to 20%. Discharges up to 160 kA with betat ˜ 20%, beta N up to ˜5, ℓi between 0.15 and 0.6, R0 ≤ 40 cm, and elongations up to 3 have been reconstructed. An operational limit has been encountered when the plasma current is approximately equal to the toroidal field rod current due to a combination of internal tearing mode activity (m/n = 2/1 and 3/2 being the most common modes) and limited ohmic volt-seconds. A loss of ohmic flux due to delayed startup at lower toroidal field accounts for about 2/3 of the decrease in plasma current. Analyses indicate that increased MHD activity at lower toroidal field degrades flux utilization and energy confinement, causing the MHD activity to contribute to the operational limit. Early mode onset at high plasma resistivity with the rational q surface in a low shear region gives the modes large extent. This limit can be avoided by maintaining q0 greater than 2 until the discharge has become hot and less resistive, inhibiting mode growth. Increased magnetic shear at the mode resonant surface also helps to mitigate the effects of the resistive tearing modes. External kink modes appear to be causing some low ℓ i discharges to
Self-Assembly and Tissue Fusion of Toroid-Shaped Minimal Building Units
Livoti, Christine M.
2010-01-01
A significant challenge of tissue engineering is to build tissues whose size is not limited by diffusion. We are investigating the use of scaffold-free lumen containing toroid-shaped microtissues as minimal building units. Monodispersed H35 cells, a rat hepatocyte cell line, were seeded onto micromolded agarose, forming self-assembled multicellular toroids within 48 h. Toroid and lumen diameter were easily controlled by micromold design, and toroid thickness was controlled by seeding density. When harvested, toroids were stable, but underwent predictable changes over time with their lumens narrowing. When brought into contact, these building units fused in the x–y plane, forming a double-lumen structure, as well as the z plane, forming a tubular structure, which completed within 72 h. Large, multi-luminal structures were assembled by multidimensional fusion of many toroids. Toroid settling was not entirely random, with most toroids lying flat with their lumens oriented along the z axis. The rapid production of toroid building units of controlled dimension and lumen size that undergo predictable changes and that can be fused to form larger structures is a step closer to tissue engineering large porous three-dimensional tissues with high cell density. PMID:20109063
Toroidal-Core Microinductors Biased by Permanent Magnets
NASA Technical Reports Server (NTRS)
Lieneweg, Udo; Blaes, Brent
2003-01-01
The designs of microscopic toroidal-core inductors in integrated circuits of DC-to-DC voltage converters would be modified, according to a proposal, by filling the gaps in the cores with permanent magnets that would apply bias fluxes (see figure). The magnitudes and polarities of the bias fluxes would be tailored to counteract the DC fluxes generated by the DC components of the currents in the inductor windings, such that it would be possible to either reduce the sizes of the cores or increase the AC components of the currents in the cores without incurring adverse effects. Reducing the sizes of the cores could save significant amounts of space on integrated circuits because relative to other integrated-circuit components, microinductors occupy large areas - of the order of a square millimeter each. An important consideration in the design of such an inductor is preventing magnetic saturation of the core at current levels up to the maximum anticipated operating current. The requirement to prevent saturation, as well as other requirements and constraints upon the design of the core are expressed by several equations based on the traditional magnetic-circuit approximation. The equations involve the core and gap dimensions and the magnetic-property parameters of the core and magnet materials. The equations show that, other things remaining equal, as the maximum current is increased, one must increase the size of the core to prevent the flux density from rising to the saturation level. By using a permanent bias flux to oppose the flux generated by the DC component of the current, one would reduce the net DC component of flux in the core, making it possible to reduce the core size needed to prevent the total flux density (sum of DC and AC components) from rising to the saturation level. Alternatively, one could take advantage of the reduction of the net DC component of flux by increasing the allowable AC component of flux and the corresponding AC component of current
Feasibility study of a conical-toroidal mirror resonator for solar-pumped thin-disk lasers
NASA Astrophysics Data System (ADS)
Endo, M.
2007-04-01
An optical resonator that is suited to a large-scale, space-based solar-pumped solid-state lasers is proposed, and it is studied by numerical simulations. The resonator consists of a conical-toroidal reflector element on which a doughnut-shaped thin-disk active medium is set, and an output coupler. Unlike the ordinary thin-disk lasers, the optical ray of the proposed resonator passes the medium radially. With this arrangement, the resonator can enjoy the benefits of the thin-disk geometry, i. e., good thermal removability and low index gradient, while getting rid of the disadvantages of them as a solar-pumped laser, low round-trip gain and poor beam quality. The output power, beam quality, thermomechanical properties, and alignment stability of the proposed resonator combined with a Nd/Cr codoped GSGG is discussed.
Feasibility study of a conical-toroidal mirror resonator for solar-pumped thin-disk lasers.
Endo, M
2007-04-30
An optical resonator that is suited to a large-scale, space-based solar-pumped solid-state lasers is proposed, and it is studied by numerical simulations. The resonator consists of a conical-toroidal reflector element on which a doughnut-shaped thin-disk active medium is set, and an output coupler. Unlike the ordinary thin-disk lasers, the optical ray of the proposed resonator passes the medium radially. With this arrangement, the resonator can enjoy the benefits of the thin-disk geometry, i. e., good thermal removability and low index gradient, while getting rid of the disadvantages of them as a solar-pumped laser, low round-trip gain and poor beam quality. The output power, beam quality, thermomechanical properties, and alignment stability of the proposed resonator combined with a Nd/Cr codoped GSGG is discussed. PMID:19532804
NASA Astrophysics Data System (ADS)
Delkhosh, Mojtaba; Saadat Foumani, Mahmoud
2013-05-01
The aim of this research is the optimisation of full-toroidal continuously variable transmission (CVT) in conjunction with the fixed ratio (FR) mechanism, while the optimisation objective is to minimise fuel consumption (FC) of the vehicle in the new European driving cycle. After the dynamic analysis of the power train, a computer model is developed to simulate contact between CVT elements and consequently calculate its efficiency. Then an algorithm is presented to calculate FC of the vehicle in the driving cycle. Then, an optimisation using particle swarm optimisation on the CVT geometry and FR mechanism (which is embedded between CVT and final drive) is carried out to minimise FC. It is found that by utilisation of the optimised CVT; FC will be about 11% and 8% lower, compared with the application of a five-speed manual transmission and conventional CVT, respectively. Finally, effects of the roller tilt angle and oil temperature on the FC are investigated.
Edge magnetohydrodynamic instability studies in the Pegasus Toroidal Experiment
NASA Astrophysics Data System (ADS)
Bongard, Michael W.
Peeling modes, an instability mechanism underlying deleterious Edge Localized Mode (ELM) activity in fusion-grade plasmas, are observed at the plasma edge in the PEGASUS Toroidal Experiment under conditions of high edge current density (Jedge(˜ 0.1 MA/m2) and low magnetic field (B ˜0.1 T) present at near-unity aspect ratio. Their macroscopic properties are measured using external Mirnov coil arrays, Langmuir probes, and high-speed visible imaging. The modest edge parameters and short pulse lengths of PEGASUS discharges permit direct measurement of the internal magnetic field structure with an insertable array of Hall-effect sensors, providing the current profile and its dynamical evolution on ELM-relevant timescales. Peeling modes generate coherent, edge-localized electromagnetic activity with low toroidal mode numbers n ≤ 3 and high poloidal mode numbers, in agreement with theoretical expectations of a low- n external kink structure. Coherent MHD fluctuation amplitudes are found to be strongly dependent on the experimentally measured J edge/B peeling instability drive, consistent with theory. An equilibrium reconstruction obtained during peeling activity with its current profile constrained by internal Hall measurements is used to test the predictions of analytic peeling stability theory and the ideal MHD stability model. Both approaches are in agreement with experiment, with the latter finding instability to an external kink. Peeling modes nonlinearly generate ELM-like, field-aligned filamentary structures. They detach from the edge and transiently accelerate radially outward, followed by propagation with constant velocity. Time-resolved Jedge measurements demonstrate that the filaments are formed from an initial current-hole perturbation and carry net toroidal currents If ˜ 100--200 A, less than 0.2% of the plasma current. Their constant-velocity radial motions are in qualitative agreement with rates given by electromagnetic blob transport theory.
Alpha particle destabilization of the toroidicity-induced Alfven eigenmodes
Cheng, C.Z.
1990-10-01
The high frequency, low mode number toroidicity-induced Alfven eigenmodes (TAE) are shown to be driven unstable by the circulating and/or trapped {alpha}-particles through the wave-particle resonances. Satisfying the resonance condition requires that the {alpha}-particle birth speed v{sub {alpha}} {ge} v{sub A}/2{vert bar}m-nq{vert bar}, where v{sub A} is the Alfven speed, m is the poloidal model number, and n is the toroidal mode number. To destabilize the TAE modes, the inverse Landau damping associated with the {alpha}-particle pressure gradient free energy must overcome the velocity space Landau damping due to both the {alpha}-particles and the core electrons and ions. The growth rate was studied analytically with a perturbative formula derived from the quadratic dispersion relation, and numerically with the aid of the NOVA-K code. Stability criteria in terms of the {alpha}-particle beta {beta}{sub {alpha}}, {alpha}-particle pressure gradient parameter ({omega}{sub {asterisk}}/{omega}{sub A}) ({omega}{sub {asterisk}} is the {alpha}-particle diamagnetic drift frequency), and (v{sub {alpha}}/v{sub A}) parameters will be presented for TFTR, CIT, and ITER tokamaks. The volume averaged {alpha}-particle beta threshold for TAE instability also depends sensitively on the core electron and ion temperature. Typically the volume averaged {alpha}-particle beta threshold is in the order of 10{sup {minus}4}. Typical growth rates of the n=1 TAE mode can be in the order of 10{sup {minus}2}{omega}{sub A}, where {omega}{sub A}=v{sub A}/qR. Other types of global Alfven waves are stable in D-T tokamaks due to toroidal coupling effects.
Observation of Central Toroidal Rotation Induced by ICRF on EAST
NASA Astrophysics Data System (ADS)
Pan, Xiayun; Wang, Fudi; Zhang, Xinjun; Lyu, Bo; Chen, Jun; Li, Yingying; Fu, Jia; Shi, Yuejiang; Yu, Yi; Ye, Minyou; Wan, Baonian
2016-02-01
Core plasma rotation of both L-mode and H-mode discharges with ion cyclotron range of frequency (ICRF) minority heating (MH) scheme was measured with a tangential X-ray imaging crystal spectrometer on EAST (Experimental Advanced Superconducting Tokamak). Co-current central impurity toroidal rotation change was observed in ICRF-heated L- and H-mode plasmas. Rotation increment as high as 30 km/s was generated at ∼1.7 MW ICRF power. Scaling results showed similar trend as the Rice scaling but with significant scattering, especially in L-mode plasmas. We varied the plasma current, toroidal field and magnetic configuration individually to study their effect on L-mode plasma rotation, while keeping the other major plasma parameters and heating unchanged during the scanning. It was found that larger plasma current could induce plasma rotation more efficiently. A scan of the toroidal magnetic field indicated that the largest rotation was obtained for on-axis ICRF heating. A comparison between lower-single-null (LSN) and double-null (DN) configurations showed that LSN discharges rendered a larger rotation change for the same power input and plasma parameters. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB112004 and 2015GB103002), National Natural Science Foundation of China (Nos. 11175208, 11305212, 11375235, 11405212 and 11261140328), the Innovative Program of Development Foundation of Hefei Center for Physical Science and Technology (2014FXCX003) and Brain Korea 21 Program for Leading Universities & Students (BK21 PLUS)
First Results from a Coherence Imaging Diagnostic for the Compact Toroidal Hybrid
NASA Astrophysics Data System (ADS)
Ennis, D. A.; Hartwell, G. J.; Johnson, C. A.; Maurer, D. A.; Allen, S. L.
2015-11-01
An optical coherence imaging diagnostic is being commissioned for time-resolved measurements (~ 10 ms) of ion emissivity, velocity, and temperature in the Compact Toroidal Hybrid (CTH) experiment. The Coherence Imaging (CI) technique measures the spectral coherence of an emission line with an imaging interferometer of fixed delay. CI has a number of advantages when compared to dispersive Doppler spectroscopy, including higher throughput and the capability to provide 2D spectral images, making it advantageous for investigating the non-axisymmetric geometry of CTH plasmas. A spectral survey of the visible and ultraviolet emission for a range of CTH discharges has identified helium and carbon impurity lines that will be utilized for CI measurements in CTH. First CI measurements of He II (468.6 nm) emission from CTH plasmas will be presented along with interferograms from a calibration light source and details of the instrument design. Results from this diagnostic will aid in characterizing the equilibrium ion parameters in both the edge and core of CTH plasmas for planned island divertor and MHD mode-locking experiments. Work supported by USDoE grant DE-FG02-00ER54610.
Fredrickson, E. D.; Bell, R. E.; Darrow, D. S.; Gorelenkov, N. N.; Kramer, G. J.; Medley, S. S.; White, R. B.; Crocker, N. A.; Kubota, S.; Levinton, F. M.; Yuh, H.; Liu, D.; Podesta, M.; Tritz, K.
2009-12-15
Experiments on the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] found strong bursts of toroidal Alfven eigenmode (TAE) activity correlated with abrupt drops in the neutron rate. A fairly complete data set offers the opportunity to benchmark the NOVA[C. Z. Cheng, Phys. Rep. 211, 1 (1992)] and ORBIT[R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)] codes in the low aspect ratio tokamak (ST) geometry. The internal structure of TAE was modeled with NOVA and good agreement is found with measurements made with an array of five fixed-frequency reflectometers. The fast-ion transport resulting from these bursts of multiple TAE was then modeled with the ORBIT code. The simulations are reasonably consistent with the observed drop in neutron rate, however, further refinements in both the simulation of the TAE structure and in the modeling of the fast-ion transport are needed. Benchmarking stability codes against present experiments is an important step in developing the predictive capability needed to plan future experiments.
Anomalous transport in toroidal plasmas. Annual report, [June 1, 1990--May 31, 1991
Punjabi, A.
1991-12-31
We have developed a Monte Carlo method to estimate the transport of different groups of particles for plasmas in toroidal geometries. This method can determine the important transport mechanisms driving the anomalous transport by comparing the numerical results with the experimental data. The important groups of particles whose transport can be estimated by this method include runaway electrons, thermal electrons, both passing and trapped diagnostic beam ions etc. The three basic mechanisms driving the anomalous transport are: spatial variation of magnetic field strength, spatial variation of electrostatic potential within the flux surfaces, and the loss of flux surfaces. The equation of motion are obtained from the drift hamiltonian. The equations of motion are developed in the canonical and in the non-canonical, practical co-ordinates as well. The effects of collisions are represented by appropriate stochastic changes in the constants of motion at each time-step. Here we present the results of application of this method to three cases: superathermal alphas in the rippled field of tokamaks, motion in the magnetic turbulence of takapole II, and transport in the stochastic fields of ZT40. This work is supported by DOE OFE and ORAU HBCU program.
Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas
Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.
1996-12-17
A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, {delta}f = f {minus} f{sub 0}, from an initial analytic distribution f{sub 0}. High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question.
Freedericksz transitions in circular toroidal layers of smectic C liquid crystals
NASA Astrophysics Data System (ADS)
Kidd, J. E.; Stewart, I. W.; Constanda, C.
2001-08-01
The aim of this paper is to consider theoretically a Freedericksz transition for concentric toroidal layers of smectic C liquid crystal arising from a simple geometric setup, thereby extending the results of Atkin & Stewart [Q. Jl Mech. Appl. Math., 47, 1994] who considered spherical layers of smectic C in the usual cone and plate geometry. Application of smectic continuum theory leads, after suitable approximations are made, to a linear governing equilibrium equation which is satisfied by both the trivial solution and a variable solution involving Bessel functions. We are able to determine the critical magnitude cH of the magnetic field H at which this variable solution exists, and a standard energy comparison reveals that the variable solution is expected to be more energetically favourable than the zero solution provided H > cH. Numerical examples of critical thresholds are given, which are comparable to those in the literature for nematics. The paper ends with a discussion section and some indication of possible future work.
White, T.L.; Bigelow, T.S.; Kimrey, H.D. Jr.
1987-01-01
The Advanced Toroidal Facility (ATF) is a moderate aspect ratio torsatron that will utilize 53.2 GHz 200 kW Electron Cyclotron Heating (ECH) to produce nearly current-free target plasmas suitable for subsequent heating by strong neutral beam injection. The initial configuration of the ECH system from the gyrotron to ATF consists of an optical arc detector, three bellows, a waveguide mode analyzer, two TiO/sub 2/ mode absorbers, two 90/sup 0/ miter bends, two waveguide pumpouts, an insulating break, a gate valve, and miscellaneous straight waveguide sections feeding a launcher radiating in the TE/sub 02/ mode. Later, a focusing Vlasov launcher will be added to beam the ECH power to the saddle point in ATF magnetic geometry for optimum power deposition. The ECH system has several unique features; namely, the entire ECH system is evacuated, the ECH system is broadband, forward power is monitored by a newly developed waveguide mode analyzer, phase correcting miter bends will be employed, and the ECH system will be capable of operating short pulse to cw. Initial high-power tests show that the overall system efficiency is 87%. The waveguide mode analyzer shows that the gyrotron mode output consists of 13% TE/sub 01/, 82.6% TE/sub 02/, 2.5% TE/sub 03/, and 1.9% TE/sub 04/. 4 refs.
Free-boundary toroidal Alfvén eigenmodes
NASA Astrophysics Data System (ADS)
Chen, Eugene Y.; Berk, H. L.; Breizman, B.; Zheng, L. J.
2011-05-01
A numerical study is presented for the n = 1 free-boundary toroidal Alfvén eigenmodes (TAE) in tokamaks, which shows that there is considerable sensitivity of n = 1 modes to the position of the conducting wall. An additional branch of the TAE is shown to emerge from the upper continuum as the ratio of conducting wall radius to plasma radius increases. Such phenomena arise in plasma equilibria with both circular and shaped cross sections, where the shaped profile studied here is similar to that found in Alcator C-Mod.
Resistive demountable toroidal-field coils for tokamak reactors
Jassby, D.L.; Jacobsen, R.A.; Kalnavarns, J.; Masson, L.S.; Sekot, J.P.
1981-07-01
Readily demountable TF (toroidal-field) coils allow complete access to the internal components of a tokamak reactor for maintenance of replacement. The requirement of readily demountable joints dictates the use of water-cooled resistive coils, which have a host of decisive advantages over superconducting coils. Previous papers have shown that resistive TF coils for tokamak reactors can operate in the steady state with acceptable power dissipation (typically, 175 to 300 MW). This paper summarizes results of parametric studies of size optimization of rectangular TF coils and of a finite-element stress analysis, and examines several candidate methods of implementing demountable joints for rectangular coils constructed of plate segments.
Evidence of Inward Toroidal Momentum Convection in the JET Tokamak
Tala, T.; Zastrow, K.-D.; Brix, M.; Corrigan, G.; Giroud, C.; Naulin, V.; Peeters, A. G.; Tardini, G.; Strintzi, D.
2009-02-20
Experiments have been carried out on the Joint European Torus tokamak to determine the diffusive and convective momentum transport. Torque, injected by neutral beams, was modulated to create a periodic perturbation in the toroidal rotation velocity. Novel transport analysis shows the magnitude and profile shape of the momentum diffusivity are similar to those of the ion heat diffusivity. A significant inward momentum pinch, up to 20 m/s, has been found. Both results are consistent with gyrokinetic simulations. This evidence is complemented in plasmas with internal transport barriers.
Observation of odd toroidal Alfvén eigenmodes.
Kramer, G J; Sharapov, S E; Nazikian, R; Gorelenkov, N N; Budny, R V
2004-01-01
Experimental evidence is presented for the existence of the theoretically predicted odd toroidicity induced Alfvén eigenmode (TAE) from the simultaneous appearance of odd and even TAEs in a normal shear discharge of the joint European torus. The modes are observed in low central magnetic shear plasmas created by injecting lower hybrid current drive. A fast ion population was created by applying ion cyclotron heating at the high-field side to excite the TAEs. The odd TAEs were identified from their frequency, mode number, and timing relative to the even TAEs. PMID:14753994
Toroidally symmetric plasma vortex at tokamak divertor null point
NASA Astrophysics Data System (ADS)
Umansky, M. V.; Ryutov, D. D.
2016-03-01
Reduced MHD equations are used for studying toroidally symmetric plasma dynamics near the divertor null point. Numerical solution of these equations exhibits a plasma vortex localized at the null point with the time-evolution defined by interplay of the curvature drive, magnetic restoring force, and dissipation. Convective motion is easier to achieve for a second-order null (snowflake) divertor than for a regular x-point configuration, and the size of the convection zone in a snowflake configuration grows with plasma pressure at the null point. The trends in simulations are consistent with tokamak experiments which indicate the presence of enhanced transport at the null point.
A flexible high-energy toroidal grating monochromator at Bessy
Bernstorff, S.; Braun, W.; Mast, M.; Peatman, W.; Schroeter, T.
1989-07-01
A toroidal grating monochromator, the HE-TGM-2, designed for medium high resolution and high transmission in the spectral range 100--730 eV, has been installed and tested at the Berlin electron storage ring BESSY. Having a conventional configuration, namely a prefocusing mirror and an entrance slit, the resolution of the HE-TGM-2 is essentially independent of the source size and position of the stored electron beam. Gas phase photoionization spectra of free atoms and molecules as well as photoemission experiments on solid surfaces have been used to characterize this monochromator.
System and method of operating toroidal magnetic confinement devices
Chance, Morrell S.; Jardin, Stephen C.; Stix, Thomas H.; Grimm, deceased, Ray C.; Manickam, Janardhan; Okabayashi, Michio
1987-01-01
For toroidal magnetic confinement devices the second region of stability against ballooning modes can be accessed with controlled operation. Under certain modes of operation, the first and second stability regions may be joined together. Accessing the second region of stability is accomplished by forming a bean-shaped plasma and increasing the indentation until a critical value of indentation is reached. A pusher coil, located at the inner-major-radius side of the device, is engaged to form a bean-shaped poloidal cross-section in the plasma.
Effect of alpha particles on Toroidal Alfven Eigenmodes
Berk, H.L.
1992-11-01
An overview is given of the analytic structure for the linear theory of the Toroidal Alfven Eigenmode (TAE), where multiple gap structures occur. A discussion is given of the alpha particle drive and the various dissipation mechanisms that can stabilize the system. A self-consistent calculation of the TAE mode, for a low-beta high-aspect-ratio plasma, indicates that though the alpha particle drive is comparable to the dissipation mechanisms, overall stability is still achieved for ignited ITER-like plasma. A brief discussion is given of the nonlinear theory for the TAE mode and how nonlinear alpha particle dynamics can be treated by mapping methods.
Theory and application of maximum magnetic energy in toroidal plasmas
Chu, T.K.
1992-02-01
The magnetic energy in an inductively driven steady-state toroidal plasma is a maximum for a given rate of dissipation of energy (Poynting flux). A purely resistive steady state of the piecewise force-free configuration, however, cannot exist, as the periodic removal of the excess poloidal flux and pressure, due to heating, ruptures the static equilibrium of the partitioning rational surfaces intermittently. The rupture necessitates a plasma with a negative q{prime}/q (as in reverse field pinches and spheromaks) to have the same {alpha} in all its force-free regions and with a positive q{prime}/q (as in tokamaks) to have centrally peaked {alpha}'s.
Theory and application of maximum magnetic energy in toroidal plasmas
Chu, T.K.
1992-02-01
The magnetic energy in an inductively driven steady-state toroidal plasma is a maximum for a given rate of dissipation of energy (Poynting flux). A purely resistive steady state of the piecewise force-free configuration, however, cannot exist, as the periodic removal of the excess poloidal flux and pressure, due to heating, ruptures the static equilibrium of the partitioning rational surfaces intermittently. The rupture necessitates a plasma with a negative q{prime}/q (as in reverse field pinches and spheromaks) to have the same {alpha} in all its force-free regions and with a positive q{prime}/q (as in tokamaks) to have centrally peaked {alpha}`s.
Variable control of neutron albedo in toroidal fusion devices
Jassby, Daniel L.; Micklich, Bradley J.
1986-01-01
An arrangement is provided for controlling neutron albedo in toroidal fusion devices having inboard and outboard vacuum vessel walls for containment of the neutrons of a fusion plasma. Neutron albedo material is disposed immediately adjacent the inboard wall, and is movable, preferably in vertical directions, so as to be brought into and out of neutron modifying communication with the fusion neutrons. Neutron albedo material preferably comprises a liquid form, but may also take pebble, stringer and curtain-like forms. A neutron flux valve, rotatable about a vertical axis is also disclosed.
Simulation of dust streaming in toroidal traps: Stationary flows
Reichstein, Torben; Piel, Alexander
2011-08-15
Molecular-dynamic simulations were performed to study dust motion in a toroidal trap under the influence of the ion drag force driven by a Hall motion of the ions in E x B direction, gravity, inter-particle forces, and friction with the neutral gas. This article is focused on the inhomogeneous stationary streaming motion. Depending on the strength of friction, the spontaneous formation of a stationary shock or a spatial bifurcation into a fast flow and a slow vortex flow is observed. In the quiescent streaming region, the particle flow features a shell structure which undergoes a structural phase transition along the flow direction.
Geodesic Acoustic Mode Induced by Toroidal Rotation in Tokamaks
Wahlberg, C.
2008-09-12
The effect of toroidal rotation on the geodesic acoustic mode (GAM) in a tokamak is studied. It is shown that, in addition to a small frequency upshift of the ordinary GAM, another GAM, with much lower frequency, is induced by the rotation. The new GAM appears as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the magnetic surfaces. Both GAMs in a rotating plasma are shown to exist both as continuum modes with finite mode numbers m and n at the rational surfaces q=m/n as well as in the form of axisymmetric modes with m=n=0.
Position indicating split toroid for the RACE experiment
NASA Astrophysics Data System (ADS)
Hurst, B.; Folkman, K.
2007-08-01
Aspects of the recent reactor accelerator coupled experiments (RACE) carried out at the University of Texas Nuclear Engineering Teaching Laboratory will be discussed. In particular, a compact instrument that allowed a continuous non-invasive means of determining the relative electron beam position was developed. The operation of the instrument is similar to an inductive current pick up toroid except that the core is sectioned radially, which allows spatial information to be derived from the induced voltages. Results of initial tests, both in beam and with a pulser, will be presented along with plans to optimize future designs.
Experimental observation of crystalline particle flows in toroidal dust clouds
Wilms, Jochen Piel, Alexander; Reichstein, Torben
2015-06-15
The dust flow in a toroidal dust trap is studied experimentally. The flow is driven by the Hall component of the ion drag force in a magnetized plasma. Dust density waves are found in a torus with a large minor radius a, which allows for several wavelength, 2a>5λ, in the (mostly) radial direction of the ion flow. Beyond an intermediate state with radial sloshing oscillations, a crystalline dust flow with suppressed wave activity could be realized for 2a<2λ. The particles arrange themselves in distinct layers with hexagonal-like local order. Smooth transitions between states with different numbers of layers are found in the inhomogeneous flow.
Toroidal constant-tension superconducting magnetic energy storage units
Herring, J.S.
1992-11-03
A superconducting magnetic energy storage unit is provided in which the magnet is wound in a toroidal fashion such that the magnetic field produced is contained only within the bore of the magnet, and thus producing a very low external field. The superconducting magnet includes a coolant channel disposed through the wire. The bore of the magnet comprises a storage volume in which cryogenic coolant is stored, and this volume supplies the coolant to be delivered to the coolant channel in the magnet. 6 figs.
Hydraulic jumps in inhomogeneous strongly coupled toroidal dust flows
NASA Astrophysics Data System (ADS)
Piel, Alexander; Wilms, Jochen
2016-07-01
The inhomogeneous flow of strongly coupled dust particles in a toroidal particle trap with harmonic radial confinement is analyzed in the incompressible fluid limit. It is shown that the flow can spontaneously generate shock-like events, which are similar to the hydraulic jump in open channel flows. A definition of the Froude number for this model is given and the critical speed is recovered as the group velocity of surface waves. This hydraulic model is compared with molecular-dynamics simulations, which show that a sudden bifurcation of the flow lines and a localized temperature peak appear just at the point where the critical condition for the hydraulic jump is located.
Linear tearing mode stability equations for a low collisionality toroidal plasma
NASA Astrophysics Data System (ADS)
Connor, J. W.; Hastie, R. J.; Helander, P.
2009-01-01
et al (1983 Phys. Fluids 26 2509) to toroidal geometry.
An introduction to Minkowski geometries
NASA Astrophysics Data System (ADS)
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
The Geometry of the Universe: Part 1
ERIC Educational Resources Information Center
Francis, Stephanie
2009-01-01
This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…
Fostering Spatial vs. Metric Understanding in Geometry
ERIC Educational Resources Information Center
Kinach, Barbara M.
2012-01-01
Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…
NASA Astrophysics Data System (ADS)
Liu, Yueqiang; Ryan, D.; Kirk, A.; Li, Li; Suttrop, W.; Dunne, M.; Fischer, R.; Fuchs, J. C.; Kurzan, B.; Piovesan, P.; Willensdorfer, M.; the ASDEX Upgrade Team; the EUROfusion MST1 Team
2016-05-01
The plasma response to the vacuum resonant magnetic perturbation (RMP) fields, produced by the ELM control coils in ASDEX Upgrade experiments, is computationally modelled using the MARS-F/K codes (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). A systematic investigation is carried out, considering various plasma and coil configurations as in the ELM control experiments. The low q plasmas, with {{q}95}∼ 3.8 (q 95 is the safety factor q value at 95% of the equilibrium poloidal flux), responding to low n (n is the toroidal mode number) field perturbations from each single row of the ELM coils, generates a core kink amplification effect. Combining two rows, with different toroidal phasing, thus leads to either cancellation or reinforcement of the core kink response, which in turn determines the poloidal location of the peak plasma surface displacement. The core kink response is typically weak for the n = 4 coil configuration at low q, and for the n = 2 configuration but only at high q ({{q}95}∼ 5.5 ). A phase shift of around 60 degrees for low q plasmas, and around 90 degrees for high q plasmas, is found in the coil phasing, between the plasma response field and the vacuum RMP field, that maximizes the edge resonant field component. This leads to an optimal coil phasing of about 100 (‑100) degrees for low (high) q plasmas, that maximizes both the edge resonant field component and the plasma surface displacement near the X-point of the separatrix. This optimal phasing closely corresponds to the best ELM mitigation observed in experiments. A strong parallel sound wave damping moderately reduces the core kink response but has minor effect on the edge peeling response. For low q plasmas, modelling shows that both the resonant electromagnetic torque and the neoclassical toroidal viscous (NTV) torque (due to the presence of 3D magnetic field perturbations) contribute to the toroidal flow damping, in particular near the