Density-shear instability in electron magneto-hydrodynamics
Wood, T. S. Hollerbach, R.; Lyutikov, M.
2014-05-15
We discuss a novel instability in inertia-less electron magneto-hydrodynamics (EMHD), which arises from a combination of electron velocity shear and electron density gradients. The unstable modes have a lengthscale longer than the transverse density scale, and a growth-rate of the order of the inverse Hall timescale. We suggest that this density-shear instability may be of importance in magnetic reconnection regions on scales smaller than the ion skin depth, and in neutron star crusts. We demonstrate that the so-called Hall drift instability, previously argued to be relevant in neutron star crusts, is a resistive tearing instability rather than an instability of the Hall term itself. We argue that the density-shear instability is of greater significance in neutron stars than the tearing instability, because it generally has a faster growth-rate and is less sensitive to geometry and boundary conditions. We prove that, for uniform electron density, EMHD is “at least as stable” as regular, incompressible MHD, in the sense that any field configuration that is stable in MHD is also stable in EMHD. We present a connection between the density-shear instability in EMHD and the magneto-buoyancy instability in anelastic MHD.
Compressibility effect on magnetic-shear-localized ideal magnetohydrodynamic interchange instability
Gupta, Sangeeta; Callen, J.D.; Hegna, C.C.
2005-08-15
Eigenmode analysis of a magnetic-shear-localized ideal magnetohydrodynamic interchange instability in the presence of plasma compressibility indicates the marginal stability criterion (D{sub I}=1/4) is not affected by the compressibility effects. Above the marginal stability criterion, plasma compressibility causes a significant reduction in the growth rate of an ideal interchange instability.
Magnetohydrodynamic instability
NASA Technical Reports Server (NTRS)
Priest, E. R.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S.
1986-01-01
There have been major advances in the theory of magnetic reconnection and of magnetic instability, with important implications for the observations, as follows: (1) Fast and slow magnetic shock waves are produced by the magnetohydrodynamics of reconnection and are potential particle accelerators. (2) The impulsive bursty regime of reconnection gives a rapid release of magnetic energy in a series of bursts. (3) The radiative tearing mode creates cool filamentary structures in the reconnection process. (4) The stability analyses imply that an arcade can become unstable when either its height or twist of plasma pressure become too great.
Gaur, Gurudatt; Das, Amita
2012-07-15
The study of electron velocity shear driven instability in electron magnetohydrodynamics (EMHD) regime in three dimensions has been carried out. It is well known that the instability is non-local in the plane defined by the flow direction and that of the shear, which is the usual Kelvin-Helmholtz mode, often termed as the sausage mode in the context of EMHD. On the other hand, a local instability with perturbations in the plane defined by the shear and the magnetic field direction exists which is termed as kink mode. The interplay of these two modes for simple sheared flow case as well as that when an external magnetic field exists has been studied extensively in the present manuscript in both linear and nonlinear regimes. Finally, these instability processes have been investigated for the exact 2D dipole solutions of EMHD equations [M. B. Isichenko and A. N. Marnachev, Sov. Phys. JETP 66, 702 (1987)] for which the electron flow velocity is sheared. It has been shown that dipoles are very robust and stable against the sausage mode as the unstable wavelengths are typically longer than the dipole size. However, we observe that they do get destabilized by the local kink mode.
Nakamura, T. K. M.; Hasegawa, H.; Shinohara, I.
2010-01-01
Ion-to-magnetohydrodynamic scale physics of the transverse velocity shear layer and associated Kelvin–Helmholtz instability (KHI) in a homogeneous, collisionless plasma are investigated by means of full particle simulations. The shear layer is broadened to reach a kinetic equilibrium when its initial thickness is close to the gyrodiameter of ions crossing the layer, namely, of ion-kinetic scale. The broadened thickness is larger in B⋅Ω<0 case than in B⋅Ω>0 case, where Ω is the vorticity at the layer. This is because the convective electric field, which points out of (into) the layer for B⋅Ω<0 (B⋅Ω>0), extends (reduces) the gyrodiameters. Since the kinetic equilibrium is established before the KHI onset, the KHI growth rate depends on the broadened thickness. In the saturation phase of the KHI, the ion vortex flow is strengthened (weakened) for B⋅Ω<0 (B⋅Ω>0), due to ion centrifugal drift along the rotational plasma flow. In ion inertial scale vortices, this drift effect is crucial in altering the ion vortex size. These results indicate that the KHI at Mercury-like ion-scale magnetospheric boundaries could show clear dawn-dusk asymmetries in both its linear and nonlinear growth. PMID:20838425
LOCAL RADIATION MAGNETOHYDRODYNAMIC INSTABILITIES IN MAGNETICALLY STRATIFIED MEDIA
Tao, Ted; Blaes, Omer
2011-11-20
We study local radiation magnetohydrodynamic instabilities in static, optically thick, vertically stratified media with constant flux mean opacity. We include the effects of vertical gradients in a horizontal background magnetic field. Assuming rapid radiative diffusion, we use the zero gas pressure limit as an entry point for investigating the coupling between the photon bubble instability and the Parker instability. Apart from factors that depend on wavenumber orientation, the Parker instability exists for wavelengths longer than a characteristic wavelength {lambda}{sub tran}, while photon bubbles exist for wavelengths shorter than {lambda}{sub tran}. The growth rate in the Parker regime is independent of the orientation of the horizontal component of the wavenumber when radiative diffusion is rapid, but the range of Parker-like wavenumbers is extended if there exists strong horizontal shear between field lines (i.e., horizontal wavenumber perpendicular to the magnetic field). Finite gas pressure introduces an additional short-wavelength limit to the Parker-like behavior, and also limits the growth rate of the photon bubble instability to a constant value at short wavelengths. We also consider the effects of differential rotation with accretion disk applications in mind. Our results may explain why photon bubbles have not yet been observed in recent stratified shearing box accretion disk simulations. Photon bubbles may physically exist in simulations with high radiation to gas pressure ratios, but higher spatial resolution will be needed to resolve the asymptotically growing unstable wavelengths.
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.
Structure Formation through Magnetohydrodynamical Instabilities in Protoplanetary Disks
NASA Astrophysics Data System (ADS)
Noguchi, K.; Tajima, T.; Horton, W.
2000-12-01
The shear flow instabilities under the presence of magnetic fields in the protoplanetary disk can greatly facilitate the formation of density structures that serve as seeds prior to the onset of the gravitational Jeans instability. Such a seeding process may explain several outstanding puzzles in the planetary genesis that are further compounded by the new discoveries of extrasolar planets and a new insight into the equation of state of dense matter. This puzzle also includes the apparent narrow window of the age difference of the Sun and the Earth. We evaluate the effects of the Parker, magnetorotational(Balbus-Hawley), and kinematic dynamo instabilities by comparing the properties of these instabilities. We calculate the mass spectra of aggregated density structures by the above mechanism in the radial direction for an axisymmetric magnetohydrodynamic(MHD) torus equiblium and power-law density profile models. The mass spectrum of the magnetorotational instability may describe the origin of giant planets away from the central star such as Jupiter. Our local three-dimentional MHD simulation indicates that the coupling of the Parker and magnetorotational instabilities creates spiral arms and gas blobs in the accretion disk, reinforcing the theory and model.
Transverse electron-scale instability in relativistic shear flows
NASA Astrophysics Data System (ADS)
Alves, E. P.; Grismayer, T.; Fonseca, R. A.; Silva, L. O.
2015-08-01
Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic (≫c /ωp e ) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales.
Magnetic control of magnetohydrodynamic instabilities in tokamaks
NASA Astrophysics Data System (ADS)
Strait, E. J.
2015-02-01
Externally applied, non-axisymmetric magnetic fields form the basis of several relatively simple and direct methods to control magnetohydrodynamic (MHD) instabilities in a tokamak, and most present and planned tokamaks now include a set of non-axisymmetric control coils for application of fields with low toroidal mode numbers. Non-axisymmetric applied fields are routinely used to compensate small asymmetries ( δB /B ˜10-3 to 10-4 ) of the nominally axisymmetric field, which otherwise can lead to instabilities through braking of plasma rotation and through direct stimulus of tearing modes or kink modes. This compensation may be feedback-controlled, based on the magnetic response of the plasma to the external fields. Non-axisymmetric fields are used for direct magnetic stabilization of the resistive wall mode—a kink instability with a growth rate slow enough that feedback control is practical. Saturated magnetic islands are also manipulated directly with non-axisymmetric fields, in order to unlock them from the wall and spin them to aid stabilization, or position them for suppression by localized current drive. Several recent scientific advances form the foundation of these developments in the control of instabilities. Most fundamental is the understanding that stable kink modes play a crucial role in the coupling of non-axisymmetric fields to the plasma, determining which field configurations couple most strongly, how the coupling depends on plasma conditions, and whether external asymmetries are amplified by the plasma. A major advance for the physics of high-beta plasmas ( β = plasma pressure/magnetic field pressure) has been the understanding that drift-kinetic resonances can stabilize the resistive wall mode at pressures well above the ideal-MHD stability limit, but also that such discharges can be very sensitive to external asymmetries. The common physics of stable kink modes has brought significant unification to the topics of static error fields at low
Magnetic control of magnetohydrodynamic instabilities in tokamaks
Strait, E. J.
2015-02-15
Externally applied, non-axisymmetric magnetic fields form the basis of several relatively simple and direct methods to control magnetohydrodynamic (MHD) instabilities in a tokamak, and most present and planned tokamaks now include a set of non-axisymmetric control coils for application of fields with low toroidal mode numbers. Non-axisymmetric applied fields are routinely used to compensate small asymmetries (δB/B∼10{sup −3} to 10{sup −4}) of the nominally axisymmetric field, which otherwise can lead to instabilities through braking of plasma rotation and through direct stimulus of tearing modes or kink modes. This compensation may be feedback-controlled, based on the magnetic response of the plasma to the external fields. Non-axisymmetric fields are used for direct magnetic stabilization of the resistive wall mode—a kink instability with a growth rate slow enough that feedback control is practical. Saturated magnetic islands are also manipulated directly with non-axisymmetric fields, in order to unlock them from the wall and spin them to aid stabilization, or position them for suppression by localized current drive. Several recent scientific advances form the foundation of these developments in the control of instabilities. Most fundamental is the understanding that stable kink modes play a crucial role in the coupling of non-axisymmetric fields to the plasma, determining which field configurations couple most strongly, how the coupling depends on plasma conditions, and whether external asymmetries are amplified by the plasma. A major advance for the physics of high-beta plasmas (β = plasma pressure/magnetic field pressure) has been the understanding that drift-kinetic resonances can stabilize the resistive wall mode at pressures well above the ideal-MHD stability limit, but also that such discharges can be very sensitive to external asymmetries. The common physics of stable kink modes has brought significant unification to the topics of static error
Instability of the magnetohydrodynamics system at vanishing Reynolds number
NASA Astrophysics Data System (ADS)
Bouya, Ismaël
2013-12-01
The aim of this note is to study the dynamo properties of the magnetohydrodynamics system at vanishing R m . Improving the analysis in Gérard-Varet (SIAM J Math Anal 37(3):815-840, 2006), we shall establish a generic Lyapunov instability result.
Diffusive Magnetohydrodynamic Instabilities beyond the Chandrasekhar Theorem
NASA Astrophysics Data System (ADS)
Rüdiger, Günther; Schultz, Manfred; Stefani, Frank; Mond, Michael
2015-10-01
We consider the stability of axially unbounded cylindrical flows that contain a toroidal magnetic background field with the same radial profile as their azimuthal velocity. For ideal fluids, Chandrasekhar had shown the stability of this configuration if the Alfvén velocity of the field equals the velocity of the background flow, i.e., if the magnetic Mach number {Mm}=1. We demonstrate that magnetized Taylor-Couette flows with such profiles become unstable against non-axisymmetric perturbations if at least one of the diffusivities is finite. We also find that for small magnetic Prandtl numbers {Pm} the lines of marginal instability scale with the Reynolds number and the Hartmann number. In the limit {Pm}\\to 0 the lines of marginal instability completely lie below the line for {Mm}=1 and for {Pm}\\to ∞ they completely lie above this line. For any finite value of {Pm}, however, the lines of marginal instability cross the line {Mm}=1, which separates slow from fast rotation. The minimum values of the field strength and the rotation rate that are needed for the instability (slightly) grow if the rotation law becomes flat. In this case, the electric current of the background field becomes so strong that the current-driven Tayler instability (which also exists without rotation) appears in the bifurcation map at low Hartmann numbers.
MHD (magnetohydrodynamics) instabilities in simple plasma configuration
Manheimer, W.M.; Lashmore-Davies, C.
1984-01-01
This work provides what, we hope, is a relatively simple, self contained description of MHD instabilities in plasmas with simple configurations. By simple configuration, we mean a plasma in which all quantities vary in only one spatial direction. We deal with such plasmas here because we want to emphasize the basic physics of MHD instabilities. Although some fusion devices are inherently two or three dimensional in nature, there are others, specifically tokamaks and reversed field pinches which are, to good approximation, one dimensional. Also, these devices both display a wealth of complex MHD activity which can be fruitfully discussed. One deceptive aspect of MHD instabilities is that the simplest ones are extremely easy to understand. However more complicated instabilities, for instance in a plasma where both an axial and azimuthal field are present are much more difficult to visualize; but they are also much more interesting. This work is divided into two parts. Chapters 2-9 describe linear theory and chapters 10-15 describe the nonlinear theory. The latter part is naturally much more speculative than the former because less is known about nonlinear theory.
de Baar, M.R.; Hogeweij, G.M.; Lopes Cardozo, N.J.; Oomens, A.A.; Schueller, F.C.
1997-06-01
In the Rijnhuizen Tokamak Project, plasmas with steady-state negative central shear (NCS) are made with off-axis electron cyclotron heating. Shifting the power deposition by 2mm results in a sharp transition of confinement. The good confinement branch features a transport barrier at the off-axis minimum of the safety factor (q) , where q{le}3, and two magnetohydrodynamic (MHD) instabilities, where one is localized at the off-axis minimum of q and one covers the entire NCS region. The low confinement branch has q{gt}3 everywhere, no transport barrier, and no MHD activity. {copyright} {ital 1997} {ital The American Physical Society}
Morrison, P. J.; Tassi, E.; Tronko, N.
2013-04-15
Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical {delta}W criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of {delta}W is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instability (MRI) for the latter model corresponds to the condition for interchange instability in CRMHD, with the Coriolis term and shear velocity playing the roles of the curvature term and pressure gradient, respectively. Using the EC method, stability conditions for the rotating disk model, for a large class of equilibria with possible non-uniform magnetic fields, are obtained. In particular, this shows it is possible for the MRI system to undergo, in addition to the MRI, another instability that is analogous to the kink instability. For vanishing magnetic field, the Rayleigh hydrodynamical stability condition is recovered.
Instability of subharmonic resonances in magnetogravity shear waves.
Salhi, A; Nasraoui, S
2013-12-01
We study analytically the instability of the subharmonic resonances in magnetogravity waves excited by a (vertical) time-periodic shear for an inviscid and nondiffusive unbounded conducting fluid. Due to the fact that the magnetic potential induction is a Lagrangian invariant for magnetohydrodynamic Euler-Boussinesq equations, we show that plane-wave disturbances are governed by a four-dimensional Floquet system in which appears, among others, the parameter ɛ representing the ratio of the periodic shear amplitude to the vertical Brunt-Väisälä frequency N(3). For sufficiently small ɛ and when the magnetic field is horizontal, we perform an asymptotic analysis of the Floquet system following the method of Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]. We determine the width and the maximal growth rate of the instability bands associated with subharmonic resonances. We show that the instability of subharmonic resonance occurring in gravity shear waves has a maximal growth rate of the form Δ(m)=(3√[3]/16)ɛ. This instability persists in the presence of magnetic fields, but its growth rate decreases as the magnetic strength increases. We also find a second instability involving a mixing of hydrodynamic and magnetic modes that occurs for all magnetic field strengths. We also elucidate the similarity between the effect of a vertical magnetic field and the effect of a vertical Coriolis force on the gravity shear waves considering axisymmetric disturbances. For both cases, plane waves are governed by a Hill equation, and, when ɛ is sufficiently small, the subharmonic instability band is determined by a Mathieu equation. We find that, when the Coriolis parameter (or the magnetic strength) exceeds N(3)/2, the instability of the subharmonic resonance vanishes.
Nonlinear electron magnetohydrodynamics physics. IV. Whistler instabilities
Urrutia, J. M.; Stenzel, R. L.; Strohmaier, K. D.
2008-06-15
A very large low-frequency whistler mode is excited with magnetic loop antennas in a uniform laboratory plasma. The wave magnetic field exceeds the ambient field causing in one polarity a field reversal, and a magnetic topology resembling that of spheromaks in the other polarity. These propagating ''whistler spheromaks'' strongly accelerate the electrons and create non-Maxwellian distributions in their toroidal current ring. It is observed that the locally energized electrons in the current ring excite new electromagnetic instabilities and emit whistler modes with frequencies unrelated to the applied frequency. Emissions are also observed from electrons excited in X-type neutral lines around the antenna. The properties of the excited waves such as amplitudes, frequency spectra, field topologies, propagation, polarization, growth, and damping have been investigated. The waves remain linear (B{sub wave}<
Theory of magnetohydrodynamic instabilities excited by energetic particles in tokamaks
Chen, L. )
1994-05-01
The resonant excitations of high-[ital n] magnetohydrodynamic instabilities by the energetic ions/alpha particles in tokamaks are theoretically analyzed. Here, [ital n] is the toroidal mode number. The magnetohydrodynamic eigenmodes, typically, consist of two-scale structures; one corresponds to the singular ( inertial'') region and the other the regular (ideal) region. Due to the finite-size orbits, the energetic particle contributions in the singular region are suppressed. Analytical dispersion relations can be derived via the asymptotic matching analysis. The dispersion relations have the generic form of the fishbone'' dispersion relation [Phys. Rev. Lett. [bold 52], 1122 (1984)] and demonstrate, in particular, the existence of two types of modes; that is, the discrete gap mode and the energetic-particle continuum mode. Specific expressions are given for both the kinetic ballooning modes and the toroidal Alfven modes.
Instabilities in shear and simple shear deformations of gold crystals
NASA Astrophysics Data System (ADS)
Pacheco, A. A.; Batra, R. C.
We use the tight-binding potential and molecular mechanics simulations to study local and global instabilities in shear and simple shear deformations of three initially defect-free finite cubes of gold single crystal containing 3480, 7813, and 58,825 atoms. Displacements on all bounding surfaces are prescribed while studying simple shear deformations, but displacements on only two opposite surfaces are assigned during simulations of shear deformations with the remaining four surfaces kept free of external forces. The criteria used to delineate local instabilities in the system include the following: (i) a component of the second-order spatial gradients of the displacement field having large values relative to its average value in the body, (ii) the minimum eigenvalue of the Hessian of the energy of an atom becoming non-positive, and (iii) structural changes represented by a high value of the common neighborhood parameter. It is found that these criteria are met essentially simultaneously at the same atomic position. Effects of free surfaces are evidenced by different deformation patterns for the same specimen deformed in shear and simple shear. The shear strength of a specimen deformed in simple shear is more than three times that of the same specimen deformed in shear. It is found that for each cubic specimen deformed in simple shear the evolution with the shear strain of the average shear stress, prior to the onset of instabilities, is almost identical to that in an equivalent hyperelastic material with strain energy density derived from the tight-binding potential and the assumption that it obeys the Cauchy-Born rule. Even though the material response of the hyperelastic body predicted from the strain energy density is stable over the range of the shear strain simulated in this work, the molecular mechanics simulations predict local and global instabilities in the three specimens.
Electrostatic ion cyclotron velocity shear instability
NASA Technical Reports Server (NTRS)
Lemons, D. S.; Winske, D.; Gary, S. P.
1992-01-01
A local electrostatic dispersion equation is derived for a shear flow perpendicular to an ambient magnetic field, which includes all kinetic effects and involves only one important parameter. The dispersion equation is cast in the form of Gordeyev integrals and is solved numerically. Numerical solutions indicate that an ion cyclotron instability is excited. The instability occurs roughly at multiples of the ion cyclotron frequency (modified by the shear), with the growth rate or the individual harmonics overlapping in the wavenumber. At large values of the shear parameter, the instability is confined to long wavelengths, but at smaller shear, a second distinct branch at shorter wavelengths also appears. The properties of the instability obtained are compared with those obtained in the nonlocal limit by Ganguli et al. (1985, 1988).
Microwave imaging of magnetohydrodynamic instabilities in fusion plasma
NASA Astrophysics Data System (ADS)
Sabot, Roland; Elbèze, Didier; Lee, Woochang; Nam, Yoonbum; Park, Hyeon; Shen, Junsong; Yun, Gunsu; Choi, Minjun; Giacalone, Jean-Claude; Nicolas, Timothée; Bottereau, Christine; Clairet, Frédéric; Lotte, Philippe; Molina, Diego
2016-11-01
Microwave imaging diagnostics are extremely useful for observing magnetohydrodynamic (MHD) instabilities in magnetic fusion plasmas. Two imaging diagnostics will be available on the WEST tokamak. A method was developed to reconstruct electron density maps from electron density profiles measured by ultrafast reflectometry, a technique based on FM-CW radar principle. It relies on plasma rotation to perform 2D reconstruction. An Electron Cyclotron Emission Imaging (ECEI) diagnostic will image directly the temperature fluctuations. It will be equivalent to 24 stacked vertically radiometers, each probing a spot of few centimetres. These two complementary techniques will contribute to the validation of MHD models.
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence
Squire, J.; Bhattacharjee, A.
2015-11-02
Here, this article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of alpha effects in the stratified regions of disks gives the puzzling result that there is nomore » strong prediction for a sign of alpha, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.« less
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence
Squire, J.; Bhattacharjee, A.
2015-11-02
Here, this article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of alpha effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of alpha, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence.
Squire, J; Bhattacharjee, A
2015-11-01
This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of α effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of α, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.
The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Wheatley, V.; Samtaney, R.; Pullin, D. I.; Gehre, R. M.
2014-01-01
The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers.
Dynamical instabilities in magnetohydrodynamic wind-cloud interactions
NASA Astrophysics Data System (ADS)
Banda-Barragan, Wladimir Eduardo; Parkin, Elliot Ross; Crocker, Roland M.; Federrath, Christoph; Bicknell, Geoffrey Vincent
2015-08-01
We report the results from a comprehensive numerical study that investigates the role of dynamical instabilities in magnetohydrodynamic interactions between winds and spherical clouds in the interstellar medium. The growth of Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities at interfaces between wind and cloud material is responsible for the disruption of clouds and the formation of filamentary tails. We show how different strengths and orientations of the initial magnetic field affect the development of unstable modes and the ultimate morphology of these filaments. In the weak field limit, for example, KH instabilities developing at the flanks of clouds are dominant, whilst they are suppressed when stronger fields are considered. On the other hand, perturbations that originate RT instabilities at the leading edge of clouds are enhanced when fields are locally stronger. The orientation of the field lines also plays an important role in the structure of filaments. Magnetic ropes are key features of systems in which fields are aligned with the wind velocity, whilst current sheets are favoured when the initial field is preferentially transverse to the wind velocity. We compare our findings with analytical predictions obtained from the linear theory of hydromagnetic stability and provide a classification of filamentary tails based on their morphology.
TURBULENT MAGNETOHYDRODYNAMIC RECONNECTION MEDIATED BY THE PLASMOID INSTABILITY
Huang, Yi-Min; Bhattacharjee, A.
2016-02-10
It has been established that the Sweet–Parker current layer in high Lundquist number reconnection is unstable to the super-Alfvénic plasmoid instability. Past two-dimensional magnetohydrodynamic simulations have demonstrated that the plasmoid instability leads to a new regime where the Sweet–Parker current layer changes into a chain of plasmoids connected by secondary current sheets, and the averaged reconnection rate becomes nearly independent of the Lundquist number. In this work, a three-dimensional simulation with a guide field shows that the additional degree of freedom allows plasmoid instabilities to grow at oblique angles, which interact and lead to self-generated turbulent reconnection. The averaged reconnection rate in the self-generated turbulent state is of the order of a hundredth of the characteristic Alfvén speed, which is similar to the two-dimensional result but is an order of magnitude lower than the fastest reconnection rate reported in recent studies of externally driven three-dimensional turbulent reconnection. Kinematic and magnetic energy fluctuations both form elongated eddies along the direction of the local magnetic field, which is a signature of anisotropic magnetohydrodynamic turbulence. Both energy fluctuations satisfy power-law spectra in the inertial range, where the magnetic energy spectral index is in the range from −2.3 to −2.1, while the kinetic energy spectral index is slightly steeper, in the range from −2.5 to −2.3. The anisotropy of turbulence eddies is found to be nearly scale-independent, in contrast with the prediction of the Goldreich–Sridhar theory for anisotropic turbulence in a homogeneous plasma permeated by a uniform magnetic field.
Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability
NASA Astrophysics Data System (ADS)
Huang, Yi-Min; Bhattacharjee, A.
2016-02-01
It has been established that the Sweet-Parker current layer in high Lundquist number reconnection is unstable to the super-Alfvénic plasmoid instability. Past two-dimensional magnetohydrodynamic simulations have demonstrated that the plasmoid instability leads to a new regime where the Sweet-Parker current layer changes into a chain of plasmoids connected by secondary current sheets, and the averaged reconnection rate becomes nearly independent of the Lundquist number. In this work, a three-dimensional simulation with a guide field shows that the additional degree of freedom allows plasmoid instabilities to grow at oblique angles, which interact and lead to self-generated turbulent reconnection. The averaged reconnection rate in the self-generated turbulent state is of the order of a hundredth of the characteristic Alfvén speed, which is similar to the two-dimensional result but is an order of magnitude lower than the fastest reconnection rate reported in recent studies of externally driven three-dimensional turbulent reconnection. Kinematic and magnetic energy fluctuations both form elongated eddies along the direction of the local magnetic field, which is a signature of anisotropic magnetohydrodynamic turbulence. Both energy fluctuations satisfy power-law spectra in the inertial range, where the magnetic energy spectral index is in the range from -2.3 to -2.1, while the kinetic energy spectral index is slightly steeper, in the range from -2.5 to -2.3. The anisotropy of turbulence eddies is found to be nearly scale-independent, in contrast with the prediction of the Goldreich-Sridhar theory for anisotropic turbulence in a homogeneous plasma permeated by a uniform magnetic field.
Electrostatic ion cyclotron velocity shear instability
Lemons, D.S.; Winske, D.; Gary, S.P. )
1992-12-01
An electrostatic ion cyclotron instability driven by sheared velocity flow perpendicular to a uniform magnetic field is investigated in the local approximation. The dispersion equation, which includes all kinetic effects and involves only one important parameter, is cast in the form of Gordeyev integrals and solved numerically. The instability occurs roughly at multiples of the ion cyclotron frequency (but modified by the shear) with the growth rate of the individual harmonics overlapping in wavenumber. At small values of the shear parameter, the instability exists in two branches, one at long wavelength, [kappa][rho][sub i] [approximately] 0.5, and one at short wavelength, [kappa][rho][sub i] > 1.5 ([kappa][rho][sub i] is the wavenumber normalized to the ion gyroradius). At larger values of the shear parameter only the longer wavelength branch persists. The growth rate of the long wavelength mode, maximized over wavenumber and frequency, increases monotonically with the shear parameter. Properties of the instability are compared to those of Ganguli et al. obtained in the nonlocal limit.
Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows
Uchava, E. S.; Shergelashvili, B. M.; Tevzadze, A. G.; Poedts, S.
2014-08-15
We present a linear stability analysis of the perturbation modes in anisotropic magnetohydrodynamic (MHD) flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model that takes into account not only the effect of pressure anisotropy but also the effect of anisotropic heat fluxes. In this model, the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow exponentially when the heat flux parameter exceeds some critical value. It seems that velocity shear makes thermo-acoustic waves overstable even at subcritical heat flux parameters. Thus, when the effect of heat fluxes is not profound acoustic waves will grow due to the velocity shear, while at supercritical heat fluxes the flow reveals compressible thermal instability. Anisotropic thermal instability should be also important in astrophysical environments, where it will limit the maximal value of magnetic field that a low density ionized anisotropic flow can sustain.
Theory of magnetohydrodynamic instabilities excited by energetic particles in tokamaks
Chen, L. )
1994-07-20
The resonant excitations of high-n magnetohydrodynamic (MHD) instabilities by the energetic ions/alpha particles in tokamaks are theoretically analyzed. Here, n is the toroidal mode number. Since, typically, the MHD modes consist of two-scale structures; one singular ( inertial'') region and one regular (ideal) region, the energetic particle contributions in the singular region are suppressed by the finite-size orbits. Analytical dispersion relations can then be derived via the asymptotic matching analysis. The dispersion relations have the generic form of the fishbone'' dispersion relation and demonstrate, in particular, the existence of two types of modes; that is, the MHD gap mode and the energetic-particle continuum mode. Specific expressions are given for both the kinetic ballooning modes (KBM) and the toroidal Alfven modes (TAM). It is suggested that the stability property may be qualitatively regarded as the hybrid'' of conventional MHD tokamaks and field reversed ion rings. [copyright]American Institute of Physics
Radiative instabilities in sheared magnetic field
NASA Technical Reports Server (NTRS)
Drake, J. F.; Sparks, L.; Van Hoven, G.
1988-01-01
The structure and growth rate of the radiative instability in a sheared magnetic field B have been calculated analytically using the Braginskii fluid equations. In a shear layer, temperature and density perturbations are linked by the propagation of sound waves parallel to the local magnetic field. As a consequence, density clumping or condensation plays an important role in driving the instability. Parallel thermal conduction localizes the mode to a narrow layer where K(parallel) is small and stabilizes short wavelengths k larger-than(c) where k(c) depends on the local radiation and conduction rates. Thermal coupling to ions also limits the width of the unstable spectrum. It is shown that a broad spectrum of modes is typically unstable in tokamak edge plasmas and it is argued that this instability is sufficiently robust to drive the large-amplitude density fluctuations often measured there.
Residual turbulence from velocity shear stabilized interchange instabilities
Hung, C. P.; Hassam, A. B.
2013-01-15
The stabilizing effect of velocity shear on the macroscopic, broad bandwidth, ideal interchange instability is studied in linear and nonlinear regimes. A 2D dissipative magnetohydrodynamic (MHD) code is employed to simulate the system. For a given flow shear, V Prime , linear growth rates are shown to be suppressed to below the shear-free level at both the small and large wavelengths. With increasing V Prime , the unstable band in wavenumber-space shrinks so that the peak growth results for modes that correspond to relatively high wavenumbers, on the scale of the density gradient. In the nonlinear turbulent steady state, a similar turbulent spectrum obtains, and the convection cells are roughly circular. In addition, the density fluctuation level and the degree of flattening of the initial inverted density profile are found to decrease as V Prime increases; in fact, unstable modes are almost completely stabilized and the density profile reverts to laminar when V Prime is a few times the classic interchange growth rate. Moreover, the turbulent particle flux diminishes with increasing velocity shear such that all the flux is carried by the classical diffusive flux in the asymptotic limit. The simulations are compared with measurements of magnetic fluctuations from the Maryland Centrifugal Experiment, MCX, which investigated interchange modes in the presence of velocity shear. The experimental spectral data, taken in the plasma edge, are in general agreement with the numerical data obtained in higher viscosity simulations for which the level of viscosity is chosen consistent with MCX Reynolds numbers at the edge. In particular, the residual turbulence in both cases is dominated by elongated convection cells. Finally, concomitant Kelvin-Helmholtz instabilities in the system are also examined. Complete stability to interchanges is obtained only in the parameter space wherein the generalized Rayleigh inflexion theorem is satisfied.
Magnetohydrodynamic Instabilities in a Simple Gasdynamic Mirror Propulsion System
NASA Technical Reports Server (NTRS)
Emrich, William J., Jr.; Hawk, Clark W.
2004-01-01
The gasdynamic mirror has been proposed as a concept which could form the basis of a highly efficient fusion rocket engine. Gasdynamic mirrors differ from most other mirror type plasma confinement schemes in that they have much larger aspect ratios and operate at somewhat higher plasma densities. To evaluate whether a gasdynamic mirror could indeed confine plasmas in a stable manner for long periods of time, a small scale experimental gasdynamic mirror was built and tested. The objective of this experiment was to determine ranges of mirror ratios and plasma densities over which gasdynamic mirror could maintain stable plasmas. Theoretical analyses indicated that plasma magnetohydrodynamic instabilities were likely to occur during subsonic to supersonic flow transitions in the mirror throat region of the gasdynamic mirror. The experimental evidence based upon data derived from the Langmuir probe measurements seems to confirm this analysis. The assumption that a gasdynamic mirror using a simple mirror geometry could be used as a propulsion system, therefore, appears questionable. Modifications to the simple mirror concept are presented which could mitigate these MHD instabilities.
Shear coaxial injector instability mechanisms
NASA Technical Reports Server (NTRS)
Puissant, C.; Kaltz, T.; Glogowski, M.; Micci, M.
1994-01-01
There is no definitive knowledge of which of several concurrent processes ultimately results in unstable combustion within liquid rocket chambers employing shear coaxial injectors. Possible explanations are a detrimental change in the atomization characteristics due to a decrease in the gas-to-liquid velocity ratio, a change in the gas side injector pressure drop allowing acoustic coupling to the propellant feed system or the disappearance of a stabilizing recirculation region at the base of the LOX post. The aim of this research effort is to investigate these proposed mechanisms under conditions comparable to actual engine operation. Spray characterization was accomplished with flash photography and planar laser imaging to examine the overall spray morphology and liquid jet breakup processes and with a PDPA to quantify the spatial distribution of droplet size and mean axial velocity. A simplified stability model based on the Rayleigh criterion was constructed for the flow dynamics occurring within the chamber and injector to evaluate the potential coupling between the chamber and injector acoustic modes and was supported by high frequency measurements of chamber and injector pressure oscillations. To examine recirculation within the LOX post recess, velocity measurements were performed in the recess region by means of LDV. Present experiments were performed under noncombusting conditions using LOX/GH2 stimulants at pressures up to 4 MPa.
NASA Astrophysics Data System (ADS)
Singh Bhatia, Tanayveer; Mukhopadhyay, Banibrata
2016-10-01
The emergence of turbulence in shear flows is a well-investigated field. Yet, there are some lingering issues that have not been sufficiently resolved. One of them is the apparent contradiction between the results of linear stability analysis showing a flow to be stable and yet experiments and simulations proving it to be otherwise. There is some success, in particular in astrophysical systems, based on magnetorotational instability (MRI), revealing turbulence. However, MRI requires the system to be weakly magnetized. Such instability is neither a feature of general magnetohydrodynamic (MHD) flows nor revealed in purely hydrodynamic flows. Nevertheless, linear perturbations of such flows are non-normal in nature, which argues for a possible origin of nonlinearity therein. The concept behind this is that non-normal perturbations could produce huge transient energy growth (TEG), which may lead to nonlinearity and further turbulence. However, so far, non-normal effects in shear flows have not been explored much in the presence of magnetic fields. In this spirit, here we consider the perturbed viscoresistive MHD shear flows with rotation in general. Basically we recast the magnetized momentum balance and associated equations into the magnetized version of Orr-Sommerfeld and Squire equations and their magnetic analogs. We also assume the flow to be incompressible and in the presence of Coriolis effect solve the equations using a pseudospectral eigenvalue approach. We investigate the possible emergence of instability and large TEG in three different types of flows, namely, the Keplerian flow, the Taylor-Couette (or constant angular momentum) flow, and plane Couette flow. We show that, above a certain value of magnetic field, instability and TEG both stop occurring. We also show that TEG is maximum in the vicinity of regions of instability in the wave number space for a given magnetic field and Reynolds number, leading to nonlinearity and plausible turbulence. Rotating
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Papini, E.; Landi, S.; Bugli, M.; Bucciantini, N.
2016-08-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula; hence, its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two-dimensional numerical simulations, the linear phase and the subsequent non-linear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics (MHD), as appropriate in situations where the Alfvén velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S-1/3 are considered, the so-called ideal tearing regime is retrieved, with modes growing independently of S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfvén velocity. In the fully non-linear stage, we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfvén speed from the X-point, and a fast reconnection rate at the predicted value {R}˜ (ln S)^{-1}.
NASA Astrophysics Data System (ADS)
Burke, B. J.; Kruger, S. E.; Hegna, C. C.; Zhu, P.; Snyder, P. B.; Sovinec, C. R.; Howell, E. C.
2010-03-01
A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n =1-20). The results use the compressible MHD model and depend on a precise representation of "ideal-like" and "vacuumlike" or "halo" regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 108 and 103 for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 105, which is much larger than experimentally measured values using Te values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.
Burke, B. J.; Kruger, S. E.; Hegna, C. C.; Zhu, P.; Snyder, P. B.; Sovinec, C. R.; Howell, E. C.
2010-03-15
A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1-20). The results use the compressible MHD model and depend on a precise representation of 'ideal-like' and 'vacuumlike' or 'halo' regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 10{sup 8} and 10{sup 3} for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 10{sup 5}, which is much larger than experimentally measured values using T{sub e} values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.
Weakening of magnetohydrodynamic interchange instabilities by Alfven waves
Benilov, E. S.; Hassam, A. B.
2008-02-15
Alfven waves, made to propagate along an ambient magnetic field and polarized transverse to a gravitational field g, with wave amplitude stratified along g, are shown to reduce the growth rate of interchange instability by increasing the effective inertia by a factor of 1+(B{sub y}{sup '}/B{sub z}k{sub z}){sup 2}, where B{sub z} is the ambient magnetic field, k{sub z} is the wavenumber, and B{sub y}{sup '} is the wave amplitude shear. Appropriately placed Alfven wave power could thus be used to enhance the stability of interchange and ballooning modes in tokamaks and other interchange-limited magnetically confined plasmas.
Plasmoid Instabilities Mediated Three-Dimensional Magnetohydrodynamic Turbulent Reconnection
Huang, Yi-min; Guo, Fan
2015-07-21
After some introductory remarks on fast reconnection in resistive MHD due to plasmoid instability, oblique tearing modes in 3D, and previous studies on 3D turbulent reconnection, the subject is presented under the following topics: 3D simulation setup, time evolution of the 3D simulation, comparison with Sweet-Parker and 2D plasmoid reconnection, and diagnostics of the turbulent state (decomposition of mean fields and fluctuations, power spectra of energy fluctuations, structure function and eddy anisotropy with respect to local magnetic field). Three primary conclusions were reached: (1) The results suggest that 3D plasmoid instabilities can lead to self-generated turbulent reconnection (evidence of energy cascade and development of inertial range, energy fluctuations preferentially align with the local magnetic field, which is one of the characteristics of MHD turbulence); (2) The turbulence is highly inhomogeneous, due to the presence of magnetic shear and outflow jets (conventional MHD turbulence theories or phenomenologies may not be applicable – e.g. scale-dependent anisotropy as predicted by Goldreich & Sridhar is not found); (3) 3D turbulent reconnection is different from 2D plasmoid-dominated reconnection in many aspects. However, in fully developed state, reconnection rates in 2D and 3D are comparable — this result needs to be further checked in higher S.
Linear instability of curved free shear layers
NASA Technical Reports Server (NTRS)
Liou, William W.
1993-01-01
The linear inviscid hydrodynamic stability of slightly curved free mixing layers is studied in this paper. The disturbance equation is solved numerically using a shooting technique. Two mean velocity profiles that represent stably and unstably curved free mixing layers are considered. Results are shown for cases of five curvature Richardson numbers. The stability characteristics of the shear layer are found to vary significantly with the introduction of the curvature effects. The results also indicate that, in a manner similar to the Goertler vortices observed in a boundary layer along a concave wall, instability modes of spatially developing streamwise vortex pairs may appear in centrifugally unstable curved mixing layers.
Effects of shear flow and transverse magnetic field on Richtmyer-Meshkov instability
Cao Jintao; Ren Haijun; Li Ding; Wu Zhengwei
2008-04-15
The effects of shear flow and transverse magnetic field on Richtmyer-Meshkov instability are examined and the expression of the interface perturbation is obtained by analytically solving the linear ideal magnetohydrodynamics equations. It shows that the perturbation evolves exponentially rather than linearly in the presence of shear flow and magnetic field when v{sub a}<{radical}(1-A{sub T}{sup 2}){delta}{sub u}/2, where v{sub a} is the modified Alfven velocity, A{sub T} is the Atwood number, and {delta}{sub u} is the relative shear velocity, respectively. The shear flow acts as a destabilizing source, while the magnetic field is a stabilizing mechanism of the shocked corrugated interface problem. The whole analysis is based on the assumption that the fluid is incompressible.
Imbalanced magnetohydrodynamic turbulence modified by velocity shear in the solar wind
NASA Astrophysics Data System (ADS)
Gogoberidze, G.; Voitenko, Y. M.
2016-11-01
We study incompressible imbalanced magnetohydrodynamic turbulence in the presence of background velocity shears. Using scaling arguments, we show that the turbulent cascade is significantly accelerated when the background velocity shear is stronger than the velocity shears in the subdominant Alfvén waves at the injection scale. The spectral transport is then controlled by the background shear rather than the turbulent shears and the Tchen spectrum with spectral index -1 is formed. This spectrum extends from the injection scale to the scale of the spectral break where the subdominant wave shear becomes equal to the background shear. The estimated spectral breaks and power spectra are in good agreement with those observed in the fast solar wind. The proposed mechanism can contribute to enhanced turbulent cascades and modified -1 spectra observed in the fast solar wind with strong velocity shears. This mechanism can also operate in many other astrophysical environments where turbulence develops on top of non-uniform plasma flows.
Shear dynamo, turbulence, and the magnetorotational instability
Squire, Jonathan
2015-09-01
The formation, evolution, and detailed structure of accretion disks remain poorly understood, with wide implications across a variety of astrophysical disciplines. While the most pressing question – what causes the high angular momentum fluxes that are necessary to explain observations? – is nicely answered by the idea that the disk is turbulent, a more complete grasp of the fundamental processes is necessary to capture the wide variety of behaviors observed in the night sky. This thesis studies the turbulence in ionized accretion disks from a theoretical standpoint, in particular focusing on the generation of magnetic fields in these processes, known as dynamo. Such fields are expected to be enormously important, both by enabling the magnetorotational instability (which evolves into virulent turbulence), and through large-scale structure formation, which may transport angular momentum in different ways and be fundamental for the formation of jets. The central result of this thesis is the suggestion of a new large-scale dynamo mechanism in shear flows – the “magnetic shear-current effect” – which relies on a positive feedback from smallscale magnetic fields. As well as being a very promising candidate for driving field generation in the central regions of accretion disks, this effect is interesting because small-scale magnetic fields have historically been considered to have a negative effect on the large-scale dynamo, damping growth and leading to dire predictions for final saturation amplitudes. Given that small-scale fields are ubiquitous in plasma turbulence above moderate Reynolds numbers, the finding that they could instead have a positive effect in some situations is interesting from a theoretical and practical standpoint. The effect is studied using direct numerical simulation, analytic techniques, and novel statistical simulation methods. In addition to the dynamo, much attention is given to the linear physics of disks and its relevance to
NASA Astrophysics Data System (ADS)
Paraschiv, Ioana; Bauer, Bruno S.; Lindemuth, Irvin R.; Makhin, Volodymyr
2007-11-01
A detailed study of the linear and nonlinear development of the m=0 instability in the presence of sheared axial flows has been performed using a two-dimensional magnetohydrodynamic numerical code, MHRDR, to solve single-fluid ideal MHD equations. In order to accurately study the sheared flow effects on the z-pinch stability, the code was modified to include periodic boundary conditions and a monotonic van Leer advection algorithm. Linear growth rates obtained with MHRDR were in good agreement with the linear theory (<10% difference). Nonlinear mode coupling and saturation of the sausage instability have been studied for z-pinch equilibria with and without sheared flows. It was found that sheared flows changed the m=0 development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to small amplitudes, and only the long wavelengths continued to grow. Full stabilization was predicted for supersonic plasma flows.
NASA Astrophysics Data System (ADS)
Pratt, J.; Busse, A.; Müller, W.-C.
2013-09-01
Intermittent large-scale high-shear flows are found to occur frequently and spontaneously in direct numerical simulations of statistically stationary turbulent Boussinesq magnetohydrodynamic (MHD) convection. The energetic steady state of the system is sustained by convective driving of the velocity field and small-scale dynamo action. The intermittent emergence of flow structures with strong velocity and magnetic shearing generates magnetic energy at an elevated rate on time scales that are longer than the characteristic time of the large-scale convective motion. The resilience of magnetic energy amplification suggests that intermittent shear bursts are a significant driver of dynamo action in turbulent magnetoconvection.
E X B instability with sheared magnetic field
NASA Astrophysics Data System (ADS)
Das, Salil; Nasrin, Shahin; Bose, Mridul
2016-10-01
The cross-field instability is ubiquitous in all electromagnetic systems. Effect of this instability is studied rigorously in plasma system with steady external magnetic field. Therefore, we have considered a sheared magnetic field to study the E X B instability which is observed in the internal transport barrier of fusion machines. Depending on the relation between y & LS we have considered three different regimes. The response of the magnetic shear, i.e. y/LS, (where, y is the magnitude of the applied magnetic field along y-direction and LS is the shear length) is then estimated which shows few interesting features.
Biglari, H.; Chen, L.; White, R.B.
1987-02-01
It is shown that, in present-day large-size tokamaks, finite resistivity modifies qualitatively the stability properties of magnetohydrodynamic instabilities resonantly excited by the unfavorable processional drift of energetic-trapped particles, i.e., the so-called ''fishbone''-type instabilities. Specifically, it is found that (1) the n = 1 energetic-trapped particle-induced internal kink (''fishbone'') instability is strongly stabilized by resistive dissipation and (2) finite resistivity lowers considerably the threshold conditions for resonant excitations of high-n ballooning/interchange modes. The possibility of exciting fishbones by alpha particles in ignition experiments is also considered.
A combined theory for magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
NASA Astrophysics Data System (ADS)
Hodgson, J. D. B.; Neukirch, T.
2017-03-01
We present a new approach to the theory of magnetohydrodynamic equilibria with anisotropic pressure, magnetic shear and translational/rotational invariance. This approach involves combining two existing formalisms in order to eliminate their individual weaknesses. The theoretical aspects of the method are explored in detail along with numerical solutions which make use of the method. Eventually, this method could be applied to model various plasma systems, such as planetary magnetospheres.
Some observations of a sheared Rayleigh-Taylor/Benard instability
NASA Technical Reports Server (NTRS)
Humphrey, J. A. C.; Marcus, D. L.
1987-01-01
An account is provided of preliminary flow visualization observations made in an unstably stratified flow with shear superimposed. The structures observed appear to be the superposition of a Rayleigh-Taylor/Benard instability and a Kelvin-Helmholtz instability. Aside from its intrinsic fundamental value, the study of these structures is of special interest to theoreticians developing nonlinear stability calculation methodologies.
Mizuno, Yosuke; Lyubarsky, Yuri; Nishikawa, Ken-Ichi; Hardee, Philip E.
2012-09-20
We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via three-dimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. We find that, in accordance with the linear stability theory, the development of the instability depends on the lateral distribution of the poloidal magnetic field. If the poloidal field significantly decreases outward from the axis, then the initial small perturbations grow strongly, and if multiple wavelengths are excited, then nonlinear interaction eventually disrupts the initial cylindrical configuration. When the profile of the poloidal field is shallow, the instability develops slowly and eventually saturates. We briefly discuss implications of our findings for Poynting-dominated jets.
Masada, Youhei; Takiwaki, Tomoya; Kotake, Kei
2015-01-01
Magnetorotational instability (MRI) in a convectively stable layer around the neutrinosphere is simulated by a three-dimensional model of a supernova core. To resolve MRI-unstable modes, a thin layer approximation considering only the radial global stratification is adopted. Our intriguing finding is that the convectively stable layer around the neutrinosphere becomes fully turbulent due to the MRI and its nonlinear penetration into the strongly stratified MRI-stable region. The intensity of the MRI-driven turbulence increases with magnetic flux threading the core, but is limited by the free energy stored in the differential rotation. The turbulent neutrinosphere is a natural consequence of rotating core-collapse and could exert a positive impact on the supernova mechanism.
Secondary instability of wall-bounded shear flows
NASA Technical Reports Server (NTRS)
Orszag, S. A.; Patera, A. T.
1983-01-01
The present analysis of a secondary instability in a wide class of wall-bounded parallel shear flows indicates that two-dimensional, finite amplitude waves are exponentially unstable to infinitessimal three-dimensional disturbances. The instability appears to be the prototype of transitional instability in such flows as Poiseuille flow, Couette flow, and flat plate boundary layers, in that it has the convective time scales observed in the typical transitions. The energetics and vorticity dynamics of the instability are discussed, and it is shown that the two-dimensional perturbation without directly providing energy to the disturbance. The three-dimensional instability requires that a threshold two-dimensional amplitude be achieved. It is found possible to identify experimental features of transitional spot structure with aspects of the nonlinear two-dimensional/linear three-dimensional instability.
Aiba, N.; Hirota, M.
2015-08-15
In a rotating toroidal plasma surrounded by a resistive wall, it is shown that linear magnetohydrodynamic (MHD) instabilities can be excited by interplay between the resistive wall mode (RWM) and stable ideal MHD modes, where the RWM can couple with not only a stable external kink mode but also various stable Alfvén eigenmodes that abound in a toroidal plasma. The RWM growth rate is shown to peak repeatedly as the rotation frequency reaches specific values for which the frequencies of the ideal MHD modes are Doppler-shifted to the small RWM frequency. Such destabilization can be observed even when the RWM in a static plasma is stable. A dispersion relation clarifies that the unstable mode changes from the RWM to the ideal MHD mode destabilized by wall resistivity when the rotation frequency passes through these specific values. The unstable mode is excited at these rotation frequencies even though plasma rotation also tends to stabilize the RWM from the combination of the continuum damping and the ion Landau damping.
NASA Astrophysics Data System (ADS)
Coon, E.; Kelemen, P.; Hirth, G.; Spiegelman, M.
2005-12-01
Kelemen and Hirth (Fall 2004 AGU) presented a model for periodic, viscous shear heating instabilities along pre-existing, fine grained shear zones. This provides an attractive alternative to dehydration embrittlement for explaining intermediate-depth earthquakes, especially those in a narrow thermal window within the mantle section of subducting oceanic plates (Hacker et al JGR03). Ductile shear zones with widths of cm to m are common in shallow mantle massifs and peridotite along oceanic fracture zones. Pseudotachylites in a mantle shear zone show that shear heating temperatures exceeded the mantle solidus (Obata & Karato Tectonophys95). Olivine grain growth in shear zones is pinned by closely spaced pyroxenes; thus, once formed, these features do not `heal' on geological time scales in the absence of melt or fluid (Warren & Hirth EPSL05). Grain-size sensitive creep will be localized within these shear zones, in preference to host rocks with olivine grain size from 1 to 10 mm. Inspired by the work of Whitehead & Gans (GJRAS74), we proposed that such pre-existing shear zones might undergo repeated shear heating instabilities. This is not a new concept; what is new is that viscous deformation is limited to a narrow shear zone, because grain boundary sliding, sensitive to both stress and grain size, may accommodate creep even at high stress and high temperature. These new ideas yield a new result: simple models for a periodic shear heating instability. Last year, we presented a 1D numerical model using olivine flow laws, assuming that viscous deformation remains localized in shear zones, surrounded by host rocks undergoing elastic deformation. Stress evolves due to elastic strain and drives viscous deformation in a shear zone of specified width. Shear heating and thermal diffusion control T. A maximum of 1400 C (substantial melting of peridotite ) was imposed. Grain size evolves due to recrystallization and diffusion. For strain rates of E-13 to E-14 per sec and
NASA Astrophysics Data System (ADS)
Jain, Neeraj; Büchner, Jörg; Muñoz, Patricio A.
2017-03-01
The dissipation mechanism by which the magnetic field reconnects in the presence of an external (guide) magnetic field in the direction of the main current is not well understood. In thin electron current sheets (half thickness close to an electron inertial length) formed in a quasi-steady state of collisionless magnetic reconnection, electron shear flow instabilities are potential candidates for providing an anomalous dissipation mechanism which can break the frozen-in condition of the magnetic field affecting the structure and rate of reconnection. We present the results of investigations of the evolution of electron shear flow instabilities, from linear to nonlinear state, in guide field magnetic reconnection. The properties of the plasma turbulence resulting from the growth of instability and their dependence on the strength of the guide field are studied. For this sake, we utilize the three dimensional electron-magnetohydrodynamic simulations of electron current sheets. We show that, unlike the case of current sheets self-consistently embedded in anti-parallel magnetic fields, the evolution of thin electron current sheets in the presence of a finite external guide field (equal to the asymptotic value of the reconnecting magnetic field or larger) is dominated by high wave number non-tearing mode instabilities. The latter causes the development of, first, a wavy structure of the current sheet. The turbulence, developed later, consists of current filaments and electron flow vortices. As a result of the nonlinear evolution of instability, the current sheet broadens simultaneously with its flattening in the central region mimicking a viscous-like turbulent dissipation. Later, the flattened current sheet bifurcates. During the time of bifurcation, the rate of the change of mean electron flow velocity is proportional to the magnitude of the flow velocity, suggesting a resistive-like dissipation. The turbulence energy cascades to shorter wavelengths preferentially in
Relativistic thermal electron scale instabilities in sheared flow plasma
NASA Astrophysics Data System (ADS)
Miller, Evan D.; Rogers, Barrett N.
2016-04-01
> The linear dispersion relation obeyed by finite-temperature, non-magnetized, relativistic two-fluid plasmas is presented, in the special case of a discontinuous bulk velocity profile and parallel wave vectors. It is found that such flows become universally unstable at the collisionless electron skin-depth scale. Further analyses are performed in the limits of either free-streaming ions or ultra-hot plasmas. In these limits, the system is highly unstable in the parameter regimes associated with either the electron scale Kelvin-Helmholtz instability (ESKHI) or the relativistic electron scale sheared flow instability (RESI) recently highlighted by Gruzinov. Coupling between these modes provides further instability throughout the remaining parameter space, provided both shear flow and temperature are finite. An explicit parameter space bound on the highly unstable region is found.
NASA Astrophysics Data System (ADS)
Zhang, Haocheng; Li, Hui; Guo, Fan; Taylor, Greg
2017-02-01
Kink instabilities are likely to occur in the current-carrying magnetized plasma jets. Recent observations of the blazar radiation and polarization signatures suggest that the blazar emission region may be considerably magnetized. While the kink instability has been studied with first-principle magnetohydrodynamic (MHD) simulations, the corresponding time-dependent radiation and polarization signatures have not been investigated. In this paper, we perform comprehensive polarization-dependent radiation modeling of the kink instability in the blazar emission region based on relativistic MHD (RMHD) simulations. We find that the kink instability may give rise to strong flares with polarization angle (PA) swings or weak flares with polarization fluctuations, depending on the initial magnetic topology and magnetization. These findings are consistent with observations. Compared with the shock model, the kink model generates polarization signatures that are in better agreement with the general polarization observations. Therefore, we suggest that kink instabilities may widely exist in the jet environment and provide an efficient way to convert the magnetic energy and produce multiwavelength flares and polarization variations.
NASA Astrophysics Data System (ADS)
Stelzer, Zacharias; Miralles, Sophie; Cébron, David; Noir, Jérôme; Vantieghem, Stijn; Jackson, Andrew
2015-08-01
We present an investigation of the stability of liquid metal flow under the influence of an imposed magnetic field by means of a laboratory experiment as well as a linear stability analysis of the setup using the finite element method. The experimental device ZUrich Cylindrical CHannel INstability Investigation is a modified cylindrical annulus with electrically driven flow of liquid GaInSn operating at Hartmann and Reynolds numbers up to M = 2022 and Re = 2.6 ṡ 105, respectively. The magnetic field gives rise to a free shear layer at the prominent inner electrode. We identify several flow regimes characterized by the nature of the instabilities. Above a critical current I c = O ( 0 . 1 A ) , the steady flow is destabilized by a Kelvin-Helmholtz mechanism at the free shear layer. The instability consists of counterrotating vortices traveling with the mean flow. For low forcing, the vortices are restricted to the free shear layer. Their azimuthal wave number m grows with M and decreases with Re. At Re/M ≈ 25, the instability becomes container-filling and energetically significant. It enhances the radial momentum transport which manifests itself in a broadening of the free shear layer width δS. We propose that this transition may be related to an unstable Hartmann layer. At R e / M 2 = O ( 1 ) , an abrupt change is observed in the mean azimuthal velocity < u ϕ ¯ > and the friction factor F, which we interpret as the transition between an inertialess and an inertial regime.
Shear Instabilities as a Probe of Jupiter's Atmosphere
NASA Technical Reports Server (NTRS)
Bosak, Tanja; Ingersoll, Andrew P.
2002-01-01
Linear wave patterns in Jupiter clouds with wavelengths strongly clustered around 300 km are commonly observed in the planet's equatorial atmosphere. We propose that the preferred wavelength is related to the thickness of an unstable shear layer within the clouds. We numerically analyze the linear stability of wavelike disturbances that have nonzero horizontal phase speeds in Jupiter's atmosphere and find that. if the static stability in the strongly clustered around 300 km are commonly observed in the planet's equatorial atmosphere. We propose that the preferred wavelength is related to the thickness of an unstable shear layer within the clouds. We numerically analyze the linear stability of wavelike disturbances that have nonzero horizontal phase speeds in Jupiter's atmosphere and find that. if the static stability in the shear layer is very low (but still nonnegative), a deep vertical shear layer like the one measured by the Galileo probe can generate the instabilities. The fastest growing waves grow exponentially within an hour, and their wavelengths match the observations. Close to zero values of static stability that permit the growth of instabilities are within the range of values measured by the Galileo probe in a hot spot. Our model probes Jupiter's equatorial atmosphere below the cloud deck and suggests that thick regions of wind shear and low static stability exist outside hot spots.
Shear flow effects on the nonlinear evolution of thermal instabilities
Leboeuf, J.; Charlton, L.A.; Carreras, B.A. )
1993-08-01
In the weak radiation drive regime, the coupling between the thermal instability driven by impurity radiation and the self-consistent flow profile modification leads to a simple dynamical system that can be approximated by the Volterra--Lotka equations. In this system the shear flow acts as a predator and the temperature fluctuations act as prey. The solutions are oscillatory, and their behavior resembles that of edge-localized modes (ELM's). The solutions of the simplified model are compared with the three-dimensional and two-dimensional nonlinear numerical results for this instability.
KELVIN-HELMHOLTZ INSTABILITY IN CORONAL MAGNETIC FLUX TUBES DUE TO AZIMUTHAL SHEAR FLOWS
Soler, R.; Terradas, J.; Oliver, R.; Ballester, J. L.; Goossens, M.
2010-04-01
Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the beta = 0 approximation and apply them to a straight and homogeneous cylindrical flux tube model embedded in a coronal environment. Azimuthal shear flows with a sharp jump of the velocity at the cylinder boundary are included in the model. We obtain an analytical expression for the dispersion relation of the unstable MHD modes supported by the configuration, and compute analytical approximations of the critical velocity shear and the KHI growth rate in the thin tube limit. A parametric study of the KHI growth rates is performed by numerically solving the full dispersion relation. We find that fluting-like modes can develop a KHI in timescales comparable to the period of kink oscillations of the flux tube. The KHI growth rates increase with the value of the azimuthal wavenumber and decrease with the longitudinal wavenumber. However, the presence of a small azimuthal component of the magnetic field can suppress the KHI. Azimuthal motions related to kink oscillations of untwisted coronal loops may trigger a KHI, but this phenomenon has not been observed to date. We propose that the azimuthal component of the magnetic field is responsible for suppressing the KHI in a stable coronal loop. The required twist is small enough to prevent the development of the pinch instability.
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.
2010-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.
NASA Astrophysics Data System (ADS)
Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Ng, C. S.; Bhattacharjee, A.
2006-10-01
A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate the problem of island coalescence instability (ICI) in 2D. The MHD solver is explicit, and uses the Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described in [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys., 215, 59-80 (2006)], allowing both statically refined and dynamically refined grids. ICI is a MHD process that can produce strong current sheets and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [cf., Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Thus, it is desirable to use adaptive refinement grids to increase resolution, and to maintain accuracy at the same time. Results are compared with simulations using finite difference method with the same refinement grid, as well as pesudo-spectral simulations using uniform grid.
NASA Astrophysics Data System (ADS)
Wang, Xian-Qu; Zhang, Rui-Bin; Qin, Liang; Wang, Xiao-Gang
2014-09-01
In this study, we theoretically explore properties of non-resonant fishbone (NRF) instabilities with a safety factor profile slightly above unity (qmin ≳ 1) in tokamak plasmas with reversed magnetic shear configuration. From the dispersion relation of the NRF mode, it is found that the growth rate of the mode in general reversed shear scenarios with qmin ≳ 1 depends on fast ion beta βh in a power law of {\\sim} \\beta_{h}^{2/3} , different from that of ˜βh in a conventional positive magnetic shear configuration. Meanwhile, due to the slow ion precession and small continuum damping in ITER-like tokamaks with reversed shear, the mode has a lower trigger threshold than those with monotonously positive magnetic shear. In addition, the ion diamagnetic drift has been found to destabilize the fast ion-driven NRF mode. Other effects such as the shape of the q-profile, characterized by values of qmin and q(0), neutral beam energy, magnetohydrodynamic potential energy and the fraction of fast ions on the instability threshold are also discussed. Nonlinear behavior of the mode is further analyzed using a modified model.
On the vertical-shear instability in astrophysical discs
NASA Astrophysics Data System (ADS)
Barker, A. J.; Latter, H. N.
2015-06-01
We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a `vertical-shear instability', which recent non-linear simulations have shown to drive hydrodynamic activity in the MRI-stable regions of protoplanetary discs. We first revisit locally isothermal discs using the quasi-global reduced model derived by Nelson et al. This analysis is then extended to global axisymmetric perturbations in a cylindrical domain. We also derive and study a reduced model describing discs with power-law radial entropy profiles (`locally polytropic discs'), which are somewhat more realistic in that they possess physical (as opposed to numerical) surfaces. The fastest growing modes have very short wavelengths and are localized at the disc surfaces (if present), where the vertical shear is maximal. An additional class of modestly growing vertically global body modes is excited, corresponding to destabilized classical inertial waves (`r modes'). We discuss the properties of both types of modes, and stress that those that grow fastest occur on the shortest available length-scales (determined either by the numerical grid or the physical viscous length). This ill-posedness makes simulations of the instability difficult to interpret. We end with some brief speculation on the non-linear saturation and resulting angular momentum transport.
NASA Astrophysics Data System (ADS)
Shukla, Chandrasekhar; Das, Amita; Patel, Kartik
2016-08-01
We carry out particle-in-cell simulations to study the instabilities associated with a 2-D sheared electron flow configuration against a neutralizing background of ions. Both weak and strong relativistic flow velocities are considered. In the weakly relativistic case, we observe the development of electromagnetic Kelvin-Helmholtz instability with similar characteristics as that predicted by the electron Magnetohydrodynamic (EMHD) model. On the contrary, in a strong relativistic case, the compressibility effects of electron fluid dominate and introduce upper hybrid electrostatic oscillations transverse to the flow which are very distinct from EMHD fluid behavior. In the nonlinear regime, both weak and strong relativistic cases lead to turbulence with broad power law spectrum.
The effect of compressibility on magnetohydrodynamic jets and Kelvin-Helmholtz instability
NASA Astrophysics Data System (ADS)
Praturi, Divya Sri; Girimaji, Sharath
2015-11-01
We investigate the effect of compressibility and magnetic field on the evolution of planar magnetohydrodynamic (MHD) jets. These jets are susceptible to Kelvin-Helmholtz (KH) instability when subjected to an in-plane transverse velocity perturbation. Various linear stability analyses have shown that compressibility and magnetic field along the jet have a stabilizing influence on the KH instability. We performed three-dimensional numerical simulations using magneto gas kinetic method (MGKM) to study the effect of the Mach number, Alfvén Mach number, and the orientation of the magnetic field with respect to the jet velocity direction on the flow-field evolution. In MGKM, the magnetic effects are added as source terms in the hydrodynamic gas kinetic scheme which also take into account the non-ideal MHD terms for finite plasma conductivity and the Hall effects. An in-depth analysis of linear and nonlinear physics is presented. The first author was supported by Texas A&M University Institute for Advanced Study HEEP fellowship.
Li, C. K.; Frenje, J. A.; Petrasso, R. D.; Seguin, F. H.; Amendt, P. A.; Landen, O. L.; Town, R. P. J.; Betti, R.; Knauer, J. P.; Meyerhofer, D. D.; Soures, J. M.
2009-07-15
Recent experiments using proton backlighting of laser-foil interactions provide unique opportunities for studying magnetized plasma instabilities in laser-produced high-energy-density plasmas. Time-gated proton radiograph images indicate that the outer structure of a magnetic field entrained in a hemispherical plasma bubble becomes distinctly asymmetric after the laser turns off. It is shown that this asymmetry is a consequence of pressure-driven, resistive magnetohydrodynamic (MHD) interchange instabilities. In contrast to the predictions made by ideal MHD theory, the increasing plasma resistivity after laser turn-off allows for greater low-mode destabilization (m>1) from reduced stabilization by field-line bending. For laser-generated plasmas presented herein, a mode-number cutoff for stabilization of perturbations with m>{approx}[8{pi}{beta}(1+D{sub m}k{sub perpendicular}{sup 2}{gamma}{sub max}{sup -1})]{sup 1/2} is found in the linear growth regime. The growth is measured and is found to be in reasonable agreement with model predictions.
Panwar, Anuraj; Ryu, Chang-Mo
2014-06-15
The modulational instability and associated rogue structures of a slow magnetosonic wave are investigated for a Hall magnetohydrodynamic plasma. Nonlinear Schrodinger equation is obtained by using the multiple scale method, which shows a modulationally unstable slow magnetosonic mode evolving into bright wavepackets. The dispersive effects induced by the Hall electron current increase with the increase in plasma β and become weaker as the angle of propagation increases. The growth rate of the modulational instability also increases with the increase in plasma β. The growth rate is greatest for the parallel propagation and drops to zero for perpendicular propagation. The envelope wavepacket of a slow magnetosonic is widened with less oscillations as plasma β increases. But the wavepacket becomes slightly narrower and more oscillatory as the angle of propagation increases. Further a non-stationary envelope solution of the Peregrine soliton is analyzed for rogue waves. The Peregrine soliton contracts temporally and expands spatially with increase in plasma β. However, the width of a slow magnetosonic Peregrine soliton decreases both temporally and spatially with increase of the propagation angle.
Experimental study of shear layer instability below a free surface
NASA Astrophysics Data System (ADS)
André, Matthieu A.; Bardet, Philippe M.
2015-11-01
Relaxation of a laminar boundary layer at a free surface is an inviscidly unstable process and can lead to millimeter-scale surface waves, influencing interfacial processes. Due to the small time- and length-scales involved, previous experimental studies have been limited to visual observations and point-wise measurements of the surface profile to determine instability onset and frequency. However, effects of viscosity, surface tension, and non-linearity of the wave profile have not been systematically studied. In fact, no data have been reported on the velocity fields associated with this instability. In the present study, planar laser induced fluorescence and particle image velocimetry provide surface profiles coupled with liquid phase velocity fields for this instability in a time resolved manner. Wave steepness (ak, with a the amplitude and k the wave number) and Reynolds and Weber numbers based on momentum thickness range from 0 to 1.2, 143 to 177, and 4.79 to 6.61, respectively. Large datasets are analyzed to gain statistical information on the surface behavior. Discrete vortices are resolved, showing that the shear layer becomes unstable and rolls up above a Reynolds number of 140. The detection onset and steepness of the subsequent surface deformation by the vortices depend upon the Weber number. Non-linear behavior such as vortex motion and wave profile asymmetry are observed at steepness larger than 0.5.
NASA Astrophysics Data System (ADS)
Klimachkov, D. A.; Petrosyan, A. S.
2017-01-01
This article deals with magnetohydrodynamic (MHD) flows of a thin rotating layer of astrophysical plasma in external magnetic field. We use the shallow water approximation to describe thin rotating plasma layer with a free surface in a vertical external magnetic field. The MHD shallow water equations with external vertical magnetic field are revised by supplementing them with the equations that are consequences of the magnetic field divergence-free conditions and reveal the existence of third component of the magnetic field in such approximation providing its relation with the horizontal magnetic field. It is shown that the presence of a vertical magnetic field significantly changes the dynamics of the wave processes in astrophysical plasma compared to the neutral fluid and plasma layer in a toroidal magnetic field. The equations for the nonlinear wave packets interactions are derived using the asymptotic multiscale method. The equations for three magneto-Poincare waves interactions, for three magnetostrophic waves interactions, for the interactions of two magneto-Poincare waves and for one magnetostrophic wave and two magnetostrophic wave and one magneto-Poincare wave interactions are obtained. The existence of parametric decay and parametric amplifications is predicted. We found following four types of parametric decay instabilities: magneto-Poincare wave decays into two magneto-Poincare waves, magnetostrophic wave decays into two magnetostrophic waves, magneto-Poincare wave decays into one magneto-Poincare wave and one magnetostrophic wave, magnetostrophic wave decays into one magnetostrophic wave and one magneto-Poincare wave. Following mechanisms of parametric amplifications are found: parametric amplification of magneto-Poincare waves, parametric amplification of magnetostrophic waves, magneto-Poincare wave amplification in magnetostrophic wave presence and magnetostrophic wave amplification in magneto-Poincare wave presence. The instabilities growth rates
Kumar Awasthi, Mukesh
2014-03-15
We study the linear magnetohydrodynamic Kelvin–Helmholtz instability of the interface between two viscous, incompressible, and electrically conducting fluids. The phases are enclosed between two coaxial cylindrical porous layers with the interface through which mass and heat transfer takes place. The fluids are subjected to a constant magnetic field parallel to the streaming direction, and the suction/injection velocities for the fluids at the permeable boundaries are also taken into account. Here, we use an irrotational theory in which the motion and pressure are irrotational, and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. We consider both asymmetric and axisymmetric disturbances in our analysis. A quadratic dispersion relation is deduced and stability criterion is given in terms of a critical value of relative velocity, as well as, magnetic field. It has been observed that in the case of permeable boundaries, heat and mass transfer phenomena play a dual in the stability analysis. The flow through porous medium is more stable than the pure flow.
Flow Instability and Wall Shear Stress Ocillation in Intracranial Aneurysms
NASA Astrophysics Data System (ADS)
Baek, Hyoungsu; Jayamaran, Mahesh; Richardson, Peter; Karniadakis, George
2009-11-01
We investigate the flow dynamics and oscillatory behavior of wall shear stress (WSS) vectors in intracranial aneurysms using high-order spectral/hp simulations. We analyze four patient- specific internal carotid arteries laden with aneurysms of different characteristics : a wide-necked saccular aneurysm, a hemisphere-shaped aneurysm, a narrower-necked saccular aneurysm, and a case with two adjacent saccular aneurysms. Simulations show that the pulsatile flow in aneurysms may be subject to a hydrodynamic instability during the decelerating systolic phase resulting in a high-frequency oscillation in the range of 30-50 Hz. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate. In particular, the WSS vectors around the flow impingement region exhibit significant spatial and temporal changes in direction as well as in magnitude.
NASA Astrophysics Data System (ADS)
Todo, Y.
2016-11-01
Magnetohydrodynamic (MHD) instabilities driven by energetic particles in tokamak plasmas and the energetic particle distribution formed with the instabilities, neutral beam injection, and collisions are investigated with hybrid simulations for energetic particles and an MHD fluid. The multi-phase simulation, which is a combination of classical simulation and hybrid simulation, is applied to examine the distribution formation process in the collisional slowing-down time scale of energetic ions for various beam deposition power ({P}{NBI}) and slowing-down time ({τ }{{s}}). The physical parameters other than {P}{NBI} and {τ }{{s}} are similar to those of a Tokamak Fusion Test Reactor (TFTR) experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874). For {P}{NBI} = 10 MW and {τ }{{s}} = 100 ms, which is similar to the TFTR experiment, the bursts of toroidal Alfvén eigenmodes take place with a time interval 2 ms, which is close to that observed in the experiment. The maximum radial velocity amplitude (v r) of the dominant TAE at the bursts in the simulation is {v}{{r}}/{v}{{A}}∼ 3× {10}-3 where v A is the Alfvén velocity at the plasma center. For {P}{NBI} = 5 MW and {τ }{{s}} = 20 ms, the amplitude of the dominant TAE is kept at a constant level {v}{{r}}/{v}{{A}}∼ 4× {10}-4. The intermittency of TAE rises with increasing {P}{NBI} and increasing {τ }{{s}} (= decreasing collision frequency). With increasing volume-averaged classical energetic ion pressure, which is well proportional to {P}{NBI}{τ }{{s}}, the energetic ion confinement degrades monotonically due to the transport by the instabilities. The volume-averaged energetic ion pressure depends only on the volume-averaged classical energetic ion pressure, not independently on {P}{NBI} or {τ }{{s}}. The energetic ion pressure profile resiliency, where the increase in energetic ion pressure profile is saturated, is found for the cases with the highest {P}{NBI}{τ }{{s}} where the TAE bursts take place.
Heinemann, Tobias; Quataert, Eliot E-mail: eliot@berkeley.edu
2014-09-01
We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low-frequency guiding center (or 'kinetic MHD') approximation, Hall magnetohydrodynamics (MHD), and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.
Instability at the Interface between Two Shearing Fluids in a Channel.
1985-02-01
INSTAWILITY AT vin.. INTERFIACE I*.VWUN , TWO SUEARING FLUIDS IN A C|UANNEL Yuriko Renardy Mathematics Research Center University of Wisconsin-Madison...RESEARCH CENTER INSTABILITY AT THE INTERFACE BETWEEN TWO SHEARING FLUIDS IN A CHANNEL Yuriko Renardy Technical Summary Report #2787 February 1985...INSTABILITY AT THE INTERFACE BETWEEN TWO SHEARING FLUIDS IN A CHANNEL Yuriko Renardy 0 §1
Firehose, Mirror, and Magnetorotational Instabilities in a Collisionless Shearing Plasma
NASA Astrophysics Data System (ADS)
Kunz, Matthew; Schekochihin, Alexander; Stone, James; Melville, Scott; Quataert, Eliot
2015-11-01
Describing the large-scale behavior of weakly collisional magnetized plasmas, such as the solar wind, black-hole accretion flows, or the intracluster medium of galaxy clusters, necessitates a detailed understanding of the kinetic-scale physics governing the dynamics of magnetic fields and the transport of momentum and heat. This physics is complicated by the fact that such plasmas are expected to exhibit particle distribution functions with unequal thermal pressures in the directions parallel and perpendicular to the local magnetic field. This pressure anisotropy can trigger fast Larmor-scale instabilities - namely, firehose and mirror - which solar-wind observations suggest to be effective at regulating the pressure anisotropy to marginally stable levels. Results from weakly nonlinear theory and hybrid-kinetic particle-in-cell simulations that address how marginal stability is achieved and maintained in a plasma whose pressure anisotropy is driven by a shearing magnetic field are presented. Fluctuation spectra and effective collisionality are highlighted. These results are placed in the context of our ongoing studies of magnetorotational turbulence in collisionless astrophysical accretion disks, in which microscale plasma instabilities regulate angular-momentum transport.
High-Energy-Density Shear Flow and Instability Experiments
NASA Astrophysics Data System (ADS)
Doss, F. W.; Flippo, K. A.; Merritt, E. C.; di Stefano, C. A.; Devolder, B. G.; Kurien, S.; Kline, J. L.
2016-10-01
High-energy-density shear experiments have been performed by LANL at the OMEGA Laser Facility and National Ignition Facility (NIF). The experiments have been simulated using the LANL radiation-hydrocode RAGE and have been used to assess turbulence models' ability to function in the high-energy-density, inertial-fusion-relevant regime. Beginning with the basic configuration of two counter-oriented shock-driven flows of > 100 km/s, which initiate a strong shear instability across an initially solid-density, 20 μm thick Al plate, variations of the experiment to details of the initial conditions have been performed. These variations have included increasing the fluid densities (by modifying the plate material from Al to Ti and Cu), imposing sinusoidal seed perturbations on the plate, and directly modifying the plate's intrinsic surface roughness. Radiography of the unseeded layer has revealed the presence of emergent Kelvin-Helmholtz structures which may be analyzed to infer fluid-mechanical properties including turbulent energy density. This work is conducted by the US DOE by LANL under contract DE-AC52-06NA25396.
Multiple shear band development and related instabilities in granular materials
NASA Astrophysics Data System (ADS)
Gajo, A.; Bigoni, D.; Wood, D. Muir
2004-12-01
A new, small-strain constitutive model, incorporating elastoplastic coupling to describe developing elastic anisotropy, and density as a state variable to capture compaction and dilation, is proposed to simulate the behaviour of granular materials, in particular sand. This developing elastic anisotropy is related to grain reorientation and is shown to be crucial to obtain localisation during strain hardening, as experiments exhibit. Post-localisation analysis is also performed under simplificative assumptions, which evinces a number of features, including softening induced by localisation, size effects and snap-back, all phenomena found in qualitative and quantitative agreement with experiments. No prior model of granular material deformation correctly captures all these behaviours. The post-localisation analysis has revealed a new form of material instability in granular materials, consisting of a saturation mechanism, in which shear bands just formed unload, permitting new bands to form. This phenomenon shares similarities with the mechanics of phase transformation in metal strips and results in a stress oscillation during increasing deformation. The investigation of this mechanism of localised deformation reveals that loose and dense sands behave in qualitatively different ways. In particular, saturation is not persistent in dense sand; rather, after several shear bands form and saturate, this process is terminated by the formation of a differently inclined shear band occurring in the material transformed by previous strain localisation. In this case, the resulting 'global' stress-strain curve exhibits a few stress oscillations followed by a strong softening. On the other hand, band saturation is found to be a persistent phenomenon in loose sand, yielding a continuing stress oscillation. This provides a consistent description of specific experimental results.
Drift-Alfven instabilities of a finite beta plasma shear flow along a magnetic field
NASA Astrophysics Data System (ADS)
Mikhailenko, V. V.; Mikhailenko, V. S.; Lee, Hae June
2016-02-01
It was derived that the drift-Alfven instabilities with the shear flow parallel to the magnetic field have significant difference from the drift-Alfven instabilities of a shearless plasma when the ion temperature is comparable with electron temperature for a finite plasma beta. The velocity shear not only modifies the frequency and the growth rate of the known drift-Alfven instability, which develops due to the inverse electron Landau damping, but also triggers a combined effect of the velocity shear and the inverse ion Landau damping, which manifests the development of the ion kinetic shear-flow-driven drift-Alfven instability. The excited unstable waves have the phase velocities along the magnetic field comparable with the ion thermal velocity, and the growth rate is comparable with the frequency. The development of this instability may be the efficient mechanism of the ion energization in shear flows.
NASA Astrophysics Data System (ADS)
Antolin, P.; De Moortel, I.; Van Doorsselaere, T.; Yokoyama, T.
2017-02-01
Magnetohydrodynamic (MHD) waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints but also by wave processes that localize the wave power in undetectable spatial scales. In this study, we conduct 3D MHD simulations and forward modeling of standing transverse MHD waves in coronal loops with uniform and non-uniform temperature variation in the perpendicular cross-section. The observed signatures are largely dominated by the combination of the Kelvin–Helmholtz instability (KHI), resonant absorption, and phase mixing. In the presence of a cross-loop temperature gradient, we find that emission lines sensitive to the loop core catch different signatures compared to those that are more sensitive to the loop boundary and the surrounding corona, leading to an out-of-phase intensity and Doppler velocity modulation produced by KHI mixing. In all of the considered models, common signatures include an intensity and loop width modulation at half the kink period, a fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, and overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.″33 and a spectral resolution of 25 km s‑1, although we do obtain severe over-estimation of the line width. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and KHI motions. We estimate this hidden wave energy to be a factor of 5–10 of the observed value.
NASA Astrophysics Data System (ADS)
Makhin, Volodymyr; Sotnikov, Vladimir; Bauer, Bruno; Lindemuth, Irvin; Sheehey, Peter
2001-10-01
1D modeling of the initial state of wire explosions (“cold start” with updated SESAME tables) was examined using 1D version of the Eulerian Magnetohydrodynamic Radiative Code (MHRDR). Simulations were carried out for two regimes: with (black body radiative model) and without radiative losses. Results of the simulations revealed strong dependence of the time of explosion and expansion speed of the wire on the implemented radiative model. This shows that it is necessary to accurately include radiative losses to model “cold start” wire explosions. 2D modeling of the m=0 sausage instability with sheared axial flow. The MHRDR simulations were used to obtain the growth rate of the m=0 sausage instability in plasma column with initial Bennett equilibrium profile with and without shear flow. These growth rates appeared to be in good agreement with growth rates calculated from the linearized MHD equations.
Flow instability and wall shear stress variation in intracranial aneurysms
Baek, H.; Jayaraman, M. V.; Richardson, P. D.; Karniadakis, G. E.
2010-01-01
We investigate the flow dynamics and oscillatory behaviour of wall shear stress (WSS) vectors in intracranial aneurysms using high resolution numerical simulations. We analyse three representative patient-specific internal carotid arteries laden with aneurysms of different characteristics: (i) a wide-necked saccular aneurysm, (ii) a narrower-necked saccular aneurysm, and (iii) a case with two adjacent saccular aneurysms. Our simulations show that the pulsatile flow in aneurysms can be subject to a hydrodynamic instability during the decelerating systolic phase resulting in a high-frequency oscillation in the range of 20–50 Hz, even when the blood flow rate in the parent vessel is as low as 150 and 250 ml min−1 for cases (iii) and (i), respectively. The flow returns to its original laminar pulsatile state near the end of diastole. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate at the aforementioned high frequencies. In particular, the WSS vectors around the flow impingement region exhibit significant spatio-temporal changes in direction as well as in magnitude. PMID:20022896
Linear Instability of a Uni-Directional Transversely Sheared Mean Flow
NASA Technical Reports Server (NTRS)
Wundrow, David W.
1996-01-01
The effect of spanwise-periodic mean-flow distortions (i.e. streamwise-vortex structures) on the evolution of small-amplitude, single-frequency instability waves in an otherwise two-dimensional shear flow is investigated. The streamwise-vortex structures are taken to be just weak enough so that the spatially growing instability waves behave (locally) like linear perturbations about a uni-directional transversely sheared mean flow. Numerical solutions are computed and discussed for both the mean flow and the instability waves. The influence of the streamwise-vortex wavelength on the properties of the most rapidly growing instability wave is also discussed.
Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks
NASA Astrophysics Data System (ADS)
Lin, Min-Kai; Youdin, Andrew N.
2015-09-01
The vertical shear instability (VSI) offers a potential hydrodynamic mechanism for angular momentum transport in protoplanetary disks (PPDs). The VSI is driven by a weak vertical gradient in the disk’s orbital motion, but must overcome vertical buoyancy, a strongly stabilizing influence in cold disks, where heating is dominated by external irradiation. Rapid radiative cooling reduces the effective buoyancy and allows the VSI to operate. We quantify the cooling timescale tc needed for efficient VSI growth, through a linear analysis of the VSI with cooling in vertically global, radially local disk models. We find the VSI is most vigorous for rapid cooling with {t}{{c}}\\lt {{{Ω }}}{{K}}-1h| q| /(γ -1) in terms of the Keplerian orbital frequency, {{{Ω }}}{{K}}, the disk’s aspect-ratio, h\\ll 1, the radial power-law temperature gradient, q, and the adiabatic index, γ. For longer tc, the VSI is much less effective because growth slows and shifts to smaller length scales, which are more prone to viscous or turbulent decay. We apply our results to PPD models where tc is determined by the opacity of dust grains. We find that the VSI is most effective at intermediate radii, from ∼5 to ∼50 AU with a characteristic growth time of ∼30 local orbital periods. Growth is suppressed by long cooling times both in the opaque inner disk and the optically thin outer disk. Reducing the dust opacity by a factor of 10 increases cooling times enough to quench the VSI at all disk radii. Thus the formation of solid protoplanets, a sink for dust grains, can impede the VSI.
Azimuthal instability of the interface in a shear banded flow by direct visual observation.
Decruppe, J P; Bécu, L; Greffier, O; Fazel, N
2010-12-17
The stability of the shear banded flow of a Maxwellian fluid is studied from an experimental point of view using rheology and flow visualization with polarized light. We show that the one-layer homogeneous flow cannot sustain shear rates corresponding to the end of the stress plateau. The high shear rate branch is not found and the shear stress oscillates at the end of the plateau. An azimuthal instability appears: the shear induced band becomes unstable and the interface between the two bands undulates in time and space with a period τ, a wavelength λ and a wave vector k parallel to the direction of the tangential velocity.
NASA Astrophysics Data System (ADS)
Sozzi, C.; Galperti, C.; Alessi, E.; Nowak, S.; Apruzzese, G.; Belli, F.; Bin, W.; Boncagni, L.; Botrugno, A.; Bruschi, A.; Buratti, P.; Calabrò, G.; Esposito, B.; Figini, L.; Garavaglia, S.; Granucci, G.; Grosso, L. A.; Marchetto, C.; Marinucci, M.; Marocco, D.; Mazzotta, C.; Mellera, V.; Minelli, D.; Mosconi, M.; Moro, A.; Piergotti, V.; Pucella, G.; Ramogida, G.; Romano, A.; Tudisco, O.
2015-08-01
Experiments on real time control of magneto-hydrodynamic (MHD) instabilities using injection of electron cyclotron waves (ECW) are being performed with a control system based on only three real time key items: an equilibrium estimator based on a statistical regression, a MHD instability marker (SVDH) using a three-dimensional array of pick-up coils and a fast ECW launcher able to poloidally steer the EC absorption volume with dρ/dt = 0.1/30 ms maximum radial speed. The MHD instability, usually a tearing mode with poloidal mode number m and toroidal mode number n such that m/n = 2/1 or 3/2 is deliberately induced either by neon gas injection or by a density ramp hitting the density limit. No diagnostics providing the radial localization of the instabilities have been used. The sensitivity of the used MHD marker allows to close the control loop solely on the effect of the actuator’s action with little elaboration. The nature of the instability triggering mechanism in these plasma prevents that the stabilization lasts longer than the ECW pulse. However when the ECW power is switched on, the instability amplitude shows a marked sensitivity to the position of the absorption volume with an increase or decrease of its growth rate. Moreover the suppression of the dominant mode by ECRH performed at high plasma density even at relatively low power level facilitates the development of a secondary mode. This minimized set of control tools aim to explore some of the difficulties which can be expected in a fusion reactor where reduced diagnostic capabilities and reduced actuator flexibility can be expected.
DOUBLE-DIFFUSIVE INSTABILITIES OF A SHEAR-GENERATED MAGNETIC LAYER
Silvers, Lara J.; Proctor, Michael R. E.; Vasil, Geoffrey M.; Brummell, Nicholas H.
2009-09-01
Previous theoretical work has speculated about the existence of double-diffusive magnetic buoyancy instabilities of a dynamically evolving horizontal magnetic layer generated by the interaction of forced vertically sheared velocity and a background vertical magnetic field. Here, we confirm numerically that if the ratio of the magnetic to thermal diffusivities is sufficiently low then such instabilities can indeed exist, even for high Richardson number shear flows. Magnetic buoyancy may therefore occur via this mechanism for parameters that are likely to be relevant to the solar tachocline, where regular magnetic buoyancy instabilities are unlikely.
NASA Astrophysics Data System (ADS)
Mikhailenko, V. V.; Mikhailenko, V. S.; Lee, Hae June
2016-11-01
The stability of the magnetic field aligned sheared flow with anisotropic ion temperatures, which have the anisotropic spatial inhomogeneities across the magnetic field and are comparable with or are above the electron temperature, is investigated numerically and analytically. The ion temperatures gradients across the magnetic field affect the instability development only when the inhomogeneous is the ion temperature along the magnetic field irrespective the inhomogeneity of the ion temperature across the magnetic field. In this case, the instability is developed due to the combined effect of the ion Landau damping, velocity shear, ion temperature anisotropy, and anisotropy of the ion temperature gradients. In the case when the ion temperature along the magnetic field is homogeneous, but the ion temperature across the magnetic field is inhomogeneous, the short wavelength instability develops with the wave length less than the thermal ion Larmor radius. This instability excites due to the coupled effect of the ion Landau damping, velocity shear and ion temperature anisotropy.
NASA Astrophysics Data System (ADS)
Kelemen, P. B.; Hirth, G.
2004-12-01
Localized ductile shear zones with widths of cm to m are observed in exposures of Earth's shallow mantle (e.g., Kelemen & Dick JGR 95; Vissers et al. Tectonophys 95) and dredged from oceanic fracture zones (e.g., Jaroslow et al. Tectonophys 96). These are mylonitic (grain size 10 to 100 microns) and record mineral cooling temperatures from 1100 to 600 C. Pseudotachylites in a mantle shear zone show that shear heating temperatures can exceed the mantle solidus (e.g., Obata & Karato Tectonophys 95). Simple shear, recrystallization, and grain boundary sliding all decrease the spacing between pyroxenes, so olivine grain growth at lower stress is inhibited; thus, once formed, these shear zones do not "heal" on geological time scales. Reasoning that grain-size sensitive creep will be localized within these shear zones, rather than host rocks (grain size 1 to 10 mm), and inspired by the work of Whitehead & Gans (GJRAS 74), we thought these might undergo repeated shear heating instabilities. In this view, as elastic stress increases, the shear zone weakens via shear heating; rapid deformation of the weak shear zone releases most stored elastic stress; lower stress and strain rate coupled with diffusion of heat into host rocks leads to cooling and strengthening, after which the cycle repeats. We constructed a simple numerical model incorporating olivine flow laws for dislocation creep, diffusion creep, grain boundary sliding, and low T plasticity. We assumed that viscous deformation remains localized in shear zones, surrounded by host rocks undergoing elastic deformation. We fixed the velocity along one side of an elastic half space, and calculated stress due to elastic strain. This stress drives viscous deformation in a shear zone of specified width. Shear heating and thermal diffusion control temperature evolution in the shear zone and host rocks. A maximum of 1400 C (where substantial melting of peridotite would occur) is imposed. Grain size evolves during dislocation
Shear flow instability generated by non-homogeneous external forcing
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1987-01-01
An experiment has been designed and conducted in order to ascertain whether instability waves can be generated by nonhomogeneous forcing, using a biconvex vane located outside the mixing layer whose oscillation was induced by an electromagnetic shaker through a linkage. The vane was oscillated at 20 Hz, and the resulting spectra were computed by a spectrum analyzer. The data are judged to provide an example of instability waves generated solely through nonhomogeneous forcing.
Minimal model for zero-inertia instabilities in shear-dominated non-Newtonian flows.
Boi, S; Mazzino, A; Pralits, J O
2013-09-01
The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The finite-time shear-induced order-disorder transition of the non-Newtonian microstructure and the corresponding viscosity change from lower to higher values are the crucial ingredients for the instabilities to emerge. The finite-time low-to-high viscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. The lack of instabilities arbitrarily close to zero Reynolds number is also observed for thixotropic fluids, in spite of the fact that the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansions (multiple-scale expansions), energy-based arguments (on the linearized equations of motion), and numerical results (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, as in microfluidic applications. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.
Effects of a weakly 3-D equilibrium on ideal magnetohydrodynamic instabilities
Hegna, C. C.
2014-07-15
The effect of a small three-dimensional equilibrium distortion on an otherwise axisymmetric configuration is shown to be destabilizing to ideal magnetohydrodynamic modes. The calculations assume that the 3-D fields are weak and that shielding physics is present so that no islands appear in the resulting equilibrium. An eigenfunction that has coupled harmonics of different toroidal mode number is constructed using a perturbation approach. The theory is applied to the case of tokamak H-modes with shielded resonant magnetic perturbations (RMPs) present indicating RMPs can be destabilizing to intermediate-n peeling-ballooning modes.
Tariq, Sabeen; Mirza, Arshad M.; Masood, W.
2010-10-15
The propagation of high and low frequency (in comparison with the cyclotron frequency) electrostatic drift-waves is investigated in a nonuniform, dense magnetoplasma (composed of electrons and ions), in the presence of parallel shear flow, by employing the quantum magnetohydrodynamic (QMHD) model. Using QMHD model, a new set of equations is presented in order to investigate linear properties of electrostatic drift-waves with sheared plasma flows for dense plasmas. In this regard, dispersion relations for coupled electron-thermal and drift-ion acoustic modes are derived and several interesting limiting cases are discussed. For instance, it is found that sheared ion flow parallel to the external magnetic field can drive the quantum drift-ion acoustic wave unstable, etc. The present investigation may have relevance in dense astrophysical environments where quantum effects are significant.
The Effect of "Wave Breakers" on the Magnetohydrodynamic Instability in Aluminum Reduction Cells
NASA Astrophysics Data System (ADS)
Pedcenko, Alex; Molokov, Sergei; Bardet, Benoit
2017-02-01
We report the results of the experiments on the suppression of the MHD instability in a model of the aluminum reduction cells (Pedchenko et al. in EPL 88:24001, 2009). The idea behind the study is to introduce obstacles in the liquid metal to suppress the propagation of the rolling-pad instability wave. As a result, in some configurations with obstacles, we detect lowering of the wave amplitude, reduction of its propagation speed, and rise of the main parameters' thresholds, responsible for the instability onset.
NASA Astrophysics Data System (ADS)
Hamlin, Nathaniel D.; Newman, William I.
2013-04-01
We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number MA. We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence
Finite-width currents, magnetic shear, and the current-driven ion-cyclotron instability
NASA Technical Reports Server (NTRS)
Bakshi, P.; Ganguli, G.; Palmadesso, P.
1983-01-01
Our earlier results that non-local effects due to even a small magnetic shear produce a significant reduction of the growth rate of the ion cyclotron instability driven by a uniform current are now generalized to finite width currents. Externally prescribed as well as self-consistent shears are considered. If the current width Lc exceeds the shear length Ls, the previous results are recovered. Shear becomes less effective with reduction of Lc, and for typical parameters, the growth rate attains its (shearless) local value for Lc/Ls approximately less than 10 to the minus 2. Non-local effects of the finite current width itself come into play if Lc is further reduced to a few ion Larmor radii and can quench the instability. Previously announced in STAR as N83-28996
Nonlinear Interaction of Shear Alfven Waves with Gradient Driven Instabilities
NASA Astrophysics Data System (ADS)
Auerbach, David William
An experimental study of the interactions between gradient-driven instabilities (GDI) and beat waves driven between two Alfven waves is presented. A cylindrical density depletion is imposed on the otherwise uniform plasma in the Large Plasma Device (LAPD) by selectively blocking the electron beam that produces the plasma. Coherent, single mode fluctuations in density, temperature, plasma potential, and magnetic field are observed to be unstable on the gradient. Measurements of the relative cross-phase between the density and potential fluctuations indicate that the fluctuations are not likely to drive significant cross field transport. Comparisons of the properties of the modes to theoretical predictions for Kelvin-Helmholtz (KH) and drift wave modes indicate that the fluctuations are likely to be a hybrid of the two instabilities. Analytic eigenmode solutions to the linearized Braginskii fluid equations using the experimentally measured gradient profiles support the conclusion that both instabilities are active. A beat wave between two driven Alfven waves is broadcast into the gradient region using a pair of loop antennas with independently controlled frequency and power. This beat wave is observed to resonantly drive the unstable mode, as well as a second otherwise stable mode slightly higher in frequency and azimuthal mode number. During the drive of the secondary stable mode, the growth of the primary instability is suppressed. The broadcast of the Alfven waves and the beat wave is also observed to drive other fluctuations in the plasma at frequencies higher than either the spontaneous instability or the second, stable mode. Both the resonant drive of the modes and the control of the mode number are observed to have non-linear threshold and saturation behavior.
The influence of fast ions on the magnetohydrodynamic stability of negative shear profiles
Helander, P.; Gimblett, C.G.; Hastie, R.J.; McClements, K.G.
1997-06-01
The influence of energetic ions on the stability of ideal double kink modes in a tokamak plasma with negative magnetic shear is investigated. It is found that the fast ions play a similar role as for the ordinary m=n=1 internal kink. In particular, phenomena analogous to sawtooth stabilization and fishbone excitation are possible.
Dampening the asymmetric instability in pipe flow of shear thinning fluids using elasticity
NASA Astrophysics Data System (ADS)
Dennis, David; Wen, Chaofan; Poole, Robert
2016-11-01
Recent experimental results have shown that the asymmetric flow of shear-thinning fluid through a cylindrical pipe, which was previously associated with the laminar-turbulent transition process, is actually a non-hysteretic and reversible, supercritical instability of the laminar base state. These experiments were performed using largely inelastic shear-thinning fluids (aqueous solutions of xanthan gum) and it was found that the greater the degree of shear-thinning the larger the magnitude of the asymmetry. In this talk we show that a viscoelastic fluid (an aqueous solution of high molecular weight polyacrylamide), with approximately the same shear-thinning characteristics as the inelastic fluid, does not exhibit the asymmetry when freshly mixed. However, once the elasticity of this fluid is degraded (by prolonged shearing) the asymmetry reappears. This suggests that the shear-thinning nature of the fluid causes the instability and the viscoelastic nature works to dampen the asymmetry. To test this hypothesis we add varyingly small amounts of polyacrylamide to xanthan gum solutions and find an inverse relationship between viscoelasticity and the magnitude of the asymmetry, although the Reynolds number at which the instability is first observed stays approximately constant.
Kelvin-Helmholtz versus Hall magnetoshear instability in astrophysical flows.
Gómez, Daniel O; Bejarano, Cecilia; Mininni, Pablo D
2014-05-01
We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well-known macroscopic and ideal shear-driven instability. In sufficiently low-density plasmas, also the microscopic Hall magnetoshear instability can take place. We performed three-dimensional simulations of the Hall-magnetohydrodynamic equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magnetoshear instability is not only non-negligible, but it actually displays growth rates larger than those of the Kelvin-Helmholtz instability.
Transverse jet shear layer instabilities and their control
NASA Astrophysics Data System (ADS)
Karagozian, Ann
2013-11-01
The jet in crossflow, or transverse jet, is a canonical flowfield that has relevance to engineering systems ranging from dilution jets and film cooling for gas turbine engines to thrust vector control and fuel injection in high speed aerospace vehicles to environmental control of effluent from chimney and smokestack plumes. Over the years, our UCLA Energy and Propulsion Research Lab's studies on this flowfield have focused on the dynamics of the vorticity associated with equidensity and variable density jets in crossflow, including the stability characteristics of the jet's upstream shear layer. A range of different experimental diagnostics have been used to study the jet's upstream shear layer, whereby a transition from convectively unstable behavior at high jet-to-crossflow momentum flux ratios to absolutely unstable flow at low momentum flux and/or density ratios is identified. These differences in shear layer stability characteristics have a profound effect on how one employs external excitation to control jet penetration, spread, and mixing, depending on the flow regime and specific engineering application. These control strategies, and challenges for future research directions, will be identified in this presentation.
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2016-01-15
A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the neutrino coupling is shown to be responsible for breaking the frozen-in magnetic field lines condition even in infinite conductivity plasmas. Simplified and ideal NMHD assumptions were adopted and analyzed in detail.
Suppression of drift wave instability due to sheared field-aligned flow and negative ions
NASA Astrophysics Data System (ADS)
Ichiki, Ryuta; Hayashi, Kenichiro; Kaneko, Toshiro; Hatakeyama, Rikizo
2006-10-01
Sheared field-aligned plasma flow is a significant topic in space/circumterrestrial plasmas. Taking into account negative ions or dust grains will make the space plasma physics more general and accurate. Using the QT-Upgrade Machine, we have conducted laboratory experiments to examine negative ion effects on shear-modified drift waves. Field-aligned K^+ ion flow and its shear strength are controlled with a concentrically segmented W hot plate. Negative ions SF6^- are produced by introducing SF6 gas in the plasma. The drift wave shows a gradual monotonic decrease in amplitude as the shear strength is increased from zero. However, as the shear strength is decreased from zero to negative values, the amplitude increases up to a certain shear strength and rapidly decreases after the peaking. The negative ion introduction, in general, suppresses this instability while retaining the dependence of the amplitude on the shear. These wave characteristics are interpreted using the theories of current-driven (kinetic) and of D’Angelo (fluid) instabilities.
Study of micro-instabilities in toroidal plasmas with negative magnetic shear
Dong, J.Q.; Zhang, Y.Z.; Mahajan, S.M.; Guzdar, P.N.
1996-03-01
The micro-instabilities driven by a parallel velocity shear, and a temperature gradient of ions are studied in toroidal plasmas with negative magnetic shear. Both the fluid and the gyro-kinetic formulations are investigated. It is found that for a broad range of parameters, the linear growth rates of the modes are lower, and the threshold temperature gradient {eta}{sub icr} is higher for plasmas with negative magnetic shear compared to plasmas with positive magnetic shear of equal magnitude. The reduction in the growth rate (with negative shear), although not insignificant, does not seem to be enough to account for the dramatic improvement in the confinement observed experimentally. Other possible physical mechanisms for the improved confinement are discussed.
Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow
NASA Technical Reports Server (NTRS)
Wundrow, David W.; Goldstein, Marvin E.
1994-01-01
It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer.
Interchange and Flow Velocity Shear Instabilities in the Presence of Finite Larmor Radius Effects
NASA Astrophysics Data System (ADS)
Sotnikov, V.; Kim, T.; Mishin, E.; Genoni, T.; Rose, D.; Mehlhorn, T.
2014-09-01
Ionospheric irregularities cause scintillations of electromagnetic signals that can severely affect navigation and transionospheric communication, in particular during Equatorial Plasma Bubbles (EPBs) events. However, the existing ionospheric models do not describe density irregularities with typical scales of several ion Larmor radii that affect UHF and L bands. These irregularities can be produced in the process of nonlinear evolution of interchange or flow velocity shear instabilities. The model of nonlinear development of these instabilities based on two-fluid hydrodynamic description with inclusion of finite Larmor radius effects will be presented. The derived nonlinear equations will be numerically solved by using the code Flute, which was originally developed for High Energy Density applications and modified to describe interchange and flow velocity shear instabilities in the ionosphere. The high-resolution simulations will be driven by the ambient conditions corresponding to the AFRL C/NOFS satellite low-resolution data during EPBs.
1989-03-01
MTL TR 89-20 [AD 00 4 THE INFLUENCE OF SECOND-PHASE DISPERSIONS ON SHEAR INSTABILITY AND FRACTURE TOUGHNESS OF ULTRAHIGH STRENGTH 4340 STEEL JOHN G...FRACTURE TOUGHNESS OF ULTRAHIGH STRENGTH 4340 STEEL 6 PERFORMING ORG. REPORT NUMBER 7. AU THOR(s) 0. CONTRACT OR GRANT NUMBERI’iI John G. Cowie 9...instability strain of UHS 4340 steel is discussed. Experimental results indicate a linear relationship exists between shear instability strain and this A/R
Lyra, Wladimir; Mac Low, Mordecai-Mark E-mail: mordecai@amnh.org
2012-09-01
It has been suggested that the transition between magnetorotationally active and dead zones in protoplanetary disks should be prone to the excitation of vortices via Rossby wave instability (RWI). However, the only numerical evidence for this has come from alpha disk models, where the magnetic field evolution is not followed, and the effect of turbulence is parameterized by Laplacian viscosity. We aim to establish the phenomenology of the flow in the transition in three-dimensional resistive-magnetohydrodynamical models. We model the transition by a sharp jump in resistivity, as expected in the inner dead zone boundary, using the PENCIL CODE to simulate the flow. We find that vortices are readily excited in the dead side of the transition. We measure the mass accretion rate finding similar levels of Reynolds stress at the dead and active zones, at the {alpha} Almost-Equal-To 10{sup -2} level. The vortex sits in a pressure maximum and does not migrate, surviving until the end of the simulation. A pressure maximum in the active zone also triggers the RWI. The magnetized vortex that results should be disrupted by parasitical magneto-elliptic instabilities, yet it subsists in high resolution. This suggests that either the parasitic modes are still numerically damped or that the RWI supplies vorticity faster than they can destroy it. We conclude that the resistive transition between the active and dead zones in the inner regions of protoplanetary disks, if sharp enough, can indeed excite vortices via RWI. Our results lend credence to previous works that relied on the alpha-disk approximation, and caution against the use of overly reduced azimuthal coverage on modeling this transition.
Squire, J.; Bhattacharjee, A.
2014-12-10
We study magnetorotational instability (MRI) using nonmodal stability techniques. Despite the spectral instability of many forms of MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very different from the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely different region of space. These ideas lead—for both axisymmetric and non-axisymmetric modes—to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary differential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using nonmodal analysis techniques, we conclude by analyzing local MRI growth over finite timescales using these methods. The strong growth over a wide range of wave-numbers suggests that nonmodal linear physics could be of fundamental importance in MRI turbulence.
J Squire, A Bhattacharjee
2014-07-01
We study the magnetorotational instability (MRI) (Balbus & Hawley 1998) using non-modal stability techniques.Despite the spectral instability of many forms of the MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very diff erent to the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely di fferent region of space. These ideas lead – for both axisymmetric and non-axisymmetric modes – to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary diff erential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using non-modal analysis techniques, we conclude by analyzing local MRI growth over finite time-scales using these methods. The strong growth over a wide range of wave-numbers suggests that non-modal linear physics could be of fundamental importance in MRI turbulence (Squire & Bhattacharjee 2014).
Nonlinear shearing modes approach to the diocotron instability of a planar electron strip
Mikhailenko, V. V. Mikhailenko, V. S.; Jo, Younghyun; Lee, Hae June
2015-09-15
The nonlinear evolution of the diocotron instability of a planar electron strip is investigated analytically by means of the nonlinear shearing mode for the solution of the initial and boundary value problems. The method is based on the sheared spatial coordinates which account for the motion of electron flow in the electrostatic field of the unstable diocotron modes in addition to the unperturbed sheared motion of the electron flow on the transformed shear coordinates. The time evolutions are studied by the solution of the initial and boundary value problems. The obtained solutions for the perturbed electrostatic potential include two nonlinear effects—the effect of the distortion of the boundaries of the planar electron strip and the effect of the coupling of the sheared nonmodal diocotron modes. It was proved by a two-dimensional particle-in-cell simulation that the developed theory is valid as long as the distortion of the boundaries of the basic shear flow does not change the frequency and growth rate of the linear diocotron instability in the transformed coordinates.
NASA Astrophysics Data System (ADS)
Wareing, C. J.; Pittard, J. M.; Falle, S. A. E. G.; Van Loo, S.
2016-06-01
We have used the adaptive mesh refinement hydrodynamic code, MG, to perform idealized 3D magnetohydrodynamical simulations of the formation of clumpy and filamentary structure in a thermally unstable medium without turbulence. A stationary thermally unstable spherical diffuse atomic cloud with uniform density in pressure equilibrium with low density surroundings was seeded with random density variations and allowed to evolve. A range of magnetic field strengths threading the cloud have been explored, from β = 0.1 to 1.0 to the zero magnetic field case (β = ∞), where β is the ratio of thermal pressure to magnetic pressure. Once the density inhomogeneities had developed to the point where gravity started to become important, self-gravity was introduced to the simulation. With no magnetic field, clouds and clumps form within the cloud with aspect ratios of around unity, whereas in the presence of a relatively strong field (β = 0.1) these become filaments, then evolve into interconnected corrugated sheets that are predominantly perpendicular to the magnetic field. With magnetic and thermal pressure equality (β = 1.0), filaments, clouds and clumps are formed. At any particular instant, the projection of the 3D structure on to a plane parallel to the magnetic field, i.e. a line of sight perpendicular to the magnetic field, resembles the appearance of filamentary molecular clouds. The filament densities, widths, velocity dispersions and temperatures resemble those observed in molecular clouds. In contrast, in the strong field case β = 0.1, projection of the 3D structure along a line of sight parallel to the magnetic field reveals a remarkably uniform structure.
New instability modes for bounded, free shear flows
NASA Technical Reports Server (NTRS)
Macaraeg, Michele G.; Streett, Craig L.
1989-01-01
A class of highly amplified supersonic disturbances are found for high-speed, bounded mixing layers at high values of streamwise wavenumber. Their amplification is an order of magnitude greater than the most amplified modes, which occur at 60-65 deg at low streamwise wavenumber. These disturbances are stabilized by increasing Mach number, viscosity, and sweep; however, the effect of sweep on the most amplified mode is not significant until the wave propagation angle reaches 30 deg. The maximum growth rate of the unstable disturbances decreases as the temperature of the higher Mach number stream is increased. The structure of these disturbances is such that the phase speed with respect to the mean flow is subsonic in a small region in the center of the shear layer, and supersonic on either side of this region.
Kelvin-Helmholtz instability of magnetohydrodynamic waves propagating on solar surges
NASA Astrophysics Data System (ADS)
Zhelyazkov, I.; Chandra, R.; Srivastava, A. K.; Mishonov, T.
2015-04-01
In the present paper, we study the evolutionary conditions for Kelvin-Helmholtz (KH) instability in a high-temperature solar surge observed in NOAA AR 11271 using the Solar Dynamics Observatory data on 2011 August 25. The jet with speed of ≈100 km s-1, width of 7 Mm, and electron number density of 4.17×109 cm-3 is assumed to be confined in an untwisted/twisted magnetic flux tube with magnetic field of 10 G. The temperature of the plasma flow is 2×106 K while that of its environment, according to the observational data, is of the order of 106 K. The electron number density of surrounding magnetized plasma is evaluated to be equal to 1.15×109 cm-3. Under these conditions, the Alfvén speed inside the flux tube is 337.6 km s-1, the sound speed is around 166 km s-1, while these characteristic speeds of the environment are ≅719 km s-1 and ≅117 km s-1, respectively. We study the propagation of normal MHD modes in the flux tube considering the two cases, notably of untwisted magnetic flux tube and the twisted one. The numerical solution to the dispersion relation shows that the kink ( m=1) wave traveling in an untwisted flux tube becomes unstable if the jet speed exceeds 1060 km s-1—a speed which is inaccessible for solar surges. A weak twist (the ratio of azimuthal to longitudinal magnetic field component) of the internal magnetic field in the range of 0.025-0.2 does not change substantially the critical flow velocity. Thus, one implies that, in general, the kink mode is stable against the KH instability. It turns out, however, that the m=-2 and m=-3 MHD modes can become unstable when the twist parameter has values between 0.2 and 0.4. Therefore, the corresponding critical jet speed for instability onset lies in the range of 93.5-99.3 km s-1. The instability wave growth rate, depending on the value of the wavelength, is of the order of several dozen inverse milliseconds. It remains to be seen whether these predictions will be observationally validated in
Li, Weidong; Gao, Yanfei; Bei, Hongbin
2016-01-01
As a commonly used method to enhance the ductility in bulk metallic glasses (BMGs), the introduction of geometric constraints blocks and confines the propagation of the shear bands, reduces the degree of plastic strain on each shear band so that the catastrophic failure is prevented or delayed, and promotes the formation of multiple shear bands. The clustering of multiple shear bands near notches is often interpreted as the reason for improved ductility. Experimental works on the shear band arrangements in notched metallic glasses have been extensively carried out, but a systematic theoretical study is lacking. Using instability theory that predicts the onset of strain localization and the free-volume-based finite element simulations that predict the evolution of shear bands, this work reveals various categories of shear band arrangements in double edge notched BMGs with respect to the mode mixity of the applied stress fields. A mechanistic explanation is thus provided to a number of related experiments and especially the correlation between various types of shear bands and the stress state. PMID:27721462
Li, Weidong; Gao, Yanfei; Bei, Hongbin
2016-10-10
As a commonly used method to enhance the ductility in bulk metallic glasses (BMGs), the introduction of geometric constraints blocks and confines the propagation of the shear bands, reduces the degree of plastic strain on each shear band so that the catastrophic failure is prevented or delayed, and promotes the formation of multiple shear bands. The clustering of multiple shear bands near notches is often interpreted as the reason for improved ductility. Experimental works on the shear band arrangements in notched metallic glasses have been extensively carried out, but a systematic theoretical study is lacking. Using instability theory that predictsmore » the onset of strain localization and the free-volume- based nite element simulations that predict the evolution of shear bands, this work reveals various categories of shear band arrangements in double edge notched BMGs with respect to the mode mixity of the applied stress fields. In conclusion, a mechanistic explanation is thus provided to a number of related experiments and especially the correlation between various types of shear bands and the stress state.« less
Li, Weidong; Gao, Yanfei; Bei, Hongbin
2016-10-10
As a commonly used method to enhance the ductility in bulk metallic glasses (BMGs), the introduction of geometric constraints blocks and confines the propagation of the shear bands, reduces the degree of plastic strain on each shear band so that the catastrophic failure is prevented or delayed, and promotes the formation of multiple shear bands. The clustering of multiple shear bands near notches is often interpreted as the reason for improved ductility. Experimental works on the shear band arrangements in notched metallic glasses have been extensively carried out, but a systematic theoretical study is lacking. Using instability theory that predicts the onset of strain localization and the free-volume- based nite element simulations that predict the evolution of shear bands, this work reveals various categories of shear band arrangements in double edge notched BMGs with respect to the mode mixity of the applied stress fields. In conclusion, a mechanistic explanation is thus provided to a number of related experiments and especially the correlation between various types of shear bands and the stress state.
NASA Astrophysics Data System (ADS)
Li, Weidong; Gao, Yanfei; Bei, Hongbin
2016-10-01
As a commonly used method to enhance the ductility in bulk metallic glasses (BMGs), the introduction of geometric constraints blocks and confines the propagation of the shear bands, reduces the degree of plastic strain on each shear band so that the catastrophic failure is prevented or delayed, and promotes the formation of multiple shear bands. The clustering of multiple shear bands near notches is often interpreted as the reason for improved ductility. Experimental works on the shear band arrangements in notched metallic glasses have been extensively carried out, but a systematic theoretical study is lacking. Using instability theory that predicts the onset of strain localization and the free-volume-based finite element simulations that predict the evolution of shear bands, this work reveals various categories of shear band arrangements in double edge notched BMGs with respect to the mode mixity of the applied stress fields. A mechanistic explanation is thus provided to a number of related experiments and especially the correlation between various types of shear bands and the stress state.
The radiation of sound by the instability waves of a compressible plane turbulent shear layer
NASA Technical Reports Server (NTRS)
Tam, C. K. W.; Morris, P. J.
1980-01-01
The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
Dynamical instability of shear-free collapsing star in extended teleparallel gravity
NASA Astrophysics Data System (ADS)
Jawad, Abdul; Rani, Shamaila
2015-11-01
We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f( T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.
Introduction to Modern Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Galtier, Sébastien
2016-10-01
Preface; Table of physical quantities; Part I. Foundations: 1. Introduction; 2. Magnetohydrodynamics; 3. Conservation laws; Part II. Fundamental Processes: 4. Magnetohydrodynamic waves; 5. Dynamo; 6. Discontinuities and shocks; 7. Magnetic reconnection; Part III. Instabilities and Magnetic Confinement: 8. Static equilibrium; 9. Linear perturbation theory; 10. Study of MHD instabilities; Part IV. Turbulence: 11. Hydrodynamic turbulence; 12. MHD turbulence; 13. Advanced MHD turbulence; Appendix 1. Solutions to the exercises; Appendix 2. Formulary; References; Index.
Localization and instability in sheared granular materials: Role of friction and vibration.
Kothari, Konik R; Elbanna, Ahmed E
2017-02-01
Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies, and variability under different loading conditions have not been fully explored. Here we use a nonequilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as the presence and absence of acoustic vibrations. Our results suggest that at low and intermediate strain rates, persistent shear bands develop only in the absence of vibrations. Vibrations tend to fluidize the granular network and delocalize slip at these rates. Stick-slip is observed only for frictional grains, and it is confined to the shear band. At high strain rates, stick-slip disappears and the different systems exhibit similar stress-slip response. Changing the vibration intensity, duration or time of application alters the system response and may cause long-lasting rheological changes. We analyze these observations in terms of possible transitions between rate strengthening and rate weakening response facilitated by a competition between shear-induced dilation and vibration-induced compaction. We discuss the implications of our results on dynamic triggering, quiescence, and strength evolution in gouge-filled fault zones.
Localization and instability in sheared granular materials: Role of friction and vibration
NASA Astrophysics Data System (ADS)
Kothari, Konik R.; Elbanna, Ahmed E.
2017-02-01
Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies, and variability under different loading conditions have not been fully explored. Here we use a nonequilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as the presence and absence of acoustic vibrations. Our results suggest that at low and intermediate strain rates, persistent shear bands develop only in the absence of vibrations. Vibrations tend to fluidize the granular network and delocalize slip at these rates. Stick-slip is observed only for frictional grains, and it is confined to the shear band. At high strain rates, stick-slip disappears and the different systems exhibit similar stress-slip response. Changing the vibration intensity, duration or time of application alters the system response and may cause long-lasting rheological changes. We analyze these observations in terms of possible transitions between rate strengthening and rate weakening response facilitated by a competition between shear-induced dilation and vibration-induced compaction. We discuss the implications of our results on dynamic triggering, quiescence, and strength evolution in gouge-filled fault zones.
Hamlin, Nathaniel D; Newman, William I
2013-04-01
We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number M(A). We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence
A Pure Hydrodynamic Instability in Shear Flows and Its Application to Astrophysical Accretion Disks
NASA Astrophysics Data System (ADS)
Nath, Sujit Kumar; Mukhopadhyay, Banibrata
2016-10-01
We provide a possible resolution for the century-old problem of hydrodynamic shear flows, which are apparently stable in linear analysis but shown to be turbulent in astrophysically observed data and experiments. This mismatch is noticed in a variety of systems, from laboratory to astrophysical flows. There are so many uncountable attempts made so far to resolve this mismatch, beginning with the early work of Kelvin, Rayleigh, and Reynolds toward the end of the nineteenth century. Here we show that the presence of stochastic noise, whose inevitable presence should not be neglected in the stability analysis of shear flows, leads to pure hydrodynamic linear instability therein. This explains the origin of turbulence, which has been observed/interpreted in astrophysical accretion disks, laboratory experiments, and direct numerical simulations. This is, to the best of our knowledge, the first solution to the long-standing problem of hydrodynamic instability of Rayleigh-stable flows.
Shear flow instability in a partially-ionized plasma sheath around a fast-moving vehicle
Sotnikov, V. I.; Mudaliar, S.; Genoni, T. C.; Rose, D. V.; Oliver, B. V.; Mehlhorn, T. A.
2011-06-15
The stability of ion acoustic waves in a sheared-flow, partially-ionized compressible plasma sheath around a fast-moving vehicle in the upper atmosphere, is described and evaluated for different flow profiles. In a compressible plasma with shear flow, instability occurs for any velocity profile, not just for profiles with an inflection point. A second-order differential equation for the electrostatic potential of excited ion acoustic waves in the presence of electron and ion collisions with neutrals is derived and solved numerically using a shooting method with boundary conditions appropriate for a finite thickness sheath in contact with the vehicle. We consider three different velocity flow profiles and find that in all cases that neutral collisions can completely suppress the instability.
2D instabilities of surface gravity waves on a linear shear current
NASA Astrophysics Data System (ADS)
Francius, Marc; Kharif, Christian
2016-04-01
Periodic 2D surface water waves propagating steadily on a rotational current have been studied by many authors (see [1] and references therein). Although the recent important theoretical developments have confirmed that periodic waves can exist over flows with arbitrary vorticity, their stability and their nonlinear evolution have not been much studied extensively so far. In fact, even in the rather simple case of uniform vorticity (linear shear), few papers have been published on the effect of a vertical shear current on the side-band instability of a uniform wave train over finite depth. In most of these studies [2-5], asymptotic expansions and multiple scales method have been used to obtain envelope evolution equations, which allow eventually to formulate a condition of (linear) instability to long modulational perturbations. It is noted here that this instability is often referred in the literature as the Benjamin-Feir or modulational instability. In the present study, we consider the linear stability of finite amplitude two-dimensional, periodic water waves propagating steadily on the free surface of a fluid with constant vorticity and finite depth. First, the steadily propagating surface waves are computed with steepness up to very close to the highest, using a Fourier series expansions and a collocation method, which constitutes a simple extension of Fenton's method [6] to the cases with a linear shear current. Then, the linear stability of these permanent waves to infinitesimal 2D perturbations is developed from the fully nonlinear equations in the framework of normal modes analysis. This linear stability analysis is an extension of [7] to the case of waves in the presence of a linear shear current and permits the determination of the dominant instability as a function of depth and vorticity for a given steepness. The numerical results are used to assess the accuracy of the vor-NLS equation derived in [5] for the characteristics of modulational
NASA Astrophysics Data System (ADS)
Schnack, D. D.; Cheng, J.; Barnes, D. C.; Parker, S. E.
2013-06-01
We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k∥/k⊥≪1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length LTi0, instability requires that either k⊥ρi or ρi/LTi0 be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue ω =ωr+iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid kinetic δf code that assumes six-dimensional Vlasov ions and isothermal fluid electrons, as functions of k⊥ρi and ρi/LTi0 using a spatially dependent equilibrium. These solutions are compared with each other, and with the predictions of the local kinetic and fluid dispersion relations. Kinetic and fluid calculations agree well at and near the marginal stability point, but diverge as k⊥ρi or ρi/LTi0 increases. There is good qualitative agreement between the models for the shape of the unstable global eigenfunction for LTi0/ρi=30 and 20. The results quantify how far fluid calculations can be extended accurately into the kinetic regime. We conclude that for the linear ITG
NASA Astrophysics Data System (ADS)
Elmegreen, Bruce G.
1991-09-01
The growth of shearing wavelets in thick galactic gas disks is studied, including the magnetic Rayleigh-Taylor instability perpendicular to the plane, various degrees of thermal instability, and the gravitational instability. Growth rates are calculated numerically for a wide range of parameter values, giving an effective dispersion relation and mass distribution function, and an approximate dispersion relation is derived analytically for the epoch of peak growth. An extensive coverage of parameter space illustrates the relative insensitivity of the gaseous shear instability to the axisymmetric stability parameter Q. The fragmentation of shearing wavelets by self-gravitational collapse parallel to the wave crest is also considered. Such fragmentation is sensitive to Q, requiring Q equal to or less than 1-2 for the growth of parallel perturbations to overcome shear inside the wavelet. Fragmentation instabilities may provide the link between shear instabilities and the formation of individual clouds. They are much more sensitive to Q than shear instabilities, and may regulate star formation so that Q approximately equals 1.
Local parametric instability near elliptic points in vortex flows under shear deformation.
Koshel, Konstantin V; Ryzhov, Eugene A
2016-08-01
The dynamics of two point vortices embedded in an oscillatory external flow consisted of shear and rotational components is addressed. The region associated with steady-state elliptic points of the vortex motion is established to experience local parametric instability. The instability forces the point vortices with initial positions corresponding to the steady-state elliptic points to move in spiral-like divergent trajectories. This divergent motion continues until the nonlinear effects suppress their motion near the region associated with the steady-state separatrices. The local parametric instability is then demonstrated not to contribute considerably to enhancing the size of the chaotic motion regions. Instead, the size of the chaotic motion region mostly depends on overlaps of the nonlinear resonances emerging in the perturbed system.
Excitation of instability waves in a two-dimensional shear layer by sound
NASA Technical Reports Server (NTRS)
Tam, C. K. W.
1978-01-01
The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for abitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach number are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analyzed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80 deg to the flow direction is most effective in exciting instability waves.
Cowee, Misa M; Winske, Dan; Gary, S Peter
2009-01-01
Two-dimensional hybrid (kinetic ions, massless fluid electrons) simulations of the Kelvin Helmholtz Instability (KHI) for a magnetopause configuration with a magnetic shear across the boundary are carried out to examine how the transport of magnetosheath plasma into the magnetosphere is affected by the shear field. Low magnetic shear conditions where the magnetosheath magnetic field is within 30{sup o} of northward is included in the simulations because KHI is thought to be important for plasma transport only for northward or near-northward interplanetary magnetic field orientations. The simulations show that coherent vortices can grow for these near-northward angles, and that they are sometimes more coherent than for pure northward conditions because the turbulence which breaks-down these vortices is reduced when there are magnetic tension forces. With increasing magnetic shear angle, the growth rate is reduced, and the vortices do not grow to as large of size which reduces the plasma transport. By tracking the individual particle motions diffusion coefficients can be obtained for the system, where the diffusion is not classical in nature but instead has a time dependence resulting from both the increasingly large-scale vortex motion and the small-scale turbulence generated in the break-down of the instabilities. Results indicate that diffusion on the order of 10{sup 9} m{sup 2}/s could possibly be generated by KHI on the flanks of the magnetosphere.
Compressibility Effect on the Rayleigh-Taylor Instability with Sheared Magnetic Fields
NASA Astrophysics Data System (ADS)
Ruderman, M. S.
2017-04-01
We study the effect of plasma compressibility on the Rayleigh-Taylor instability of a magnetic interface with a sheared magnetic field. We assume that the plasma is ideal and the equilibrium quantities are constant above and below the interface. We derive the dispersion equation. Written in dimensionless variables, it contains seven dimensionless parameters: the ratio of plasma densities above and below the interface ζ, the ratio of magnetic field magnitude squared χ, the shear angle α, the plasma beta above and below the interface, β2 and β1, the angle between the perturbation wave number and the magnetic field direction above the interface φ, and the dimensionless wave number κ. Only six of these parameters are independent because χ, β1, and β2 are related by the condition of total pressure continuity at the interface. Only perturbations with the wave number smaller than the critical wave number are unstable. The critical wave number depends on φ, but it is independent of β1 and β2, and is the same as that in the incompressible plasma approximation. The dispersion equation is solved numerically with ζ= 100, χ= 1, and β1 = β2 = β. We obtain the following results. When β decreases, so does the maximum instability increment. However, the effect is very moderate. It is more pronounced for high values of α. We also calculate the dependence on φ of the maximum instability increment with respect to κ. The instability increment takes its maximum at φ= φm. Again, the decrease of β results in the reduction of the instability increment. This reduction is more pronounced for high values of |φ- φm|. When both α and |φ- φm| are small, the reduction effect is practically negligible. The theoretical results are applied to the magnetic Rayleigh-Taylor instability of prominence threads in the solar atmosphere.
Hanasaki, Itsuo; Walther, Jens H; Kawano, Satoyuki; Koumoutsakos, Petros
2010-11-01
We study shear-induced instabilities of lipid bilayers immersed in water using coarse-grained molecular dynamics simulations. The shear imposed by the flow of the water induces initially microscopic structural changes of the membrane, starting with tilting of the molecules in the direction of the shear. The tilting propagates in the spanwise direction when the shear rate exceeds a critical value and the membrane undergoes a bucklinglike deformation in the direction perpendicular to the shear. The bucklinglike undulation continues until a localized Kelvin-Helmholtz-like instability leads to membrane rupture. We study the different modes of membrane undulation using membranes of different geometries and quantify the relative importance of the bucklinglike bending and the Kelvin-Helmholtz-like instability of the membrane.
NASA Astrophysics Data System (ADS)
Hanasaki, Itsuo; Walther, Jens H.; Kawano, Satoyuki; Koumoutsakos, Petros
2010-11-01
We study shear-induced instabilities of lipid bilayers immersed in water using coarse-grained molecular dynamics simulations. The shear imposed by the flow of the water induces initially microscopic structural changes of the membrane, starting with tilting of the molecules in the direction of the shear. The tilting propagates in the spanwise direction when the shear rate exceeds a critical value and the membrane undergoes a bucklinglike deformation in the direction perpendicular to the shear. The bucklinglike undulation continues until a localized Kelvin-Helmholtz-like instability leads to membrane rupture. We study the different modes of membrane undulation using membranes of different geometries and quantify the relative importance of the bucklinglike bending and the Kelvin-Helmholtz-like instability of the membrane.
Prediction of plastic instabilities under thermo-mechanical loadings in tension and simple shear
NASA Astrophysics Data System (ADS)
Manach, P. Y.; Mansouri, L. F.; Thuillier, S.
2016-08-01
Plastic instabilities like Portevin-Le Châtelier were quite thoroughly investigated experimentally in tension, under a large range of strain rates and temperatures. Such instabilities are characterized both by a jerky flow and a localization of the strain in bands. Similar phenomena were also recorded for example in simple shear [1]. Modelling of this phenomenon is mainly performed at room temperature, taking into account the strain rate sensitivity, though an extension of the classical Estrin-Kubin-McCormick was proposed in the literature, by making some of the material parameters dependent on temperature. A similar approach is considered in this study, furthermore extended for anisotropic plasticity with Hill's 1948 yield criterion. Material parameters are identified at 4 different temperatures, ranging from room temperature up to 250°C. The identification procedure is split in 3 steps, related to the elasticity, the average stress level and the magnitude of the stress drops. The anisotropy is considered constant in this temperature range, as evidenced by experimental results [2]. The model is then used to investigate the temperature dependence of the critical strain, as well as its capability to represent the propagation of the bands. Numerical predictions of the instabilities in tension and simple shear at room temperature and up to 250°C are compared with experimental results [3]. In the case of simple shear, a monotonic loading followed by unloading and reloading in the reverse direction (“Bauschinger-type” test) is also considered, showing that (i) kinematic hardening should be taken into account to fully describe the transition at re-yielding (ii) the modelling of the critical strain has to be improved.
Three-dimensional flow instability near ion selective membrane under shear flow
NASA Astrophysics Data System (ADS)
Kwon, Hyukjin J.; Pham, Sang Van; Kim, Bumjoo; Lim, Geunbae; White, Jacob; Han, Jongyoon
2015-11-01
Ion transport through ion selective membranes is critically determined by concentration polarization in bulk solutions near the membrane, which is a complicated multiphysics phenomena. For the first time, we report a full experimental and numerical characterization of three-dimensional electrokinetic instability near ion selective membrane under a DC bias and shear flow. A new pattern of instability vortex is found, which was shown to be critically affected by the confinement geometry of the system. It is also found that the onset of over-limiting current and over-limiting resistance can be controlled by geometry of the system, which has significant implications on the optimization of electrodialysis and other electrochemical systems. This work is supported by ARPA-E grant (DE-AR0000294), and also by Kuwait-MIT Center for Natural Resources and the Environment (CNRE), which was funded by Kuwait Foundation for the Advancement of Sciences (KFAS). V. S. Pham was partially supported by SMAR.
Kinetic shear Alfvén instability in the presence of impurity ions in tokamak plasmas
Lu, Gaimin; Shen, Y.; Xie, T.; He, Zhixiong; He, Hongda; Qi, Longyu; Cui, Shaoyan
2013-10-15
The effects of impurity ions on the kinetic shear Alfvén (KSA) instability in tokamak plasmas are investigated by numerically solving the integral equations for the KSA eigenmode in the toroidal geometry. The kinetic effects of hydrogen and impurity ions, including transit motion, finite ion Larmor radius, and finite-orbit-width, are taken into account. Toroidicity induced linear mode coupling is included through the ballooning-mode representation. Here, the effects of carbon, oxygen, and tungsten ions on the KSA instability in toroidal plasmas are investigated. It is found that, depending on the concentration and density profile of the impurity ions, the latter can be either stabilizing or destabilizing for the KSA modes. The results here confirm the importance of impurity ions in tokamak experiments and should be useful for analyzing experimental data as well as for understanding anomalous transport and control of tokamak plasmas.
Sheared Flow Driven Drift Instability and Vortices in Dusty Plasmas with Opposite Polarity
NASA Astrophysics Data System (ADS)
Mushtaq, A.; Shah, AttaUllah; Ikram, M.; Clark, R. E. H.
2016-02-01
Low-frequency electrostatic drift waves are studied in an inhomogeneous dust magnetoplasma containing dust with components of opposite polarity. The drift waves are driven by the magnetic-field-aligned (parallel) sheared flows in the presence of electrons and ions. Due to sheared flow in the linear regime, the electrostatic dust drift waves become unstable. The conditions of mode instability, with the effects of dust streaming and opposite polarity, are studied. These are excited modes which gain large amplitudes and exhibit interactions among themselves. The interaction is governed by the Hasegawa-Mima (HM) nonlinear equation with vector nonlinearity. The stationary solutions of the HM equation in the form of a vortex chain and a dipolar vortex, including effects of dust polarity and electron (ion) temperatures, are studied. The relevance of the present work to space and laboratory four component dusty plasmas is noted.
Experimental and numerical study of plastic shear instability under high-speed loading conditions
Sokovikov, Mikhail E-mail: naimark@icmm.ru; Chudinov, Vasiliy E-mail: naimark@icmm.ru; Bilalov, Dmitry E-mail: naimark@icmm.ru; Oborin, Vladimir E-mail: naimark@icmm.ru; Uvarov, Sergey E-mail: naimark@icmm.ru; Plekhov, Oleg E-mail: naimark@icmm.ru; Terekhina, Alena E-mail: naimark@icmm.ru; Naimark, Oleg E-mail: naimark@icmm.ru
2014-11-14
The behavior of specimens dynamically loaded during the split Hopkinson (Kolsky) bar tests in a regime close to simple shear conditions was studied. The lateral surface of the specimens was investigated in a real-time mode with the aid of a high-speed infra-red camera CEDIP Silver 450M. The temperature field distribution obtained at different time made it possible to trace the evolution of plastic strain localization. The process of target perforation involving plug formation and ejection was examined using a high-speed infra-red camera and a VISAR velocity measurement system. The microstructure of tested specimens was analyzed using an optical interferometer-profilometer and a scanning electron microscope. The development of plastic shear instability regions has been simulated numerically.
Instability of a Lamellar Phase under Shear Flow: Formation of Multilamellar Vesicles
NASA Astrophysics Data System (ADS)
Courbin, L.; Delville, J. P.; Rouch, J.; Panizza, P.
2002-09-01
The formation of closed-compact multilamellar vesicles (referred to in the literature as the ``onion texture'') obtained upon shearing lamellar phases is studied using small-angle light scattering and cross-polarized microscopy. By varying the shear rate γ ˙, the gap cell D, and the smectic distance d, we show that: (i)the formation of this structure occurs homogeneously in the cell at a well-defined wave vector qi, via a strain-controlled process, and (ii)the value of qi varies as (dγ ˙/D)1/3. These results strongly suggest that formation of multilamellar vesicles may be monitored by an undulation (buckling) instability of the membranes, as expected from theory.
NASA Technical Reports Server (NTRS)
Van Hoven, G.; Mok, Y.
1984-01-01
The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.
Inflectional instabilities in the wall region of bounded turbulent shear flows
NASA Technical Reports Server (NTRS)
Swearingen, Jerry D.; Blackwelder, Ron F.; Spalart, Philippe R.
1987-01-01
The primary thrust of this research was to identify one or more mechanisms responsible for strong turbulence production events in the wall region of bounded turbulent shear flows. Based upon previous work in a transitional boundary layer, it seemed highly probable that the production events were preceded by an inflectional velocity profile which formed on the interface between the low-speed streak and the surrounding fluid. In bounded transitional flows, this unstable profile developed velocity fluctuations in the streamwise direction and in the direction perpendicular to the sheared surface. The rapid growth of these instabilities leads to a breakdown and production of turbulence. Since bounded turbulent flows have many of the same characteristics, they may also experience a similar type of breakdown and turbulence production mechanism.
Impacts of Shear Flow on the Low-n Kink Instabilities
NASA Astrophysics Data System (ADS)
Chen, Jianguo; Xu, Xueqiao
2016-10-01
We report the progress on studies of the effects of shear flow on the edge instabilities using the reduced 3-field two fluid MHD model under the BOUT + + framework. Using the equilibrium profiles in JET-like Tokamak geometry with a circular cross section, the results of simulations demonstrate that: (1) the low-n peeling modes are mainly driven by the gradient of parallel current and the large pressure gradient leads to high-n ballooning modes; (2) in low density cases, the low-n kink modes are sensitive to the Er shear; (3) using the shear flow's profiles measured from DIII-D experiment, the intermediate-n modes (n 20) are triggered firstly and the peak of it shifts to low-n mode with narrower mode spectrum when increasing the shear flow in the linear simulation; (4) the nonlinear results show the enhanced nonlinear mode-mode interaction in saturate phase and are quantitatively consistent with the transition from coherent harmonic oscillation(EHO) to the broad band turbulence state discovered in DIII-D discharge with net-zero NBI torque and the QH-mode can be achieved by NBI in both co- and counter direction. It's significant for understanding the mechanism of EHO and QH-mode.
Origin of intermittent plastic flow and instability of shear band sliding in bulk metallic glasses.
Sun, B A; Pauly, S; Hu, J; Wang, W H; Kühn, U; Eckert, J
2013-05-31
Intermittent or serrated plastic flow is widely observed in the deformation of bulk metallic glasses (BMGs) or other disordered solids at low temperatures. However, the underlying physical process responsible for the phenomena is still poorly understood. Here, we give an interpretation of the serrated flow behavior in BMGs by relating the atomic-scale deformation with the macroscopic shear band behavior. Our theoretical analysis shows that serrated flow in fact arises from an intrinsic dynamic instability of the shear band sliding, which is determined by a critical stiffness parameter in stick-slip dynamics. Based on this, the transition from serrated to nonserrated flow with the strain rate or the temperature is well predicted and the effects of various extrinsic and intrinsic factors on shear band stability can be quantitatively analyzed in BMGs. Our results, which are verified by a series of compression tests on various BMGs, provide key ingredients to fundamentally understand serrated flow and may bridge the gap between the atomic-scale physics and the larger-scale shear band dynamics governing the deformation of BMGs.
Jayakumar, R.J.; Austin, M.E.; Brennan, D.P.; Chu, M.S.; Luce, T.C.; Strait, E.J.; Turnbull, A.D.
2002-07-01
In DIII-D plasmas with L-mode edge and negative central shear (q{sub axis}-q{sub min} {approx}0.3 to 0.5), an interchange-like instability has been observed [1]. The instability and a subsequent tearing mode cause reduction of the core electron temperature and plasma rotation, and therefore the instability affects discharge evolution and the desired high performance is not achieved. Stability analyses indicate robust ideal stability, while the Resistive Interchange Mode criterion is marginal and the instability appears to be localized initially. Based on this, we believe that the mode is, most likely, a Resistive Interchange Mode. The amplitude of the instability is correlated with the location of the q{sub min} surface and inversely with the fast-ion pressure. There is indication that the interchange-like instability may be ''seeding'' the tearing mode that sometimes follows the interchange-like instability.
Shear-driven instabilities and shocks in the atmospheres of hot Jupiters
NASA Astrophysics Data System (ADS)
Fromang, Sébastien; Leconte, Jeremy; Heng, Kevin
2016-07-01
Context. General circulation models of the atmosphere of hot Jupiters have shown the existence of a supersonic eastward equatorial jet. These results have been obtained using numerical schemes that filter out vertically propagating sound waves and assume vertical hydrostatic equilibrium, or were acquired with fully compressive codes that use large dissipative coefficients. Aims: We remove these two limitations and investigate the effects of compressibility on the atmospheric dynamics by solving the standard Euler equations. Methods: This was done by means of a series of simulations performed in the framework of the equatorial β-plane approximation using the finite-volume shock-capturing code RAMSES. Results: At low resolution, we recover the classical results described in the literature: we find a strong and steady supersonic equatorial jet of a few km s-1 that displays no signature of shocks. We next show that the jet zonal velocity depends significantly on the grid meridional resolution. When this resolution is fine enough to properly resolve the jet, the latter is subject to a Kelvin-Helmholtz instability. The jet zonal mean velocity displays regular oscillations with a typical timescale of a few days and a significant amplitude of about 15% of the jet velocity. We also find compelling evidence for the development of a vertical shear instability at pressure levels of a few bars. It seems to be responsible for an increased downward kinetic energy flux that significantly affects the temperature of the deep atmosphere and appears to act as a form of drag on the equatorial jet. This instability also creates velocity fluctuations that propagate upward and steepen into weak shocks at pressure levels of a few mbars. Conclusions: We conclude that hot-Jupiter equatorial jets are potentially unstable to both a barotropic Kelvin-Helmholtz instability and a vertical shear instability. Upon confirmation using more realistic models, these two instabilities could result in
Magnetohydrodynamic stability of stochastically driven accretion flows.
Nath, Sujit Kumar; Mukhopadhyay, Banibrata; Chattopadhyay, Amit K
2013-07-01
We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.
The Effects of Contact Conditions on the Onset of Shear Instability in Cold-Spray
NASA Astrophysics Data System (ADS)
Meng, Fanchao; Aydin, Huseyin; Yue, Stephen; Song, Jun
2015-04-01
Using ABAQUS/Explicit, the effects of contact conditions between the particle and substrate, including tangential friction, normal constraint, and contact geometry on the plastic deformation during the cold-spray process are studied. It was found that the onset of shear instability, an event often used to indicate the establishment of bonding, is very sensitive to the choice of contact conditions. This suggests that the onset of shear instability does not serve as an accurate means to identify the plasticity threshold responsible for bonding. On the other hand, it is demonstrated that the evolution of the overall equivalent plastic strain (i.e., ) and the overall von Mises stress, being linearly proportional to each other, are both independent of contact conditions. Furthermore, it is shown that an energy value, defined as the product of the and the von Mises stress integrated over all particle elements, can quantitatively represent the energy dissipated via plastic deformation while being independent of contact conditions. The and associated energy value as defined may provide robust tools to assess the plasticity and the consequent bonding during cold-spray.
Mikhailenko, V. V.; Mikhailenko, V. S.; Lee, Hae June; Koepke, M. E.
2014-07-15
The cross-magnetic-field (i.e., perpendicular) profile of ion temperature and the perpendicular profile of the magnetic-field-aligned (parallel) plasma flow are sometimes inhomogeneous for space and laboratory plasma. Instability caused either by a gradient in the ion-temperature profile or by shear in the parallel flow has been discussed extensively in the literature. In this paper, (1) hydrodynamic plasma stability is investigated, (2) real and imaginary frequency are quantified over a range of the shear parameter, the normalized wavenumber, and the ratio of density-gradient and ion-temperature-gradient scale lengths, and (3) the role of inverse Landau damping is illustrated for the case of combined ion-temperature gradient and parallel-flow shear. We find that increasing the ion-temperature gradient reduces the instability threshold for the hydrodynamic parallel-flow shear instability, also known as the parallel Kelvin-Helmholtz instability or the D'Angelo instability. We also find that a kinetic instability arises from the coupled, reinforcing action of both free-energy sources. For the case of comparable electron and ion temperature, we illustrate analytically the transition of the D'Angelo instability to the kinetic instability as (a) the shear parameter, (b) the normalized wavenumber, and (c) the ratio of density-gradient and ion-temperature-gradient scale lengths are varied and we attribute the changes in stability to changes in the amount of inverse ion Landau damping. We show that near a normalized wavenumber k{sub ⊥}ρ{sub i} of order unity (i) the real and imaginary values of frequency become comparable and (ii) the imaginary frequency, i.e., the growth rate, peaks.
Stick-slip instabilities and shear strain localization in amorphous materials.
Daub, Eric G; Carlson, Jean M
2009-12-01
We study the impact of strain localization on the stability of frictional slipping in dense amorphous materials. We model the material using shear transformation zone (STZ) theory, a continuum approximation for plastic deformation in amorphous solids. In the STZ model, the internal state is quantified by an effective disorder temperature, and the effective temperature dynamics capture the spontaneous localization of strain. We study the effect of strain localization on stick-slip instabilities by coupling the STZ model to a noninertial spring slider system. We perform a linear stability analysis to generate a phase diagram that connects the small scale physics of strain localization to the macroscopic stability of sliding. Our calculations determine the values of spring stiffness and driving velocity where steady sliding becomes unstable and we confirm our results through numerical integration. We investigate both homogeneous deformation, where no shear band forms, and localized deformation, where a narrow shear band spontaneously forms and accommodates all of the deformation. Our results show that at a given velocity, strain localization leads to unstable frictional sliding at a much larger spring stiffness compared to homogeneous deformation, and that localized deformation cannot be approximated by a homogeneous model with a narrower material. We also find that strain localization provides a physical mechanism for irregular stick-slip cycles in certain parameter ranges. Our results quantitatively connect the internal physics of deformation in amorphous materials to the larger scale frictional dynamics of stick-slip.
Shear instabilities in metallic nanoparticles: hydrogen-stabilized structure of Pt37 on carbon.
Wang, Lin-Lin; Johnson, D D
2007-03-28
Using density functional theory calculations, we have studied the morphology of a Pt37 nanoparticle supported on carbon with and without hydrogen (H) passivation that arises with postprocessing of nanoparticles before characterization. Upon heating in an anneal cycle, we find that without H (e.g., in a helium atmosphere or evacuation at high temperature), the morphology change of a truncated cuboctahedral Pt37 is driven by the shearing of (100) to (111) facets to lower the surface energy, a remnant shear instability that drives surface reconstruction in semi-infinite Pt(100). With H passivation from a postprocessing anneal, we show that the sheared structure automatically reverts to the observed truncated cuboctahedral structure and the average first nearest-neighbor Pt-Pt bond length increases by 3%, agreeing well with experiment. We explain the stabilization of the truncated cuboctahedral structure due to H passivation via adsorption energetics of hydrogen on Pt(100) and (111) facets, specifically, the preference for H adsorption at bridge sites on (100) facets, which should be considered in a realistic model for H adsorption on Pt nanoparticles. We find that dramatic morphological change of a nanoparticle can occur even with small changes to first-shell Pt-Pt coordination number. The implications of our findings when comparing to experimental data are discussed.
Generation of auroral Omega bands by shear instability of the neutral winds
NASA Technical Reports Server (NTRS)
Lyons, L. R.; Walterscheid, R. L.
1985-01-01
Thermospheric neutral wind acceleration via ion drag in the conducting E-region of the ionosphere is greatly increased by electron precipitation associated with auroras. This increased acceleration can lead to the development of significant horizontal wind shears, which were found to be unstable to the Kelvin-Helmholtz shear instability. Numerical simulation of the neutral response to an intense, postmidnight, diffuse aurora shows tne formation of an E-region 'jet stream' within the aurora, with peak winds speeds greather than 700 m/s after one hour. It is proposed that this jet stream produces unstable Kelvin-Helmholtz waves, which can drive waves of discrete aurora along the poleward boundary of the preexisting diffuse aurora. It is suggested that such auroral waves, driven by the neutral winds, form eastward propagating waves (omega bands) occasionally observed along the poleward boundary of postmidnight diffuse auroras. It was found that neutral wind shears that develop in response to discrete auroral arcs are unstable; however, the resulting wind waves are not expected to drive significant auroral waves along discrete arcs.
Khan, Arshad; Khan, Ilyas; Shafie, Sharidan
2014-06-19
This article studies the radiation and porosity effects on the unsteady magnetohydrodynamic free convection flow of an incompressible viscous fluid past an infinite vertical plate that applies a shear stress f(t) to the fluid. Conjugate phenomenon of heat and mass transfer is considered. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. The solution of velocity is presented as a sum of mechanical and non mechanical parts. These solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. The results for embedded parameters are shown graphically. Numerical results for skin friction, Nusselt number and Sherwood number are computed and presented in tabular forms.
Nonlinear magnetohydrodynamic stability
NASA Technical Reports Server (NTRS)
Bauer, F.; Betancourt, O.; Garabedian, P.
1981-01-01
The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.
NASA Technical Reports Server (NTRS)
Blackaby, Nicholas D.; Choudhari, Meelan
1993-01-01
We consider the inviscid instability of three-dimensional boundary-layer flows with a small crossflow over locally concave or convex walls, along with the inviscid instability of stratified shear flows. We show how these two problems are closely related through the forms of their governing equations. A proposed definition of a generalized Richardson number for the neutrally stable inviscid vortex motions is given. Implications of the similarity between the two problems are discussed.
Coupling of the Okuda-Dawson model with a shear current-driven wave and the associated instability
NASA Astrophysics Data System (ADS)
Masood, W.; Saleem, H.; Saleem
2013-12-01
It is pointed out that the Okuda-Dawson mode can couple with the newly proposed current-driven wave. It is also shown that the Shukla-Varma mode can couple with these waves if the density inhomogeneity is taken into account in a plasma containing stationary dust particles. A comparison of several low-frequency electrostatic waves and instabilities driven by shear current and shear plasma flow in an electron-ion plasma with and without stationary dust is also presented.
NASA Astrophysics Data System (ADS)
Mikhailenko, V. V.; Mikhailenko, V. S.; Lee, Hae June
2016-06-01
The temporal evolution of the kinetic ion temperature gradient driven instability and of the related anomalous transport of the ion thermal energy of plasma shear flow across the magnetic field is investigated analytically. This instability develops in a steady plasma due to the inverse ion Landau damping and has the growth rate of the order of the frequency when the ion temperature is equal to or above the electron temperature. The investigation is performed employing the non-modal methodology of the shearing modes which are the waves that have a static spatial structure in the frame of the background flow. The solution of the governing linear integral equation for the perturbed potential displays that the instability experiences the non-modal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the non-modal structure with vanishing frequency and growth rate with time. The obtained solution of the nonlinear integral equation, which accounts for the random scattering of the angle of the ion gyro-motion due to the interaction of ions with ensemble of shearing waves, reveals similar but accelerated process of the transformations of the perturbations into the zero frequency structures. It was obtained that in the shear flow the anomalous ion thermal conductivity decays with time. It is a strictly non-modal effect, which originates from the temporal evolution of the shearing modes turbulence.
Lao, L.L.; Burrell, K.H.; Casper, T.S.
1996-08-01
The confinement and the stability properties of the DIII-D tokamak high performance discharges are evaluated in terms of rotational and magnetic shear with emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped- electron-{eta}{sub i}mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the {eta}{sub i} mode suggests that the large core {bold E x B} flow shear can stabilize this mode and broaden the region of reduced core transport . Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low {Beta}{sub N} {lt} 2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges which has a broad region of weak or slightly negative magnetic shear (WNS) is described. The WNS discharges have broader pressure profiles and higher values than the NCS discharges together with high confinement and high fusion reactivity.
NASA Astrophysics Data System (ADS)
Choi, M. J.; Park, H. K.; Yun, G. S.; Nam, Y. B.; Choe, G. H.; Lee, W.; Jardin, S.
2016-01-01
The electron cyclotron emission imaging (ECEI) instrument is widely used to study the local electron temperature (Te) fluctuations by measuring the ECE intensity IECE ∝ Te in tokamak plasmas. The ECEI measurement is often processed in a normalized fluctuation quantity against the time averaged value due to complication in absolute calibration. In this paper, the ECEI channels are relatively calibrated using the flat Te assumption of the sawtooth crash or the tearing mode island and a proper extrapolation. The 2-D relatively calibrated electron temperature (Te,rel) images are reconstructed and the displacement amplitude of the magnetohydrodynamic modes can be measured for the accurate quantitative growth analysis.
Earthquakes initiation and thermal shear instability in the Hindu Kush intermediate depth nest
NASA Astrophysics Data System (ADS)
Poli, Piero; Prieto, German; Rivera, Efrain; Ruiz, Sergio
2016-02-01
Intermediate depth earthquakes often occur along subducting lithosphere, but despite their ubiquity the physical mechanism responsible for promoting brittle or brittle-like failure is not well constrained. Large concentrations of intermediate depth earthquakes have been found to be related to slab break-off, slab drip, and slab tears. The intermediate depth Hindu Kush nest is one of the most seismically active regions in the world and shows the correlation of a weak region associated with ongoing slab detachment process. Here we study relocated seismicity in the nest to constraint the geometry of the shear zone at the top of the detached slab. The analysis of the rupture process of the Mw 7.5 Afghanistan 2015 earthquake and other several well-recorded events over the past 25 years shows an initially slow, highly dissipative rupture, followed by a dramatic dynamic frictional stress reduction and corresponding large energy radiation. These properties are typical of thermal driven rupture processes. We infer that thermal shear instabilities are a leading mechanism for the generation of intermediated-depth earthquakes especially in presence of weak zone subjected to large strain accumulation, due to ongoing detachment process.
Rotational instability of the electric polarization and divergence of the shear elastic compliance
NASA Astrophysics Data System (ADS)
Cordero, F.; Langhammer, H. T.; Müller, T.; Buscaglia, V.; Nanni, P.
2016-02-01
The rotational instability of the electric polarization P during phase transformations between ferroelectric phases is of great practical interest, since it may be accompanied by extremely large values of the piezoelectric coefficient, and a divergence of the coupled shear compliance contributes to such enhancements. In the literature, this has been explicitly calculated in the framework of the Landau theory and discussed with specific numerical simulations involving tetragonal, orthorhombic, and rhombohedral ferroelectric phases. When monoclinic phases are involved, such an approach is practically impossible, and an approximated treatment has been proposed, based on the observation that in those cases there are shear strains almost linearly coupled to the transverse component of P , implying a divergence of the Curie-Weiss type in the associated compliances. Here the argument is extended to the general case of transitions whose major effect is a rotation of the polarization, and the limits of its validity are discussed. As experimental verification, the elastic response of BaTiO3 is measured and analyzed, together with those of other ferroelectric perovskites available in the literature, such as KNN.
Mikhailenko, V. V. Mikhailenko, V. S.; Lee, Hae June
2015-10-15
The developed kinetic theory for the stability of a magnetic-field-aligned (parallel) shear flow with inhomogeneous ion temperature [Mikhailenko et al., Phys. Plasmas 21, 072117 (2014)] predicted that a kinetic instability arises from the coupled reinforcing action of the flow velocity shear and ion temperature gradient in the cases where comparable ion and electron temperatures exist. In the present paper, the nonlinear theory was developed for the instability caused by the combined effects of ion-temperature-gradient and shear-flow (ITG–SF). The level of the electrostatic turbulence is determined for the saturation state of the instability on the basis of the nonlinear dispersion equation, which accounts for a nonlinear scattering of ions by the developed turbulence in a sheared flow. The renormalized quasilinear equation for the ion distribution function, which accounts for the turbulent scattering of ions by ITG–SF driven turbulence, was derived and employed for the estimation of the turbulent ion viscosity, the anomalous ion thermal conductivity, and anomalous ion heating rate at the saturation state of the instability.
Lao, L.L.; Burrell, K.H.; Casper, T.S.; Chan, V.S.; Chu, M.S.; DeBoo, J.C.; Doyle, E.J.; Durst, R.D.; Forest, C.B.; Greenfield, C.M.; Groebner, R.J.; Hinton, F.L.; Kawano, Y.; Lazarus, E.A.; Lin-Liu, Y.R.; Mauel, M.E.; Meyer, W.H.; Miller, R.L.; Navratil, G.A.; Osborne, T.H.; Peng, Q.; Rettig, C.L.; Rewoldt, G.; Rhodes, T.L.; Rice, B.W.; Schissel, D.P.; Stallard, B.W.; Strait, E.J.; Tang, W.M.; Taylor, T.S.; Turnbull, A.D.; Waltz, R.E.; the DIII-D Team
1996-05-01
The confinement and the stability properties of the DIII-D tokamak [{ital Plasma} {ital Physics} {ital and} {ital Controlled} {ital Nuclear} {ital Fusion} {ital Research} 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high-performance discharges are evaluated in terms of rotational and magnetic shear, with an emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped-electron-{eta}{sub {ital i}} mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the {eta}{sub {ital i}} mode suggests that the large core {ital E}{times}{ital B} flow shear can stabilize this mode and broaden the region of reduced core transport. Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low {beta}{sub {ital N}}{le}2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges, which has a broad region of weak or slightly negative magnetic shear (WNS), is described. The WNS discharges have broader pressure profiles and higher {beta} values than the NCS discharges, together with high confinement and high fusion reactivity. {copyright} {ital 1996 American Institute of Physics.}
Linear and non-linear evolution of the vertical shear instability in accretion discs
NASA Astrophysics Data System (ADS)
Nelson, Richard P.; Gressel, Oliver; Umurhan, Orkan M.
2013-11-01
We analyse the stability and non-linear dynamics of power-law accretion disc models. These have mid-plane densities that follow radial power laws and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high-resolution 2D axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the disc scaleheight, the thermal relaxation time of the fluid and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to guide our interpretation of the simulation results. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of perturbations whose most obvious character is modes with horizontal and vertical wavenumbers that satisfy |kR/kZ| ≫ 1. Instability occurs only when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time-scale. These discs appear to exhibit the Goldreich-Schubert-Fricke or `vertical shear' linear instability. Closer inspection of the simulation results uncovers the growth of two distinct modes. The first are characterized by very short radial wavelength perturbations that grow rapidly at high latitudes in the disc, and descend down towards the mid-plane on longer time-scales. We refer to these as `finger modes' because they display kR/kZ ≫ 1. The second appear at slightly later times in the main body of the disc, including near the mid-plane. These `body modes' have somewhat longer radial wavelengths. Early on they manifest themselves as fundamental breathing modes, but quickly become corrugation modes as symmetry about the mid-plane is broken. The corrugation modes are a prominent feature
Choi, M. J.; Park, H. K.; Yun, G. S.; Nam, Y. B.; Choe, G. H.; Lee, W.; Jardin, S.
2016-01-15
The electron cyclotron emission imaging (ECEI) instrument is widely used to study the local electron temperature (T{sub e}) fluctuations by measuring the ECE intensity I{sub ECE} ∝ T{sub e} in tokamak plasmas. The ECEI measurement is often processed in a normalized fluctuation quantity against the time averaged value due to complication in absolute calibration. In this paper, the ECEI channels are relatively calibrated using the flat T{sub e} assumption of the sawtooth crash or the tearing mode island and a proper extrapolation. The 2-D relatively calibrated electron temperature (T{sub e,rel}) images are reconstructed and the displacement amplitude of the magnetohydrodynamic modes can be measured for the accurate quantitative growth analysis.
NASA Astrophysics Data System (ADS)
Ming, Yue; Zhou, Deng
2017-01-01
The effect of the poloidal equilibrium flow and flow shear on the tearing mode instabilities for tokamak plasmas is investigated. The vorticity equation is derived and approximately solved for large poloidal mode numbers (m). Asymptotic matching of the inner solution to the outer solution can approximately give the classical tearing mode stability index Δ' . For typical plasma parameters with positive flow shear, we notice that the poloidal mean flows have a beneficial effect on the classical tearing mode and vice versa. To study the modes with arbitrary poloidal mode numbers, we numerically solve the vorticity equation for delta prime ( Δ' ) for typical plasma parameters with positive flow shear at the rational surface and the resulting Δ' with large m also decreases with increasing poloidal flow velocity, consistent with the approximate analytical large m results. Our numerical calculations indicate that the poloidal mean flow with positive flow shear has beneficial influence on the stabilization of classical tearing modes in tokamak plasmas.
Particle dynamics in discs with turbulence generated by the vertical shear instability
NASA Astrophysics Data System (ADS)
Stoll, Moritz H. R.; Kley, Wilhelm
2016-10-01
Context. Among the candidates for generating turbulence in accretion discs in situations with low intrinsic ionization, the vertical shear instability (VSI) has become an interesting candidate, since it relies purely on a vertical gradient in the angular velocity. Existing numerical simulations have shown that α-values a few times 10-4 can be generated. Aims: The particle growth in the early planet formation phase is determined by the dynamics of embedded dust particles. Here, we address, in particular, the efficiency of VSI-turbulence in concentrating particles to generate overdensities and low collision velocities. Methods: We perform three-dimensional (3D) numerical hydrodynamical simulations of accretion discs around young stars that include radiative transport and irradiation from the central star. The motion of embedded particles within a size range of a fraction of mm up to several m is followed using standard drag formula. Results: We confirm that, under realistic conditions, the VSI is able to generate turbulence in full 3D protoplanetary discs. The irradiated disc shows turbulence within 10 to 60 au. The mean radial motion of the gas is such that it is directed inward near the midplane and outward in the surface layers. We find that large particles drift inward with the expected speed, while small particles can experience phases of outward drift. Additionally, the particles show bunching behaviour with overdensities reaching five times the average value, which is strongest for dimensionless stopping times around unity. Conclusions: Particles in a VSI-turbulent discs are concentrated in large-scale turbulent eddies and show low relative speeds that allow for growing collisions. The reached overdensities will also enable the onset of streaming instabilities, further enhancing particle growth. The outward drift for small particles at higher disk elevations enable the transport of processed high temperature material in the solar system to greater distances.
NASA Astrophysics Data System (ADS)
Sherman, James P.; She, Chiao-Yao
2006-06-01
One thousand three hundred and eleven 15-min profiles of nocturnal mesopause region (80 105 km) temperature and horizontal wind, observed by Colorado State University sodium lidar over Fort Collins, CO (41°N, 105°W), between May 2002 and April 2003, were analyzed. From these profiles, taken over 390 h and each possessing vertical resolution of 2 km, a statistical analysis of seasonal variations in wind shears, convective and dynamical instabilities was performed. Large wind shears were most often observed near 100 km and during winter months. Thirty-five percent of the winter profiles contained wind shears exceeding 40 m/s per km at some altitude. In spite of large winds and shears, the mesopause region (at a resolution of 2 km and 15 min) is a very stable region. At a given altitude, the probability for convective instability is less than 1.4% for all seasons and the probability for dynamic instability (in the sense of Richardson number) ranges from 2.7% to 6.0%. Wind shear measurements are compared with four decades of chemical release measurements, compiled in a study by Larson [2002. Winds and shears in the mesosphere and lower thermosphere: results from four decades of chemical release wind measurements. Journal of Geophysical Research 107(A8), 1215]. Instability results are compared with those deduced from an annual lidar study conducted with higher spatial and temporal resolution at the Starfire Optical Range (SOR) in Albuquerque, NM, by Zhao et al. [2003. Measurements of atmospheric stability in the mesopause region at Starfire Optical Range, NM. Journal of Atmospheric and Solar-Terrestrial Physics 65, 219 232], and from a study by Li et al. [2005b. Characteristics of instabilities in the mesopause region over Maui, Hawaii. Journal of Geophysical Research 110, D09S12] with 19 days of data acquired from Maui Mesosphere and Lower Thermosphere (Maui MALT) Campaign . The Fort Collins lidar profiles were also analyzed using 1-h temporal resolution to compare
Mazur, V. A. Chuiko, D. A.
2013-12-15
The coefficient of reflection of a fast magnetosonic wave incident on the magnetosphere from the solar wind is studied analytically in the framework of a plane-stratified model of the medium with allowance for the transverse inhomogeneity of the magnetosphere and a jump of the plasma parameters at the magnetopause. Three factors decisively affecting the properties of reflection are taken into account: the shear flow of the solar wind plasma relative to the magnetosphere; the presence of a magnetospheric magnetohydrodynamic waveguide caused by the transverse plasma inhomogeneity; and the presence of an Alfvén resonance deep in the magnetosphere, where the oscillation energy dissipates. If the solar wind velocity exceeds the wave phase velocity along the magnetopause, then the wave energy in the solar wind is negative and such a wave experiences overreflection. In the opposite case, the wave energy is positive and the wave is reflected only partially. The wave reflection has a pronounced resonant character: the reflection coefficient has deep narrow minima or high narrow maxima at the eigenfrequencies of the magnetospheric waveguide. For other frequencies, the reflection coefficient only slightly differs from unity. The wave energy influx into the magnetosphere is positive for waves with both positive and negative energies. For waves with a negative energy, this is a consequence of their overreflection, because the flux of negative energy carried away by the reflected wave exceeds the incident flux of negative energy.
Garcia-Munoz, M.; Fahrbach, H.-U.; Zohm, H.; Collaboration: ASDEX Upgrade Team
2009-05-15
A scintillator based detector for fast-ion losses has been designed and installed on the ASDEX upgrade (AUG) tokamak [A. Herrmann and O. Gruber, Fusion Sci. Technol. 44, 569 (2003)]. The detector resolves in time the energy and pitch angle of fast-ion losses induced by magnetohydrodynamics (MHD) fluctuations. The use of a novel scintillator material with a very short decay time and high quantum efficiency allows to identify the MHD fluctuations responsible for the ion losses through Fourier analysis. A Faraday cup (secondary scintillator plate) has been embedded behind the scintillator plate for an absolute calibration of the detector. The detector is mounted on a manipulator to vary its radial position with respect to the plasma. A thermocouple on the inner side of the graphite protection enables the safety search for the most adequate radial position. To align the scintillator light pattern with the light detectors a system composed by a lens and a vacuum-compatible halogen lamp has been allocated within the detector head. In this paper, the design of the scintillator probe, as well as the new technique used to analyze the data through spectrograms will be described. A last section is devoted to discuss the diagnosis prospects of this method for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)].
Mazur, V. A. Chuiko, D. A.
2013-06-15
Oscillations of the 'magnetosphere-solar wind' system are studied analytically in the framework of a plane-stratified model of the medium. The properties of oscillations are determined by three phenomena: Kelvin-Helmholtz instability on the tangential discontinuity (magnetopause) separating the magnetosphere and the solar wind, the presence of a waveguide for fast magnetosonic waves in the magnetosphere, and the Alfven resonance-a sharp increase in the amplitude of oscillations having the properties of Alfven waves-in the inner magnetosphere. The oscillations of the system form a discrete spectrum of eigenmodes. Analytical expressions are obtained for the frequency and growth rate of instability of each mode, as well as for the functions describing the spatial structure of these modes. All these characteristics of the eigenmodes are shown to depend on the velocity of the solar wind as a parameter. The dependences of the main mode characteristics (such as the instability thresholds, the points of the maximum and minimum growth rate, and the spatial distributions of the oscillation energy) on this parameter are determined for each eigenmode.
NASA Astrophysics Data System (ADS)
Pamuk, Onur; Akyol, Altan; Aslan, Zafer
2013-04-01
Spatial and temporal distributions of wind and solar energy potential are function of atmospheric stability, wind shear exponent, aerosol contents, heat fluxes etc. Richardson number is one of the indicators of the evolution of atmospheric instability. It is a function of the static stability and wind shear exponent. The logarithmic wind profile is commonly used for wind energy evaluation processes in the atmospheric surface layer. Definition of the vertical variation of horizontal wind speeds above the ground by logarithmic profile is limited by 100 meters. The main objective of this study is to take into account atmospheric instability and wind shear exponent in wind power assessment. In the first part of this paper, stability parameters and wind shear exponent have been calculated by using radiosonde data and the wind measuring system for the local area of Istanbul; northwestern part of Turkey between 2011 and 2012. These data were analyzed to define hourly, daily, monthly and seasonal variations of the Richardson number and wind shear exponent. Analyses of early morning soundings produced negative skewwness and afternoon soundings produced a positive skewwness for Ri numbers. The larger negative values of Ri numbers (extremely unstable conditions) have been observed in early morning in winter at the lower levels of atmosphere. The second part of this study covers temporal variations of wind speed and daily total radiation in Istanbul. By using time series and wavelet techniques, small, meso and large scale factors and their roles on wind speed and total daily solar radiation variations have been analyzed. The second part of the paper underlines the role of atmospheric stability and importance of wind shear exponent on variations of wind and solar energy potential. The results of this study would be applicable in the field of wind and solar combined energy systems. Keywords: Wind shear exponent, total daily radiation, wavelet wind and solar energy. Corresponding
NASA Technical Reports Server (NTRS)
Massaglia, S.; Ferrari, A.; Bodo, G.; Kalkofen, W.; Rosner, R.
1985-01-01
The stability of current-driven filamentary modes in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE and in hydrostatic equilibrium is discussed. Within the tube, energy transport by radiation only is considered. The dominant contribution to the opacity is due to H- ions and H atoms (in the Paschen continuum). A region in the parameter space of the equilibrium configuration in which the instability is effective is delimited, and the relevance of this process for the formation of structured coronae in late-type stars and accretion disks is discussed.
NASA Astrophysics Data System (ADS)
Bhat, Pallavi; Ebrahimi, Fatima; Blackman, Eric G.
2016-10-01
We study the dynamo generation (exponential growth) of large-scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal (x-y) averaging, we also demonstrate the presence of large-scale fields when vertical (y-z) averaging is employed instead. By computing space-time planar averaged fields and power spectra, we find large-scale dynamo action in the early MRI growth phase - a previously unidentified feature. Non-axisymmetric linear MRI modes with low horizontal wavenumbers and vertical wavenumbers near that of expected maximal growth, amplify the large-scale fields exponentially before turbulence and high wavenumber fluctuations arise. Thus the large-scale dynamo requires only linear fluctuations but not non-linear turbulence (as defined by mode-mode coupling). Vertical averaging also allows for monitoring the evolution of the large-scale vertical field and we find that a feedback from horizontal low wavenumber MRI modes provides a clue as to why the large-scale vertical field sustains against turbulent diffusion in the non-linear saturation regime. We compute the terms in the mean field equations to identify the individual contributions to large-scale field growth for both types of averaging. The large-scale fields obtained from vertical averaging are found to compare well with global simulations and quasi-linear analytical analysis from a previous study by Ebrahimi & Blackman. We discuss the potential implications of these new results for understanding the large-scale MRI dynamo saturation and turbulence.
Magnetohydrodynamic Turbulence
NASA Astrophysics Data System (ADS)
Montgomery, David C.
2004-01-01
Magnetohydrodynamic (MHD) turbulence theory is modeled on neutral fluid (Navier-Stokes) turbulence theory, but with some important differences. There have been essentially no repeatable laboratory MHD experiments wherein the boundary conditions could be controlled or varied and a full set of diagnostics implemented. The equations of MHD are convincingly derivable only in the limit of small ratio of collision mean-free-paths to macroscopic length scales, an inequality that often goes the other way for magnetofluids of interest. Finally, accurate information on the MHD transport coefficients-and thus, the Reynolds-like numbers that order magnetofluid behavior-is largely lacking; indeed, the algebraic expressions used for such ingredients as the viscous stress tensor are often little more than wishful borrowing from fluid mechanics. The one accurate thing that has been done extensively and well is to solve the (strongly nonlinear) MHD equations numerically, usually in the presence of rectangular periodic boundary conditions, and then hope for the best when drawing inferences from the computations for those astrophysical and geophysical MHD systems for which some indisputably turbulent detailed data are available, such as the solar wind or solar prominences. This has led to what is perhaps the first field of physics for which computer simulations are regarded as more central to validating conclusions than is any kind of measurement. Things have evolved in this way due to a mixture of the inevitable and the bureaucratic, but that is the way it is, and those of us who want to work on the subject have to live with it. It is the only game in town, and theories that have promised more-often on the basis of some alleged ``instability''-have turned out to be illusory.
Influence of equilibrium shear flow on peeling-ballooning instability and edge localized mode crash
Xi, P. W.; Xu, X. Q.; Wang, X. G.; Xia, T. Y.
2012-09-15
The E Multiplication-Sign B shear flow plays a dual role on peeling-ballooning modes and their subsequently triggered edge localized mode (ELM) crashes. On one hand, the flow shear can stabilize high-n modes and twist the mode in the poloidal direction, constraining the mode's radial extent and reducing the size of the corresponding ELM. On the other hand, the shear flow also introduces the Kelvin-Helmholtz drive, which can destabilize peeling-ballooning modes. The overall effect of equilibrium shear flow on peeling-ballooning modes and ELM crashes depends on the competition between these two effects. When the flow shear is either small or very large, it can reduce ELM size. However, for moderate values of flow shear, the destabilizing effect from the Kelvin-Helmholtz term is dominant and leads to larger ELM crashes.
Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability
NASA Astrophysics Data System (ADS)
Belyaev, Mikhail A.
2017-02-01
We present an instability for exciting incompressible modes (e.g., gravity or Rossby modes) at the surface of a star accreting through a boundary layer. The instability excites a stellar mode by sourcing an acoustic wave in the disk at the boundary layer, which carries a flux of energy and angular momentum with the opposite sign as the energy and angular momentum density of the stellar mode. We call this instability the acoustic Chandrasekhar–Friedman–Schutz (CFS) instability, because of the direct analogy to the CFS instability for exciting modes on a rotating star by emission of energy in the form of gravitational waves. However, the acoustic CFS instability differs from its gravitational wave counterpart in that the fluid medium in which the acoustic wave propagates (i.e., the accretion disk) typically rotates faster than the star in which the incompressible mode is sourced. For this reason, the instability can operate even for a non-rotating star in the presence of an accretion disk. We discuss applications of our results to high-frequency quasi-periodic oscillations in accreting black hole and neutron star systems and dwarf nova oscillations in cataclysmic variables.
Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity
NASA Technical Reports Server (NTRS)
Ofman, L.; Morrison, P. J.; Steinolfson, R. S.
1993-01-01
The effect of shear flow on the nonlinear evolution of the tearing mode is investigated via numerical solutions of the resistive MHD equations in slab geometry, using a finite-difference alternative-direction implicit method. It was found that, when the shear flow is small (V less than 0.3), the tearing mode saturates within one resistive time, whereas for larger flows the nonlinear saturation develops on longer time scales. The magnetic energy release decreases and the saturation time increases with increasing values of V for both small and large resistivity. Shear flow was found to decrease the saturated magnetic island width and to generate currents far from the tearing layer. Results suggest that equilibrium shear flow may improve the confinement of tokamak plasma.
NASA Astrophysics Data System (ADS)
Jo, Young Hyun; Lee, Hae June; Mikhailenko, Vladimir V.; Mikhailenko, Vladimir S.
2016-01-01
It was derived that the drift-Alfven instabilities with the shear flow parallel to the magnetic field have significant difference from the drift-Alfven instabilities of a shearless plasma when the ion temperature is comparable with electron temperature for a finite plasma beta. The velocity shear not only modifies the frequency and the growth rate of the known drift-Alfven instability, which develops due to the inverse electron Landau damping, but also triggers a combined effect of the velocity shear and the inverse ion Landau damping, which manifests the development of the ion kinetic shear-flow-driven drift-Alfven instability. The excited unstable waves have the phase velocities along the magnetic field comparable with the ion thermal velocity, and the growth rate is comparable with the frequency. The development of this instability may be the efficient mechanism of the ion energization in shear flows. The levels of the drift--Alfven turbulence, resulted from the development of both instabilities, are determined from the renormalized nonlinear dispersion equation, which accounts for the nonlinear effect of the scattering of ions by the electromagnetic turbulence. The renormalized quasilinear equation for the ion distribution function, which accounts for the same effect of the scattering of ions by electromagnetic turbulence, is derived and employed for the analysis of the ion viscosity and ions heating, resulted from the interactions of ions with drift-Alfven turbulence. In the same way, the phenomena of the ion cyclotron turbulence and anomalous anisotropic heating of ions by ion cyclotron plasma turbulence has numerous practical applications in physics of the near-Earth space plasmas. Using the methodology of the shearing modes, the kinetic theory of the ion cyclotron turbulence of the plasma with transverse current with strong velocity shear has been developed.
Magnetohydrodynamic Simulations of Barred Galaxies
NASA Astrophysics Data System (ADS)
Kim, W.-T.
2013-04-01
Magnetic fields are pervasive in barred galaxies, especially in gaseous substructures such as dust lanes and nuclear rings. To explore the effects of magnetic fields on the formation of the substructures as well as on the mass inflow rates to the galaxy center, we run two-dimensional, ideal magnetohydrodynamic simulations. We use a modified version of the Athena code whose numerical magnetic diffusivity is shown to be of third order in space. In the bar regions, magnetic fields are compressed and abruptly bent around the dust-lane shocks. The associated magnetic stress not only reduces the peak density of the dust-lane shocks but also removes angular momentum further from the gas that is moving radially in. Nuclear rings that form at the location of centrifugal barrier rather than resonance with the bar are smaller and more radially distributed, and the mass flow rate to the galaxy center is correspondingly larger in models with stronger magnetic fields. Outside the bar regions, the bar potential and strong shear conspire to amplify the field strength near the corotation resonance. The amplified fields transport angular momentum outward, producing trailing magnetic arms with strong fields and low density. The base of the magnetic arms are found to be unstable to a tearing-mode instability of magnetic reconnection. This produces numerous magnetic islands that eventually make the outer regions highly chaotic.
NASA Astrophysics Data System (ADS)
Sayag, Roiy; Tziperman, Eli
2008-05-01
A significant portion of the ice discharge in ice sheets is drained through ice streams, with subglacial sediment (till) acting as a lubricant. The known importance of horizontal friction in shear margins to ice stream dynamics suggests a critical role of longitudinal stresses. The effects of subglacial till and longitudinal stresses on the stability of an ice sheet flow are studied by linear stability analysis of an idealized ice-till model in two horizontal dimensions. A power law-viscous constitutive relation is used, explicitly including longitudinal shear stresses. The till, which has compressible viscous rheology, affects the ice flow through bottom friction. We examine the possibility that pure ice streams develop via a spontaneous instability of ice flow. We demonstrate that this model can be made intrinsically unstable for a seemingly relevant range of parameters and that the wavelengths and growth rates that correspond to the most unstable modes are in rough agreement with observed pure ice streams. Instabilities occur owing to basal friction and meltwater production at the ice-till interface. The most unstable wavelength arise because of selective dissipation of both short and long perturbation scales. Longitudinal stress gradients stabilize short transverse wavelengths, while Nye diffusion stabilizes long transverse wavelengths. The selection of an intermediate unstable wavelength occurs, however, only for certain parameter and perturbation structure choices. These results do not change qualitatively for a Newtonian ice flow law, indicating no significant role to shear thinning, although this may very well be due to the restrictive assumptions of the model and analysis.
First Laboratory Observation of a Shear Alfvén Wave Parametric Instability
NASA Astrophysics Data System (ADS)
Dorfman, S.; Carter, T.; Vincena, S.; Pribyl, P.; Rossi, G.; Lin, Y.; Sydora, R.
2016-10-01
Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in lab and space. The non-linear behavior of these modes is thought to play a key role in important problems such as the heating of the solar corona, solar wind turbulence, and Alfvén eigenmodes in tokamaks. In particular, theoretical predictions show that these Alfvén waves may be unstable to various parametric instabilities. Recent results from the Large Plasma Device at UCLA have recorded the first observation of a sheer Alfvén wave parametric instability in the laboratory [Dorfman and Carter, PRL 2016]. When a single finite ω /Ωi , finite k⊥ Alfvén wave is launched above a threshold amplitude, three daughter waves are observed: two sideband Alfvén waves co-propagating with the pump and a low frequency nonresonant mode. Frequency and parallel wave number matching relations are satisfied. Although these features are consistent with the k⊥ = 0 modulational instability theory, the theoretical growth rate is too small to explain observations. Efforts are underway to determine the nature of the perpendicular (to the background magnetic field) nonlinear drive, conduct comparative simulation studies, and identify parametric instabilities in spacecraft data. Supported by DOE, NSF, and NASA Eddy Postdoctoral Fellowship.
Palermo, F.; Garbet, X.; Cartier-Michaud, T.; Ghendrih, P.; Grandgirard, V.; Sarazin, Y.; Ghizzo, A.
2015-04-15
One important issue in turbulence self-organization is the interplay between the Kelvin–Helmholtz (KH) instability and streamers and/or zonal flows. This question has been debated for a long time. The effects of the KH instability and its position in the sequence of events between streamers, turbulence, and zonal flows have been investigated with a reduced gyro-bounce averaged kinetic code devoted to study the primary ion temperature gradient (ITG) instability linked to trapped ion modes (TIM). In toroidal geometry, the specific dynamics of TIM linked to trapped particles becomes important when the frequency of ITG modes falls below the ion bounce frequency, allowing one to average on both the cyclotron and bounce motion fast time scales. This reduction of the number of degrees of freedom leads to a strong reduction of computer resources (memory and computation time). Bounce-averaged gyrokinetic code can be considered as a toy model able to describe basic structures of turbulent transport in tokamak devices. In particular, by means of this code, we have observed that the energy injected in the system by the TIM instability is exchanged between streamers and zonal flows by means of KH vortices that grow along these structures in the nonlinear phase. The energy transfer occurs throughout the relaxation phase of the streamer growth leading to a modification of the KH modes and to the generation of the zonal flows.
Ng Sheungwah; Hassam, A.B.
2005-06-15
Finite Larmor radius (FLR) effects, originally shown to stabilize magnetized plasma interchange modes at short wavelength, are shown to assist velocity shear stabilization of long wavelength interchanges. It is shown that the FLR effects result in stabilization with roughly the same efficacy as the stabilization from dissipative (resistive and viscous) effects found earlier.
EXPLOSIVE INSTABILITY AND CORONAL HEATING
Dahlburg, R. B.; Liu, J.-H.; Klimchuk, J. A.; Nigro, G.
2009-10-20
The observed energy-loss rate from the solar corona implies that the coronal magnetic field has a critical angle at which energy is released. It has been hypothesized that at this critical angle an 'explosive instability' would occur, leading to an enhanced conversion of magnetic energy into heat. In earlier investigations, we have shown that a shear-dependent magnetohydrodynamic process called 'secondary instability' has many of the distinctive features of the hypothetical 'explosive instability'. In this paper, we give the first demonstration that this 'secondary instability' occurs in a system with line-tied magnetic fields and boundary shearing-basically the situation described by Parker. We also show that, as the disturbance due to secondary instability attains finite amplitude, there is a transition to turbulence which leads to enhanced dissipation of magnetic and kinetic energy. These results are obtained from numerical simulations performed with a new parallelized, viscoresistive, three-dimensional code that solves the cold plasma equations. The code employs a Fourier collocation-finite difference spatial discretization, and uses a third-order Runge-Kutta temporal discretization.
NASA Astrophysics Data System (ADS)
Wang, Meng; Huerre, Patrick; Jiang, Chung-Hsiang; Pei, Suyang; Rui, Maryann; Marcus, Philip
2015-11-01
It has been found recently that baroclinic critical layers are responsible for a new finite-amplitude instability, called the Zombie Vortex Instability (ZVI), in stratified (with Brunt-Väisälä frequency N) flows, rotating with angular velocity Ω and shear σ. ZVI occurs via baroclinic critical layers that create linearly unstable vortex layers, which roll-up into vortices. Those vortices excite new baroclinic critical layers, which form new generations of vortices, resulting in ``vortex self-replication'' that fills the fluid with turbulent vortices. To understand the role of baroclinic critical layers in ZVI, we analyze their structures with matched asymptotic expansions, assuming viscosity determines the magnitude and thickness of the critical layer. We verify our analytically obtained leading order inner and outer layer solutions with numerical simulations. In addition, maps of the control parameter space (Reynolds number, N/ Ω and σ/ Ω) are presented that show two regimes where ZVI occurs, and the physics that determines the boundaries of the two regimes is interpreted. The parameter map and its underlying physics provide guidance for designing practical laboratory experiments in which ZVI could be observed.
NASA Astrophysics Data System (ADS)
Hussain, Fazle
1998-11-01
We study a rectilinear vortex normal to a uniform shear - a prototypical coherent structure in shear flows. A newly found instability of the vortex due to core size variations, absent without shear, is shown to result from stretching by shear of helically twisted vortex lines. Core Dynamics (CD)-induced strong axial flow generates a large low-enstrophy bubble, surrounded by a thin sheath of vorticity, which rolls up into fine-scale vortices due to localized instability. Additionally, fine-scale 3D vorticity fluctuations are generated within the bubble by vortex filament folding and reconnection. Despite its smaller linear growth rate compared to vortex bending modes, the CD instability (CDI) is shown to dominate transition and cascade when both modes are present. In particular, CDI of spanwise rolls by oblique modes dominates transition in a mixing layer (ML) even in the presence of well developed ribs. Interestingly, initiation of CDI in a ML closely resembles streak instability in fully-developed near-wall turbulence, the latter producing streamwise vortices and hence enhanced drag.
Magnetic viscosity by localized shear flow instability in magnetized accretion disks
Matsumoto, R.; Tajima, T.
1995-01-01
Differentially rotating disks are subject to the axisymmetric instability for perfectly conducting plasma in the presence of poloidal magnetic fields. For nonaxisymmetric perturbations, the authors find localized unstable eigenmodes whose eigenfunction is confined between two Alfven singularities at {omega}{sub d} = {+-} {omega}{sub A}, where {omega}{sub d} is the Doppler-shifted wave frequency, and {omega}{sub A} = k{parallel}v{sub A} is the Alfven frequency. The radial width of the unstable eigenfunction is {Delta}x {approximately} {omega}{sub A}/(Ak{sub y}), where A is the Oort`s constant, and k{sub y} is the azimuthal wave number. The growth rate of the fundamental mode is larger for smaller value of k{sub y}/k{sub z}. The maximum growth rate when k{sub y}/k{sub z} {approximately} 0.1 is {approximately} 0.2{Omega} for the Keplerian disk with local angular velocity {Omega}. It is found that the purely growing mode disappears when k{sub y}/k{sub z} > 0.12. In a perfectly conducting disk, the instability grows even when the seed magnetic field is infinitesimal. Inclusion of the resistivity, however, leads to the appearance of an instability threshold. When the resistivity {eta} depends on the instability-induced turbulent magnetic fields {delta}B as {eta}([{delta}B{sup 2}]), the marginal stability condition self-consistently determines the {alpha} parameter of the angular momentum transport due to the magnetic stress. For fully ionized disks, the magnetic viscosity parameter {alpha}{sub B} is between 0.001 and 1. The authors` three-dimensional MHD simulation confirms these unstable eigenmodes. It also shows that the {alpha} parameter observed in simulation is between 0.01 and 1, in agreement with theory. The observationally required smaller {alpha} in the quiescent phase of accretion disks in dwarf novae may be explained by the decreased ionization due to the temperature drop.
NASA Astrophysics Data System (ADS)
Rogister, André L.; Singh, Raghvendra
2005-11-01
By keeping account of the trapped electron ∇B and curvature drifts, it is found that the spatial decay of the collisionless electron drift wave is governed either by the trapped electron response or by the resonant interaction of ions with the sidebands of the primary oscillation. In the former case, pairs of spatially bounded unstable and damped solutions are obtained for negative magnetic shear (ŝ<0) if, as usual, LTe=1/∂rlnTe<0; there are no bounded solutions if ŝLTe<0. In the latter case, there is either a set of bounded damped solutions if ηi>0 or a set of bounded unstable solutions if ηi<0. The unstable modes have a radiating character and the growth rates are γ ˜(2n+1)√1+2q2 ∣ŝ∣∣LNωe*/qR∣ (n is the Hermite polynomial solution index, q the safety factor, ŝ the magnetic shear parameter, R the major radius, ωe* the electron diamagnetic frequency, LN=1/∂rlnNe, and ηi=LN/LTi).The sidebands are responsible for unusually large ratios Qe/TeΓe, where Qe and Γe are the anomalous electron energy flux and the particle flux. These results may explain the box-type Te profile observed in lower hybrid current drive reversed magnetic shear plasmas on the Japan Atomic Energy Research Institute Tokamak 60 Upgrade (JT-60U) [H. Ninomiya and the JT-60U Team, Phys. Fluids B 4, 2070 (1992)]. It is finally demonstrated that the ballooning hypothesis generally leads to conflicting requirements: it is thus hardly relevant for the electron drift branch! The "radiating" boundary condition that has formerly been imposed on the slab solution is finally discussed.
Singing sand as an instability arising from a shear-plug flow
NASA Astrophysics Data System (ADS)
Dagois-Bohy, Simon; Courrech Du Pont, Sylvain; Douady, Stéphane
2010-05-01
Desert sand dunes can have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this is the song of the dunes. After the early travelers who first mentioned it (Darwin, Marco-Polo, ...) later scientific observations have shown that if not all dunes sing, all the singing dunes are composed of dry, well-sorted and coated sand; this sound occurs when the sand is sheared, and particularly on field during avalanches on a slip face of a singing dune? Several observations—recent and less recent—have shown that the sound frequency is likely equal to the shear rate of the flow, or at least is varying in the same way. We have been able to reproduce these avalanches in laboratory on an inclined plane with singing sand from Morocco and Oman, which has made possible to study them more accurately than on the field. Signals of accelerometers measuring local vertical oscillations of the flowing surface show that the phenomenon does not require resonance in the depth or in the dune. Measures of velocity and flow rate during avalanches enhance the co-existence of a plug flow with a large shear band underneath, both strongly correlated to the sound emission. A new model has been developed, based on the mechanical interaction between the plug area and the transient force chains in the flow. This model predicts a threshold that depends on the compacity of the granular media and on the surface friction and adhesion properties of the grains, and the value predicted fits quantitively well the data collected from avalanches, as well as from other experimental set-up of singing sand.
NASA Astrophysics Data System (ADS)
Rouhnia, M.; Strom, K.
2015-12-01
Sediment removal rates from buoyant river discharges are typically scaled with particle settling velocity. However, some field and laboratory data suggest that removal can take place at rates higher than those predicted by individual particle settling. It is possible that these enhanced removal rates could potentially be due, at least in part, to mass settling of fluid and sediment near the fresh and saltwater interface. Fluid shear at the interface can mix the freshwater and sediment with the underlying saltwater and lead to pockets or bands of saltwater and sediment that are more dense than the underlying clear saltwater; resulting in an unstable configuration that can lead to rapid vertical transport of sediment. In this study, we perform laboratory experiments to study the enhancement of sediment removal from buoyant plumes under the effect of shear-driven gravitational instabilities. To do this, we ran a 5 cm deep layer of freshwater with flocculated kaolinite over a 50 cm deep basin of clear saltwater in a 1 m long glass flume under a range of upper layer velocities, concentrations, and initial stratification ratios. A Vectrino profiler is placed such that it constantly records velocity profiles from 2 cm above to 2 cm below the original interface. The velocity of the buoyant layer is controlled using a vertical head pipe at the flume inlet, and the Richardson number is varied from 0.05 to 0.25. The interface is monitored with a digital camera and a laser sheet, and Rhodamine B is added to the buoyant layer for better visualization. Snapshots from the video are used to observe the overall dynamics and developments of instabilities at the interface. The sediment concentration of the inflow and outflow of the system are continuously measured with a pair of OBS sensors, and floc size is measured with a floc imaging system and converted to a floc settling velocity. The difference in sediment concentration between the two OBS sensors is used along with a mass
Influence of Magnetic Shear on the Collisional Current Driven Ion Cyclotron Instability.
1984-07-05
I DRIVEN ION CYCLOTRON INSTA9ILITY(U) NAVAL RESEARCH LAB MASHINOTON DC P SATYRNARAYRNA ET AL. S5 JUL 64 UNCLASSIFIED NRLD-NR-5345 FIG 2/9 L II 13J6...These results are verified by directly solving Eq. (14) using a numerical shooting code. We present the former results in the following. In Fig . 1 we...some light on the magnetic shear required to significantly reduce the growth rate, we plot in Fig . 2, the normalized growth rate versus the normalized
Formation of Kinneyia via shear-induced instabilities in microbial mats
NASA Astrophysics Data System (ADS)
Thomas, Katherine; Herminghaus, Stephan; Porada, Hubertus; Goehring, Lucas
2013-03-01
Kinneyia are a class of microbially mediated sedimentary fossils. Characterised by clearly defined ripple structures, Kinneyia are generally found in areas that were formally littoral habitats and covered by microbial mats. To date there has been no conclusive explanation as to the processes involved in the formation of these fossils. Microbial mats behave like viscoelastic fluids. We propose that the key mechanism involved in the formation of Kinneyia is a Kelvin-Helmholtz instability induced in a viscoelastic film under flowing water. A ripple corrugation is spontaneously induced in the film and grows in amplitude over time. Theoretical predictions show that the ripple instability has a wavelength proportional to the thickness of the film. Experiments carried out using viscoelastic films confirm this prediction. The ripple pattern that forms has a wavelength roughly three times the thickness of the film. This behaviour is independent of the viscosity of the film and the flow conditions. Well-ordered patterns form, with both honeycomb-like and parallel ridges being observed, depending on the flow speed. These patterns correspond well with those found in Kinneyia fossils, with similar morphologies, wavelengths and amplitudes being observed.
GRIM: General Relativistic Implicit Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Chandra, Mani; Foucart, Francois; Gammie, Charles F.
2017-02-01
GRIM (General Relativistic Implicit Magnetohydrodynamics) evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. GRIM, which runs on CPUs as well as on GPUs, combines time evolution and primitive variable inversion needed for conservative schemes into a single step using only the residuals of the governing equations as inputs. This enables the code to be physics agnostic as well as flexible regarding time-stepping schemes.
Flow Shear Effects in the Onset Physics of Resistive MHD Instabilities in Tokamaks. Final report
Brennan, Dylan P.
2013-04-24
The progress in this research centers around the computational analysis of flow shear effects in the onset of a 3/2 mode driven by a 1/1 mode in DIII-D equilibria. The initial idea was to try and calculate, via nonlinear simulations with NIMROD, the effects of rotation shear on driven 3/2 and 2/1 seed island physics, in experimentally relevant DIIID equilibria. The simulations indicated that very small seed islands were directly driven, as shielding between the sawtooth and the surfaces is significant at the high Lundquist numbers of the experiment. Instead, long after the initial crash the difference in linear stability of the 3/2, which remained prevalent despite the flattening of the core profiles from the sawtooth, contributed to a difference in the eventual seed island evolution. Essentially the seed islands grew or decayed long after the sawtooth crash, and not directly from it. Effectively the dominant 1/1 mode was found to be dragging the coupled modes surrounding it at a high rate through the plasma at their surfaces. The 1/1 mode is locked to the local frame of the plasma in the core, where the flow rate is greatest. The resonant perturbations at the surrounding surfaces propagate in the 'high slip regime' in the language of Fitzpatrick. Peaked flux averaged jxb forces (see Figs. 1 and 2) agree with localized flow modifications at the surfaces in analogy with Ebrahimi, PRL 2007. We track the mode into nonlinear saturation and have found oscillatory states in the evolution. During a visit (11/09) to Tulsa by R.J. LaHaye (GA), it became clear that similar oscillatory states are observed in DIII-D for these types of discharges.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mohseni, F.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1 / 2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Boquist, Carl W.; Marchant, David D.
1978-01-01
A ceramic-metal composite suitable for use in a high-temperature environment consists of a refractory ceramic matrix containing 10 to 50 volume percent of a continuous high-temperature metal reinforcement. In a specific application of the composite, as an electrode in a magnetohydrodynamic generator, the one surface of the electrode which contacts the MHD fluid may have a layer of varying thickness of nonreinforced refractory ceramic for electrode temperature control. The side walls of the electrode may be coated with a refractory ceramic insulator. Also described is an electrode-insulator system for a MHD channel.
NASA Technical Reports Server (NTRS)
Davis, J. G.; Scoggins, J. R.
1981-01-01
Data from the Fourth Atmospheric Variability Experiment were used to investigate conditions/factors responsible for the development (local time rate-of-change) of convective instability, wind shear, and vertical motion in areas with varying degrees of convective activity. AVE IV sounding data were taken at 3 or 6 h intervals during a 36 h period on 24-25 April 1975 over approximately the eastern half of the United States. An error analysis was performed for each variable studied.
Marchant, David D.; Killpatrick, Don H.
1978-01-01
An electrode capable of withstanding high temperatures and suitable for use as a current collector in the channel of a magnetohydrodynamic (MHD) generator consists of a sintered powdered metal base portion, the upper surface of the base being coated with a first layer of nickel aluminide, an intermediate layer of a mixture of nickel aluminide - refractory ceramic on the first layer and a third or outer layer of a refractory ceramic material on the intermediate layer. The sintered powdered metal base resists spalling by the ceramic coatings and permits greater electrode compliance to thermal shock. The density of the powdered metal base can be varied to allow optimization of the thermal conductivity of the electrode and prevent excess heat loss from the channel.
Merritt, E. C.; Doss, F. W.; Loomis, E. N.; Flippo, K. A.; Kline, J. L.
2015-06-24
Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varying two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. In addition, we also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths.
Merritt, E. C.; Doss, F. W.; Loomis, E. N.; ...
2015-06-24
Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varyingmore » two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. In addition, we also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths.« less
Merritt, E. C. Doss, F. W.; Loomis, E. N.; Flippo, K. A.; Kline, J. L.
2015-06-15
Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varying two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. We also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths.
Casanellas, Laura; Alves, Manuel A.; Poole, Robert J.; Lerouge, Sandra
2016-01-01
We determine both experimentally and numerically the onset of elastic flow instabilities in viscoelastic polymer solutions with different levels of shear thinning. Previous experiments realized in microfluidic serpentine channels using dilute polymeric solutions showed that the onset of elastic instabilities strongly depends on the channel curvature. The scaling dependence is well captured by the general instability scaling criterion proposed by Pakdel and McKinley [Phys. Rev. Lett., 1996, 76, 2459:1–4]. We determine here the influence of fluid shear thinning on the onset of such purely-elastic flow instabilities. By testing a set of polyethylene oxide solutions of high molecular weight at different polymer concentrations in microfluidic serpentine channels we observe that shear thinning has a stabilizing effect on the microfluidic flow. Three-dimensional numerical simulations performed using the White–Metzner model predict similar trends, which are not captured by a simple scaling analysis using the Pakdel–McKinley criterion. PMID:27265240
Nonlinear evolution of the Kelvin-Helmholtz instability in the double current sheet configuration
NASA Astrophysics Data System (ADS)
Mao, Aohua; Li, Jiquan; Liu, Jinyuan; Kishimoto, Yasuaki
2016-03-01
The nonlinear evolution of the Kelvin-Helmholtz (KH) instability driven by a radially antisymmetric shear flow in the double current sheet configuration is numerically investigated based on a reduced magnetohydrodynamic model. Simulations reveal different nonlinear fate of the KH instability depending on the amplitude of the shear flow, which restricts the strength of the KH instability. For strong shear flows far above the KH instability threshold, the linear electrostatic-type KH instability saturates and achieves a vortex flow dominated quasi-steady state of the electromagnetic (EM) KH turbulence with large-amplitude zonal flows as well as zonal fields. The magnetic surfaces are twisted significantly due to strong vortices but without the formation of magnetic islands. However, for the shear flow just over the KH instability threshold, a weak EM-type KH instability is saturated and remarkably damped by zonal flows through modifying the equilibrium shear flow. Interestingly, a secondary double tearing mode (DTM) is excited subsequently in highly damped KH turbulence, behaving as a pure DTM in a flowing plasma as described in Mao et al. [Phys. Plasmas 21, 052304 (2014)]. However, the explosive growth phenomenon is replaced by a gradually growing oscillation due to the extremely twisted islands. As a result, the release of the magnetic energy becomes slow and the global magnetic reconnection tends to be gentle. A complex nonlinear interaction between the EM KH turbulence and the DTMs occurs for the medium shear flows above the KH instability threshold, turbulent EM fluctuations experience oscillatory nonlinear growth of the DTMs, finally achieves a quasi-steady state with the interplay of the fluctuations between the DTMs and the EM KH instability.
DISCO: A 3D Moving-mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks
NASA Astrophysics Data System (ADS)
Duffell, Paul C.
2016-09-01
This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.
Magnetohydrodynamic mechanism for pedestal formation.
Guazzotto, L; Betti, R
2011-09-16
Time-dependent two-dimensional magnetohydrodynamic simulations are carried out for tokamak plasmas with edge poloidal flow. Differently from conventional equilibrium theory, a density pedestal all around the edge is obtained when the poloidal velocity exceeds the poloidal sound speed. The outboard pedestal is induced by the transonic discontinuity, the inboard one by mass redistribution. The density pedestal follows the formation of a highly sheared flow at the transonic surface. These results may be relevant to the L-H transition and pedestal formation in high performance tokamak plasmas.
Single-fluid stability of stationary plasma equilibria with velocity shear and magnetic shear
Miura, Akira
2009-10-15
By using incompressible single-fluid equations with a generalized Ohm's law neglecting the electron inertia, a linear eigenmode equation for a magnetic field perturbation is derived for stationary equilibria in a slab geometry with velocity and magnetic shears. The general eigenmode equation contains a fourth-order derivative of the perturbation in the highest order and contains Alfven and whistler mode components for a homogeneous plasma. The ratio of the characteristic ion inertia length to the characteristic inhomogeneity scale length is chosen as a small parameter for expansion. Neglecting whistler mode in the lowest order, the eigenmode equation becomes a second-order differential equation similar to the ideal magnetohydrodynamic eigenmode equation except for the fact that the unperturbed perpendicular velocity contains both electric and ion diamagnetic drifts. A sufficient condition for stability against the Kelvin-Helmholtz instability driven by shear in the ion diamagnetic drift velocity is derived and then applied to tokamaks.
Feedback instability in the magnetosphere-ionosphere coupling system: Revisited
Watanabe, T.-H.
2010-02-15
A coupled set of the reduced magnetohydrodynamic and the two-fluid equations is applied to the magnetosphere-ionosphere (M-I) feedback interactions in relation to growth of quite auroral arcs. A theoretical analysis revisiting the linear feedback instability reveals asymptotic behaviors of the dispersion relation and a non-Hermite property in the M-I coupling. A nonlinear simulation of the feedback instability in the M-I coupling system manifests growth of the Kelvin-Helmholtz-like mode in the magnetosphere as the secondary instability. The distorted vortex and field-aligned current profiles propagating as the shear Alfven waves lead to spontaneous deformation of ionospheric density and current structures associated with auroral arcs.
Feedback instability in the magnetosphere-ionosphere coupling system: Revisited
NASA Astrophysics Data System (ADS)
Watanabe, T.-H.
2010-02-01
A coupled set of the reduced magnetohydrodynamic and the two-fluid equations is applied to the magnetosphere-ionosphere (M-I) feedback interactions in relation to growth of quite auroral arcs. A theoretical analysis revisiting the linear feedback instability reveals asymptotic behaviors of the dispersion relation and a non-Hermite property in the M-I coupling. A nonlinear simulation of the feedback instability in the M-I coupling system manifests growth of the Kelvin-Helmholtz-like mode in the magnetosphere as the secondary instability. The distorted vortex and field-aligned current profiles propagating as the shear Alfvén waves lead to spontaneous deformation of ionospheric density and current structures associated with auroral arcs.
Magnetoconvection in sheared magnetic fields
Bian, N. H.; Garcia, O. E.
2008-10-15
The development of magnetoconvection in a sheared magnetic field is investigated. The equilibrium magnetic field B{sub 0} is horizontal and its orientation varies linearly along the vertical axis. Preliminary consideration of the transition from the inertial to the viscous regime of the gravitational resistive interchange instability, reveals that the latter is characterized by the existence of viscoresistive boundary layers of vertical width which scales as Q{sup -1/6}, where Q is the Chandrasekhar number. The situation is analogous to the one encountered in magnetically confined laboratory plasmas, where convective flows are constrained by the magnetic shear to develop in boundary layers located around resonant magnetic surfaces in order to fulfill the 'interchange condition'k{center_dot}B{sub 0}=0, where k is the wave vector of the magnetic perturbation. It follows that when the effect of thermal diffusion is taken into account in the process, convection can only occur above a certain critical value of the Rayleigh number which scales as Q{sup 2/3} for large Q. At the onset, the convection pattern is a superposition of identically thin convective rolls everywhere aligned with the local magnetic field lines and which therefore adopt the magnetic field geometry, a situation also reminiscent of the penumbra of sunspots. Using this degeneracy, equations describing the weakly nonlinear state are obtained and discussed. A reduced magnetohydrodynamic description of magnetoconvection is introduced. Since it is valid for arbitrary magnetic field configurations, it allows a simple extension to the case where there exists an inclination between the direction of gravity and the plane spanned by the equilibrium magnetic field. These reduced magnetohydrodynamic equations are proposed as a powerful tool for further investigations of magnetoconvection in more complex field line geometries.
Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.
Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane
2011-03-11
We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
NASA Technical Reports Server (NTRS)
Basu, Sunanda; Mackenzie, E.; Basu, S.; Coley, W. R.; Sharber, J. R.; Hoegy, W. R.
1990-01-01
Using results of the in situ measurements made by the DE 2 satellite, the nature of plasma structuring at high latitudes, caused by the gradient drift instability process, is described. Using noon-midnight and dawn-dusk orbits of the DE 2 satellite, it was possible to examine the simultaneous density and electric field spectra of convecting large-scale plasma density enhancements in the polar cap known as 'patches', in directions parallel and perpendicular to their antisunward convection. The results provide evidence for the existence of at least two generic classes of instabilities operating in the high-latitude ionosphere: one driven by large-scale density gradients in a homogeneous convection field with respect to the neutrals, and the other driven by the structured convection field itself in an ambient ionosphere where density fluctuations are ubiquitous.
NASA Technical Reports Server (NTRS)
Cain, A. B.; Thompson, M. W.
1986-01-01
The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.
Compressible magnetohydrodynamic sawtooth crash
NASA Astrophysics Data System (ADS)
Sugiyama, Linda E.
2014-02-01
In a toroidal magnetically confined plasma at low resistivity, compressible magnetohydrodynamic (MHD) predicts that an m = 1/n = 1 sawtooth has a fast, explosive crash phase with abrupt onset, rate nearly independent of resistivity, and localized temperature redistribution similar to experimental observations. Large scale numerical simulations show that the 1/1 MHD internal kink grows exponentially at a resistive rate until a critical amplitude, when the plasma motion accelerates rapidly, culminating in fast loss of the temperature and magnetic structure inside q < 1, with somewhat slower density redistribution. Nonlinearly, for small effective growth rate the perpendicular momentum rate of change remains small compared to its individual terms ∇p and J × B until the fast crash, so that the compressible growth rate is determined by higher order terms in a large aspect ratio expansion, as in the linear eigenmode. Reduced MHD fails completely to describe the toroidal mode; no Sweet-Parker-like reconnection layer develops. Important differences result from toroidal mode coupling effects. A set of large aspect ratio compressible MHD equations shows that the large aspect ratio expansion also breaks down in typical tokamaks with rq =1/Ro≃1/10 and a /Ro≃1/3. In the large aspect ratio limit, failure extends down to much smaller inverse aspect ratio, at growth rate scalings γ =O(ɛ2). Higher order aspect ratio terms, including B˜ϕ, become important. Nonlinearly, higher toroidal harmonics develop faster and to a greater degree than for large aspect ratio and help to accelerate the fast crash. The perpendicular momentum property applies to other transverse MHD instabilities, including m ≥ 2 magnetic islands and the plasma edge.
NASA Astrophysics Data System (ADS)
Gallaire, Francois; Zhu, Lailai
2016-11-01
While the deformation regimes under flow of anuclear cells, like red blood cells, have been widely analyzed, the dynamics of nuclear cells are less explored. The objective of this work is to investigate the interplay between the stiff nucleus, modeled here as a rigid spherical particle and the surrounding deformable cell membrane, modeled for simplicity as an immiscible droplet, subjected to an external unbounded plane shear flow. A three-dimensional boundary integral implementation is developed to describe the interface-structure interaction characterized by two dimensionless numbers: the capillary number Ca , defined as the ratio of shear to capillary forces and and the particle-droplet size ratio. For large Ca , i.e. very deformable droplets, the particle has a stable equilibrium position at the center of the droplet. However, for smaller Ca , both the plane symmetry and the time invariance are broken and the particle migrates to a closed orbit located off the symmetry plane, reaching a limit cycle. For even smaller capillary numbers, the time invariance is restored and the particle reaches a steady equilibrium position off the symmetry plane. This series of bifurcations is analyzed and possible physical mechanisms from which they originate are discussed. Financial support by ERC Grant SimCoMiCs 280117 is gratefully acknowledged.
Electron Inertia Effects in Hall-Driven Magnetic Field Penetration in Electron-Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Richardson, Andrew; Angus, Justin; Swanekamp, Stephen; Schumer, Joseph; Ottinger, Paul
2015-11-01
Magnetic field penetration in electron-magnetohydrodynamics (EMHD) can be driven by density gradients through the Hall term. Here we describe the effect of electron inertia on simplified one- and two- dimensional models of a magnetic front. Nonlinear effects due to inertia cause the 1D model to develop peaked solitary waves, while in 2D a shear-driven Kelvin-Helholtz like instability causes the front to break into a series of vortices which propagate into the plasma. The combination of these two effects means that in 2D, Hall driven magnetic field penetration will typically happen in the form of complex vortex-dominated penetration, rather than as a transversely-smooth shock front. This work was supported by the Naval Research Laboratory Base Program.
Bodo, G.; Rossi, P.; Cattaneo, F.; Ferrari, A.; Mignone, A.
2011-10-01
We consider the problem of convergence in homogeneous shearing-box simulations of magneto-rotationally driven turbulence. When there is no mean magnetic flux, if the equations are non-dimensionalized with respect to the diffusive scale, the only free parameter in the problem is the size of the computational domain. The problem of convergence then relates to the asymptotic form of the solutions as the computational box size becomes large. By using a numerical code with a high order of accuracy we show that the solutions become asymptotically independent of domain size. We also show that cases with weak magnetic flux join smoothly to the zero-flux cases as the flux vanishes. These results are consistent with the operation of a subcritical small-scale dynamo driving the turbulence. We conclude that for this type of turbulence the angular momentum transport is proportional to the diffusive flux and therefore has limited relevance in astrophysical situations.
NASA Astrophysics Data System (ADS)
Meng, Guo; Wang, Xian-Qu; Wang, Xiaogang; Zhang, Rui-Bin
2015-09-01
Double fishbone mode excited by energetic particles at q = 1 rational surfaces is studied, with the minimum of the safety factor q min < 1 . The dispersion relation of the mode is derived based on energy principle and the radial displacement structure is calculated by an iterative method self-consistently. It is found that the double fishbone mode has a two-step mode structure similar to that of double kink modes. For q min → 1 , the sharp slope of the ξ r distribution at the rational surfaces is smoothened. The effects of the magnetic shear, the minimum of safety factor, the fast ion beta, and the precession frequency on the plasma displacement and growth rate are also analyzed, respectively.
Experiments in Magnetohydrodynamics
ERIC Educational Resources Information Center
Rayner, J. P.
1970-01-01
Describes three student experiments in magnetohydrodynamics (MHD). In these experiments, it was found that the electrical conductivity of the local water supply was sufficient to demonstrate effectively some of the features of MHD flowmeters, generators, and pumps. (LC)
Magnetohydrodynamic cellular automata
NASA Technical Reports Server (NTRS)
Montgomery, David; Doolen, Gary D.
1987-01-01
A generalization of the hexagonal lattice gas model of Frisch, Hasslacher and Pomeau is shown to lead to two-dimensional magnetohydrodynamics. The method relies on the ideal point-wise conservation law for vector potential.
Magnetohydrodynamic power generation
NASA Technical Reports Server (NTRS)
Smith, J. L.
1984-01-01
Magnetohydrodynamic (MHD) Power Generation is a concise summary of MHD theory, history, and future trends. Results of the major international MHD research projects are discussed. Data from MHD research is included. Economics of initial and operating costs are considered.
Gyroscopic analog for magnetohydrodynamics
Holm, D.D.
1981-01-01
The gross features of plasma equilibrium and dynamics in the ideal magnetohydrodynamics (MHD) model can be understood in terms of a dynamical system which closely resembles the equations for a deformable gyroscope.
Magnetohydrodynamic fluidic system
Lee, Abraham P.; Bachman, Mark G.
2004-08-24
A magnetohydrodynamic fluidic system includes a reagent source containing a reagent fluid and a sample source containing a sample fluid that includes a constituent. A reactor is operatively connected to the supply reagent source and the sample source. MHD pumps utilize a magnetohydrodynamic drive to move the reagent fluid and the sample fluid in a flow such that the reagent fluid and the sample fluid form an interface causing the constituent to be separated from the sample fluid.
NASA Technical Reports Server (NTRS)
Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.
1992-01-01
The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.
Zonal flow dynamics in the double tearing mode with antisymmetric shear flows
Mao, Aohua; Li, Jiquan; Liu, Jinyuan; Kishimoto, Yasuaki
2014-05-15
The generation dynamics and the structural characteristics of zonal flows are investigated in the double tearing mode (DTM) with antisymmetric shear flows. Two kinds of zonal flow oscillations are revealed based on reduced resistive magnetohydrodynamics simulations, which depend on the shear flow amplitudes corresponding to different DTM eigen mode states, elaborated by Mao et al. [Phys. Plasmas 20, 022114 (2013)]. For the weak shear flows below an amplitude threshold, v{sub c}, at which two DTM eigen states with antisymmetric or symmetric magnetic island structure are degenerated, the zonal flows grow oscillatorily in the Rutherford regime during the nonlinear evolution of the DTMs. It is identified that the oscillation mechanism results from the nonlinear interaction between the distorted islands and the zonal flows through the modification of shear flows. However, for the medium shear flows above v{sub c} but below the critical threshold of the Kelvin-Helmholtz instability, an oscillatory growing zonal flow occurs in the linear phase of the DTM evolution. It is demonstrated that the zonal flow oscillation originates from the three-wave mode coupling or a modulation instability pumped by two DTM eigen modes with the same frequency but opposite propagating direction. With the shear flows increasing, the amplitude of zonal flow oscillation increases first and then decreases, whilst the oscillation frequency as twice of the Doppler frequency shift increases. Furthermore, impacts of the oscillatory zonal flows on the nonlinear evolution of DTM islands and the global reconnection are also discussed briefly.
Magnetohydrodynamic effects in liquid metal batteries
NASA Astrophysics Data System (ADS)
Stefani, F.; Galindo, V.; Kasprzyk, C.; Landgraf, S.; Seilmayer, M.; Starace, M.; Weber, N.; Weier, T.
2016-07-01
Liquid metal batteries (LMBs) consist of two liquid metal electrodes and a molten salt ionic conductor sandwiched between them. The density ratios allow for a stable stratification of the three layers. LMBs were already considered as part of energy conversion systems in the 1960s and have recently received renewed interest for economical large-scale energy storage. In this paper, we concentrate on the magnetohydrodynamic aspects of this cell type with special focus on electro-vortex flows and possible effects of the Tayler instability.
Gómez, Daniel O.; DeLuca, Edward E.; Mininni, Pablo D.
2016-02-20
Recent high-resolution Atmospheric Imaging Assembly/Solar Dynamics Observatory images show evidence of the development of the Kelvin–Helmholtz (KH) instability, as coronal mass ejections (CMEs) expand in the ambient corona. A large-scale magnetic field mostly tangential to the interface is inferred, both on the CME and on the background sides. However, the magnetic field component along the shear flow is not strong enough to quench the instability. There is also observational evidence that the ambient corona is in a turbulent regime, and therefore the criteria for the development of the instability are a priori expected to differ from the laminar case. To study the evolution of the KH instability with a turbulent background, we perform three-dimensional simulations of the incompressible magnetohydrodynamic equations. The instability is driven by a velocity profile tangential to the CME–corona interface, which we simulate through a hyperbolic tangent profile. The turbulent background is generated by the application of a stationary stirring force. We compute the instability growth rate for different values of the turbulence intensity, and find that the role of turbulence is to attenuate the growth. The fact that KH instability is observed sets an upper limit on the correlation length of the coronal background turbulence.
Guiding Center Equations for Ideal Magnetohydrodynamic Modes
Roscoe B. White
2013-02-21
Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through δ~B = ∇ X (ξ X B) however perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement ξ are derived which perserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.
Guiding center equations for ideal magnetohydrodynamic modes
White, R. B.
2013-04-15
Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through {delta}B-vector={nabla} Multiplication-Sign ({xi}-vector Multiplication-Sign B-vector), however, perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories, the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement {xi}-vector are derived which preserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.
Shear coaxial injector instability mechanisms
NASA Technical Reports Server (NTRS)
Kaltz, T.; Glogowski, M.; Micci, M. M.
1993-01-01
Although stable operating regimes for cryogenic coaxial injectors have been empirically determined, there is no knowledge of the spray characteristics corresponding to stable operation, or the physical processes which produce the atomization patterns that result in stable or unstable operation. The current engineering method for determining the stable operating regime of a cryogenic coaxial injector is the 'hydrogen temperature ramping' method, however there is no definitive knowledge of whether the hydrogen temperature influences the chamber stability by decreasing the injected gas velocity, by affecting a recirculation region at the base of the LOX Post, or by changing the pressure drop across the injector, allowing chamber pressure oscillations to couple to the fuel feed system. Results for the injector response from a linearized lumped-element model are presented as a function of temperature and frequency. LDV measurements in the recess region at the base of the LOX post show reverse flow indicative of a recirculation region. Finally, Phase Doppler Particle Analyzer (PDPA) measurements of droplet size and velocity distributions are discussed for a coaxial injector element similar to the SSME preburner element operating with water and air at atmospheric pressure and liquid and gaseous nitrogen at 20 bars.
On the nature of magnetic turbulence in rotating, shearing flows
NASA Astrophysics Data System (ADS)
Walker, Justin; Lesur, Geoffroy; Boldyrev, Stanislav
2016-03-01
The local properties of turbulence driven by the magnetorotational instability (MRI) in rotating, shearing flows are studied in the framework of a shearing-box model. Based on numerical simulations, we propose that the MRI-driven turbulence comprises two components: the large-scale shear-aligned strong magnetic field and the small-scale fluctuations resembling magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale component is close to k-2, whereas the spectrum of the small-scale component agrees with the spectrum of strong MHD turbulence k-3/2. While the spectrum of the fluctuations is universal, the outer-scale characteristics of the turbulence are not; they depend on the parameters of the system, such as the net magnetic flux. However, there is remarkable universality among the allowed turbulent states - their intensity v0 and their outer scale λ0 satisfy the balance condition v0/λ0 ˜ dΩ/dln r, where dΩ/dln r is the local orbital shearing rate of the flow. Finally, we find no sustained dynamo action in the Pm = 1 zero net-flux case for Reynolds numbers as high as 45 000, casting doubts on the existence of an MRI dynamo in the Pm ≤ 1 regime.
The role of the magnetorotational instability in the sun
Kagan, Daniel; Wheeler, J. Craig E-mail: wheel@astro.as.utexas.edu
2014-05-20
We calculate growth rates for nonaxisymmetric instabilities including the magnetorotational instability (MRI) throughout the Sun. We first derive a dispersion relation for nonaxisymmetric instability including the effects of shear, convective buoyancy, and three diffusivities (thermal conductivity, resistivity, and viscosity). We then use a solar model evolved with the stellar evolution code MESA and angular velocity profiles determined by Global Oscillations Network Group helioseismology to determine the unstable modes present at each location in the Sun and the associated growth rates. The overall instability has unstable modes throughout the convection zone and also slightly below it at middle and high latitudes. It contains three classes of modes: large-scale hydrodynamic convective modes, large-scale hydrodynamic shear modes, and small-scale magnetohydrodynamic shear modes, which may be properly called MRI modes. While large-scale convective modes are the most rapidly growing modes in most of the convective zone, MRI modes are important in both stably stratified and convectively unstable locations near the tachocline at colatitudes θ < 53°. Nonaxisymmetric MRI modes grow faster than the corresponding axisymmetric modes; for some poloidal magnetic fields, the nonaxisymmetric MRI growth rates are similar to the angular rotation frequency Ω, while axisymmetric modes are stabilized. We briefly discuss the saturation of the field produced by MRI modes, finding that the implied field at the base of the convective zone in the Sun is comparable to that derived based on dynamos active in the tachocline and that the saturation of field resulting from the MRI may be of importance even in the upper convection zone.
Waves and instabilities in plasmas
Chen, L.
1987-01-01
The contents of this book are: Plasma as a Dielectric Medium; Nyquist Technique; Absolute and Convective Instabilities; Landau Damping and Phase Mixing; Particle Trapping and Breakdown of Linear Theory; Solution of Viasov Equation via Guilding-Center Transformation; Kinetic Theory of Magnetohydrodynamic Waves; Geometric Optics; Wave-Kinetic Equation; Cutoff and Resonance; Resonant Absorption; Mode Conversion; Gyrokinetic Equation; Drift Waves; Quasi-Linear Theory; Ponderomotive Force; Parametric Instabilities; Problem Sets for Homework, Midterm and Final Examinations.
Thermoacoustic magnetohydrodynamic electrical generator
Wheatley, John C.; Swift, Gregory W.; Migliori, Albert
1986-01-01
A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1,000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.
Thermoacoustic magnetohydrodynamic electrical generator
Wheatley, J.C.; Swift, G.W.; Migliori, A.
1984-11-16
A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.
AC magnetohydrodynamic microfluidic switch
Lemoff, A V; Lee, A P
2000-03-02
A microfluidic switch has been demonstrated using an AC Magnetohydrodynamic (MHD) pumping mechanism in which the Lorentz force is used to pump an electrolytic solution. By integrating two AC MHD pumps into different arms of a Y-shaped fluidic circuit, flow can be switched between the two arms. This type of switch can be used to produce complex fluidic routing, which may have multiple applications in {micro}TAS.
Interactions between magnetohydrodynamical discontinuities
Dai, W.; Woodward, P.R. )
1994-11-01
Interactions between magnetohydrodynamical (MHD) discontinuities are studied through numerical simulations for the set of one-dimensional MHD equations. The interactions include the impact of a shock on a contact discontinuity, the collision of two shocks, and the catchup of a shock over another shock. The shocks involved in the interactions may be very strong. Each shock in an interaction may be either a fast or a slow shock.
Joiner, N.; Hirose, A.
2008-08-15
The kinetic ballooning mode (KBM) has been shown in previous work to be unstable within the magnetohydrodynamic (MHD) region (in s-{alpha} space) of second stability [Hirose et al., Phys. Rev. Lett. 72, 3993 (2004)]. In this work we verify this result using the gyrokinetic code GS2 [Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1996)] treating both ions and electrons as kinetic species and retaining the magnetosonic perturbation B{sub parallel}. Growth rates calculated using GS2 differ significantly from the previous differential/shooting code analysis. Calculations without B{sub parallel} find the stability region is preserved, while the addition of B{sub parallel} causes the mode to be more unstable than previously calculated within the region of MHD second stability. The inclusion of parallel ion current and B{sub parallel} into the shooting code does not account for the GS2 results. The evidence presented in this paper leads us to the conclusion that the adiabatic electron approximation employed in previous studies is found to be unsuitable for this type of instability. Based on the findings of this work, the KBM becomes an interesting instability in the context of internal transport barriers, where {alpha} is often large and magnetic shear is small (positive or negative)
Future of Magnetohydrodynamic Ship Propulsion,
1983-08-16
83 FOREIGN TECHNOLOGY DIVISION FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION by A.P. Baranov DTIQ ~E tJ Approved for public release; 0.. distribution...MAGNETOHYDRODYNAMIC SHIP PROPULSION By: A.P. Baranov -,English pages: 10 Source: Sudostroyeniye, Nr. 12, December 1966, pp. 3-6 . Country of origin: USSR X...equations, etc. merged into this translation were extracted from the best quality copy available. FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION A. P
Numerical simulations of magnetic Kelvin-Helmholtz instability at a twisted solar flux tube
NASA Astrophysics Data System (ADS)
Murawski, K.; Chmielewski, P.; Zaqarashvili, T. V.; Khomenko, E.
2016-07-01
The paper aims to study the response of a solar small-scale and weak magnetic flux tube to photospheric twisting motions. We numerically solve three-dimensional ideal magnetohydrodynamic equations to describe the evolution of the perturbation within the initially static flux tube, excited by twists in the azimuthal component of the velocity. These twists produce rotation of the magnetic field lines. Perturbation of magnetic field lines propagates upwardly, driving vertical and azimuthal flow as well as plasma compressions and rarefactions in the form of eddies. We conclude that these eddies result from the sheared azimuthal flow which seeds Kelvin-Helmholtz instability (KHI) between the flux tube and the ambient medium. Numerically obtained properties of the KHI confirm the analytical predictions for the occurrence of the instability.
Material Instabilities in Particulate Systems
NASA Technical Reports Server (NTRS)
Goddard, J. D.
1999-01-01
Following is a brief summary of a theoretical investigation of material (or constitutive) instability associated with shear induced particle migration in dense particulate suspensions or granular media. It is shown that one can obtain a fairly general linear-stability analysis, including the effects of shear-induced anisotropy in the base flow as well as Reynolds dilatancy. A criterion is presented here for simple shearing instability in the absence of inertia and dilatancy.
Linear growth of the Kelvin-Helmholtz instability with an adiabatic cosmic-ray gas
Suzuki, Akihiro; Takahashi, Hiroyuki R.; Kudoh, Takahiro
2014-06-01
We investigate effects of cosmic rays on the linear growth of the Kelvin-Helmholtz instability. Cosmic rays are treated as an adiabatic gas and allowed to diffuse along magnetic field lines. We calculated the dispersion relation of the instability for various sets of two free parameters, the ratio of the cosmic-ray pressure to the thermal gas pressure, and the diffusion coefficient. Including cosmic-ray effects, a shear layer is more destabilized and the growth rates can be enhanced in comparison with the ideal magnetohydrodynamical case. Whether the growth rate is effectively enhanced or not depends on the diffusion coefficient of cosmic rays. We obtain the criterion for effective enhancement by comparing the growing timescale of the instability with the diffusion timescale of cosmic rays. These results can be applied to various astrophysical phenomena where a velocity shear is present, such as outflows from star-forming galaxies, active galactic nucleus jet, channel flows resulting from the nonlinear development of the magnetorotational instability, and galactic disks.
Shearing box simulations in the Rayleigh unstable regime
NASA Astrophysics Data System (ADS)
Nauman, Farrukh; Blackman, Eric G.
2017-01-01
We study the stability properties of Rayleigh unstable flows both in the purely hydrodynamic and magnetohydrodynamic (MHD) regimes for two different values of the shear q = 2.1, 4.2 (q = -dln Ω/dln r) and compare it with the Keplerian case q = 1.5. We find that the q > 2 regime is unstable both in the hydrodynamic and in the MHD limit (with an initially weak magnetic field). In this regime, the velocity fluctuations dominate the magnetic fluctuations. In contrast, in the q < 2 (magnetorotational instability (MRI)) regime the magnetic fluctuations dominate. This highlights two different paths to MHD turbulence implied by the two regimes, suggesting that in the q > 2 regime the instability produces primarily velocity fluctuations that cause magnetic fluctuations, with the causality reversed for the q < 2 MRI unstable regime. We also find that the magnetic field correlation is increasingly localized as the shear is increased in the Rayleigh unstable regime. In calculating the time evolution of spatial averages of different terms in the MHD equations, we find that the q > 2 regime is dominated by terms which are nonlinear in the fluctuations, whereas for q < 2, the linear terms play a more significant role.
Magnetohydrodynamic simulations of global accretion disks with vertical magnetic fields
Suzuki, Takeru K.; Inutsuka, Shu-ichiro
2014-04-01
We report results of three-dimensional magnetohydrodynamical (MHD) simulations of global accretion disks threaded with weak vertical magnetic fields. We perform the simulations in the spherical coordinates with different temperature profiles and accordingly different rotation profiles. In the cases with a spatially constant temperature, because the rotation frequency is vertically constant in the equilibrium condition, general properties of the turbulence excited by magnetorotational instability are quantitatively similar to those obtained in local shearing box simulations. On the other hand, in the cases with a radially variable temperature profile, the vertical differential rotation, which is inevitable in the equilibrium condition, winds up the magnetic field lines in addition to the usual radial differential rotation. As a result, the coherent wound magnetic fields contribute to the Maxwell stress in the surface regions. We obtain nondimensional density and velocity fluctuations ∼0.1-0.2 at the midplane. The azimuthal power spectra of the magnetic fields show shallower slopes, ∼m {sup 0} – m {sup –1}, than those of velocity and density. The Poynting flux associated with the MHD turbulence drives intermittent and structured disk winds as well as sound-like waves toward the midplane. The mass accretion mainly occurs near the surfaces, and the gas near the midplane slowly moves outward in the time domain of the present simulations. The vertical magnetic fields are also dragged inward in the surface regions, while they stochastically move outward and inward around the midplane. We also discuss an observational implication of induced spiral structure in the simulated turbulent disks.
Two-dimensional Magnetohydrodynamic Simulations of Barred Galaxies
NASA Astrophysics Data System (ADS)
Kim, Woong-Tae; Stone, James M.
2012-06-01
Barred galaxies are known to possess magnetic fields that may affect the properties of bar substructures such as dust lanes and nuclear rings. We use two-dimensional high-resolution magnetohydrodynamic (MHD) simulations to investigate the effects of magnetic fields on the formation and evolution of such substructures, as well as on the mass inflow rates to the galaxy center. The gaseous medium is assumed to be infinitesimally thin, isothermal, non-self-gravitating, and threaded by initially uniform, azimuthal magnetic fields. We find that there exists an outermost x 1-orbit relative to which gaseous responses to an imposed stellar bar potential are completely different between inside and outside. Inside this orbit, gas is shocked into dust lanes and infalls to form a nuclear ring. Magnetic fields are compressed in dust lanes, reducing their peak density. Magnetic stress removes further angular momentum of the gas at the shocks, temporarily causing the dust lanes to bend into an "L" shape and eventually leading to a smaller and more centrally distributed ring than in unmagnetized models. The mass inflow rates in magnetized models correspondingly become larger, by more than two orders of magnitude when the initial fields have an equipartition value with thermal energy, than in the unmagnetized counterparts. Outside the outermost x 1-orbit, on the other hand, an MHD dynamo due to the combined action of the bar potential and background shear operates near the corotation and bar-end regions, efficiently amplifying magnetic fields. The amplified fields shape into trailing magnetic arms with strong fields and low density. The base of the magnetic arms has a thin layer in which magnetic fields with opposite polarity reconnect via a tearing-mode instability. This produces numerous magnetic islands with large density that propagate along the arms to turn the outer disk into a highly chaotic state.
Magnetohydrodynamics of fractal media
Tarasov, Vasily E.
2006-05-15
The fractal distribution of charged particles is considered. An example of this distribution is the charged particles that are distributed over the fractal. The fractional integrals are used to describe fractal distribution. These integrals are considered as approximations of integrals on fractals. Typical turbulent media could be of a fractal structure and the corresponding equations should be changed to include the fractal features of the media. The magnetohydrodynamics equations for fractal media are derived from the fractional generalization of integral Maxwell equations and integral hydrodynamics (balance) equations. Possible equilibrium states for these equations are considered.
Accurate, meshless methods for magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.; Raives, Matthias J.
2016-01-01
Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.
Electron magnetohydrodynamics: Dynamics and turbulence
NASA Astrophysics Data System (ADS)
Lyutikov, Maxim
2013-11-01
We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector k1=k2 do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade ∝k-2. The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.
Ideal magnetohydrodynamic interchanges in low density plasmas
Huang Yimin; Goel, Deepak; Hassam, A.B.
2005-03-01
The ideal magnetohydrodynamic equations are usually derived under the assumption V{sub A}<
Ideal magnetohydrodynamic stability of the spheromak configuration
Jardin, S.C.
1982-01-19
Results are presented of a parametric study of the ideal magnetohydrodynamic stability properties of the spheromak, or compact torus, configuration. In the absence of a nearby conducting wall, the spheromak is always unstable to at least one current driven mode. With a conducting wall at the surface, the spheromak can be unstable to current driven modes if the current is too peaked, i.e., q/sub o/(R/a) less than or equal to 2/3, or if the shear is too low at the origin. The Mercier criterion sets an upper limit on the pressure gradient everywhere, but configurations that are everywhere Mercier stable can be unstable to pressure driven low-n modes. Stable toroidal configurations exist with a spherical wall separated by half a minor radius, and with ..beta../sub theta/ = 30%.
Castillo-Tejas, Jorge; Alvarado, Juan F J; González-Alatorre, Guillermo; Luna-Bárcenas, Gabriel; Sanchez, Isaac C; Macias-Salinas, Ricardo; Manero, Octavio
2005-08-01
Nonequilibrium molecular-dynamics simulations are performed for linear and branched chain molecules to study their rheological and structural properties under simple shear and Poiseuille flows. Molecules are described by a spring-monomer model with a given intermolecular potential. The equations of motion are solved for shear and Poiseuille flows with Lees and Edward's [A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972)] periodic boundary conditions. A multiple time-scale algorithm extended to nonequilibrium situations is used as the integration method, and the simulations are performed at constant temperature using Nose-Hoover [S. Nose, J. Chem. Phys. 81, 511 (1984)] dynamics. In simple shear, molecules with flow-induced ellipsoidal shape, having significant segment concentrations along the gradient and neutral directions, exhibit substantial flow resistance. Linear molecules have larger zero-shear-rate viscosity than that of branched molecules, however, this behavior reverses as the shear rate is increased. The relaxation time of the molecules is associated with segment concentrations directed along the gradient and neutral directions, and hence it depends on structure and molecular weight. The results of this study are in qualitative agreement with other simulation studies and with experimental data. The pressure (Poiseuille) flow is induced by an external force F(e) simulated by confining the molecules in the region between surfaces which have attractive forces. Conditions at the boundary strongly influence the type of the slip flow predicted. A parabolic velocity profile with apparent slip on the wall is predicted under weakly attractive wall conditions, independent of molecular structure. In the case of strongly attractive walls, a layer of adhered molecules to the wall produces an abrupt distortion of the velocity profile which leads to slip between fluid layers with magnitude that depends on the molecular structure. Finally, the molecular deformation
The plasmoid instability during asymmetric inflow magnetic reconnection
Murphy, Nicholas A.; Young, Aleida K.; Shen, Chengcai; Lin, Jun; Ni, Lei
2013-06-15
Theoretical studies of the plasmoid instability generally assume that the reconnecting magnetic fields are symmetric. We relax this assumption by performing two-dimensional resistive magnetohydrodynamic simulations of the plasmoid instability during asymmetric inflow magnetic reconnection. Magnetic asymmetry modifies the onset, scaling, and dynamics of this instability. Magnetic islands develop preferentially into the weak magnetic field upstream region. Outflow jets from individual X-points impact plasmoids obliquely rather than directly as in the symmetric case. Consequently, deposition of momentum by the outflow jets into the plasmoids is less efficient, the plasmoids develop net vorticity, and shear flow slows down secondary merging between islands. Secondary merging events have asymmetry along both the inflow and outflow directions. Downstream plasma is more turbulent in cases with magnetic asymmetry because islands are able to roll around each other after exiting the current sheet. As in the symmetric case, plasmoid formation facilitates faster reconnection for at least small and moderate magnetic asymmetries. However, when the upstream magnetic field strengths differ by a factor of 4, the reconnection rate plateaus at a lower value than expected from scaling the symmetric results. We perform a parameter study to investigate the onset of the plasmoid instability as a function of magnetic asymmetry and domain size. There exist domain sizes for which symmetric simulations are stable but asymmetric simulations are unstable, suggesting that moderate magnetic asymmetry is somewhat destabilizing. We discuss the implications for plasmoid and flux rope formation in solar eruptions, laboratory reconnection experiments, and space plasmas. The differences between symmetric and asymmetric simulations provide some hints regarding the nature of the three-dimensional plasmoid instability.
Conservation of circulation in magnetohydrodynamics
Bekenstein; Oron
2000-10-01
We demonstrate at both the Newtonian and (general) relativistic levels the existence of a generalization of Kelvin's circulation theorem (for pure fluids) that is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
Magnetohydrodynamic Augmented Propulsion Experiment
NASA Technical Reports Server (NTRS)
Litchford, Ron J.; Cole, John; Lineberry, John; Chapman, Jim; Schmidt, Harold; Cook, Stephen (Technical Monitor)
2002-01-01
A fundamental obstacle to routine space access is the specific energy limitations associated with chemical fuels. In the case of vertical take-off, the high thrust needed for vertical liftoff and acceleration to orbit translates into power levels in the 10 GW range. Furthermore, useful payload mass fractions are possible only if the exhaust particle energy (i.e., exhaust velocity) is much greater than that available with traditional chemical propulsion. The electronic binding energy released by the best chemical reactions (e.g., LOX/LH2 for example, is less than 2 eV per product molecule (approx. 1.8 eV per H2O molecule), which translates into particle velocities less than 5 km/s. Useful payload fractions, however, will require exhaust velocities exceeding 15 km/s (i.e., particle energies greater than 20 eV). As an added challenge, the envisioned hypothetical RLV (reusable launch vehicle) should accomplish these amazing performance feats while providing relatively low acceleration levels to orbit (2-3g maximum). From such fundamental considerations, it is painfully obvious that planned and current RLV solutions based on chemical fuels alone represent only a temporary solution and can only result in minor gains, at best. What is truly needed is a revolutionary approach that will dramatically reduce the amount of fuel and size of the launch vehicle. This implies the need for new compact high-power energy sources as well as advanced accelerator technologies for increasing engine exhaust velocity. Electromagnetic acceleration techniques are of immense interest since they can be used to circumvent the thermal limits associated with conventional propulsion systems. This paper describes the Magnetohydrodynamic Augmented Propulsion Experiment (MAPX) being undertaken at NASA Marshall Space Flight Center (MSFC). In this experiment, a 1-MW arc heater is being used as a feeder for a 1-MW magnetohydrodynamic (MHD) accelerator. The purpose of the experiment is to demonstrate
NASA Technical Reports Server (NTRS)
Bechert, D. W.
1982-01-01
The generation of instability waves in free shear layers is investigated. The model assumes an infinitesimally thin shear layer shed from a semi-infinite plate which is exposed to sound excitation. The acoustical shear layer excitation by a source further away from the plate edge in the downstream direction is very weak while upstream from the plate edge the excitation is relatively efficient. A special solution is given for the source at the plate edge. The theory is then extended to two streams on both sides of the shear layer having different velocities and densities. Furthermore, the excitation of a shear layer in a channel is calculated. A reference quantity is found for the magnitude of the excited instability waves. For a comparison with measurements, numerical computations of the velocity field outside the shear layer were carried out.
Belyaev, Mikhail A.; Rafikov, Roman R.; Stone, James M.
2013-06-10
We perform global unstratified three-dimensional magnetohydrodynamic simulations of an astrophysical boundary layer (BL)-an interface region between an accretion disk and a weakly magnetized accreting object such as a white dwarf-with the goal of understanding the effects of magnetic field on the BL. We use cylindrical coordinates with an isothermal equation of state and investigate a number of initial field geometries including toroidal, vertical, and vertical with zero net flux. Our initial setup consists of a Keplerian disk attached to a non-rotating star. In a previous work, we found that in hydrodynamical simulations, sound waves excited by shear in the BL were able to efficiently transport angular momentum and drive mass accretion onto the star. Here we confirm that in MHD simulations, waves serve as an efficient means of angular momentum transport in the vicinity of the BL, despite the magnetorotational instability (MRI) operating in the disk. In particular, the angular momentum current due to waves is at times larger than the angular momentum current due to MRI. Our results suggest that angular momentum transport in the BL and its vicinity is a global phenomenon occurring through dissipation of waves and shocks. This point of view is quite different from the standard picture of transport by a local anomalous turbulent viscosity. In addition to angular momentum transport, we also study magnetic field amplification within the BL. We find that the field is indeed amplified in the BL, but only by a factor of a few, and remains subthermal.
Suzuki, Kentaro; Ogawa, Takayuki; Matsumoto, Yosuke; Matsumoto, Ryoji E-mail: ogawa@astro.s.chiba-u.ac.jp E-mail: matumoto@astro.s.chiba-u.ac.jp
2013-05-10
We carried out three-dimensional magnetohydrodynamic simulations to study the effects of plasma viscosity on the formation of sharp discontinuities of density and temperature distributions, cold fronts, in clusters of galaxies. By fixing the gravitational potential that confines the cool, dense plasma in a moving subcluster, we simulated its interaction with the hot, lower density plasma around the subcluster. At the initial state, the intracluster medium (ICM) is assumed to be threaded by uniform magnetic fields. The enhancement of plasma viscosity along the direction of magnetic fields is incorporated as anisotropic viscosity depending on the direction of magnetic fields. We found that the Kelvin-Helmholtz instability at the surface of the subcluster grows even in models with anisotropic viscosity, because its effects on the velocity shear across the magnetic field lines are suppressed. We also found that magnetic fields around the interface between the subcluster and ICM are amplified even in the presence of viscosity, while magnetic fields behind the subcluster are amplified up to {beta}{sup -1} {approx} 0.01 in models with viscosity, whereas they are amplified up to {beta}{sup -1} {approx} 0.1 in models without viscosity, where {beta} is the ratio of gas pressure to magnetic pressure.
Multi-symplectic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.; McKenzie, J. F.; Zank, G. P.; Zank
2014-10-01
A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on the Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by constraints using Lagrange multipliers that ensure mass conservation, entropy advection with the flow, the Lin constraint, and Faraday's equation (i.e. the magnetic flux is Lie dragged with the flow). The analysis is also carried out using the magnetic vector potential Ã where α=Ã. d x is Lie dragged with the flow, and B=∇×Ã. The multi-symplectic conservation laws give rise to the Eulerian momentum and energy conservation laws. The symplecticity or structural conservation laws for the multi-symplectic system corresponds to the conservation of phase space. It corresponds to taking derivatives of the momentum and energy conservation laws and combining them to produce n(n-1)/2 extra conservation laws, where n is the number of independent variables. Noether's theorem for the multi-symplectic MHD system is derived, including the case of non-Cartesian space coordinates, where the metric plays a role in the equations.
Filamentary magnetohydrodynamic plasmas
Kinney, R.; Tajima, T.; Petviashvili, N.; McWilliams, J.C.
1993-05-01
A filamentary construct of magnetohydrodynamical plasma dynamics, based on the Elsasser variables was developed. This approach is modeled after discrete vortex models of hydrodynamical turbulence, which cannot be expected in general to produce results identical to ones based on a Fourier decomposition of the fields. In a highly intermittent plasma, the induction force is small compared to the convective motion, and when this force is neglected. the plasma vortex system is described by a Hamiltonian. For a system with many such vortices we present a statistical treatment of a collection of discrete current-vorticity concentrations. Canonical and microcanonical statistical calculations show that both the vorticity and the current spectra are peaked at long wavelengths, and the expected states revert to known hydrodynamical states as the magnetic field vanishes. These results differ from previous Fourier-based statistical theories. but it is found that when the filament calculation is expanded to include the inductive force, the results approach the Fourier equilibria in the low-temperature limit, and the previous Hamiltonian plasma vortex results in the high-temperature limit. Numerical simulations of a large number of filaments are carried out and support the theory. A three-dimensional vortex model is outlined as well, which is also Hamiltonian when the inductive force is neglected.
Magnetohydrodynamics in Materials Processing
NASA Astrophysics Data System (ADS)
Davidson, P. A.
1999-01-01
Magnetic fields can be used to melt, pump, stir, and stabilize liquid metals. This provides a nonintrusive means of controlling the flow of metal in commercial casting and refining operations. The quest for greater efficiency and more control in the production of steel, aluminum, and high-performance superalloys has led to a revolution in the application of magnetohydrodynamics (MHD) to process metallurgy. Three typical applications are described here, chosen partially on the basis of their general interest to fluid dynamicists, and partially because of their considerable industrial importance. We look first at magnetic stirring, where a rotating magnetic field is used to agitate and homogenize the liquid zone of a partially-solidified ingot. This is a study in Ekman pumping. Next, we consider magnetic damping, where an intense, static magnetic field is used to suppress fluid motion. In particular, we look at the damping of jets, vortices, and turbulence. We conclude with a discussion of the magnetic destabilization of liquid-liquid interfaces. This is of particular importance in aluminum production.
Modeling eruptive coronal magnetohydrodynamic systems with FLUX
NASA Astrophysics Data System (ADS)
Rachmeler, L. A.
In this dissertation I explore solar coronal energetic eruptions in the context of magnetic reconnection, which is commonly thought to be a required trigger mechanism for solar eruptions. Reconnection is difficult to directly observe in the corona, and current numerical methods cannot model reconnectionless control cases. Thus, it is not possible to determine if reconnection is a necessary component of these eruptions. I have executed multiple controlled simulations to determine the importance of reconnection for initiation and evolution of several eruptive systems using FLUX, a numerical model that uses the comparatively new fluxon technique. I describe two types of eruptions modeled with FLUX: a metastable confined flux rope theory for coronal mass ejection (CME) initiation, and symmetrically twisted coronal jets in a uniform vertical background field. In the former, I identified an ideal magnetohydrodynamic (MHD) instability that allows metastable twisted flux rope systems to suddenly lose stability and erupt even in the absence of reconnection, contradicting previous conjecture. The CME result is in contrast to the azimuthally symmetric coronal jet initiation model, where jet-like behavior does not manifest without reconnection. My work has demonstrated that some of the observed eruptive phenomena may be triggered by non-reconnective means such as ideal MHD instabilities, and that magnetic reconnection is not a required element in all coronal eruptions.
Jain, Neeraj; Büchner, Jörg
2014-06-15
In collisionless magnetic reconnection, electron current sheets (ECS) with thickness of the order of an electron inertial length form embedded inside ion current sheets with thickness of the order of an ion inertial length. These ECS's are susceptible to a variety of instabilities which have the potential to affect the reconnection rate and/or the structure of reconnection. We carry out a three dimensional linear eigen mode stability analysis of electron shear flow driven instabilities of an electron scale current sheet using an electron-magnetohydrodynamic plasma model. The linear growth rate of the fastest unstable mode was found to drop with the thickness of the ECS. We show how the nature of the instability depends on the thickness of the ECS. As long as the half-thickness of the ECS is close to the electron inertial length, the fastest instability is that of a translational symmetric two-dimensional (no variations along flow direction) tearing mode. For an ECS half thickness sufficiently larger or smaller than the electron inertial length, the fastest mode is not a tearing mode any more and may have finite variations along the flow direction. Therefore, the generation of plasmoids in a nonlinear evolution of ECS is likely only when the half-thickness is close to an electron inertial length.
Microphysics of Cosmic Ray Driven Plasma Instabilities
NASA Astrophysics Data System (ADS)
Bykov, A. M.; Brandenburg, A.; Malkov, M. A.; Osipov, S. M.
2013-10-01
Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.
Microphysics of Cosmic Ray Driven Plasma Instabilities
NASA Astrophysics Data System (ADS)
Bykov, A. M.; Brandenburg, A.; Malkov, M. A.; Osipov, S. M.
Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.
Solar Flares: Magnetohydrodynamic Processes
NASA Astrophysics Data System (ADS)
Shibata, Kazunari; Magara, Tetsuya
2011-12-01
This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD) processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 1032 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence), local enhancement of electric current in the corona (formation of a current sheet), and rapid dissipation of electric current (magnetic reconnection) that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely), while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.
Identification of Mercier instabilities in Alcator C-Mod tokamak
In, Y.; Ramos, J. J.; Hastie, R. J.; Catto, P. J.; Hubbard, A. E.; Hutchinson, I. H.; Marmar, E.; Porkolab, M.; Snipes, J.; Wolfe, S.
2000-12-01
During current ramp-up discharges, highly localized magnetohydrodynamic (MHD) fluctuations were observed on the electron cyclotron emission diagnostics of Alcator C-Mod tokamak [I. H. Hutchinson , Phys. Plasmas 1, 1511 (1994)]. The electron temperature profile was hollow, while the density profile was weakly decreasing. Assuming that the equilibration time was short enough to quickly thermalize ions the pressure profile was also found to be hollow. Using this pressure profile as an additional constraint to the EFIT program, an equilibrium with reversed shear was constructed having a q(0)>>1. The localized MHD activity was observed near the inner q=5 rational surface in this reconstructed equilibrium, where the Mercier criterion for ideal MHD stability was violated because of the reversed pressure gradient (dp/dr>0), q>1 and moderate shear. When kinetic effects were added, the ideal Mercier mode was finite ion Larmor radius stabilized. However, ion Landau damping was found to be strong enough to drive a kinetic Mercier instability.
Structures in magnetohydrodynamic turbulence: Detection and scaling
NASA Astrophysics Data System (ADS)
Uritsky, V. M.; Pouquet, A.; Rosenberg, D.; Mininni, P. D.; Donovan, E. F.
2010-11-01
We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 15363 points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, the so-called Orszag-Tang vortex, or an Arn’old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic-field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with magnetohydrodynamics. We suggest that this range can be governed by turbulence dynamics as opposed to criticality and propose an interpretation of intermittency in terms of propagation of local instabilities.
[Nonlinear magnetohydrodynamics]. Final report
Montgomery, D.C.
1998-11-01
This is a final report on the research activities carried out under the above grant at Dartmouth. During the period considered, the grant was identified as being for nonlinear magnetohydrodynamics, considered as the most tractable theoretical framework in which the plasma problems associated with magnetic confinement of fusion plasmas could be studied. During the first part of the grant`s lifetime, the author was associated with Los Alamos National Laboratory as a consultant and the work was motivated by the reversed-field pinch. Later, when that program was killed at Los Alamos, the problems became ones that could be motivated by their relation to tokamaks. Throughout the work, the interest was always on questions that were as fundamental as possible, compatible with those motivations. The intent was always to contribute to plasma physics as a science, as well as to the understanding of mission-oriented confined fusion plasmas. Twelve Ph.D. theses were supervised during this period and a comparable number of postdoctoral research associates were temporarily supported. Many of these have gone on to distinguished careers, though few have done so in the context of the controlled fusion program. Their work was a combination of theory and numerical computation, in gradually less and less idealized settings, moving from rectangular periodic boundary conditions in two dimensions, through periodic straight cylinders and eventually, before the grant was withdrawn, to toroids, with a gradually more prominent role for electrical and mechanical boundary conditions. The author never had access to a situation where he could initiate experiments and relate directly to the laboratory data he wanted. Computers were the laboratory. Most of the work was reported in referred publications in the open literature, copies of which were transmitted one by one to DOE at the time they appeared. The Appendix to this report is a bibliography of published work which was carried out under the
High conductivity magnetic tearing instability. [of neutral plasma sheets
NASA Technical Reports Server (NTRS)
Cross, M. A.; Van Hoven, G.
1976-01-01
Linearized equations of magnetohydrodynamics are used to investigate the tearing mode, for arbitrary values of the conductivity, through a consideration of the additional effect of the electron-inertia contribution to Ohm's law. A description is provided of the equilibrium and subsequent instability in the magnetohydrodynamic approximation. A method for solving the perturbation equations in the linear approximation is discussed and attention is given to the results in the high conductivity limit.
The parametric decay of Alfven waves into shear Alfven waves and dust lower hybrid waves
Jamil, M.; Shah, H. A.; Zubia, K.; Zeba, I.; Uzma, Ch.; Salimullah, M.
2010-07-15
The parametric decay instability of Alfven wave into low-frequency electrostatic dust-lower-hybrid and electromagnetic shear Alfven waves has been investigated in detail in a dusty plasma in the presence of external/ambient uniform magnetic field. Magnetohydrodynamic fluid equations of plasmas have been employed to find the linear and nonlinear response of the plasma particles for this three-wave nonlinear coupling in a dusty magnetoplasma. Here, relatively high frequency electromagnetic Alfven wave has been taken as the pump wave. It couples with other two low-frequency internal possible modes of the dusty magnetoplasma, viz., the dust-lower-hybrid and shear Alfven waves. The nonlinear dispersion relation of the dust-lower-hybrid wave has been solved to obtain the growth rate of the parametric decay instability. The growth rate is maximum for small value of external magnetic field B{sub s}. It is noticed that the growth rate is proportional to the unperturbed electron number density n{sub oe}.
Stability of negative central magnetic shear discharges in the DIII-D tokamak
Strait, E.J.; Chu, M.S.; Ferron, J.R.
1996-12-01
Discharges with negative central magnetic shear (NCS) hold the promise of enhanced fusion performance in advanced tokamaks. However, stability to long wavelength magnetohydrodynamic modes is needed to take advantage of the improved confinement found in NCS discharges. The stability limits seen in DIII-D experiments depend on the pressure and current density profiles and are in good agreement with stability calculations. Discharges with a strongly peaked pressure profile reach a disruptive limit at low beta, {beta}{sub N} = {beta} (I/aB){sup -1} {le} 2.5 (% m T/MA), caused by an n = 1 ideal internal kink mode or a global resistive instability close to the ideal stability limit. Discharges with a broad pressure profile reach a soft beta limit at significantly higher beta, {beta}{sub N} = 4 to 5, usually caused by instabilities with n > 1 and usually driven near the edge of the plasma. With broad pressure profiles, the experimental stability limit is independent of the magnitude of negative shear but improves with the internal inductance, corresponding to lower current density near the edge of the plasma. Understanding of the stability limits in NCS discharges has led to record DIII-D fusion performance in discharges with a broad pressure profile and low edge current density.
Action Principle for Relativistic Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
D'Avignon, Eric; Morrison, Philip; Pegoraro, Francesco
2015-11-01
A covariant action principle for ideal relativistic magnetohydrodynamics in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al., which uses a noncanonical bracket to implement constrained variations of an action functional. Various implications and extensions of this action principle are also discussed.
Energy decay laws in strongly anisotropic magnetohydrodynamic turbulence.
Bigot, Barbara; Galtier, Sébastien; Politano, Hélène
2008-02-22
We investigate the influence of a uniform magnetic field B(0)=B(0)e( parallel) on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along B(0) is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology of Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong B(0), with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.
Magnetic reconnection from a multiscale instability cascade
NASA Astrophysics Data System (ADS)
Moser, Auna L.; Bellan, Paul M.
2012-02-01
Magnetic reconnection, the process whereby magnetic field lines break and then reconnect to form a different topology, underlies critical dynamics of magnetically confined plasmas in both nature and the laboratory. Magnetic reconnection involves localized diffusion of the magnetic field across plasma, yet observed reconnection rates are typically much higher than can be accounted for using classical electrical resistivity. It is generally proposed that the field diffusion underlying fast reconnection results instead from some combination of non-magnetohydrodynamic processes that become important on the `microscopic' scale of the ion Larmor radius or the ion skin depth. A recent laboratory experiment demonstrated a transition from slow to fast magnetic reconnection when a current channel narrowed to a microscopic scale, but did not address how a macroscopic magnetohydrodynamic system accesses the microscale. Recent theoretical models and numerical simulations suggest that a macroscopic, two-dimensional magnetohydrodynamic current sheet might do this through a sequence of repetitive tearing and thinning into two-dimensional magnetized plasma structures having successively finer scales. Here we report observations demonstrating a cascade of instabilities from a distinct, macroscopic-scale magnetohydrodynamic instability to a distinct, microscopic-scale (ion skin depth) instability associated with fast magnetic reconnection. These observations resolve the full three-dimensional dynamics and give insight into the frequently impulsive nature of reconnection in space and laboratory plasmas.
A drift model of interchange instability
Benilov, E. S.; Power, O. A.
2007-08-15
A set of asymptotic equations is derived, describing the dynamics of the flute mode in a magnetized plasma with cold ions, under a 'local' approximation (i.e., near a particular point). The asymptotic set is then used to calculate the growth rate of interchange instability in the slab model. It is shown that, unlike the magnetohydrodynamic ordering, the drift one allows instability to occur for either sign of the pressure gradient (i.e., for both 'bad' and 'good' curvature of the magnetic field). It is also demonstrated that finite beta gives rise to an extra instability that does not exist in the small-beta limit.
Magnetohydrodynamic Numerical Simulations of Magnetic Reconnection in Interstellar Medium
NASA Astrophysics Data System (ADS)
Tanuma, Syuniti
2000-03-01
In this thesis, we perform two-dimensional (2D) resistive magnetohydrodynamic (MHD) numerical simulations of the magnetic reconnection in interstellar medium. Part I is introduction. The motivation of the study is to investigate the origin of hot gas in interstellar medium. A scenario for generating X-ray gas in Galaxy is proposed, and examined by performing 2D MHD simulations with simple assumptions (Part II). The magnetic reconnection triggered by a supernova (Part III) and Parker instability (Part IV) are studied in detail, by performing 2D MHD simulations. Furthermore, the magnetic reconnection is also studied by performing three-dimensional (3D) MHD numerical simulation in (Part V). % Finally, we discuss and summarize the thesis (Parts VI and VII). Part I First, we review observation of Galactic Ridge X-ray Emission (GRXE) and its problems. Second, we describe observation of interstellar magnetic field briefly. Third, we review magnetic reconnection, theoretical models, numerical simulations, observations and experiments, and tearing instability. Forth, Parker instability (undular mode of magnetobuoyancy instability) is mentioned. Finally, we show the purpose of this thesis. Part II We present a scenario for the origin of the hot plasma in Galaxy as a model of strong X-ray emission [sim 3-10 keV; LX(2-10 keV) sim 1038 erg s-1], called GRXE, which has been observed near to the galactic plane. GRXE is thermal emission from a hot component (sim 7 keV) and a cool component (sim 0.8 keV). Observations suggest that the hot component is diffuse, and that it is not escaping away freely. Both what heats the hot component and what confines it in Galactic ridge still remain puzzling, while the cool component is believed to be created by supernovae. We propose a new scenario: the hot component is heated by magnetic reconnection, and confined by a helical magnetic field produced by magnetic reconnection. We solved 2D MHD equations numerically to study how magnetic
LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE
Masada, Youhei; Takiwaki, Tomoya; Kotake, Kei; Sano, Takayoshi E-mail: kkotake@th.nao.ac.jp
2012-11-10
Bearing in mind the application of core-collapse supernovae, we study the nonlinear properties of the magnetorotational instability (MRI) by means of three-dimensional simulations in the framework of a local shearing box approximation. By systematically changing the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear-vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress (((w {sub tot}))) and the shear-vorticity ratio (g{sub q} ) as ((w {sub tot})){proportional_to}g {sup {delta}} {sub q} with an index of {delta} {approx} 0.5. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has a slightly smaller power-law index ({approx}0.36). By modeling the effect of viscous heating rates from MRI turbulence, we show that the stronger magnetic fields, or the larger shear rates initially imposed, lead to higher dissipation rates. For a rapidly rotating PNS with a spin period in milliseconds and with strong magnetic fields of 10{sup 15} G, the energy dissipation rate is estimated to exceed 10{sup 51} erg s{sup -1}. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by MRI-driven turbulence, which we speculate, on the one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface; or, on the other hand, its energy deposition might be potentially favorable for the working of the neutrino-heating mechanism.
MAGNETOHYDRODYNAMIC SIMULATION OF A SIGMOID ERUPTION OF ACTIVE REGION 11283
Jiang Chaowei; Feng Xueshang; Wu, S. T.; Hu Qiang E-mail: fengx@spaceweather.ac.cn E-mail: qh0001@uah.edu
2013-07-10
Current magnetohydrodynamic (MHD) simulations of the initiation of solar eruptions are still commonly carried out with idealized magnetic field models, whereas the realistic coronal field prior to eruptions can possibly be reconstructed from the observable photospheric field. Using a nonlinear force-free field extrapolation prior to a sigmoid eruption in AR 11283 as the initial condition in an MHD model, we successfully simulate the realistic initiation process of the eruption event, as is confirmed by a remarkable resemblance to the SDO/AIA observations. Analysis of the pre-eruption field reveals that the envelope flux of the sigmoidal core contains a coronal null and furthermore the flux rope is prone to a torus instability. Observations suggest that reconnection at the null cuts overlying tethers and likely triggers the torus instability of the flux rope, which results in the eruption. This kind of simulation demonstrates the capability of modeling the realistic solar eruptions to provide the initiation process.
Viscous, resistive magnetohydrodynamic stability computed by spectral techniques
Dahlburg, R. B.; Zang, T. A.; Montgomery, D.; Hussaini, M. Y.
1983-01-01
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasiequilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfvén speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow. PMID:16593375
Jain, Neeraj; Büchner, Jörg
2014-07-15
Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =d{sub e}=c/ω{sub pe}), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheets (half thickness ∼5 d{sub e}), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.
Energetic particle effects on global magnetohydrodynamic modes
NASA Astrophysics Data System (ADS)
Cheng, C. Z.
1990-06-01
The effects of energetic particles on magnetohydrodynamic (MHD) type modes are studied using analytical theories and the nonvariational kinetic-MHD stability code (nova-k) [Workshop on Theory of Fusion Plasmas, (Societa Italiana di Fisica, Bologna, 1987), p. 185]. In particular, the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ``fishbone'' internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfvén eigenmodes (TAE) via transit resonances are addressed. Analytical theories are presented to help explain the nova-k results. For energetic trapped particles generated by neutral beam injection or ion cyclotron resonant heating, a stability window for the n=1 internal kink mode in the hot particle beta space exists even in the absence of core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.
Energetic particle effects on global magnetohydrodynamic modes
Cheng, C.Z. )
1990-06-01
The effects of energetic particles on magnetohydrodynamic (MHD) type modes are studied using analytical theories and the nonvariational kinetic-MHD stability code (NOVA-K) ({ital Workshop} {ital on} {ital Theory} {ital of} {ital Fusion} {ital Plasmas}, (Societa Italiana di Fisica, Bologna, 1987), p. 185). In particular, the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant fishbone'' internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances are addressed. Analytical theories are presented to help explain the NOVAresults. For energetic trapped particles generated by neutral beam injection or ion cyclotron resonant heating, a stability window for the {ital n}=1 internal kink mode in the hot particle beta space exists even in the absence of core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to resonantly excite instability of the {ital n}=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.
Micromechanics of shear banding
Gilman, J.J.
1992-08-01
Shear-banding is one of many instabilities observed during the plastic flow of solids. It is a consequence of the dislocation mechanism which makes plastic flow fundamentally inhomogeneous, and is exacerbated by local adiabatic heating. Dislocation lines tend to be clustered on sets of neighboring glide planes because they are heterogeneously generated; especially through the Koehler multiple-cross-glide mechanism. Factors that influence their mobilities also play a role. Strain-hardening decreases the mobilities within shear bands thereby tending to spread (delocalize) them. Strain-softening has the inverse effect. This paper reviews the micro-mechanisms of these phenomena. It will be shown that heat production is also a consequence of the heterogeneous nature of the microscopic flow, and that dislocation dipoles play an important role. They are often not directly observable, but their presence may be inferred from changes in thermal conductivity. It is argued that after deformation at low temperatures dipoles are distributed a la Pareto so there are many more small than large ones. Instability at upper yield point, the shapes of shear-band fronts, and mechanism of heat generation are also considered. It is shown that strain-rate acceleration plays a more important role than strain-rate itself in adiabatic instability.
Towards the detection of magnetohydrodynamics instabilities in a fusion reactor
NASA Astrophysics Data System (ADS)
Sozzi, Carlo; Alessi, E.; Figini, L.; Galperti, G.; Lazzaro, E.; Marchetto, C.; Mosconi, M.; Nowak, S.
2014-08-01
Various active control strategies of the Neoclassical tearing modes are being studied in present tokamaks using established detection techniques which exploit the measurements of the fluctuations of the magnetic field and of the electron temperature. The extrapolation of such techniques to the fusion reactor scale is made problematic by the neutron fluence and by the physics conditions related to the high plasma temperature and density which degrade the spatial resolution of such measurements.
Dynamic multiscaling in magnetohydrodynamic turbulence.
Ray, Samriddhi Sankar; Sahoo, Ganapati; Pandit, Rahul
2016-11-01
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Non-conventional Fishbone Instabilities
Ya.I. Kolesnichenko; V.V. Lutsenko; V.S. Marchenko; R.B. White
2004-11-10
New instabilities of fishbone type are predicted. First, a trapped-particle-induced m = n = 1 instability with the mode structure having nothing to do with the conventional rigid kink displacement. This instability takes place when the magnetic field is weak, so that the precession frequency of the energetic ions is not small as compared to the frequency of the corresponding Alfven continuum at r = 0 and the magnetic shear is small inside the q = 1 radius [the case relevant to spherical tori]. Second, an Energetic Particle Mode fishbone instability driven by circulating particles. Third, a double-kink-mode instability driven by the circulating energetic ions. In particular, the latter can have two frequencies simultaneously: we refer to it as ''doublet'' fishbones. This instability can occur when the radial profile of the energetic ions has an off-axis maximum inside the region of the mode localization.
NASA Astrophysics Data System (ADS)
Stelzer, Zacharias; Cébron, David; Miralles, Sophie; Vantieghem, Stijn; Noir, Jérôme; Scarfe, Peter; Jackson, Andrew
2015-07-01
Shear layers in confined liquid metal magnetohydrodynamic (MHD) flow play an important role in geo- and astrophysical bodies as well as in engineering applications. We present an experimental and numerical study of liquid metal MHD flow in a modified cylindrical annulus that is driven by an azimuthal Lorentz force resulting from a forced electric current under an imposed axial magnetic field. Hartmann and Reynolds numbers reach Mmax ≈ 2000 and Remax ≈ 1.3 × 104, respectively, in the steady regime. The peculiarity of our model geometry is the protruding inner disk electrode which gives rise to a free Shercliff layer at its edge. The flow of liquid GaInSn in the experimental device ZUCCHINI (ZUrich Cylindrical CHannel INstability Investigation) is probed with ultrasound Doppler velocimetry. We establish the base flow in ZUCCHINI and study the scaling of velocities and the free Shercliff layer in both experiment and finite element simulations. Experiment and numerics agree well on the mean azimuthal velocity uϕ(r) following the prediction of a large-M theoretical model. The large-M limit, which is equivalent to neglecting inertial effects, appears to be reached for M ≳ 30 in our study. In the numerics, we recover the theoretical scaling of the free Shercliff layer δS ˜ M-1/2 whereas δS appears to be largely independent of M in the experiment.
Vortex simulation of reacting shear flow
NASA Astrophysics Data System (ADS)
Ghoniem, Ahmed F.
Issues involved in the vortex simulation of reacting shear flow are discussed. It is shown that maintaining accuracy in the vortex methods requires the application of elaborate vorticity-updating schemes as vortex elements are moved along particle trajectories when shear or a strong strain field is represented. Solutions using 2D and 3D methods are discussed to illustrate some of the most common instabilities encountered in nonreacting and reacting shear flows and to reveal the mechanisms by which the maturation of these instabilities enhance mixing and hence burning in a reacting flow. The transport element method is developed and its application to compute scalar mixing in a shear layer is reviewed. The method is then combined with the vortex method to solve the problem of nonuniform-density shear flow. The results of incompressible reacting flow models are used to examine reaction extinction due to the formation of localized regions of strong strains as instabilities grow into their nonlinear range.
Stability of an accelerated shear layer
Mjolsness, R.C.; Ruppel, H.M.
1986-07-01
A fluid shear layer with free boundary conditions is subject to a Kelvin--Helmholtz-like instability. When the shear layer is accelerated by a difference in applied pressures it is also subject to a Rayleigh--Taylor-like instability. The combined action of these instabilities leads to at most one unstable mode at each wavelength, whose behavior depends in detail on fluid parameters, the fluid acceleration and the perturbation wavelength. Typically, at longest wavelengths the instability is essentially of Rayleigh--Taylor form; its behavior resembles the Kelvin--Helmholtz-like mode at shorter wavelengths, near the thickness of the shear layer, cutting off when the Kelvin--Helmholtz-like mode does. At still shorter wavelengths, the shear layer is subject to a Rayleigh--Taylor-like instability. Careful control of fluid parameters could place the most unstable wavelength for Rayleigh--Taylor instability, calculated from viscous theory, in the range of wavelengths where the accelerated shear layer has no unstable mode. However, this may be difficult to achieve in practice. If this can be realized, the most unstable growth rate may be reduced by about an order of magnitude by the presence of shear.
Shear Alfven waves with Landau and collisional effects
Hedrick, C.L.; Leboeuf, J.; Spong, D.A.
1995-06-01
Shear Alfven waves can be driven unstable by hot particles such as alpha particles in an ignited fusion device or hot ions in existing devices. Motivated by rather collisional Wendelstein 7 Advanced Stellarator (W7-AS) [Phys. Rev. Lett. {bold 72}, 1220 (1994)] beam-driven global Alfven instability experiments, the effect of electron and ion collisions on these modes has been examined. Collisions broaden and suppress the peak associated with Landau effects. This broadening makes ion damping more important, while the electron damping is suppressed. Additional resistive effects provide increased damping for the main part of the spectrum, which can have a rather high phase velocity. Of more general interest is the fact that collisional and collisionless resistivity has a numerically stabilizing effect that is known to be important for nonlinear resistive magnetohydrodynamics (MHD). This can preclude the need for introducing and testing the sensitivity to similar ad hoc effects. Numerical and analytic results for both a particle-conserving Krook collision operator and a Lorentz (pitch angle) collision operator are compared and contrasted.
PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. II. IMPLEMENTATION AND TESTS
McNally, Colin P.; Mac Low, Mordecai-Mark; Maron, Jason L. E-mail: jmaron@amnh.org
2012-05-01
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to ensure the particles fill the computational volume and gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. We have parallelized the code by adapting the framework provided by GADGET-2. A set of standard test problems, including 10{sup -6} amplitude linear magnetohydrodynamics waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented. Finally, we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. This paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.
Data assimilation for magnetohydrodynamics systems
NASA Astrophysics Data System (ADS)
Mendoza, O. Barrero; de Moor, B.; Bernstein, D. S.
2006-05-01
Prediction of solar storms has become a very important issue due to the fact that they can affect dramatically the telecommunication and electrical power systems at the earth. As a result, a lot of research is being done in this direction, space weather forecast. Magnetohydrodynamics systems are being studied in order to analyse the space plasma dynamics, and techniques which have been broadly used in the prediction of earth environmental variables like the Kalman filter (KF), the ensemble Kalman filter (EnKF), the extended Kalman filter (EKF), etc., are being studied and adapted to this new framework. The assimilation of a wide range of space environment data into first-principles-based global numerical models will improve our understanding of the physics of the geospace environment and the forecasting of its behaviour. Therefore, the aim of this paper is to study the performance of nonlinear observers in magnetohydrodynamics systems, namely, the EnKF.The EnKF is based on a Monte Carlo simulation approach for propagation of process and measurement errors. In this paper, the EnKF for a nonlinear two-dimensional magnetohydrodynamic (2D-MHD) system is considered. For its implementation, two software packages are merged, namely, the Versatile Advection Code (VAC) written in Fortran and Matlab of Mathworks. The 2D-MHD is simulated with the VAC code while the EnKF is computed in Matlab. In order to study the performance of the EnKF in MHD systems, different number of measurement points as well as ensemble members are set.
Method for manufacturing magnetohydrodynamic electrodes
Killpatrick, D.H.; Thresh, H.R.
1980-06-24
A method of manufacturing electrodes for use in a magnetohydrodynamic (MHD) generator is described comprising the steps of preparing a billet having a core of a first metal, a tubular sleeve of a second metal, and an outer sheath of an extrusile metal; evacuating the space between the parts of the assembled billet; extruding the billet; and removing the outer jacket. The extruded bar may be made into electrodes by cutting and bending to the shape required for an MHD channel frame. The method forms a bond between the first metal of the core and the second metal of the sleeve strong enough to withstand a hot and corrosive environment.
Action principle for relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
D'Avignon, Eric; Morrison, P. J.; Pegoraro, F.
2015-04-01
A covariant action principle for ideal relativistic magnetohydrodynamics in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al. [Ann. Phys. 169, 29 (1986)], which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant byproducts of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory.
Magneto-Hydrodynamics Based Microfluidics
Qian, Shizhi; Bau, Haim H.
2009-01-01
In microfluidic devices, it is necessary to propel samples and reagents from one part of the device to another, stir fluids, and detect the presence of chemical and biological targets. Given the small size of these devices, the above tasks are far from trivial. Magnetohydrodynamics (MHD) offers an elegant means to control fluid flow in microdevices without a need for mechanical components. In this paper, we review the theory of MHD for low conductivity fluids and describe various applications of MHD such as fluid pumping, flow control in fluidic networks, fluid stirring and mixing, circular liquid chromatography, thermal reactors, and microcoolers. PMID:20046890
PARTICLE TRAPPING AND STREAMING INSTABILITY IN VORTICES IN PROTOPLANETARY DISKS
Raettig, Natalie; Klahr, Hubert; Lyra, Wladimir E-mail: klahr@mpia.de
2015-05-01
We analyze the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, e.g., baroclinic vortex growth. Besides the gas drag acting on particles, we also allow for back-reaction from dust onto the gas. This becomes important when the local dust-to-gas ratio approaches unity. In our two-dimensional, local, shearing sheet simulations, we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, St. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for St = 1.0. The increased dust-to-gas ratio triggers the streaming instability, thus counter-intuitively limiting the maximal achievable overdensities. We find that particle trapping inside vortices opens the possibility for gravity assisted planetesimal formation even for small particles (St = 0.01) and a low initial dust-to-gas ratio of 1:10{sup 4}, e.g., much smaller than in the previously studied magnetohydrodynamic zonal flow case.
Role of Shear Instability in Ballistic Penetration
1989-12-01
example of this is shown in Figure 1 (taken from Reference 1). Two sets of targets were made from the same steel alloy ( 4340 ), processed in the same way...Figure 3 shows that for both VIM and ESR steels , the drop in ballistic performance is clearly associated with the change in failure mode from plastic flow...diabticshea bads n ths pper -Or A R * Failure by Plastic Flow A. * Failure by Plugging i 1.4 a Failure by Discing 6 1.3 ,0 A ESR Steel % 1.2 A A ~1.1 06 0 acr
Sustained turbulence and magnetic energy in nonrotating shear flows
NASA Astrophysics Data System (ADS)
Nauman, Farrukh; Blackman, Eric G.
2017-03-01
From numerical simulations, we show that nonrotating magnetohydrodynamic shear flows are unstable to finite amplitude velocity perturbations and become turbulent, leading to the growth and sustenance of magnetic energy, including large scale fields. This supports the concept that sustained magnetic energy from turbulence is independent of the driving mechanism for large enough magnetic Reynolds numbers.
Variational integrators for reduced magnetohydrodynamics
Kraus, Michael; Tassi, Emanuele; Grasso, Daniela
2016-09-15
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Variational integrators for reduced magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Kraus, Michael; Tassi, Emanuele; Grasso, Daniela
2016-09-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
On stability criteria for kinetic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Ramos, J. J.
2016-12-01
The existence of a potential energy functional in the zero-Larmor-radius collisionless plasma theory of Kruskal & Oberman (Phys. Fluids, vol. 1, 1958 p. 275), Rosenbluth & Rostoker (Phys. Fluids, vol. 2, 1959, p. 23) allows us to derive easily sufficient conditions for linear stability. However, this kinetic magnetohydrodynamics (KMHD) theory does not have a self-adjointness property, making it difficult to derive necessary conditions. In particular, the standard methods to prove that an instability follows if some trial perturbation makes the incremental potential energy negative, which rely on the self-adjointness of the force operator or on the existence of a complete basis of normal modes, are not applicable to KMHD. This paper investigates KMHD linear stability criteria based on the time evolution of initial-value solutions, without recourse to the classic bounds or comparison theorems of Kruskal-Oberman and Rosenbluth-Rostoker for the KMHD potential energy. The adopted approach does not solve the kinetic equations by integration along characteristics and does not require that the particle orbits be periodic or nearly periodic. Most importantly, the investigation of a necessary condition for stability does not require the self-adjointness of the force operator or the existence of a complete basis of normal modes. It is thereby shown that stability in isothermal ideal-MHD is a sufficient condition for stability in KMHD and that, with a proviso on the long-time behaviour of oscillations about stable equilibria, stability in the double-adiabatic fluid theory, including the variation of the parallel fluid displacement, would be a necessary condition for stability in KMHD.
NASA Astrophysics Data System (ADS)
Lyu, L.; Lai, S.
2003-12-01
Simulation results of Kelvin-Helmholtz (K-H) instability at a magnetohydrodynamic (MHD) tangential discontinuity (TD) show asymmetric development of nonlinear waves when magnetic field is perpendicular to the velocity shear on one side of the TD but parallel to the velocity shear on the other side of the TD. To explain these simulation results, an analytic study is carried out to obtain generalized solutions of K-H instability. Both incompressibility and pure surface wave conditions are removed from our basic assumptions. Nonlinear waves in our model are allowed to propagate at directions both tangent and normal to the surface of TD. Plasma is assumed to follow an adiabatic process. Nonlinear waves on two sides of the TD have a common tangential wavelength, but may have different normal wavelengths. Wave amplitude is assumed to decay exponentially away from the surface of TD. Our solutions indicate that the exponential decay length increases with increasing normal wavelength. On the other hand, the normal wavelength will decrease with increasing velocity shear. Our simulation results are in good agreement with the analytic solutions. For magnetic field parallel or anti-parallel to the velocity shear direction, the normal wavelength is much longer than the tangential wavelength. Thus, nonlinear waves are developed from the TD like a toothbrush with wave normal nearly perpendicular to the normal of the TD. With flow energy converted into wave energy and carried away from the TD, amplification of the surface wave become stabilized. Only a finite amplitude disturbance can be found at surface of the TD in our simulation. Our analytic solutions and simulation results indicate possible existence of another type of nonlinear waves in magnetosheath and in the tail lobes as a result of solar wind-magnetopause interactions.
Dynamo quenching due to shear flow.
Leprovost, Nicolas; Kim, Eun-jin
2008-04-11
We provide a theory of dynamo (alpha effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the alpha effect is reduced by the shear even in the absence of magnetic field. The alpha effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun.
Hall diffusion and the magnetorotational instability in protoplanetary discs
NASA Astrophysics Data System (ADS)
Wardle, Mark; Salmeron, Raquel
2012-06-01
The destabilizing effect of Hall diffusion in a weakly ionized Keplerian disc allows the magnetorotational instability (MRI) to occur for much lower ionization levels than would otherwise be possible. However, simulations incorporating Hall and Ohm diffusion give the impression that the consequences of this for the non-linear saturated state are not as significant as suggested by the linear instability. Close inspection reveals that this is not actually the case as the simulations have not yet probed the Hall-dominated regime. Here we revisit the effect of Hall diffusion on the MRI and the implications for the extent of magnetohydrodynamic (MHD) turbulence in protoplanetary discs, where Hall diffusion dominates over a large range of radii. We conduct a local, linear analysis of the instability for a vertical, weak magnetic field subject to axisymmetric perturbations with a purely vertical wave vector. In contrast to previous analyses, we express the departure from ideal MHD in terms of Hall and Pedersen diffusivities ηH and ηP, which provide transparent notation that is directly connected to the induction equation. This allows us to present a crisp overview of the dependence of the instability on magnetic diffusivity. We present analytic expressions and contours in the ηH-ηP plane for the maximum growth rate and corresponding wavenumber, the upper cut-off for unstable wavenumbers and the loci that divide the plane into regions of different characteristic behaviour. We find that for ?, where vA is the Alfvén speeds and Ω is the Keplerian frequency, Hall diffusion suppresses the MRI irrespective of the value of ηP. In the highly diffusive limit, the magnetic field decouples from the fluid perturbations and simply diffuses in the background Keplerian shear flow. The diffusive MRI reduces to a diffusive plane-parallel shear instability with effective shear rate (3/2)Ω. We give simple analytic expressions for the growth rate and wavenumber of the most unstable
Coherent motion in excited free shear flows
NASA Technical Reports Server (NTRS)
Wygnanski, Israel J.; Petersen, Robert A.
1987-01-01
The application of the inviscid instability approach to externally excited turbulent free shear flows at high Reynolds numbers is explored. Attention is given to the cases of a small-deficit plane turbulent wake, a plane turbulent jet, an axisymmetric jet, the nonlinear evolution of instabilities in free shear flows, the concept of the 'preferred mode', vortex pairing in turbulent mixing layers, and experimental results for the control of free turbulent shear layers. The special features often attributed to pairing or to the preferred mode are found to be difficult to comprehend; the concept of feedback requires further substantiation in the case of incompressible flow.
Some Basic Aspects of Magnetohydrodynamic Boundary-Layer Flows
NASA Technical Reports Server (NTRS)
Hess, Robert V.
1959-01-01
An appraisal is made of existing solutions of magnetohydrodynamic boundary-layer equations for stagnation flow and flat-plate flow, and some new solutions are given. Since an exact solution of the equations of magnetohydrodynamics requires complicated simultaneous treatment of the equations of fluid flow and of electromagnetism, certain simplifying assumptions are generally introduced. The full implications of these assumptions have not been brought out properly in several recent papers. It is shown in the present report that for the particular law of deformation which the magnetic lines are assumed to follow in these papers a magnet situated inside the missile nose would not be able to take up any drag forces; to do so it would have to be placed in the flow away from the nose. It is also shown that for the assumption that potential flow is maintained outside the boundary layer, the deformation of the magnetic lines is restricted to small values. The literature contains serious disagreements with regard to reductions in heat-transfer rates due to magnetic action at the nose of a missile, and these disagreements are shown to be mainly due to different interpretations of reentry conditions rather than more complicated effects. In the present paper the magnetohydrodynamic boundary-layer equation is also expressed in a simple form that is especially convenient for physical interpretation. This is done by adapting methods to magnetic forces which in the past have been used for forces due to gravitational or centrifugal action. The simplified approach is used to develop some new solutions of boundary-layer flow and to reinterpret certain solutions existing in the literature. An asymptotic boundary-layer solution representing a fixed velocity profile and shear is found. Special emphasis is put on estimating skin friction and heat-transfer rates.
Migrational Instabilities in Particle Suspensions
NASA Technical Reports Server (NTRS)
Goddard, Joe D.
1996-01-01
This work deals with an instability arising from the shear-induced migration of particles in dense suspensions coupled with a dependence of viscosity on particle concentration. The analysis summarized here treats the inertialess (Re = O) linear stability of homogeneous simple shear flows for a Stokesian suspension model of the type proposed by Leighton and Acrivos (1987). Depending on the importance of shear-induced migration relative to concentration-driven diffusion, this model admits short-wave instability arising from wave-vector stretching by the base flow and evolving into particle-depleted shear bands. Moreover, this instability in the time-dependent problem corresponds to loss of ellipticity in the associated static problem (Re = O, Pe = O). While the isotropic version of the Leighton-Acrivos model is found to be stable with their experimentally determined parameters for simple shear, it is known that the stable model does not give a good quantitative description of particle clustering in the core of pipe flow (Nott and Brady 1994). This leads to the conjecture that an appropriate variant on the above model could explain such clustering as a two-phase bifurcation in the base flow.
Falceta-Gonçalves, D.; Kowal, G.
2015-07-20
In this work we report on a numerical study of the cosmic magnetic field amplification due to collisionless plasma instabilities. The collisionless magnetohydrodynamic equations derived account for the pressure anisotropy that leads, in specific conditions, to the firehose and mirror instabilities. We study the time evolution of seed fields in turbulence under the influence of such instabilities. An approximate analytical time evolution of the magnetic field is provided. The numerical simulations and the analytical predictions are compared. We found that (i) amplification of the magnetic field was efficient in firehose-unstable turbulent regimes, but not in the mirror-unstable models; (ii) the growth rate of the magnetic energy density is much faster than the turbulent dynamo; and (iii) the efficient amplification occurs at small scales. The analytical prediction for the correlation between the growth timescales and pressure anisotropy is confirmed by the numerical simulations. These results reinforce the idea that pressure anisotropies—driven naturally in a turbulent collisionless medium, e.g., the intergalactic medium, could efficiently amplify the magnetic field in the early universe (post-recombination era), previous to the collapse of the first large-scale gravitational structures. This mechanism, though fast for the small-scale fields (∼kpc scales), is unable to provide relatively strong magnetic fields at large scales. Other mechanisms that were not accounted for here (e.g., collisional turbulence once instabilities are quenched, velocity shear, or gravitationally induced inflows of gas into galaxies and clusters) could operate afterward to build up large-scale coherent field structures in the long time evolution.
ANALYSIS OF MAGNETOROTATIONAL INSTABILITY WITH THE EFFECT OF COSMIC-RAY DIFFUSION
Kuwabara, Takuhito; Ko, Chung-Ming E-mail: cmko@astro.ncu.edu.tw
2015-01-10
We present the results obtained from the linear stability analysis and 2.5 dimensional magnetohydrodynamic (MHD) simulations of magnetorotational instability (MRI), including the effects of cosmic rays (CRs). We took into account the CR diffusion along the magnetic field but neglected the cross-field-line diffusion. Two models are considered in this paper: the shearing box model and differentially rotating cylinder model. We studied how MRI is affected by the initial CR pressure (i.e., energy) distribution. In the shearing box model, the initial state is uniform distribution. Linear analysis shows that the growth rate of MRI does not depend on the value of the CR diffusion coefficient. In the differentially rotating cylinder model, the initial state is a constant angular momentum polytropic disk threaded by a weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both results are confirmed by MHD simulations. The MHD simulation results show that the outward movement of matter by the growth of MRI is not impeded by the CR pressure gradient, and the centrifugal force that acts on the concentrated matter becomes larger. Consequently, the growth rate of MRI is increased. On the other hand, if the initial CR pressure is uniform, then the growth rate of the MRI barely depends on the value of the CR diffusion coefficient.
Numerical Investigations of Magnetohydrodynamic Turbulence
NASA Astrophysics Data System (ADS)
Mueller, W. C.
2006-12-01
Incompressible magnetohydrodynamic turbulence studied by large-scale direct numerical simulations has revealed a number of new interesting facets. The Goldreich-Sridhar phenomenology partly breaks down in turbulence subject to a strong mean magnetic field. This leads to a measureable anisotropy of two-point statistics. The nonlinear dynamics of kinetic (E^K) and magnetic energy (E^M) is the result of a dynamical equilibrium of Alfvén effect and a small-sale dynamo leading to a scaling relation between total and residual energy: (E^M-E^K)~ k(E^K+E^M)2. The probability density functions of cascading quantities are found to exhibit mono-scaling.
Magnetohydrodynamic Turbulence and the Geodynamo
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2014-01-01
The ARES Directorate at JSC has researched the physical processes that create planetary magnetic fields through dynamo action since 2007. The "dynamo problem" has existed since 1600, when William Gilbert, physician to Queen Elizabeth I, recognized that the Earth was a giant magnet. In 1919, Joseph Larmor proposed that solar (and by implication, planetary) magnetism was due to magnetohydrodynamics (MHD), but full acceptance did not occur until Glatzmaier and Roberts solved the MHD equations numerically and simulated a geomagnetic reversal in 1995. JSC research produced a unique theoretical model in 2012 that provided a novel explanation of these physical observations and computational results as an essential manifestation of broken ergodicity in MHD turbulence. Research is ongoing, and future work is aimed at understanding quantitative details of magnetic dipole alignment in the Earth as well as in Mercury, Jupiter and its moon Ganymede, Saturn, Uranus, Neptune, and the Sun and other stars.
Method for manufacturing magnetohydrodynamic electrodes
Killpatrick, Don H.; Thresh, Henry R.
1982-01-01
A method of manufacturing electrodes for use in a magnetohydrodynamic (MHD) generator comprising the steps of preparing a billet having a core 10 of a first metal, a tubular sleeve 12 of a second metal, and an outer sheath 14, 16, 18 of an extrusile metal; evacuating the space between the parts of the assembled billet; extruding the billet; and removing the outer jacket 14. The extruded bar may be made into electrodes by cutting and bending to the shape required for an MDH channel frame. The method forms a bond between the first metal of the core 10 and the second metal of the sleeve 12 strong enough to withstand a hot and corrosive environment.
Magnetohydrodynamic production of relativistic jets.
Meier, D L; Koide, S; Uchida, Y
2001-01-05
A number of astronomical systems have been discovered that generate collimated flows of plasma with velocities close to the speed of light. In all cases, the central object is probably a neutron star or black hole and is either accreting material from other stars or is in the initial violent stages of formation. Supercomputer simulations of the production of relativistic jets have been based on a magnetohydrodynamic model, in which differential rotation in the system creates a magnetic coil that simultaneously expels and pinches some of the infalling material. The model may explain the basic features of observed jets, including their speed and amount of collimation, and some of the details in the behavior and statistics of different jet-producing sources.
Magnetohydrodynamic turbulence: Observation and experiment
Brown, M. R.; Schaffner, D. A.; Weck, P. J.
2015-05-15
We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations E{sub B}(f). We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.
Micromachined magnetohydrodynamic actuators and sensors
Lee, Abraham P.; Lemoff, Asuncion V.
2000-01-01
A magnetohydrodynamic (MHD) micropump and microsensor which utilizes micromachining to integrate the electrodes with microchannels and includes a magnet for producing magnetic fields perpendicular to both the electrical current direction and the fluid flow direction. The magnet can also be micromachined and integrated with the micropump using existing technology. The MHD micropump, for example, can generate continuous, reversible flow, with readily controllable flow rates. The flow can be reversed by either reversing the electrical current flow or reversing the magnetic field. By mismatching the electrodes, a swirling vortex flow can be generated for potential mixing applications. No moving parts are necessary and the dead volume is minimal. The micropumps can be placed at any position in a fluidic circuit and a combination of micropumps can generate fluidic plugs and valves.
ANISOTROPIC INTERMITTENCY OF MAGNETOHYDRODYNAMIC TURBULENCE
Osman, K. T.; Kiyani, K. H.; Chapman, S. C.; Hnat, B.
2014-03-10
A higher-order multiscale analysis of spatial anisotropy in inertial range magnetohydrodynamic turbulence is presented using measurements from the STEREO spacecraft in fast ambient solar wind. We show for the first time that, when measuring parallel to the local magnetic field direction, the full statistical signature of the magnetic and Elsässer field fluctuations is that of a non-Gaussian globally scale-invariant process. This is distinct from the classic multiexponent statistics observed when the local magnetic field is perpendicular to the flow direction. These observations are interpreted as evidence for the weakness, or absence, of a parallel magnetofluid turbulence energy cascade. As such, these results present strong observational constraints on the statistical nature of intermittency in turbulent plasmas.
Relativistic magnetohydrodynamics in one dimension
NASA Astrophysics Data System (ADS)
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Magnetohydrodynamic Turbulence and the Geodynamo
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Magnetohydrodynamic turbulence: Observation and experimenta)
NASA Astrophysics Data System (ADS)
Brown, M. R.; Schaffner, D. A.; Weck, P. J.
2015-05-01
We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations EB(f ) . We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.
Weakly nonlinear magnetohydrodynamic wave interactions
Webb, G.M.; Brio, M.; Kruse, M.T.; Zank, G.P.
1999-06-01
Equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of: (a) three-wave resonant interactions in which high frequency waves, may evolve on long space and time scales if the wave phases satisfy the resonance conditions; (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. For wave propagation in non-uniform media, further linear wave mixing terms appear in the equations. The equations describe four types of resonant triads: slow-fast magnetosonic wave interaction; Alfv{acute e}n-entropy wave interaction; Alfv{acute e}n-magnetosonic wave interaction; and magnetosonic-entropy wave interaction. The formalism is restricted to coherent wave interactions. {copyright} {ital 1999 American Institute of Physics.}
Three-dimensional force-free looplike magnetohydrodynamic equilibria
NASA Technical Reports Server (NTRS)
Finn, John M.; Guzdar, Parvez N.; Usikov, Daniel
1994-01-01
Computations of three-dimensional force-free magnetohydrodynamic (MHD) equilibria, del x B = lambdaB with lambda = lambda(sub 0), a constant are presented. These equilibria are determined by boundary conditions on a surface corresponding to the solar photosphere. The specific boundary conditions used correspond to looplike magnetic fields in the corona. It is found that as lambda(sub 0) is increased, the loops of flux become kinked, and for sufficiently large lambda(sub 0), develop knots. The relationship between the kinking and knotting properties of these equilibria and the presence of a kink instability and related loss of equilibrium is explored. Clearly, magnetic reconnection must be involved for an unknotted loop equilibrium to become knotted, and speculations are made about the creation of a closed hyperbolic field line (X-line) about which this reconnection creating knotted field lines is centered.
Implicit Methods for the Magnetohydrodynamic Description of Magnetically Confined Plasmas
Jardin, S C
2010-09-28
Implicit algorithms are essential for predicting the slow growth and saturation of global instabilities in today’s magnetically confined fusion plasma experiments. Present day algorithms for obtaining implicit solutions to the magnetohydrodynamic (MHD) equations for highly magnetized plasma have their roots in algorithms used in the 1960s and 1970s. However, today’s computers and modern linear and non-linear solver techniques make practical much more comprehensive implicit algorithms than were previously possible. Combining these advanced implicit algorithms with highly accurate spatial representations of the vector fields describing the plasma flow and magnetic fields and with improved methods of calculating anisotropic thermal conduction now makes possible simulations of fusion experiments using realistic values of plasma parameters and actual configuration geometry.
K.Y. Ng
2003-08-25
The lecture covers mainly Sections 2.VIII and 3.VII of the book ''Accelerator Physics'' by S.Y. Lee, plus mode-coupling instabilities and chromaticity-driven head-tail instability. Besides giving more detailed derivation of many equations, simple interpretations of many collective instabilities are included with the intention that the phenomena can be understood more easily without going into too much mathematics. The notations of Lee's book as well as the e{sup jwt} convention are followed.
Development of magnetohydrodynamic modes during sawteeth in tokamak plasmas
Firpo, M.-C.; Ettoumi, W.; Farengo, R.; Ferrari, H. E.; García-Martínez, P. L.; Lifschitz, A. F.
2013-07-15
A dynamical analysis applied to a reduced resistive magnetohydrodynamics model is shown to explain the chronology of the nonlinear destabilization of modes observed in tokamak sawteeth. A special emphasis is put on the nonlinear self-consistent perturbation of the axisymmetric m = n = 0 mode that manifests through the q-profile evolution. For the very low fusion-relevant resistivity values, the q-profile is shown to remain almost unchanged on the early nonlinear timescale within the central tokamak region, which supports a partial reconnection scenario. Within the resistive region, indications for a local flattening or even a local reversed-shear of the q-profile are given. The impact of this ingredient in the occurrence of the sawtooth crash is discussed.
Pattern formation induced by a differential shear flow
NASA Astrophysics Data System (ADS)
Stucchi, L.; Vasquez, Desiderio A.
2013-02-01
Fluid flow advecting one substance while others are immobilized can generate an instability in a homogeneous steady state of a reaction-diffusion-advection system. This differential-flow instability leads to the formation of steady spatial patterns in a moving reference frame. We study the effects of shear flow on this instability by considering two layers of fluid moving independently from each other, but allowing the substances to diffuse along and across the layers. We find that shear flow can generate instabilities even if the average flow velocity is zero for both substances. These instabilities are strongly dependent on which substance is advected by the shear flow. We explain these effects using the results of Taylor dispersion, where an effective diffusivity is enhanced by shear flow.
The collisionless magnetoviscous-thermal instability
Islam, Tanim
2014-05-20
It is likely that nearly all central galactic massive and supermassive black holes are nonradiative: their accretion luminosities are orders of magnitude below what can be explained by efficient black hole accretion within their ambient environments. These objects, of which Sagittarius A* is the best-known example, are also dilute (mildly collisional to highly collisionless) and optically thin. In order for accretion to occur, magnetohydrodynamic (MHD) instabilities must develop that not only transport angular momentum, but also gravitational energy generated through matter infall, outward. A class of new magnetohydrodynamical fluid instabilities—the magnetoviscous-thermal instability (MVTI)—was found to transport angular momentum and energy along magnetic field lines through large (fluid) viscosities and thermal conductivities. This paper describes the analog to the MVTI, the collisionless MVTI (CMVTI), that similarly transports energy and angular momentum outward, expected to be important in describing the flow properties of hot, dilute, and radiatively inefficient accretion flows around black holes. We construct a local equilibrium for MHD stability analysis in this differentially rotating disk. We then find and characterize specific instabilities expected to be important in describing their flow properties, and show their qualitative similarities to instabilities derived using the fluid formalism. We conclude with further work needed in modeling this class of accretion flow.
Submesoscale baroclinic instability and the Balance Equations
NASA Astrophysics Data System (ADS)
Grooms, Ian
2015-11-01
Ocean submesoscale baroclinic instability is studied in the framework of the Balance Equations. The Balance Equations are an intermediate model that includes balanced ageostrophic effects with higher accuracy than the quasigeostrophic approximation, but rules out unbalanced wave motions; as such, they are particularly suited to the study of baroclinic instability in submesoscale ocean dynamics. The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. The primary finding is that at low Richardson numbers the growth rate of some instability modes is increased compared to larger-scale quasigeostrophic dynamics, and that the increase can be attributed to both ageostrophic baroclinic production and shear production of perturbation energy. This suggests that the nonlinear development of submesoscale baroclinic instability will proceed more vigorously than mesoscale/quasigeostrophic, and may include a downscale/forward transfer of kinetic energy.
Computational Methods for Ideal Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Kercher, Andrew D.
Numerical schemes for the ideal magnetohydrodynamics (MHD) are widely used for modeling space weather and astrophysical flows. They are designed to resolve the different waves that propagate through a magnetohydro fluid, namely, the fast, Alfven, slow, and entropy waves. Numerical schemes for ideal magnetohydrodynamics that are based on the standard finite volume (FV) discretization exhibit pseudo-convergence in which non-regular waves no longer exist only after heavy grid refinement. A method is described for obtaining solutions for coplanar and near coplanar cases that consist of only regular waves, independent of grid refinement. The method, referred to as Compound Wave Modification (CWM), involves removing the flux associated with non-regular structures and can be used for simulations in two- and three-dimensions because it does not require explicitly tracking an Alfven wave. For a near coplanar case, and for grids with 213 points or less, we find root-mean-square-errors (RMSEs) that are as much as 6 times smaller. For the coplanar case, in which non-regular structures will exist at all levels of grid refinement for standard FV schemes, the RMSE is as much as 25 times smaller. A multidimensional ideal MHD code has been implemented for simulations on graphics processing units (GPUs). Performance measurements were conducted for both the NVIDIA GeForce GTX Titan and Intel Xeon E5645 processor. The GPU is shown to perform one to two orders of magnitude greater than the CPU when using a single core, and two to three times greater than when run in parallel with OpenMP. Performance comparisons are made for two methods of storing data on the GPU. The first approach stores data as an Array of Structures (AoS), e.g., a point coordinate array of size 3 x n is iterated over. The second approach stores data as a Structure of Arrays (SoA), e.g. three separate arrays of size n are iterated over simultaneously. For an AoS, coalescing does not occur, reducing memory efficiency
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
Magnetohydrodynamic Propulsion for the Classroom
NASA Astrophysics Data System (ADS)
Font, Gabriel I.; Dudley, Scott C.
2004-10-01
The cinema industry can sometimes prove to be an ally when searching for material with which to motivate students to learn physics. Consider, for example, the electromagnetic force on a current in the presence of a magnetic field. This phenomenon is at the heart of magnetohydrodynamic (MHD) propulsion systems. A submarine employing this type of propulsion was immortalized in the movie Hunt for Red October. While mentioning this to students certainly gets their attention, it often elicits comments that it is only fiction and not physically possible. Imagine their surprise when a working system is demonstrated! It is neither difficult nor expensive to construct a working system that can be demonstrated in the front of a classroom.2 In addition, all aspects of the engineering hurdles that must be surmounted and myths concerning this "silent propulsion" system are borne out in a simple apparatus. This paper details how to construct an inexpensive MHD propulsion boat that can be demonstrated for students in the classroom.
Magnetohydrodynamic (MHD) driven droplet mixer
Lee, Abraham P.; Lemoff, Asuncion V.; Miles, Robin R.
2004-05-11
A magnetohydrodynamic fluidic system mixes a first substance and a second substance. A first substrate section includes a first flow channel and a first plurality of pairs of spaced electrodes operatively connected to the first flow channel. A second substrate section includes a second flow channel and a second plurality of pairs of spaced electrodes operatively connected to the second flow channel. A third substrate section includes a third flow channel and a third plurality of pairs of spaced electrodes operatively connected to the third flow channel. A magnetic section and a control section are operatively connected to the spaced electrodes. The first substrate section, the second substrate section, the third substrate section, the first plurality of pairs of spaced electrodes, the second plurality of pairs of spaced electrodes, the third plurality of pairs of spaced electrodes, the magnetic section, and the control section are operated to move the first substance through the first flow channel, the second substance through the second flow channel, and both the first substance and the second substance into the third flow channel where they are mixed.
Shell models of magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Plunian, Franck; Stepanov, Rodion; Frick, Peter
2013-02-01
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfvén waves and the Hall effect.
Linear study of the precessional fishbone instability
NASA Astrophysics Data System (ADS)
Idouakass, M.; Faganello, M.; Berk, H. L.; Garbet, X.; Benkadda, S.
2016-10-01
The precessional fishbone instability is an m = n = 1 internal kink mode destabilized by a population of trapped energetic particles. The linear phase of this instability is studied here, analytically and numerically, with a simplified model. This model uses the reduced magneto-hydrodynamics equations for the bulk plasma and the Vlasov equation for a population of energetic particles with a radially decreasing density. A threshold condition for the instability is found, as well as a linear growth rate and frequency. It is shown that the mode frequency is given by the precession frequency of the deeply trapped energetic particles at the position of strongest radial gradient. The growth rate is shown to scale with the energetic particle density and particle energy while it is decreased by continuum damping.
The effect of plasma flow on line-tied magnetohydrodynamic modes
Arcudi, Francesco; Delzanno, Gian Luca; Finn, John M.
2010-06-15
The linear stability of a linear pinch to kink modes with line-tying boundary conditions and equilibrium axial flow is studied. Numerical results in visco-resistive magnetohydrodynamics show that for long plasmas, in which the line-tying stabilization effect is weak, plasma flow is stabilizing. For shorter plasmas, near the length at which line-tying stabilizes the mode for zero flow, the flow can be destabilizing. A simple model using reduced ideal magnetohydrodynamics with a step-function current density and an even simpler one-dimensional sound wave model with equilibrium flow elucidate these effects. It is concluded that: (1) The stabilization in long plasmas is due to convective stabilization; (2) the destabilization for short plasmas can be explained using a picture involving the coupling of two stable waves, one propagating in the forward direction and one in the backward direction; and (3) strong magnetic shear suppresses the flow destabilization for short plasmas.
BOOK REVIEW: Magnetohydrodynamics of Plasma Relaxation
NASA Astrophysics Data System (ADS)
Connor, J. W.
1998-06-01
This monograph on magnetohydrodynamic (MHD) relaxation in plasmas by Ortolani and Schnack occupies a fascinating niche in the plasma physics literature. It is rare in the complex and often technically sophisticated subject of plasma physics to be able to isolate a topic and deal with it comprehensively in a mere 180 pages. Furthermore, it brings a refreshingly original and personal approach to the treatment of plasma relaxation, synthesizing the experiences of the two authors to produce a very readable account of phenomena appearing in such diverse situations as laboratory reversed field pinches (RFPs) and the solar corona. Its novelty lies in that, while it does acknowledge the seminal Taylor theory of relaxation as a general guide, it emphasizes the role of large scale numerical MHD simulations in developing a picture for the relaxation phenomena observed in experiment and nature. Nevertheless, the volume has some minor shortcomings: a tendency to repetitiveness and some omissions that prevent it being entirely self-contained. The monograph is divided into nine chapters, with the first a readable, `chatty', introduction to the physics and phenomena of relaxation discussed in the later chapters. Chapter 2 develops the tools for describing relaxation processes, namely the resistive MHD model, leading to a discussion of resistive instabilities and the stability properties of RFPs. This chapter demonstrates the authors' confessed desire to avoid mathematical detail with a rather simplified discussion of Δ' and magnetic islands; it also sets the stage for their own belief, or thesis, that numerical simulation of the non-linear consequences of the MHD model is the best approach to explaining the physics of relaxation. Nevertheless, in Chapter 3 they provide a reasonably good account and critique of one analytic approach that is available, and which is the commonly accepted picture for relaxation in pinches - the Taylor relaxation theory based on the conservation of
Observations and Simulations of Magnetohydrodynamic Turbulence in the Solar Wind
NASA Astrophysics Data System (ADS)
Goldstein, M. L.
2006-12-01
Alfvénic fluctuations are a ubiquitous component of the solar wind. Evidence from many spacecraft indicates that the fluctuations are convected out of the solar corona with relatively flat power spectra and constitute a source of free energy for a turbulent cascade of magnetic and kinetic energy to high wave numbers. Observations and simulations support the conclusion that the cascade evolves most rapidly in the vicinity of velocity shears and current sheets. Numerical solutions of the magnetohydrodynamic equations have elucidated the role of expansion on the evolution of the turbulence. Such studies are clarifying not only how a turbulent cascade develops, but also the nature of the symmetries of the turbulence. Of particular interest is the origin of the two-component correlation function of magnetic fluctuations that was deduced from ISEE-3 data. A central issue to be resolved is whether the correlation function indicates the existence of a quasi-two- dimensional component of the turbulence, or reflects another origin, such as pressure-balanced structures or small velocity shears. In our efforts to simulate solar wind turbulence we have included a tilted rotating current heliospheric sheet as well as variety of waves (e.g., Alfvénic, quasi-two-dimensional, pressure balance structures) and microstreams. These simulations have replicated many of the observations, but challenges remain.
From the Einstein-Szilard Patent to Modern Magnetohydrodynamics.
ERIC Educational Resources Information Center
Povh, I. L.; Barinberg, A. D.
1979-01-01
Examines present-day and future prospects of the applications of modern magnetohydrodynamics in a number of countries. Explains how the electromagnetic pump, which was invented by Einstein and Leo Szilard, led to the development of applied magnetohydrodynamics. (HM)
Localization in inelastic rate dependent shearing deformations
NASA Astrophysics Data System (ADS)
Katsaounis, Theodoros; Lee, Min-Gi; Tzavaras, Athanasios
2017-01-01
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, indicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing structure and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions.
Variational Integrators for Ideal and Reduced Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Kraus, Michael; Maj, Omar; Tassi, Emanuele; Grasso, Daniela
2016-10-01
Ideal and reduced magnetohydrodynamics are simplified sets of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their geometrical character. The resulting integrators preserve important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As these integrators are free of numerical resistivity, the magnetic field line topology is preserved and spurious reconnection is absent in the ideal case. Only when effects of finite electron mass are added, magnetic reconnection takes place. The excellent conservation properties of the methods are exemplified with numerical examples in 2D. We conclude with an outlook towards the treatment of general geometries in 3D and full magnetohydrodynamics.
New approach to nonrelativistic ideal magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Kumar, Kuldeep
2016-07-01
We provide a novel action principle for nonrelativistic ideal magnetohydrodynamics in the Eulerian scheme exploiting a Clebsch-type parametrisation. Both Lagrangian and Hamiltonian formulations have been considered. Within the Hamiltonian framework, two complementary approaches have been discussed using Dirac's constraint analysis. In one case the Hamiltonian is canonical involving only physical variables but the brackets have a noncanonical structure, while the other retains the canonical structure of brackets by enlarging the phase space. The special case of incompressible magnetohydrodynamics is also considered where, again, both the approaches are discussed in the Hamiltonian framework. The conservation of the stress tensor reveals interesting aspects of the theory.
The magnetohydrodynamics of current sheets
NASA Technical Reports Server (NTRS)
Priest, E. R.
1985-01-01
Examples of current sheets are summarized and their formation is described. A universal phenomenon in cosmic plasmas is the creation of sheets off intense current near X-type neutral points (where the magnetic field vanishes). These sheets are important as sites where the magnetic-field energy is converted efficiently into heat and bulk kinetic energy and where particles can be accelerated to high energies. Examples include disruptions in laboratory tokamaks, substorms in the earth's magnetosphere, and flares on the sun. The basic behavior of a one-dimensional sheet is presented, together with an account of the linear tearing-mode instability that can cause the field lines in such a sheet to reconnect. Such reconnection may develop in different ways: it may arise from a spontaneous instability or it may be driven, either from outside by motions or locally by a resistivity enhancement. Various processes are described that may occur during the nonlinear development of tearing, along with the many numerical and laboratory experiments that are aiding our understanding of this intriguing cosmical process.
Disruption of a helmet streamer by photospheric shear
NASA Technical Reports Server (NTRS)
Linker, Jon A.; Mikic, Zoran
1995-01-01
Helmet streamers on the Sun have been observed to be the site of coronal mass ejections, dynamic events that eject coronal plasma and magnetic fields into the solar wind. We develop a two-dimensional (azimuthally symmetric) helmet streamer configuration by computing solutions of the time-dependent magnetohydrodynamic (MHD) equations, and we investigate the evolution of the configuration when photospheric shearing motions are imposed. We find that the configuration disrupts when a critical shear is exceeded, ejecting a plasmoid into the solar wind. The results are similar to the case of a sheared dipole magnetic field in a hydrostatic atmosphere (Mikic & Linker 1994). However, the presence of the outflowing solar wind makes the disruption significantly more energetic when a helmet streamer is sheared. Our resutls suggest that shearing of helmet streamers may initiate coronal mass ejections.
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.
MHD Instabilities Occurring Near/AT the Transport Barrier, Including Loss of Confinement in H-Modes
L. L. Lao
1999-09-01
In configurations with transport barriers the improved edge and core confinement leads to large pressure gradient and large edge bootstrap current density which often drive magnetohydrodynamic (MHD) instabilities terminating the discharge or reducing the discharge performance. The edge and the core transport barriers deteriorate or are completely lost. In this presentation, recent experimental and theoretical developments concerning MHD instabilities occurring near/at the edge and the core transport barriers are summarized emphasizing the dominant instabilities and the comparison with theory.
Stability of magnetohydrodynamic Dean Flow as applied to centrifugally confined plasmas
Hassam, A.B.
1999-10-01
Dean Flow is the azimuthal flow of fluid between static concentric cylinders. In a magnetized plasma, there may also be radial stratification of the pressure. The ideal magnetohydrodynamic stability of such a flow in the presence of a strong axial magnetic field and an added radial gravitational force is examined. It is shown that both the Kelvin{endash}Helmholtz instability and pressure-gradient-driven interchanges can be stabilized if the flow is driven by a unidirectional external force and if the plasma annulus is sufficiently thin (large aspect ratio). These results find application in schemes using centrifugal confinement of plasma for fusion. {copyright} {ital 1999 American Institute of Physics.}
Variational integration for ideal magnetohydrodynamics with built-in advection equations
Zhou, Yao; Burby, J. W.; Bhattacharjee, A.; Qin, Hong
2014-10-15
Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum-preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
NASA Astrophysics Data System (ADS)
Morrison, P. J.; Andreussi, T.; Pegoraro, F.
2016-10-01
In a series of papers we have investigated general properties of equilibria and their stability in each of the Lagrangian, Eulerian, and Dynamically Accessible stability formulations of magnetohydrodynamics. In our latest work we compare and contrast stability results with these formulations for two applications: stratified convection and rotating pinch equilibrium configurations. The former example, emphasizes the role played entropy, while the later demonstrates the utility of a relabeling transformation that we introduced in our earlier work. Comparisons to classical works, in particular on interchange instability, are made. DOE DE-FG02-04ER-54742.
On energy conservation in extended magnetohydrodynamics
Kimura, Keiji; Morrison, P. J.
2014-08-15
A systematic study of energy conservation for extended magnetohydrodynamic models that include Hall terms and electron inertia is performed. It is observed that commonly used models do not conserve energy in the ideal limit, i.e., when viscosity and resistivity are neglected. In particular, a term in the momentum equation that is often neglected is seen to be needed for conservation of energy.
Solar-driven liquid metal magnetohydrodynamic generator
NASA Technical Reports Server (NTRS)
Lee, J. H.; Hohl, F.
1981-01-01
A solar oven heated by concentrated solar radiation as the heat source of a liquid metal magnetohydrodynamic (LMMHD) power generation system is proposed. The design allows the production of electric power in space, as well as on Earth, at high rates of efficiency. Two types of the solar oven suitable for the system are discussed.
Potential vorticity formulation of compressible magnetohydrodynamics.
Arter, Wayne
2013-01-04
Compressible ideal magnetohydrodynamics is formulated in terms of the time evolution of potential vorticity and magnetic flux per unit mass using a compact Lie bracket notation. It is demonstrated that this simplifies analytic solution in at least one very important situation relevant to magnetic fusion experiments. Potentially important implications for analytic and numerical modelling of both laboratory and astrophysical plasmas are also discussed.
Physical consistency in modeling interplanetary magnetohydrodynamic fluctuations
NASA Technical Reports Server (NTRS)
Zhou, Y.; Matthaeus, W. H.; Roberts, D. A.; Goldstein, M. L.
1990-01-01
The validity of the Velli, Grappin and Mangeney (1989) model is evaluated. It is argued that the model is incorrect because it mixes different dynamical models, assumes weak nonlinearities, makes predictions that vary with observations, and violates causality. It is proposed that self-similar behavior in the coronal source region of the magnetohydrodynamic fluctuations cause the Kolmogorov-like spectra.
Global Magnetohydrodynamic Modeling of the Solar Corona
NASA Technical Reports Server (NTRS)
Linker, Jon A.
2001-01-01
This report describes the progress made in the investigation of the solar corona using magnetohydrodynamic (MHD) simulations. Coronal mass ejections (CME) are believed to be the primary cause of nonrecurrent geomagnetic storms and these have been investigated through the use of three-dimensional computer simulation.
Combustion and Magnetohydrodynamic Processes in Advanced Pulse Detonation Rocket Engines
NASA Astrophysics Data System (ADS)
Cole, Lord Kahil
A number of promising alternative rocket propulsion concepts have been developed over the past two decades that take advantage of unsteady combustion waves in order to produce thrust. These concepts include the Pulse Detonation Rocket Engine (PDRE), in which repetitive ignition, propagation, and reflection of detonations and shocks can create a high pressure chamber from which gases may be exhausted in a controlled manner. The Pulse Detonation Rocket Induced Magnetohydrodynamic Ejector (PDRIME) is a modification of the basic PDRE concept, developed by Cambier (1998), which has the potential for performance improvements based on magnetohydrodynamic (MHD) thrust augmentation. The PDRIME has the advantage of both low combustion chamber seeding pressure, per the PDRE concept, and efficient energy distribution in the system, per the rocket-induced MHD ejector (RIME) concept of Cole, et al. (1995). In the initial part of this thesis, we explore flow and performance characteristics of different configurations of the PDRIME, assuming quasi-one-dimensional transient flow and global representations of the effects of MHD phenomena on the gas dynamics. By utilizing high-order accurate solvers, we thus are able to investigate the fundamental physical processes associated with the PDRIME and PDRE concepts and identify potentially promising operating regimes. In the second part of this investigation, the detailed coupling of detonations and electric and magnetic fields are explored. First, a one-dimensional spark-ignited detonation with complex reaction kinetics is fully evaluated and the mechanisms for the different instabilities are analyzed. It is found that complex kinetics in addition to sufficient spatial resolution are required to be able to quantify high frequency as well as low frequency detonation instability modes. Armed with this quantitative understanding, we then examine the interaction of a propagating detonation and the applied MHD, both in one-dimensional and two
The possibility of Kelvin-Helmholtz instability in solar spicules
NASA Astrophysics Data System (ADS)
Ajabshirizadeh, A.; Ebadi, H.; Vekalati, R. E.; Molaverdikhani, K.
2015-05-01
Transversal oscillations of spicules axes may be related to the propagation of magnetohydrodynamic waves along them. These waves may become unstable and the instability can be of the Kelvin-Helmholtz type. We use the dispersion relation of kink mode derived from linearized magnetohydrodynamic equations. The input parameters of the derived dispersion equation, namely, spicules and their ambient medium densities ratios as well as their corresponding magnetic fields ratios, are considered to be within the range 0-1. By solving the dispersion equation numerically, we show that for higher densities and lower magnetic fields ratios within the range mentioned, the KHI onset in type ii spicules conditions is possible. This possibility decreases with an increase in Alfvén velocity inside spicules. A rough criterion for appearing of Kelvin-Helmholtz instability is obtained. We also drive a more reliable and exact criterion for KHI onset of kink waves.
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.
NASA Astrophysics Data System (ADS)
Raphaldini, Breno; Raupp, Carlos F. M.
2015-01-01
The solar dynamo is known to be associated with several periodicities, with the nearly 11/22 yr cycle being the most pronounced one. Even though these quasiperiodic variations of solar activity have been attributed to the underlying dynamo action in the Sun's interior, a fundamental theoretical description of these cycles is still elusive. Here, we present a new possible direction in understanding the Sun's cycles based on resonant nonlinear interactions among magnetohydrodynamic (MHD) Rossby waves. The WKB theory for dispersive waves is applied to magnetohydrodynamic shallow-water equations describing the dynamics of the solar tachocline, and the reduced dynamics of a resonant triad composed of MHD Rossby waves embedded in constant toroidal magnetic field is analyzed. In the conservative case, the wave amplitudes evolve periodically in time, with periods on the order of the dominant solar activity timescale (~11 yr). In addition, the presence of linear forcings representative of either convection or instabilities of meridionally varying background states appears to be crucial in balancing dissipation and thus sustaining the periodic oscillations of wave amplitudes associated with resonant triad interactions. Examination of the linear theory of MHD Rossby waves embedded in a latitudinally varying mean flow demonstrates that MHD Rossby waves propagate toward the equator in a waveguide from -35° to 35° in latitude, showing a remarkable resemblance to the structure of the butterfly diagram of the solar activity. Therefore, we argue that resonant nonlinear magnetohydrodynamic Rossby wave interactions might significantly contribute to the observed cycles of magnetic solar activity.
Instability of finite volumes of magnetic fluid in channels
Bashtovoi, V.G.; Mikhalev, V.P.; Reks, A.G.; Taits, E.M.
1987-07-01
The instability and magnetohydrodynamic behavior of a magnetic liquid comprised of a suspension of magnetite particles in transformer oil and in droplet form are assessed under experimental conditions in a tube under the effect of a magnetic field of varying strength. Flow visualization is used to monitor the behavior of the liquid. A flow model is constructed based on the experimental data which depicts, along with the above properties, the dependence of the critical magnetization on the dimensions of the capillary tube.
Collisionless Zonal Flow Saturation for Weak Magnetic Shear
NASA Astrophysics Data System (ADS)
Lu, Zhixin; Wang, Weixing; Diamond, Patrick; Ashourvan, Arash; Tynan, George
2015-11-01
The damping of the zonal flow, either collisional or collisionless, plays an important role in regulating the drift wave-zonal flow system, and can affect the transport and confinement. The tertiary instability, e.g., a generalized Kelvin-Helmholtz (KH) instability driven by flow shear, has been suggested theoretically as a possible damping mechanism [Rogers 2000 PRL, Diamond 2005 PPCF]. The sensitivity of the tertiary mode to magnetic shear has not been quantified, especially in weak magnetic shear regimes. In this work, parametric scans using gyrokinetic simulation demonstrate that the zonal electric field energy normalized by the turbulence electric field energy decreases as magnetic shear decreases. With ITG drive artificially eliminated, the time evolution of the zonal structure indicates that the zonal electric field damps more rapidly at weak shear. This suggests larger collisionless zonal flow damping or larger effective turbulent viscosity at weak magnetic shear. The effects of the zonal components of specific variables, e.g., the parallel shear flow and the radial electric field, on tertiary instability, are also studied. Quantitative studies on the magnetic shear scaling of tertiary instability excitation and the collisionless zonal flow saturation are ongoing.
Dynamic shear deformation in high purity Fe
Cerreta, Ellen K; Bingert, John F; Trujillo, Carl P; Lopez, Mike F; Gray, George T
2009-01-01
The forced shear test specimen, first developed by Meyer et al. [Meyer L. et al., Critical Adiabatic Shear Strength of Low Alloyed Steel Under Compressive Loading, Metallurgical Applications of Shock Wave and High Strain Rate Phenomena (Marcel Decker, 1986), 657; Hartmann K. et al., Metallurgical Effects on Impact Loaded Materials, Shock Waves and High Strain rate Phenomena in Metals (Plenum, 1981), 325-337.], has been utilized in a number of studies. While the geometry of this specimen does not allow for the microstructure to exactly define the location of shear band formation and the overall mechanical response of a specimen is highly sensitive to the geometry utilized, the forced shear specimen is useful for characterizing the influence of parameters such as strain rate, temperature, strain, and load on the microstructural evolution within a shear band. Additionally, many studies have utilized this geometry to advance the understanding of shear band development. In this study, by varying the geometry, specifically the ratio of the inner hole to the outer hat diameter, the dynamic shear localization response of high purity Fe was examined. Post mortem characterization was performed to quantify the width of the localizations and examine the microstructural and textural evolution of shear deformation in a bcc metal. Increased instability in mechanical response is strongly linked with development of enhanced intergranular misorientations, high angle boundaries, and classical shear textures characterized through orientation distribution functions.
Gillon, K.A.; Wooten, R.M.; Latham, R.L.; Witt, A.W.; Douglas, T.J.; Bauer, J.B.; Fuemmeler, S.J.
2009-01-01
Landslide hazard maps of Watauga County identify >2200 landslides, model debris flow susceptibility, and evaluate a 14km x 0.5km zone of existing and potential rock slope instability (ZEPRSI) near the Town of Boone. The ZEPRSI encompasses west-northwest trending (WNWT) topographic ridges where 14 active/past-active rock/weathered rock slides occur mainly in rocks of the Grandfather Mountain Window (GMW). The north side of this ridgeline is the GMW / Linville Falls Fault (LFF) contact. Sheared rocks of the Linville Falls Shear Zone (LFSZ) occur along the ridge and locally in the valley north of the contact. The valley is underlain principally by layered granitic gneiss comprising the Linville Falls/Beech Mountain/Stone Mountain Thrust Sheet. The integration of ArcGIS??? - format digital geologic and lineament mapping on a 6m LiDAR (Light Detecting and Ranging) digital elevation model (DEM) base, and kinematic analyses of site specific rock slope data (e.g., presence and degree of ductile and brittle deformation fabrics, rock type, rock weathering state) indicate: WNWT lineaments are expressions of a regionally extensive zone of fractures and faults; and ZEPRSI rock slope failures concentrate along excavated, north-facing LFF/LFSZ slopes where brittle fabrics overprint older metamorphic foliations, and other fractures create side and back release surfaces. Copyright 2009 ARMA, American Rock Mechanics Association.
Bora, Madhurjya P.; Buzar Baruah, Manasi
2011-01-15
A linear stability analysis of a thin rotating Keplerian disk is presented in the framework of Hall-magnetohydrodynamics with equilibrium pressure stratification and radiative cooling. Anisotropic pressure is considered in view of a stronger axial magnetic field. The analysis is relevant in studying the stability of protoplanetary disks. It has been shown that the equilibrium pressure stratification determines the growth rate of the Hall instability. With radiative loss, the thermal modes are affected by the Hall mode and the classical instability conditions.
Jeans instability of rotating magnetized quantum plasma: Influence of radiation
Joshi, H.; Pensia, R. K.
2015-07-31
The effect of radiative heat-loss function and rotation on the Jeans instability of quantum plasma is investigated. The basic set of equations for this problem is constructed by considering quantum magnetohydrodynamic (QMHD) model. Using normal mode analysis, the general dispersion relation is obtained. This dispersion relation is studied in both, longitudinal and transverse direction of propagations. In both case of longitudinal and transverse direction of propagation, the Jeans instability criterion is modified due to presence of radiative heat-loss function and quantum correction.
Interfacial Instabilities on a Droplet
NASA Astrophysics Data System (ADS)
Jalaal, Maziyar; Mehravaran, Kian
2013-11-01
The fragmentation of droplets is an essential stage of several natural and industrial applications such as fuel atomization and rain phenomena. In spite of its relatively long history, the mechanism of fragmentation is not clear yet. This is mainly due to small length and time scales as well as the non-linearity of the process. In the present study, two and three-dimensional numerical simulations have been performed to understand the early stages of the fragmentation of an initially spherical droplet. Simulations are performed for high Reynolds and a range of relatively high Weber numbers (shear breakup). To resolve the small-scale instabilities generated over the droplet, a second-order adaptive finite volume/volume of fluids (FV/VOF) method is employed, where the grid resolution is increased with the curvature of the gas-liquid interface as well as the vorticity magnitude. The study is focused on the onset and growth of interfacial instabilities. The role of Kelvin-Helmholtz instability (in surface wave formation) and Rayleigh-Taylor instability (in azimuthal transverse modulation) are shown and the obtained results are compared with the linear instability theories for zero and non-zero vorticity layers. Moreover, the analogy between the fragmentation of a single drop and a co-axial liquid jet is discussed. The current results can be used for the further development of the current secondary atomization models.
Explosive Instability of Prominence Flux Ropes
Hurricane, O; Fong, R H L; Cowley, S C
2002-09-04
The rapid, Alfvenic, time scale of erupting solar-prominences has been an enigma ever since they where first identified. Investigators have proposed a variety of different mechanisms in an effort to account for the abrupt reconfiguration observed. No one mechanism clearly stands out as the single cause of these explosive events. Recent analysis has demonstrated that field lines in the solar atmosphere are metastable to ballooning type instabilities. It has been found previously that in ideal MHD plasmas marginally unstable ballooning modes inevitably become ''explosive'' evolving towards a finite time singularity via a nonlinear 3D instability called ''Nonlinear Magnetohydrodynamic Detonation.'' Thus, this mechanism is a good candidate to explain explosive events observed in the solar atmosphere of our star or in others.
Magnetohydrodynamic Simulation of Solid-Deuterium - Z-Pinch Experiments
NASA Astrophysics Data System (ADS)
Sheehey, Peter Trogdon
Solid-deuterium-initiated Z-pinch experiments are numerically simulated using a two-dimensional resistive magnetohydrodynamic model, which includes many important experimental details, such as "cold-start" initial conditions, thermal conduction, radiative energy loss, actual discharge current vs. time, and grids of sufficient size and resolution to allow realistic development of the plasma. The alternating -direction-implicit numerical technique used meets the substantial demands presented by such a computational task. Simulations of fiber-initiated experiments show that when the fiber becomes fully ionized (at a time depending on current ramp and fiber thickness), rapidly developing m = 0 instabilities, which originated in the coronal plasma generated from the ablating fiber, drive intense non-uniform heating and rapid expansion of the plasma column. The possibility that inclusion of additional physical effects would improve stability is explored. Finite-Larmor-radius-ordered Hall and diamagnetic pressure terms in the magnetic field evolution equation, corresponding energy equation terms, and separate ion and electron energy equations are included; these do not change the basic results. Model diagnostics, such as shadowgrams and interferograms, generated from simulation results, are in good agreement with experiment. Two alternative experimental approaches are explored: high-current magnetic implosion of hollow cylindrical deuterium shells, and "plasma -on wire" (POW) implosion of low-density plasma onto a central deuterium fiber. By minimizing instability problems, these techniques may allow attainment of higher temperatures and densities than possible with bare fiber-initiated Z -pinches. Conditions for significant D-D or D-T fusion neutron production may be realizable with these implosion -based approaches.
Magnetohydrodynamic modeling of the solar eruption on 2010 April 8
Kliem, B.; Su, Y. N.; Van Ballegooijen, A. A.; DeLuca, E. E.
2013-12-20
The structure of the coronal magnetic field prior to eruptive processes and the conditions for the onset of eruption are important issues that can be addressed through studying the magnetohydrodynamic (MHD) stability and evolution of nonlinear force-free field (NLFFF) models. This paper uses data-constrained NLFFF models of a solar active region (AR) that erupted on 2010 April 8 as initial conditions in MHD simulations. These models, constructed with the techniques of flux rope insertion and magnetofrictional relaxation (MFR), include a stable, an approximately marginally stable, and an unstable configuration. The simulations confirm previous related results of MFR runs, particularly that stable flux rope equilibria represent key features of the observed pre-eruption coronal structure very well, and that there is a limiting value of the axial flux in the rope for the existence of stable NLFFF equilibria. The specific limiting value is located within a tighter range, due to the sharper discrimination between stability and instability by the MHD description. The MHD treatment of the eruptive configuration yields a very good agreement with a number of observed features, like the strongly inclined initial rise path and the close temporal association between the coronal mass ejection and the onset of flare reconnection. Minor differences occur in the velocity of flare ribbon expansion and in the further evolution of the inclination; these can be eliminated through refined simulations. We suggest that the slingshot effect of horizontally bent flux in the source region of eruptions can contribute significantly to the inclination of the rise direction. Finally, we demonstrate that the onset criterion, formulated in terms of a threshold value for the axial flux in the rope, corresponds very well to the threshold of the torus instability in the considered AR.
An adaptive mesh magneto-hydrodynamic analysis of interstellar clouds
NASA Astrophysics Data System (ADS)
Kominsky, Paul J.
Interstellar clouds play a key role in many astrophysical events. The interactions of dense interstellar clouds with shock waves and interstellar wind were investigated using an adaptive three-dimensional Cartesian mesh approach to the magneto-hydrodynamic equations. The mixing of the cloud material with the post-shock material results in complex layers of current density. In both the shock and wind interactions, a tail develops similar to the tail found with comets due to the solar wind. The orientation of this tail structure changes with the direction of the magnetic field, and may be useful to observationally determining the orientation of magnetic fields in the interstellar medium. The octree data structure was analyzed in regard to parallel work units. Larger block sizes have a higher volume to surface ratio and support a higher percentage of computational cells to non-computational cells, but require more cells at the finest grid resolution. Keeping the minimum resolution of the grid fixed, and averaging over all possible grids, the analysis confirms experience that block sizes larger than 8 × 8 × 8 cells do not improve storage efficiency. A novel algorithm was developed to implement rotationally periodic boundary conditions on quadtree and octree data, structures. Astrophysical flows wit h symmetric circulation, such as accretion disks, or periodic instabilities, such supernova remnants, may be able to take advantage of such boundary conditions while maintaining the other benefits of a Cartesian grid.
Some topics in the magnetohydrodynamics of accreting magnetic compact objects
NASA Technical Reports Server (NTRS)
Aly, J. J.
1986-01-01
Magnetic compact objects (neutron stars or white dwarfs) are currently thought to be present in many accreting systems that are releasing large amounts of energy. The magnetic field of the compact star may interact strongly with the accretion flow and play an essential role in the physics of these systems. Some magnetohydrodynamic (MHD) problems that are likely to be relevant in building up self-consistent models of the interaction between the accreting plasma and the star's magnetosphere are addressed in this series of lectures. The basic principles of MHD are first introduced and some important MHD mechanisms (Rayleigh-Taylor and Kelvin-Helmholtz instabilities; reconnection) are discussed, with particular reference to their role in allowing the infalling matter to penetrate the magnetosphere and mix with the field. The structure of a force-free magnetosphere and the possibility of quasistatic momentum and energy transfer between regions linked by field-aligned currents are then studied in some detail. Finally, the structure of axisymmetric accretion flows onto magnetic compact objects is considered.
Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe?
NASA Astrophysics Data System (ADS)
Wurster, James; Price, Daniel J.; Bate, Matthew R.
2016-03-01
We investigate whether or not the low ionization fractions in molecular cloud cores can solve the `magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionization chemistry assuming 0.1 μm grains. When including only ambipolar diffusion or Ohmic resistivity, discs do not form in the presence of strong magnetic fields, similar to the cases using ideal MHD. With the Hall effect included, disc formation depends on the direction of the magnetic field with respect to the rotation vector of the gas cloud. When the vectors are aligned, strong magnetic braking occurs and no disc is formed. When the vectors are anti-aligned, a disc with radius of 13 au can form even in strong magnetic when all three non-ideal terms are present, and a disc of 38 au can form when only the Hall effect is present; in both cases, a counter-rotating envelope forms around the first hydrostatic core. For weaker, anti-aligned fields, the Hall effect produces massive discs comparable to those produced in the absence of magnetic fields, suggesting that planet formation via gravitational instability may depend on the sign of the magnetic field in the precursor molecular cloud core.
Criticality and turbulence in a resistive magnetohydrodynamic current sheet
NASA Astrophysics Data System (ADS)
Klimas, Alexander J.; Uritsky, Vadim M.
2017-02-01
Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.
Criticality and turbulence in a resistive magnetohydrodynamic current sheet.
Klimas, Alexander J; Uritsky, Vadim M
2017-02-01
Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.
Anisotropic diffusion in mesh-free numerical magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.
2017-04-01
We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.
The interaction of a magnetohydrodynamical shock with a filament
NASA Astrophysics Data System (ADS)
Goldsmith, K. J. A.; Pittard, J. M.
2016-09-01
We present 3D magnetohydrodynamic numerical simulations of the adiabatic interaction of a shock with a dense, filamentary cloud. We investigate the effects of various filament lengths and orientations on the interaction using different orientations of the magnetic field, and vary the Mach number of the shock, the density contrast of the filament χ, and the plasma beta, in order to determine their effect on the evolution and lifetime of the filament. We find that in a parallel magnetic field filaments have longer lifetimes if they are orientated more `broadside' to the shock front, and that an increase in χ hastens the destruction of the cloud, in terms of the modified cloud-crushing time-scale, tcs. The combination of a mild shock and a perpendicular or oblique field provides the best condition for extending the life of the filament, with some filaments able to survive almost indefinitely since they are cocooned by the magnetic field. A high value for χ does not initiate large turbulent instabilities in either the perpendicular or oblique field cases but rather draws the filament out into long tendrils which may eventually fragment. In addition, flux ropes are only formed in parallel magnetic fields. The length of the filament is, however, not as important for the evolution and destruction of a filament.
High-. beta. operation and MHD (magnetohydrodynamic) activity on TFTR
McGuire, K.
1990-04-01
Magnetohydrodynamic (MHD) activity within three zones (core, half- radius, and edge) of TFTR (Plasma Physics and Controlled Nuclear Fusion Research (1986), (IAEA, Vienna, 1987), Vol. 1, P. 51) tokamak plasmas are discussed. Near the core of the plasma column, sawteeth are often observed. Two types of sawteeth are studied in detail: one with complete, and the other with incomplete magnetic reconnection. Their characteristics are determined by the shape of the q profile. Near the half-radius the m/n = 3/2 and 2/1 resistive ballooning modes are found to correlate with a beta collapse. The pressure and the pressure gradient at the mode rational surface are found to play an important role in stability. MHD activity is also studied at the plasma edge during limiter H-modes. The Edge Localized Mode (ELMs) are found to have a precursor mode with a frequency between 50--200 kHz and a mode number m/n = 1/0. The mode does not show a ballooning structure. While these instabilities have been studied on many other machines, on TFTR the studies have been extended to high pressure (plasma pressure greater than 4 {times} 10{sup 5} Pa) and low collisionality. 16 refs., 3 figs.
Cosmos++: Relativistic Magnetohydrodynamics on Unstructured Grids with Local Adaptive Refinement
Anninos, P; Fragile, P C; Salmonson, J D
2005-05-06
A new code and methodology are introduced for solving the fully general relativistic magnetohydrodynamic (GRMHD) equations using time-explicit, finite-volume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. it provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threated oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. A number of tests are presented to demonstrate robustness of the numerical algorithms and adaptive mesh framework over a wide spectrum of problems, boosts, and astrophysical applications, including relativistic shock tubes, shock collisions, magnetosonic shocks, Alfven wave propagation, blast waves, magnetized Bondi flow, and the magneto-rotational instability in Kerr black hole spacetimes.
Magnetohydrodynamic flow of a binary electrolyte in a concentric annulus
NASA Astrophysics Data System (ADS)
Qin, M.; Bau, H. H.
2012-03-01
We study theoretically magnetohydrodynamic (MHD) motion of a binary electrolyte in a concentric annulus subjected to a uniform, axial magnetic field. The annulus' cylindrical surfaces serve as electrodes. When a potential difference is imposed across the cylindrical electrodes, radial electric current flows in the solution and interacts with the axial magnetic field to induce a Lorentz body force that drives azimuthal fluid flow. When the annulus is infinitely long, a purely azimuthal flow (analogous to the classical Dean flow) is possible. We determine the velocity profile, ion concentration fields, and current density as functions of the electrodes' potential difference and study the linear stability of the azimuthal flow. Of particular interest is the effect of the ions' concentration fields on the centrifugal Dean instability. When the current is directed outwardly, electrochemical effects destabilize the flow, and the MHD flow loses stability at a Dean number much lower than its analogous, pressure driven flow. The supercritical flow consists of convective cells in the transverse plane. In contrast, when the current is directed inwardly, electrochemical effects stabilize the flow and the azimuthal flow is linearly stable for all Dean numbers. When the annulus is capped, purely azimuthal flow is no longer possible, and the flow in the annulus is always three-dimensional. In this case, the secondary flow is mostly driven by pressure gradients induced by the no-slip floor and ceiling. The intensity of the transverse convection depends then only weakly on the current's direction.
Low-frequency instabilities of collisionless plasma and the 16-moment approximation
Dzhalilov, N. S. Kuznetsov, V. D.
2013-12-15
Using the 16-moment equations that take into account heat fluxes in anisotropic collisionless plasma, the properties of magnetohydrodynamic (MHD) instabilities are investigated. For all instabilities occurring in the MHD approach (the normal incompressible firehose instability, the second compressible almost longitudinal firehose instability, and the almost transverse mirror instability of slow magnetosonic modes, as well as thermal instability caused by the heat flux directed along the magnetic field), their kinetic analogs are considered. The kinetic dispersion relation in the low-frequency range in the vicinity of the ion thermal velocity is analyzed. The flow of plasma ions along the magnetic field is taken into account. The thresholds and instability growth rates obtained in the MHD and kinetic approaches are found to be in good agreement. This indicates that the 16-moment MHD equations adequately describe the dynamics of collisionless plasma.
The classification of magnetohydrodynamic regimes of thermonuclear combustion
Remming, Ian S.; Khokhlov, Alexei M.
2014-10-10
Physical properties of magnetohydrodynamic (MHD) reaction fronts are studied as functions of the thermodynamic conditions, and the strength and orientation of the magnetic field in the unburned matter through which the fronts propagate. We determine the conditions for the existence of the various types of MHD reaction fronts and the character of the changes in physical quantities across these reaction fronts. The analysis is carried out in general for a perfect gas equation of state and a constant energy release, and then extended to thermonuclear reaction fronts in degenerate carbon-oxygen mixtures and degenerate helium in conditions typical of Type Ia supernova explosions. We find that as unburned matter enters perpendicular to a reaction front, the release of energy through burning generates shear velocity in the reacting gas that, depending on the type of reaction front, strengthens or weakens the magnetic field. In addition, we find that the steady-state propagation of a reaction front is impossible for certain ranges of magnetic field direction. Our results provide insight into the phenomena of MHD thermonuclear combustion that is relevant to the interpretation of future simulations of SN Ia explosions that have magnetic fields systematically incorporated.
Nonlinear wave interaction and spin models in the magnetohydrodynamic regime
NASA Astrophysics Data System (ADS)
Brodin, G.; Lundin, J.; Zamanian, J.; Stefan, M.
2011-08-01
Here we consider the influence on the electron spin in the magnetohydrodynamic (MHD) regime. Recently developed models that include spin-velocity correlations are taken as the starting point. A theoretical argument is presented, suggesting that in the MHD regime a single-fluid electron model with spin correlations is equivalent to a model with spin-up and spin-down electrons constituting different fluids, but where the spin-velocity correlations are omitted. Three-wave interaction of two shear Alfvén waves and a compressional Alfvén wave is then taken as a model problem to evaluate the asserted equivalence. The theoretical argument turns out to be supported, because the predictions of the two models agree completely. Furthermore, the three-wave coupling coefficients obey the Manley-Rowe relations, which further support the soundness of the models and the validity of the assumptions made in the derivation. Finally, we point out that the proposed two-fluid model can be incorporated in standard particle-in-cell schemes with only minor modifications.
Multi-region relaxed magnetohydrodynamics with flow
Dennis, G. R. Dewar, R. L.; Hole, M. J.; Hudson, S. R.
2014-04-15
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Hall-magnetohydrodynamic turbulence with electron inertia
NASA Astrophysics Data System (ADS)
Martin, L. N.; Andres, N.; Dmitruk, P.; Gomez, D. O.
2013-12-01
The magnetohydrodynamic (one-fluid) model is often regarded as a reasonable description of the dynamics of a plasma. One-fluid models are useful in the context of large scale dynamics, but when a more detailed description is needed (for instance, when the physical context favors the development of small scales) it is most appropriate to consider two-fluid models. Within the framework of two-fluid MHD for a fully ionized hydrogen plasma, we study the effect of the Hall term and electron inertia in MHD turbulence, observing whether these effects change the energy cascade, the characteristic scales of the flow and the dynamics of global magnitudes, with particular interest in the dissipation processes. Numerical simulations of freely evolving three-dimensional reduced magnetohydrodynamics (RHMHD) and 2.5-D Hall-MHD including electron inertia are performed for different values of the ion and electron skin depth (controlling the impact of the Hall term and the electron inertia).
Multi-fluid problems in magnetohydrodynamics with applications to astrophysical processes
NASA Astrophysics Data System (ADS)
Greenfield, Eric John
2016-01-01
I begin this study by presenting an overview of the theory of magnetohydrodynamics and the necessary conditions to justify the fluid treatment of a plasma. Upon establishing the fluid description of a plasma we move on to a discussion of magnetohydrodynamics in both the ideal and Hall regimes. This framework is then extended to include multiple plasmas in order to consider two problems of interest in the field of theoretical space physics. The first is a study on the evolution of a partially ionized plasma, a topic with many applications in space physics. A multi-fluid approach is necessary in this case to account for the motions of an ion fluid, electron fluid and neutral atom fluid; all of which are coupled to one another by collisions and/or electromagnetic forces. The results of this study have direct application towards an open question concerning the cascade of Kolmogorov-like turbulence in the interstellar plasma which we will discuss below. The second application of multi-fluid magnetohydrodynamics that we consider in this thesis concerns the amplification of magnetic field upstream of a collisionless, parallel shock. The relevant fluids here are the ions and electrons comprising the interstellar plasma and the galactic cosmic ray ions. Previous works predict that the streaming of cosmic rays lead to an instability resulting in significant amplification of the interstellar magnetic field at supernova blastwaves. This prediction is routinely invoked to explain the acceleration of galactic cosmic rays up to energies of 1015 eV. I will examine this phenomenon in detail using the multi-fluid framework outlined below. The purpose of this work is to first confirm the existence of an instability using a purely fluid approach with no additional approximations. If confirmed, I will determine the necessary conditions for it to operate.
Global modes of flute instability of a rotating cylindrical plasma
Sorokina, E. A.
2009-05-15
The influence of rotation on the flute instability of a cylindrical gravitating plasma in a straight inhomogeneous magnetic field is studied in the framework of one-fluid magnetohydrodynamics. The dispersion relation and integral expression for the instability growth rate of eigenmodes are derived. It is shown that, in the framework of the given problem, rotation is a destabilizing factor, and the corresponding theorem is proved for the general case. For a linear radial profile of the rotation frequency, the structure of eigenmodes is calculated. The growth rate of these modes is shown to increase with increasing rotation velocity and azimuthal mode number. It is found that plasma rotation in the eigenmode localization region leads to the displacement of perturbation from the rotation region, which results in a decrease in the instability growth rate. The absence of eigenmodes (i.e., exponential instability of the system) for certain profiles of the density and rotation frequency is demonstrated.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Lattice Boltzmann model for simulation of magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William
1991-01-01
A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.
New cellular automaton model for magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Hudong; Matthaeus, William H.
1987-01-01
A new type of two-dimensional cellular automation method is introduced for computation of magnetohydrodynamic fluid systems. Particle population is described by a 36-component tensor referred to a hexagonal lattice. By appropriate choice of the coefficients that control the modified streaming algorithm and the definition of the macroscopic fields, it is possible to compute both Lorentz-force and magnetic-induction effects. The method is local in the microscopic space and therefore suited to massively parallel computations.
Nuclear Electric Magnetohydrodynamic Propulsion for Submarine
1989-05-01
Magnetohydrodynamic Theory 24 2.3 MHD Pump Analysis 29 2.4 Maximum Pump Efficiency and Power 33 2.5 MHD Electrical Generator 40 2.6 MHD Generator Requirements 44 3...propulsion was first demon- strated by Stewart Way who published a very complete and mathematically rigorous analysis of an external duct, DC...in simple analysis and still apply in a complicated cases which require computer or physical modeling. As mentioned before, the MHD generator works on
Geomagnetic main field modeling using magnetohydrodynamic constraints
NASA Technical Reports Server (NTRS)
Estes, R. H.
1985-01-01
The influence of physical constraints are investigated which may be approximately satisfied by the Earth's liquid core on models of the geomagnetic main field and its secular variation. A previous report describes the methodology used to incorporate nonlinear equations of constraint into the main field model. The application of that methodology to the GSFC 12/83 field model to test the frozen-flux hypothesis and the usefulness of incorporating magnetohydrodynamic constraints for obtaining improved geomagnetic field models is described.
Two-dimensional magnetohydrodynamic simulations of poloidal flows in tokamaks and MHD pedestal
NASA Astrophysics Data System (ADS)
Guazzotto, L.; Betti, R.
2011-09-01
Poloidal rotation is routinely observed in present-day tokamak experiments, in particular near the plasma edge and in the high-confinement mode of operation. According to the magnetohydrodynamic (MHD) equilibrium theory [R. Betti and J. P. Freidberg, Phys. Plasmas 7, 2439 (2000)], radial discontinuities form when the poloidal velocity exceeds the poloidal sound speed (or rather, more correctly, the poloidal magneto-slow speed). Two-dimensional compressible magnetohydrodynamic simulations show that the transonic discontinuities develop on a time scale of a plasma poloidal revolution to form an edge density pedestal and a localized velocity shear layer at the pedestal location. While such an MHD pedestal surrounds the entire core, the outboard side of the pedestal is driven by the transonic discontinuity while the inboard side is caused by a poloidal redistribution of the mass. The MHD simulations use a smooth momentum source to drive the poloidal flow. Soon after the flow exceeds the poloidal sound speed, the density pedestal and the velocity shear layer form and persist into a quasi steady state. These results may be relevant to the L-H transition, the early stages of the pedestal and edge transport barrier formation.
Two-dimensional magnetohydrodynamic simulations of poloidal flows in tokamaks and MHD pedestal
Guazzotto, L.; Betti, R.
2011-09-15
Poloidal rotation is routinely observed in present-day tokamak experiments, in particular near the plasma edge and in the high-confinement mode of operation. According to the magnetohydrodynamic (MHD) equilibrium theory [R. Betti and J. P. Freidberg, Phys. Plasmas 7, 2439 (2000)], radial discontinuities form when the poloidal velocity exceeds the poloidal sound speed (or rather, more correctly, the poloidal magneto-slow speed). Two-dimensional compressible magnetohydrodynamic simulations show that the transonic discontinuities develop on a time scale of a plasma poloidal revolution to form an edge density pedestal and a localized velocity shear layer at the pedestal location. While such an MHD pedestal surrounds the entire core, the outboard side of the pedestal is driven by the transonic discontinuity while the inboard side is caused by a poloidal redistribution of the mass. The MHD simulations use a smooth momentum source to drive the poloidal flow. Soon after the flow exceeds the poloidal sound speed, the density pedestal and the velocity shear layer form and persist into a quasi steady state. These results may be relevant to the L-H transition, the early stages of the pedestal and edge transport barrier formation.
On the preferred mode of jet instability
NASA Technical Reports Server (NTRS)
Petersen, R. A.; Samet, M. M.
1988-01-01
The preferred mode of instability was investigated in an axisymmetric air jet of moderate Reynolds number. Natural instabilities are shown to scale with local shear-layer thickness and the preferred mode is shown to be a shear-layer instability. The spatial evolution of the preferred mode was examined by exciting the flow acoustically and then mapping the phase-locked velocity fluctuations. Throughout the potential core region the phase-locked profiles are shown to agree with the eigensolutions of the Orr-Sommerfeld stability equations provided the calculations are based on measured, mean velocity profiles. The excitation intensity was varied from low levels, where the flow was merely tagged, to high levels where the mean flow was substantially distorted, and over that range of excitation there was no apparent deterioration in the agreement with stability predictions.
NASA Astrophysics Data System (ADS)
Stone, James M.; Norman, Michael L.
1992-06-01
In this, the second of a series of three papers, we continue a detailed description of ZEUS-2D, a numerical code for the simulation of fluid dynamical flows in astrophysics including a self-consistent treatment of the effects of magnetic fields and radiation transfer. In this paper, we give a detailed description of the magnetohydrodynamical (MHD) algorithms in ZEUS-2D. The recently developed constrained transport (CT) algorithm is implemented for the numerical evolution of the components of the magnetic field for MHD simulations. This formalism guarantees the numerically evolved field components will satisfy the divergence-free constraint at all times. We find, however, that the method used to compute the electromotive forces must be chosen carefully to propagate accurately all modes of MHD wave families (in particular shear Alfvén waves). A new method of computing the electromotive force is developed using the method of characteristics (MOC). It is demonstrated through the results of an extensive series of MHD test problems that the resulting hybrid MOC-CT method provides for the accurate evolution of all modes of MHD wave families.
Thermal instability of a radiative and resistive coronal plasma
NASA Technical Reports Server (NTRS)
Sparks, L.; Van Hoven, G.
1988-01-01
Thermal instability is believed to determine the evolution and formation of cool structures in the solar atmosphere such as the transition region and prominences (or filaments). The linear modes that arise in a sheared, force-free, magnetic field due to thermal instability are studied numerically. Previous studies have considered separately modes that arise due to the effects of radiation, compression, anisotropic thermal conduction, and ohmic heating. Here the results of such studies are integrated, first by presenting simple arguments that illustrate the essential physics of ideal, sheared-field, condensation modes, and second by showing numerically how finite resistivity affects the condensational instability in parameter regimes applicable to the solar corona.
Control of low-frequency plasma instabilities by a nonuniform radial electric field
Komori, A.; Watanabe, K.; Kawai, Y.
1988-01-01
Flute instability of a magnetoplasma is generated and controlled experimentally by a nonuniform weak radial electric field. Six concentric electrodes, biased separately, are used to change the radial electric field. The instability, which is different from the velocity shear flute instability, is observed in a plasma with well-type potential and hill-type density profiles.
Modeling the effect of toroidal plasma rotation on drift-magnetohydrodynamic modes in tokamaks
NASA Astrophysics Data System (ADS)
Chapman, I. T.; Sharapov, S. E.; Huysmans, G. T. A.; Mikhailovskii, A. B.
2006-06-01
A new code, MISHKA-F (Flow), has been developed as an extension of the ideal magneto-hydrodynamic (MHD) code MISHKA-1 [Mikhailovskii et al., Plasma Phys. Rep. 23, 844 (1997)] in order to investigate the linear MHD stability of ideal and resistive eigenmodes with respect to the effects of toroidal rotation in tokamaks in general toroidal geometry with the ion diamagnetic drift effect taken into account. Benchmark test results of the MISHKA-F code show good agreement with analytic theory [A. B. Mikhailovskii and S. E. Sharapov, Plasma Phys. Controlled Fusion 42, 57 (2000)] for the stability limits of the ideal n /m=1/1 internal kink mode. The combined stabilizing effects of the ion diamagnetic drift frequency, ω*i, and the toroidal flow shear are also studied. The ω*i stabilization of the internal kink mode is found to be more effective at finite flow shear. Finite-n ballooning modes are studied in plasmas with the toroidal flow shear effect included. The stabilization of the ballooning modes by toroidal rotation is found to agree well with earlier predictions [Webster et al., Phys. Plasmas 11, 2135 (2004)]. The effect of high flow shear is analyzed for a sawtoothing discharge typical in the Mega Ampère Spherical Tokamak (MAST) [Sykes et al., Nucl. Fusion 41, 1423 (2001)]. It is found that the ideal n =1 internal kink mode can be stabilized by toroidal rotation at values observed experimentally.
Modeling the effect of toroidal plasma rotation on drift-magnetohydrodynamic modes in tokamaks
Chapman, I.T.; Sharapov, S.E.; Huysmans, G.T.A.; Mikhailovskii, A. B.
2006-06-15
A new code, MISHKA-F (Flow), has been developed as an extension of the ideal magneto-hydrodynamic (MHD) code MISHKA-1 [Mikhailovskii et al., Plasma Phys. Rep. 23, 844 (1997)] in order to investigate the linear MHD stability of ideal and resistive eigenmodes with respect to the effects of toroidal rotation in tokamaks in general toroidal geometry with the ion diamagnetic drift effect taken into account. Benchmark test results of the MISHKA-F code show good agreement with analytic theory [A. B. Mikhailovskii and S. E. Sharapov, Plasma Phys. Controlled Fusion 42, 57 (2000)] for the stability limits of the ideal n/m=1/1 internal kink mode. The combined stabilizing effects of the ion diamagnetic drift frequency, {omega}{sub *i}, and the toroidal flow shear are also studied. The {omega}{sub *i} stabilization of the internal kink mode is found to be more effective at finite flow shear. Finite-n ballooning modes are studied in plasmas with the toroidal flow shear effect included. The stabilization of the ballooning modes by toroidal rotation is found to agree well with earlier predictions [Webster et al., Phys. Plasmas 11, 2135 (2004)]. The effect of high flow shear is analyzed for a sawtoothing discharge typical in the Mega Ampere Spherical Tokamak (MAST) [Sykes et al., Nucl. Fusion 41, 1423 (2001)]. It is found that the ideal n=1 internal kink mode can be stabilized by toroidal rotation at values observed experimentally.
Evolution of accretion discs around a kerr black hole using extended magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Foucart, Francois; Chandra, Mani; Gammie, Charles F.; Quataert, Eliot
2016-02-01
Black holes accreting well below the Eddington rate are believed to have geometrically thick, optically thin, rotationally supported accretion discs in which the Coulomb mean free path is large compared to GM/c2. In such an environment, the disc evolution may differ significantly from ideal magnetohydrodynamic (MHD) predictions. We present non-ideal global axisymmetric simulations of geometrically thick discs around a rotating black hole. The simulations are carried out using a new code GRIM, which evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal MHD. Non-ideal effects are modelled through heat conduction along magnetic field lines, and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. We find that the pressure anisotropy grows to match the magnetic pressure, at which point it saturates due to the mirror instability. The pressure anisotropy produces outward angular momentum transport with a magnitude comparable to that of MHD turbulence in the disc, and a significant increase in the temperature in the wall of the jet. We also find that, at least in our axisymmetric simulations, conduction has a small effect on the disc evolution because (1) the heat flux is constrained to be parallel to the field and the field is close to perpendicular to temperature gradients, and (2) the heat flux is choked by an increase in effective collisionality associated with the mirror instability.
NASA Astrophysics Data System (ADS)
Mutabazi, Innocent; Bai, Yang; Crumeyrolle, Olivier
2015-11-01
The analogy between viscoelastic instability in the Taylor-Couette flow and the magnetorotational instability (MRI) has been found by Ogilvie & Potter. It relies on the similarity between the governing equations of viscoelastic flows of constant viscosity (Oldroyd-B model equations)and those of Magnetohydrodynamics (MHD). We have performed linear stability analysis of the Taylor-Couette flow with a polymer solution obeying the Oldroyd-B model. A diagram of critical states shows the existence of stationary and helicoidal modes depending on the elasticity of the polymer solution. A generalized Rayleigh criterion determines the potentially unstable zone to pure elasticity-driven perturbations. Experimental results yield four type of modes : one pure elasticity mode and three elastorotational modes that are the MRI-analog modes. Anti-Keplerian case has also been investigated. There is a good agreement between experimental and theoretical results. Work supported by the CPER and ANR-LABEX EMC3.
Broken symmetry in ideal magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1993-01-01
A numerical study of the long-time evolution of a number of cases of inviscid, isotropic, incompressible, three-dimensional fluid, and magneto-fluid turbulence has been completed. The results confirm that ideal magnetohydrodynamic turbulence is non-ergodic if there is no external magnetic field present. This is due essentially to a canonical symmetry being broken in an arbitrary dynamical representation. The broken symmetry manifests itself as a coherent structure, i.e., a non-zero time-averaged part of the turbulent magnetic field. The coherent structure is observed, in one case, to contain about eighteen percent of the total energy.
Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay
NASA Astrophysics Data System (ADS)
Brandenburg, Axel; Kahniashvili, Tina
2017-02-01
We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wave number k ), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k4).
Nonlinear magnetohydrodynamics by Galerkin-method computation
NASA Technical Reports Server (NTRS)
Shan, Xiaowen; Montgomery, David; Chen, Hudong
1991-01-01
A fully spectral numerical code is used to explore the properties of voltage-driven dissipative magnetofluids inside a periodic cylinder with circular cross section. The trial functions are orthonormal eigenfunctions of the curl (Chandrasekhar-Kendall functions). Transitions are observed from axisymmetric resistive equilibria without flow to helically deformed laminar states with flow, and between pairs of helical laminar states with different pairs of poloidal and toroidal m and n numbers. States of minimum energy dissipation rate seem to be preferred. At high values of the pinch ratio, fully developed magnetohydrodynamic turbulence is observed.
Janvier, M; Kishimoto, Y; Li, J Q
2011-11-04
The onset of abrupt magnetic reconnection events, observed in the nonlinear evolution of double tearing modes (DTM), is investigated via reduced resistive magnetohydrodynamic simulations. We have identified the critical threshold for the parameters characterizing the linear DTM stability leading to the bifurcation to the explosive dynamics. A new type of secondary instability is discovered that is excited once the magnetic islands on each rational surface reach a critical structure characterized here by the width and the angle rating their triangularization. This new instability is an island structure-driven nonlinear instability, identified as the trigger of the subsequent nonlinear dynamics which couples flow and flux perturbations. This instability only weakly depends on resistivity.
Shear-Driven Reconnection in Kinetic Models
NASA Astrophysics Data System (ADS)
Black, C.; Antiochos, S. K.; Germaschewski, K.; Karpen, J. T.; DeVore, C. R.; Bessho, N.
2015-12-01
The explosive energy release in solar eruptive phenomena is believed to be due to magnetic reconnection. In the standard model for coronal mass ejections (CME) and/or solar flares, the free energy for the event resides in the strongly sheared magnetic field of a filament channel. The pre-eruption force balance consists of an upward force due to the magnetic pressure of the sheared field countered by a downward tension due to overlying unsheared field. Magnetic reconnection disrupts this force balance; therefore, it is critical for understanding CME/flare initiation, to model the onset of reconnection driven by the build-up of magnetic shear. In MHD simulations, the application of a magnetic-field shear is a trivial matter. However, kinetic effects are dominant in the diffusion region and thus, it is important to examine this process with PIC simulations as well. The implementation of such a driver in PIC methods is challenging, however, and indicates the necessity of a true multiscale model for such processes in the solar environment. The field must be sheared self-consistently and indirectly to prevent the generation of waves that destroy the desired system. Plasma instabilities can arise nonetheless. In the work presented here, we show that we can control this instability and generate a predicted out-of-plane magnetic flux. This material is based upon work supported by the National Science Foundation under Award No. AGS-1331356.
Observation of Rayleigh-Taylor-instability evolution in a plasma with magnetic and viscous effects
Adams, Colin S.; Moser, Auna L.; Hsu, Scott C.
2015-11-06
We present time-resolved observations of Rayleigh-Taylor-instability (RTI) evolution at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time (~10μs) is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density (~1014cm–3) and deceleration (~109 m/s2). The observed mode wavelength (≳1 cm) nearly doubles within a linear growth time. Furthermore, theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodynamic simulations including a physical viscosity model both suggest that the observed instability evolution is subject to magnetic and/or viscous effects.
Flute instability in a plasma confined by perfectly reflecting end walls
Farina, D.; Pozzoli, R.; Ryutov, D. )
1993-11-01
The magnetohydrodynamic stability of a low-pressure plasma confined along the magnetic field by the end walls that are perfectly reflecting the impinging particles is considered. It is shown that, if the magnetic field lines do not intersect the walls along the normal, a fast instability can develop. An explicit expression for the growth rate has been derived, and an analogy with the usual flute instability has been traced. The instability can play some role in the scrape-off layers of tokamaks with poloidal limiter.
Impact response of shear thickening suspensions
NASA Astrophysics Data System (ADS)
Brown, Eric; Ozgen, Oktar; Kallmann, Marcelo; Allen, Benjamin
2013-11-01
Dense suspensions of hard particles such as cornstarch in water exhibit shear thickening, in which the energy dissipation rate under shear dramatically increases with increasing shear rate. Recent work has established that in steady-state shear this phenomena is a result of a dynamic jamming of the particles in suspension. Several dynamic phenomena observed in such suspensions have long been assumed to be a consequence of this shear thickening; strong impact resistance, the ability of a person to run on the fluid surface, fingering and hole instabilities under vibration, and oscillations in the speed of sinking of an object in the fluid. However, I will present results of experiments consisting of an indenter impacting a dense suspension which demonstrate that the strong impact resistance cannot be explained by existing models for steady-state shear thickening. I will show these dynamic phenomena can be reproduced by graphical simulations based on a minimal phenomenological model in which the fluid has a stiffness with a dependence on velocity history. These and other recent results suggest a need for new models to understand the dynamic phenomena associated with shear thickening fluids.
Shear-flow Effects in Open Traps
Beklemishev, A. D.
2008-11-01
Interaction between shear flows and plasma instabilities and turbulence in open traps can lead to improved confinement both in experiments and in simulations. Shear flows, driven by biasing end-plates and limiters or by off-axis electron heating, in combination with the finite-larmor-radius (FLR) effects are shown to be efficient in confining plasmas even with unstable flute modes. Interpretation of the observed effects as the ''vortex confinement,'' i.e., confinement of the plasma core in the dead-flow zone of the driven vortex, is shown to agree well with simulations.
Unstable transition properties of the driven magnetohydrodynamic sheet pinch
NASA Technical Reports Server (NTRS)
Dahlburg, R. B.; Zang, T. A.; Montgomery, D.
1986-01-01
The unstable transition behavior of a bounded current-carrying two-dimensional magnetofluid is explored, using the hydrodynamic theory developed for parallel shear flows as a guide. Nonlinear excitation of the higher wavenumbers results in the development of electric current sheets of finite extent, as well as the formation of 'attraction currents' centered at the magnetic O-points. A secondary instability mechanism, the dynamic tearing of the electric current sheet, is also observed. This dynamic tearing leads to sawtoothlike temporal oscillations in certain global quantities. The long-time state of the system resembles a nonlinearly saturated state with significant excitation of many wavenumbers. Some features of this state can be understood by means of a Landau nonlinear stability theory based on certain assumptions about the perturbation energy balance.
Lamppa, Derek C.; Haill, Thomas A.; Alexander, C. Scott; Asay, James Russell
2010-09-01
A new experimental technique to measure material shear strength at high pressures has been developed for use on magneto-hydrodynamic (MHD) drive pulsed power platforms. By applying an external static magnetic field to the sample region, the MHD drive directly induces a shear stress wave in addition to the usual longitudinal stress wave. Strength is probed by passing this shear wave through a sample material where the transmissible shear stress is limited to the sample strength. The magnitude of the transmitted shear wave is measured via a transverse VISAR system from which the sample strength is determined.
Double-duct liquid metal magnetohydrodynamic engine
Haaland, Carsten M.
1997-01-01
An internal combustion, liquid metal (LM) magnetohydrodynamic (MHD) engine and an alternating current (AC) magnetohydrodynamic generator, are used in combination to provide useful AC electric energy output. The engine design has four pistons and a double duct configuration, with each duct containing sodium potassium liquid metal confined between free pistons located at either end of the duct. The liquid metal is forced to flow back and forth in the duct by the movement of the pistons, which are alternatively driven by an internal combustion process. In the MHD generator, the two LM-MHD ducts pass in close proximity through a Hartmann duct with output transformer. AC power is produced by operating the engine with the liquid metal in the two generator ducts always flowing in counter directions. The amount of liquid metal maintained in the ducts may be varied. This provides a variable stroke length for the pistons. The engine/generator provides variable AC power at variable frequencies that correspond to the power demands of the vehicular propulsion. Also the engine should maintain nearly constant efficiency throughout the range of power usage. Automobiles and trucks could be powered by the invention, with no transmission or power converter devices being required.
Double-duct liquid metal magnetohydrodynamic engine
Haaland, Carsten M.
1995-01-01
An internal combustion, liquid metal (LM) magnetohydrodynamic (MHD) engine and an alternating current (AC) magnetohydrodynamic generator, are used in combination to provide useful AC electric energy output. The engine design has-four pistons and a double duct configuration, with each duct containing sodium potassium liquid metal confined between free pistons located at either end of the duct. The liquid metal is forced to flow back and forth in the duct by the movement of the pistons, which are alternatively driven by an internal combustion process. In the MHD generator, the two LM-MHD ducts pass in close proximity through a Hartmann duct with output transformer. AC power is produced by operating the engine with the liquid metal in the two generator ducts always flowing in counter directions. The amount of liquid metal maintained in the ducts may be varied. This provides a variable stroke length for the pistons. The engine/generator provides variable AC power at variable frequencies that correspond to the power demands of the vehicular propulsion. Also the engine should maintain nearly constant efficiency throughout the range of power usage. Automobiles and trucks could be powered by the invention, with no transmission or power converter devices being required.
Analytical study of magnetohydrodynamic propulsion stability
NASA Astrophysics Data System (ADS)
Abdollahzadeh Jamalabadi, M. Y.
2014-09-01
In this paper an analytical solution for the stability of the fully developed flow drive in a magneto-hydro-dynamic pump with pulsating transverse Eletro-magnetic fields is presented. To do this, a theoretical model of the flow is developed and the analytical results are obtained for both the cylindrical and Cartesian configurations that are proper to use in the propulsion of marine vessels. The governing parabolic momentum PDEs are transformed into an ordinary differential equation using approximate velocity distribution. The numerical results are obtained and asymptotic analyses are built to discover the mathematical behavior of the solutions. The maximum velocity in a magneto-hydro-dynamic pump versus time for various values of the Stuart number, electro-magnetic interaction number, Reynolds number, aspect ratio, as well as the magnetic and electrical angular frequency and the shift of the phase angle is presented. Results show that for a high Stuart number there is a frequency limit for stability of the fluid flow in a certain direction of the flow. This stability frequency is dependent on the geometric parameters of a channel.
Efficient acceleration of relativistic magnetohydrodynamic jets
NASA Astrophysics Data System (ADS)
Toma, Kenji; Takahara, Fumio
2013-08-01
Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although the conversion mechanism from the Poynting into the particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloidal magnetic field line just inside the external boundary, without treating the transfield force balance in detail. We find some examples of the poloidal field structure and corresponding external pressure profile for an efficient and rapid energy conversion as required by observations, and that the rapid acceleration requires a rapid decrease of the external pressure above the accretion disk. We also clarify the differences between the fast magnetosonic point of the MHD flow and the sonic point of the de Laval nozzle.
Global Magnetohydrodynamic Modeling of the Solar Corona
NASA Technical Reports Server (NTRS)
Linker, Jon A.
1997-01-01
Under this contract, we have continued our investigations of the large scale structure of the solar corona and inner heliosphere using global magnetohydrodynamic (MHD) simulations. These computations have also formed the basis for studies of coronal mass ejections (CMES) using realistic coronal configurations. We have developed a technique for computing realistic magnetohydrodynamic (MHD) computations of the solar corona and inner heliosphere. To perform computations that can be compared with specific observations, it is necessary to incorporate solar observations into the boundary conditions. We have used the Wilcox Solar Observatory synoptic maps (collected during a solar rotation by daily measurements of the line-of-sight magnetic field at central meridian) to specify the radial magnetic field (B,) at the photosphere. For the initial condition, we use a potential magnetic field consistent with the specified distribution of B, at the lower boundary, and a wind solution consistent with the specified plasma density and temperature at the solar surface. Together this initial condition forms a (non-equilibrium) approximation of the state of the solar corona for the time-dependent MHD computation. The MHD equations are then integrated in time to steady state. Here we describe solutions relevant to a recent solar eclipse, as well as Ulysses observations. We have also developed a model configuration of solar minimum, useful for studying CME initiation and propagation.
NASA Astrophysics Data System (ADS)
Madraki, Yasaman; Hormozi, Sarah; Ovarlez, Guillaume; Guazzelli, Élisabeth; Pouliquen, Olivier
2017-03-01
A cornstarch suspension is the quintessential particulate system that exhibits shear thickening. By adding large non-Brownian spheres to a cornstarch suspension, we show that shear thickening can be significantly enhanced. More precisely, the shear-thickening transition is found to be increasingly shifted to lower critical shear rates. This influence of the large particles on the discontinuous shear-thickening transition is shown to be more dramatic than that on the viscosity or the yield stress of the suspension.
Study of Magnetohydrodynamic Surface Waves on Liquid Gallium
Hantao Ji; William Fox; David Pace; H.L. Rappaport
2004-05-13
Magnetohydrodynamic (MHD) surface waves on liquid gallium are studied theoretically and experimentally in the small magnetic Reynolds number limit. A linear dispersion relation is derived when a horizontal magnetic field and a horizontal electric current is imposed. No wave damping is found in the shallow liquid limit while waves always damp in the deep liquid limit with a magnetic field parallel to the propagation direction. When the magnetic field is weak, waves are weakly damped and the real part of the dispersion is unaffected, while in the opposite limit waves are strongly damped with shortened wavelengths. In a table-top experiment, planar MHD surface waves on liquid gallium are studied in detail in the regime of weak magnetic field and deep liquid. A non-invasive diagnostic accurately measures surface waves at multiple locations by reflecting an array of lasers off the surface onto a screen, which is recorded by an Intensified-CCD camera. The measured dispersion relation is consistent with the linear theory with a reduced surface tension likely due to surface oxidation. In excellent agreement with linear theory, it is observed that surface waves are damped only when a horizontal magnetic field is imposed parallel to the propagation direction. No damping is observed under a perpendicular magnetic field. The existence of strong wave damping even without magnetic field suggests the importance of the surface oxide layer. Implications to the liquid metal wall concept in fusion reactors, especially on the wave damping and a Rayleigh-Taylor instability when the Lorentz force is used to support liquid metal layer against gravity, are discussed.
On the performance of exponential integrators for problems in magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Einkemmer, Lukas; Tokman, Mayya; Loffeld, John
2017-02-01
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.
Radiation-magnetohydrodynamic simulations of the photoionization of magnetized globules
NASA Astrophysics Data System (ADS)
Henney, William J.; Arthur, S. Jane; de Colle, Fabio; Mellema, Garrelt
2009-09-01
We present the first three-dimensional radiation-magnetohydrodynamic simulations of the photoionization of a dense, magnetized molecular globule by an external source of ultraviolet radiation. We find that, for the case of a strong ionizing field, significant deviations from the non-magnetic evolution are seen when the initial magnetic field threading the globule has an associated magnetic pressure that is greater than 100 times the gas pressure. In such a strong-field case, the photoevaporating globule will adopt a flattened or `curled up' shape, depending on the initial field orientation, and magnetic confinement of the ionized photoevaporation flow can lead to recombination and subsequent fragmentation during advanced stages of the globule evolution. We find suggestive evidence that such magnetic effects may be important in the formation of bright, bar-like emission features in HII regions. We include simple but realistic fits to heating and cooling rates in the neutral and molecular gas in the vicinity of a high-mass star cluster, and show that the frequently used isothermal approximation can lead to an overestimate of the importance of gravitational instability in the radiatively imploded globule. For globules within 2 pc of a high-mass star cluster, we find that heating by stellar X-rays prevents the molecular gas from cooling below 50 K. Based in part on numerical simulations carried out using the Kan Balam supercomputer, operated by the Departamento de Supercómputo, Dirección General de Servicios de Cómputo Académico, Universidad Nacional Autónoma de México. E-mail: w.henney@astrosmo.unam.mx
Magnetic interchange instability in accretion disks
NASA Astrophysics Data System (ADS)
Lubow, Stephen H.; Spruit, Hendrik C.
1995-05-01
We investigate the stability of a disk to magnetic interchange in the disk plane, when a poloidal magentic field provides some radial support of the disk. The disk is assumed to be geometrically thin and may possess rotation and shear. We assume the unperturbed magnetic field vertically threads the disk and has a comparable radial component at the disk surface. We formulate the linear stability problem as an initial value problem in shearing coordinates and ignore any effects of winds. Shear stabilizes the interchange instability strongly compared to the uniformly rotating case studied previously and makes the growth algebraic rather than exponential. A second form of instability with long wavelengths is identified, whose growth appears to be transient. If the field strength is measured by the travel time tauA of an Alfven wave across the disk thickness, significant amplification for both forms of instability requires (tauA Omega)-2 greater than or approximately equal to L/H, where L is the radial length scale of the field gradient and H is the disk thickness. Field strengths such that 1 less than or approximately equal (tauA Omega)-2 less than or approximately equal L/H are stable to these instabilities as well as the instability recently investigated by Balbus & Hawley (1991). The results suggest that in dark environments in which the magnetic energy density is greater than the thermal energy density, disks are stable over a substantial range of parameter space, with radial advection of magnetic flux limited by the interchange instability possibly near the disk center. Such environments may be relevant for the production of magnetic winds or jets in young stars or active galactic nuclei.
Electromagnetic interchange-like mode and zonal flow in electron-magnetohydrodynamic plasma
Chakrabarti, Nikhil; Horiuchi, Ritoku
2006-10-15
A numerical simulation of the nonlinear state of interchange instability associated with electron inertia in an unmagnetized plasma is studied. It is shown that a self-consistent sheared transverse electron current flow is generated due to nonlinear mechanisms. This zonal flow can reduce the growth rate of the magnetic interchange-like instability and reach a steady state. The zonal flow generation mechanisms are discussed by truncated Fourier mode representation. In the truncated model, three mode equations are considered that have an exact analytic solution that matches well with the numerical solution. The effect of different boundary conditions in such investigations is also discussed.
Pfirsch, D.; Sudan, R.N.
1996-01-01
It is observed that the recently developed magnetic flux-averaged magnetohydrodynamics (AMHD) [Phys. Plasmas {bold 1}, 2488 (1994)] is incompatible with Taylor{close_quote}s theorem, which states that the lowest-energy state of force-free equilibria based on the conservation of the helicity integral is absolutely stable for vanishingly small resistivity. By a modification of the Lagrangian from which AMHD is derived, a modified version of AMHD that is compatible with Taylor{close_quote}s theorem is obtained. It also provides an energy principle for examining the linear instability of resistive equilibria, which has a great advantage over resistive MHD. {copyright} {ital 1996 American Institute of Physics.}
Raphaldini, Breno; Raupp, Carlos F. M. E-mail: carlos.raupp@iag.usp.br
2015-01-20
The solar dynamo is known to be associated with several periodicities, with the nearly 11/22 yr cycle being the most pronounced one. Even though these quasiperiodic variations of solar activity have been attributed to the underlying dynamo action in the Sun's interior, a fundamental theoretical description of these cycles is still elusive. Here, we present a new possible direction in understanding the Sun's cycles based on resonant nonlinear interactions among magnetohydrodynamic (MHD) Rossby waves. The WKB theory for dispersive waves is applied to magnetohydrodynamic shallow-water equations describing the dynamics of the solar tachocline, and the reduced dynamics of a resonant triad composed of MHD Rossby waves embedded in constant toroidal magnetic field is analyzed. In the conservative case, the wave amplitudes evolve periodically in time, with periods on the order of the dominant solar activity timescale (∼11 yr). In addition, the presence of linear forcings representative of either convection or instabilities of meridionally varying background states appears to be crucial in balancing dissipation and thus sustaining the periodic oscillations of wave amplitudes associated with resonant triad interactions. Examination of the linear theory of MHD Rossby waves embedded in a latitudinally varying mean flow demonstrates that MHD Rossby waves propagate toward the equator in a waveguide from –35° to 35° in latitude, showing a remarkable resemblance to the structure of the butterfly diagram of the solar activity. Therefore, we argue that resonant nonlinear magnetohydrodynamic Rossby wave interactions might significantly contribute to the observed cycles of magnetic solar activity.
NASA Astrophysics Data System (ADS)
Merkin, V. G.; Lyon, J.; Claudepierre, S. G.
2013-12-01
The Kelvin-Helmholtz Instability (KHI) has long been suggested to operate on the magnetospheric boundary, where the magnetosheath plasma streams past the magnetosphere. The instability is thought to be responsible for inducing various wave populations in the magnetosphere and for mass, momentum and energy transport across the magnetospheric boundary. Waves attributed to the KHI have been observed at the Earth's magnetosphere flanks as well as at Saturn and Mercury during spacecraft crossings, and remotely at boundaries of Coronal Mass Ejections (CMEs). Recent high-resolution global 3D magnetohydrodynamic (MHD) simulations of the magnetosphere confirm the existence of pronounced perturbations of the magnetospheric boundary, which are thought to be due to KHI. Such global simulations had been challenging in the past because of the need to encompass the entire magnetosphere, while sufficiently resolving the boundary layer. Here we present results of such a high-resolution simulation of the magnetosphere, using the Lyon-Fedder-Mobarry (LFM) model, under steady northward Interplanetary Magnetic Field (IMF) conditions. We find the magnetospheric boundary to be globally unstable, including the high-latitude boundary layer (meridional plane), where magnetic tension is apparently not sufficient to stabilize the growth of oscillations. Roughly beyond the terminator, global modes, coupled into the surface modes, become apparent, so that the entire body of the magnetosphere is engaged in an oscillatory motion. The wave vector of the surface oscillations has a component perpendicular to the background flow and tangential to the shear layer (in the equatorial plane, k_z component of the wave vector), which is consistent with the generation of field-aligned currents that flow on closed field lines between the inner portion of the boundary layer and the ionosphere. We calculate the distribution of wave power in the equatorial plane and find it consistent with the existence of a
Shear Stabilization of a Solidifying Front
NASA Technical Reports Server (NTRS)
Davis, Stephen H.; Schulze, Timothy P.
1996-01-01
The manufacturing of multi-component single crystals with uniform material properties is frequently hampered by the presence of morphological instabilities during the solidification. We discuss the influence of shear flows on the linear and nonlinear stability of the solid/liquid interface during the directional solidification of binary alloys. The flows are generated by nonplanar harmonic translations of the crystal parallel to the mean interface position. Oscillations with physically realizable amplitudes and frequencies are found useful for stabilization purposes.
Fan-structure waves in shear ruptures
NASA Astrophysics Data System (ADS)
Tarasov, Boris
2016-04-01
This presentation introduces a recently identified shear rupture mechanism providing a paradoxical feature of hard rocks - the possibility of shear rupture propagation through the highly confined intact rock mass at shear stress levels significantly less than frictional strength. According to the fan-mechanism the shear rupture propagation is associated with consecutive creation of small slabs in the fracture tip which, due to rotation caused by shear displacement of the fracture interfaces, form a fan-structure representing the fracture head. The fan-head combines such unique features as: extremely low shear resistance (below the frictional strength), self-sustaining stress intensification in the rupture tip (providing easy formation of new slabs), and self-unbalancing conditions in the fan-head (making the failure process inevitably spontaneous and violent). An important feature of the fan-mechanism is the fact that for the initial formation of the fan-structure an enhanced local shear stress is required, however, after completion of the fan-structure it can propagate as a dynamic wave through intact rock mass at shear stresses below the frictional strength. Paradoxically low shear strength of pristine rocks provided by the fan-mechanism determines the correspondingly low transient strength of the lithosphere, which favours generation of new earthquake faults in the intact rock mass adjoining pre-existing faults in preference to frictional stick-slip instability along these faults. The new approach reveals an alternative role of pre-existing faults in earthquake activity: they represent local stress concentrates in pristine rock adjoining the fault where special conditions for the fan-mechanism nucleation are created, while further dynamic propagation of the new fault (earthquake) occurs at low field stresses even below the frictional strength.
The genesis of adiabatic shear bands
Landau, P.; Osovski, S.; Venkert, A.; Gärtnerová, V.; Rittel, D.
2016-01-01
Adiabatic shear banding (ASB) is a unique dynamic failure mechanism that results in an unpredicted catastrophic failure due to a concentrated shear deformation mode. It is universally considered as a material or structural instability and as such, ASB is hardly controllable or predictable to some extent. ASB is modeled on the premise of stability analyses. The leading paradigm is that a competition between strain (rate) hardening and thermal softening determines the onset of the failure. It was recently shown that microstructural softening transformations, such as dynamic recrystallization, are responsible for adiabatic shear failure. These are dictated by the stored energy of cold work, so that energy considerations can be used to macroscopically model the failure mechanism. The initial mechanisms that lead to final failure are still unknown, as well as the ASB formation mechanism(s). Most of all - is ASB an abrupt instability or rather a gradual transition as would be dictated by microstructural evolutions? This paper reports thorough microstructural characterizations that clearly show the gradual character of the phenomenon, best described as a nucleation and growth failure mechanism, and not as an abrupt instability as previously thought. These observations are coupled to a simple numerical model that illustrates them. PMID:27849023
Zakharov, Leonid E.; Li, Xujing
2015-06-15
This paper formulates the Tokamak Magneto-Hydrodynamics (TMHD), initially outlined by X. Li and L. E. Zakharov [Plasma Science and Technology 17(2), 97–104 (2015)] for proper simulations of macroscopic plasma dynamics. The simplest set of magneto-hydrodynamics equations, sufficient for disruption modeling and extendable to more refined physics, is explained in detail. First, the TMHD introduces to 3-D simulations the Reference Magnetic Coordinates (RMC), which are aligned with the magnetic field in the best possible way. The numerical implementation of RMC is adaptive grids. Being consistent with the high anisotropy of the tokamak plasma, RMC allow simulations at realistic, very high plasma electric conductivity. Second, the TMHD splits the equation of motion into an equilibrium equation and the plasma advancing equation. This resolves the 4 decade old problem of Courant limitations of the time step in existing, plasma inertia driven numerical codes. The splitting allows disruption simulations on a relatively slow time scale in comparison with the fast time of ideal MHD instabilities. A new, efficient numerical scheme is proposed for TMHD.
Simplified variational principles for non-barotropic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Yahalom, Asher
2016-04-01
> Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic magnetohydrodynamics can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary barotropic flows. This is less than the eight variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field the velocity field , the entropy and the density .
Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model
Hameiri, Eliezer
2013-02-15
It is shown that shocks and contact discontinuities in the Hall-magnetohydrodynamics (HMHD) model must satisfy solvability conditions that replace some of the familiar Rankine-Hugoniot jump conditions when the latter do not apply due to singular behavior of fluxes of conserved quantities. Some of these conditions depend on the larger topology of the plasma and magnetic field and are not merely 'local.' The contact discontinuity which separates two adjoining plasma regions or plasma and vacuum regions is the simplest case where the new jump conditions are applicable and is discussed for a toroidal plasma with sheared magnetic field such as the tokamak, but with no initial mass flow. It is proven that a static discontinuous tokamak-like equilibrium is linearly stable in the HMHD model if it is linearly stable within the ideal magnetohydrodynamics model, provided that the electron pressure depends only on the density, and some other restrictions on the ratio of pressure to density gradients also apply. When the electron pressure does depend on two thermodynamic variables, a sufficient condition for Hall-MHD plasma stability is derived as well.
Thermal effects in dislocation theory. II. Shear banding
NASA Astrophysics Data System (ADS)
Langer, J. S.
2017-01-01
The thermodynamic dislocation theory presented in previous papers is used here to describe shear-banding instabilities. Central ingredients of the theory are a thermodynamically defined effective configurational temperature and a formula for the plastic strain rate determined by thermally activated depinning of entangled dislocations. This plastic strain rate is extremely sensitive to variations of the stress and the ordinary temperature. As a result of this sensitivity, the system undergoes rapid shear banding instabilities when ordinary thermal relaxation is slow. It also undergoes rapid changes from elastic to plastic behaviors at yielding transitions.
Magnetohydrodynamic Modeling of the Jovian Magnetosphere
NASA Technical Reports Server (NTRS)
Walker, Raymond
2005-01-01
Under this grant we have undertaken a series of magnetohydrodynamic (MHD) simulation and data analysis studies to help better understand the configuration and dynamics of Jupiter's magnetosphere. We approached our studies of Jupiter's magnetosphere in two ways. First we carried out a number of studies using our existing MHD code. We carried out simulation studies of Jupiter s magnetospheric boundaries and their dependence on solar wind parameters, we studied the current systems which give the Jovian magnetosphere its unique configuration and we modeled the dynamics of Jupiter s magnetosphere following a northward turning of the interplanetary magnetic field (IMF). Second we worked to develop a new simulation code for studies of outer planet magnetospheres.
Hall magneto-hydrodynamics in protoplanetary discs
NASA Astrophysics Data System (ADS)
Béthune, W.; Lesur, G.; Ferreira, J.
2016-12-01
Protoplanetary discs exhibit large-scale, organised structures. Because they are dense and cold, they should be weakly ionized, and hence concerned by non-ideal plasma effects, such as the Hall effect. We perform numerical simulations of non-stratified Keplerian discs, in the non-ideal magnetohydrodynamic framework. We show that the Hall effect causes self-organisation through three distinct stages. A weak Hall effect enhances turbulent transport. At intermediate strength, it produces magnetized vortices. A strong Hall effect generates axisymmetric zonal flows. These structures may trap dust particles, and thus influence planetary formation. The transport of angular momentum is quenched in the organised state, impugning the relevance of magneto-rotational turbulence as a driving mechanism of accretion in Hall dominated regions.
Exploring Astrophysical Magnetohydrodynamics in the Laboratory
NASA Astrophysics Data System (ADS)
Manuel, Mario
2014-10-01
Plasma evolution in many astrophysical systems is dominated by magnetohydrodynamics. Specifically of interest to this talk are collimated outflows from accretion systems. Away from the central object, the Euler equations can represent the plasma dynamics well and may be scaled to a laboratory system. We have performed experiments to investigate the effects of a background magnetic field on an otherwise hydrodynamically collimated plasma. Laser-irradiated, cone targets produce hydrodynamically collimated plasma jets and a pulse-powered solenoid provides a constant background magnetic field. The application of this field is shown to completely disrupt the original flow and a new magnetically-collimated, hollow envelope is produced. Results from these experiments and potential implications for their astrophysical analogs will be discussed.
Geometrical shock dynamics of fast magnetohydrodynamic shocks
NASA Astrophysics Data System (ADS)
Mostert, Wouter; Pullin, Dale I.; Samtaney, Ravi; Wheatley, Vincent
2016-11-01
We extend the theory of geometrical shock dynamics (GSD, Whitham 1958), to two-dimensional fast magnetohydrodynamic (MHD) shocks moving in the presence of nonuniform magnetic fields of general orientation and strength. The resulting generalized area-Mach number rule is adapted to MHD shocks moving in two spatial dimensions. A partially-spectral numerical scheme developed from that of Schwendeman (1993) is described. This is applied to the stability of plane MHD fast shocks moving into a quiescent medium containing a uniform magnetic field whose field lines are inclined to the plane-shock normal. In particular, we consider the time taken for an initially planar shock subject to an initial perturbed magnetosonic Mach number distribution, to first form shock-shocks. Supported by KAUST OCRF Award No. URF/1/2162-01.
Lagrangian simulation of explosively driven magnetohydrodynamic generator
NASA Astrophysics Data System (ADS)
Kim, Deok-Kyu; Seo, Min Su; Kim, Inho
2003-06-01
A series of time-dependent one-dimensional simulations has been carried out on the hydrodynamic behavior of argon and air plasmas in an explosively driven magnetohydrodynamic power generator. The thermodynamic properties of plasma gases are computed using equation-of-state data obtained from a detailed theoretical model. The plasma conductivities are given by a mixture rule, which comprises the fully and weakly ionized plasma approximations. The effects of the initial pressure and the magnetic field strength on the plasma behavior in the flow channel are examined over a moderate range of operating conditions, and then the computed results are compared with the experimental measurements, showing good agreement for the case of low magnetic Reynolds number.
Rarefaction wave in relativistic steady magnetohydrodynamic flows
Sapountzis, Konstantinos Vlahakis, Nektarios
2014-07-15
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.
On the kinetic foundations of Kaluza's magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Sandoval-Villalbazo, Alfredo; Sagaceta-Mejía, Alma R.; García-Perciante, Ana L.
2015-06-01
Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field [J. Non-Equilib. Thermodyn. 38 (2013), 141-151]. The treatment in that work was limited to a four-dimensional Minkowski space-time in which the Boltzmann equation was treated in a special relativistic approach. The more complete framework of general relativity can be introduced to kinetic theory in order to describe transport processes associated to electromagnetic fields. In this context, the original Kaluza's formalism is a promising approach [Sitz. Ber. Preuss. Akad. Wiss. (1921), 966-972; Gen. Rel. Grav. 39 (2007), 1287-1296; Phys. Plasmas 7 (2000), 4823-4830]. The present work contains a kinetic theory basis for Kaluza's magnetohydrodynamics and gives a novel description for the establishment of thermodynamic forces beyond the special relativistic description.
RESISTIVE MAGNETOHYDRODYNAMIC SIMULATIONS OF RELATIVISTIC MAGNETIC RECONNECTION
Zenitani, Seiji; Hesse, Michael; Klimas, Alex
2010-06-20
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten-Lan-van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfvenic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the 'diamond-chain' structure due to multiple shock reflections. Under a uniform resistivity, Sweet-Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
NASA Technical Reports Server (NTRS)
Zenitani, Seiji; Hesse, Michael; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten-Lan-van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv enic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond-chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet-Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Action principles for extended magnetohydrodynamic models
NASA Astrophysics Data System (ADS)
Keramidas Charidakos, I.; Lingam, M.; Morrison, P. J.; White, R. L.; Wurm, A.
2014-09-01
The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.
Remarkable connections between extended magnetohydrodynamics models
Lingam, M. Morrison, P. J. Miloshevich, G.
2015-07-15
Through the use of suitable variable transformations, the commonality of all extended magnetohydrodynamics (MHD) models is established. Remarkable correspondences between the Poisson brackets of inertialess Hall MHD and inertial MHD (which has electron inertia, but not the Hall drift) and extended MHD (which has both effects) are established. The helicities (two in all) for each of these models are obtained through these correspondences. The commonality of all the extended MHD models is traced to the existence of two Lie-dragged 2-forms, which are closely associated with the canonical momenta of the two underlying species. The Lie-dragging of these 2-forms by suitable velocities also leads to the correct equations of motion. The Hall MHD Poisson bracket is analyzed in detail, the Jacobi identity is verified through a detailed proof, and this proof ensures the Jacobi identity for the Poisson brackets of all the models.
A photolithographic fabrication technique for magnetohydrodynamic micropumps
NASA Astrophysics Data System (ADS)
Kuenstner, Stephen; Baylor, Martha-Elizabeth
2014-03-01
Magnetohydrodynamic (MHD) devices use perpendicular electric and magnetic fields to exert a Lorentz body force on a conducting fluid. Miniaturized MHD devices have been used to create pumps, stirrers, heat exchangers, and microfluidic networks. Compared to mechanical micropumps, MHD micropumps are appealing because they require no moving parts, which simplifies fabrication, and because they are amenable to electronic control. This abstract reports the fabrication and testing of a centimeter-scale MHD pump using a thiol-ene/methacrylate-based photopolymer and mask-based photolithographic technique. Pumps like this one could simplify the fabrication of sophisticated optofluidic devices, including liquid-core, liquid cladding (L2) waveguides, which are usually created with PDMS using stamps, or etched into silicon wafers. The photolithographic technique demonstrated here requires only one masking step to create fluid channels with complex geometries.
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
NASA Astrophysics Data System (ADS)
Zenitani, Seiji; Hesse, Michael; Klimas, Alex
2010-06-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten-Lan-van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfvénic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond-chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet-Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Multidimensional numerical scheme for resistive relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Komissarov, Serguei S.
2007-12-01
The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric field is kept consistent with the electric charge distribution via the method of Generalized Lagrange Multiplier. The hyperbolic fluxes are computed using the Harten-Lax-van Leer (HLL) prescription and the source terms are accounted via the time-splitting technique. The results of test simulations show that the scheme can handle equally well both resistive current sheets and shock waves, and thus can be a useful tool for studying phenomena of relativistic astrophysics that involve both colliding supersonic flows and magnetic reconnection.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
MAGNETOHYDRODYNAMICS OF THE WEAKLY IONIZED SOLAR PHOTOSPHERE
Cheung, Mark C. M.; Cameron, Robert H.
2012-05-01
We investigate the importance of ambipolar diffusion and Hall currents for high-resolution comprehensive ({sup r}ealistic{sup )} photospheric simulations. To do so, we extended the radiative magnetohydrodynamics code MURaM to use the generalized Ohm's law under the assumption of local thermodynamic equilibrium. We present test cases comparing analytical solutions with numerical simulations for validation of the code. Furthermore, we carried out a number of numerical experiments to investigate the impact of these neutral-ion effects in the photosphere. We find that, at the spatial resolutions currently used (5-20 km per grid point), the Hall currents and ambipolar diffusion begin to become significant-with flows of 100 m s{sup -1} in sunspot light bridges, and changes of a few percent in the thermodynamic structure of quiet-Sun magnetic features. The magnitude of the effects is expected to increase rapidly as smaller-scale variations are resolved by the simulations.
Numerical models for high beta magnetohydrodynamic flow
Brackbill, J.U.
1987-01-01
The fundamentals of numerical magnetohydrodynamics for highly conducting, high-beta plasmas are outlined. The discussions emphasize the physical properties of the flow, and how elementary concepts in numerical analysis can be applied to the construction of finite difference approximations that capture these features. The linear and nonlinear stability of explicit and implicit differencing in time is examined, the origin and effect of numerical diffusion in the calculation of convective transport is described, and a technique for maintaining solenoidality in the magnetic field is developed. Many of the points are illustrated by numerical examples. The techniques described are applicable to the time-dependent, high-beta flows normally encountered in magnetically confined plasmas, plasma switches, and space and astrophysical plasmas. 40 refs.
Acceleration of particles in imbalanced magnetohydrodynamic turbulence.
Teaca, Bogdan; Weidl, Martin S; Jenko, Frank; Schlickeiser, Reinhard
2014-08-01
The present work investigates the acceleration of test particles, relevant to the solar-wind problem, in balanced and imbalanced magnetohydrodynamic turbulence (terms referring here to turbulent states possessing zero and nonzero cross helicity, respectively). These turbulent states, obtained numerically by prescribing the injection rates for the ideal invariants, are evolved dynamically with the particles. While the energy spectrum for balanced and imbalanced states is known, the impact made on particle heating is a matter of debate, with different considerations giving different results. By performing direct numerical simulations, resonant and nonresonant particle accelerations are automatically considered and the correct turbulent phases are taken into account. For imbalanced turbulence, it is found that the acceleration rate of charged particles is reduced and the heating rate diminished. This behavior is independent of the particle gyroradius, although particles that have a stronger adiabatic motion (smaller gyroradius) tend to experience a larger heating.
Bifurcation of resistive wall mode dynamics predicted by magnetohydrodynamic-kinetic hybrid theory
Yang, S. X.; Wang, Z. X.; Wang, S.; Hao, G. Z. Song, X. M.; Wang, A. K.; Liu, Y. Q.
2015-09-15
The magnetohydrodynamic-kinetic hybrid theory has been extensively and successfully applied for interpreting experimental observations of macroscopic, low frequency instabilities, such as the resistive wall mode, in fusion plasmas. In this work, it is discovered that an analytic version of the hybrid formulation predicts a bifurcation of the mode dynamics while varying certain physical parameters of the plasma, such as the thermal particle collisionality or the ratio of the thermal ion to electron temperatures. This bifurcation can robustly occur under reasonably large parameter spaces as well as with different assumptions, for instance, on the particle collision model. Qualitatively similar bifurcation features are also observed in full toroidal computations presented in this work, based on a non-perturbative hybrid formulation.
Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions
NASA Astrophysics Data System (ADS)
Olmi, B.; Del Zanna, L.; Amato, E.; Bucciantini, N.; Mignone, A.
2016-12-01
In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisp motions as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.
Magnetohydrodynamic stability in the electromagnetic levitation of horizontal molten-metal sheets
NASA Astrophysics Data System (ADS)
Hull, John R.; Wiencek, Tom; Rote, Donald M.
1989-06-01
High-frequency electromagnetic (EM) fields are investigated for the levitation of thin horizontal sheets of liquid metal. A magnetic configuration is analyzed in which inductance stabilization provides global stability and magnetic flux compression provides local stability. Stability analysis indicates that frequencies greater than about 24 kHz are desirable to stably levitate 6 mm thick steel. For stability in systems without active feedback, a conducting screen is required below the metal, with a gap between the screen and the molten metal of no more than twice the metal thickness. Experiments in which 10 kHz EM fields were used to statically levitate sheets of molten tin indicate that dominant magnetohydrodynamic instabilities are of the Rayleigh-Taylor type and correspond to theory.
Instability in electromagnetically driven flows. II
NASA Astrophysics Data System (ADS)
Rodriguez Imazio, Paola; Gissinger, Christophe
2016-03-01
In a previous paper, we have reported numerical simulations of the magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel, at low Reynolds number. It was shown that the stalling of such induction pump is strongly related to magnetic flux expulsion. In the present article, we show that for larger hydrodynamic Reynolds number, and with more realistic boundary conditions, this instability takes the form of a large axisymmetric vortex flow in the (r, z)-plane, in which the fluid is locally pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability of this vortex flow, a low-frequency pulsation is generated. Finally, these results are compared to theoretical predictions and are discussed within the framework of experimental annular linear induction electromagnetic pumps.
Observations of velocity shear driven plasma turbulence
NASA Technical Reports Server (NTRS)
Kintner, P. M., Jr.
1976-01-01
Electrostatic and magnetic turbulence observations from HAWKEYE-1 during the low altitude portion of its elliptical orbit over the Southern Hemisphere are presented. The magnetic turbulence is confined near the auroral zone and is similar to that seen at higher altitudes by HEOS-2 in the polar cusp. The electrostatic turbulence is composed of a background component with a power spectral index of 1.89 + or - .26 and an intense component with a power spectral index of 2.80 + or - .34. The intense electrostatic turbulence and the magnetic turbulence correlate with velocity shears in the convective plasma flow. Since velocity shear instabilities are most unstable to wave vectors perpendicular to the magnetic field, the shear correlated turbulence is anticipated to be two dimensional in character and to have a power spectral index of 3 which agrees with that observed in the intense electrostatic turbulence.
Vorticity structuring and velocity rolls triggered by gradient shear bands.
Fielding, Suzanne M
2007-07-01
We suggest a mechanism by which vorticity structuring and velocity rolls can form in complex fluids, triggered by the linear instability of one-dimensional gradient shear banded flow. We support this with a numerical study of the diffusive Johnson-Segalman model. In the steady vorticity structured state, the thickness of the interface between the bands remains finite in the limit of zero stress diffusivity, presenting a possible challenge to the accepted theory of shear banding.
NASA Astrophysics Data System (ADS)
Hilburn, Guy Louis
Results from several studies are presented which detail explorations of the physical and spectral properties of low luminosity active galactic nuclei. An initial Sagittarius A* general relativistic magnetohydrodynamic simulation and Monte Carlo radiation transport model suggests accretion rate changes as the dominant flaring method. A similar study on M87 introduces new methods to the Monte Carlo model for increased consistency in highly energetic sources. Again, accretion rate variation seems most appropriate to explain spectral transients. To more closely resolve the methods of particle energization in active galactic nuclei accretion disks, a series of localized shearing box simulations explores the effect of numerical resolution on the development of current sheets. A particular focus on numerically describing converged current sheet formation will provide new methods for consideration of turbulence in accretion disks.
Large-scale magnetic field generation by randomly forced shearing waves.
Heinemann, T; McWilliams, J C; Schekochihin, A A
2011-12-16
A rigorous theory for the generation of a large-scale magnetic field by random nonhelically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low magnetic Reynolds number (Rm) and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wave number and growth rate of the fastest-growing mode, previously not understood, are derived analytically. The simplicity of the model suggests that shear dynamo action may be a generic property of sheared magnetohydrodynamic turbulence.
NASA Astrophysics Data System (ADS)
Rembiasz, T.; Obergaulinger, M.; Cerdá-Durán, P.; Müller, E.; Aloy, M. A.
2016-03-01
The magnetorotational instability (MRI) can be a powerful mechanism amplifying the magnetic field in core-collapse supernovae. Whether initially weak magnetic fields can be amplified by this instability to dynamically relevant strengths is still a matter of debate. One of the main uncertainties concerns the process that terminates the growth of the instability. Parasitic instabilities of both Kelvin-Helmholtz and tearing-mode type have been suggested to play a crucial role in this process, disrupting MRI channel flows and quenching magnetic field amplification. We perform two-dimensional and three-dimensional sheering-disc simulations of a differentially rotating protoneutron star layer in non-ideal magnetohydrodynamics with unprecedented high numerical accuracy, finding that Kelvin-Helmholtz parasitic modes dominate tearing modes in the regime of large hydrodynamic and magnetic Reynolds numbers, as encountered close to the surface of protoneutron stars. They also determine the maximum magnetic field stress achievable during the exponential growth of the MRI. Our results are consistent with the theory of parasitic instabilities based on a local stability analysis. To simulate the Kelvin-Helmholtz instabilities properly, a very high numerical resolution is necessary. Using ninth-order spatial reconstruction schemes, we find that at least eight grid zones per MRI channel are necessary to simulate the growth phase of the MRI and reach an accuracy of ˜10 per cent in the growth rate, while more than ˜60 zones per channel are required to achieve convergent results for the value of the magnetic stress at MRI termination.
Dodelson, Scott; Shapiro, Charles; White, Martin J.; /UC, Berkeley, Astron. Dept. /UC, Berkeley
2005-08-01
Measurements of ellipticities of background galaxies are sensitive to the reduced shear, the cosmic shear divided by (1-{kappa}) where {kappa} is the projected density field. They compute the difference between shear and reduced shear both analytically and with simulations. The difference becomes more important an smaller scales, and will impact cosmological parameter estimation from upcoming experiments. A simple recipe is presented to carry out the required correction.
Viscosity and Vorticity in Reduced Magneto-Hydrodynamics
Joseph, Ilon
2015-08-12
Magneto-hydrodynamics (MHD) critically relies on viscous forces in order for an accurate determination of the electric eld. For each charged particle species, the Braginskii viscous tensor for a magnetized plasma has the decomposition into matrices with special symmetries.
Rotatable shear plate interferometer
Duffus, Richard C.
1988-01-01
A rotatable shear plate interferometer comprises a transparent shear plate mounted obliquely in a tubular supporting member at 45.degree. with respect to its horizontal center axis. This tubular supporting member is supported rotatably around its center axis and a collimated laser beam is made incident on the shear plate along this center axis such that defocus in different directions can be easily measured.
An AC magnetohydrodynamic micropump: towards a true integrated microfluidic system
Lee, A P; Lemoff, A V; McConaghy, C F; Miles, R R
1999-03-01
An AC Magnetohydrodynamic (MHD) micropump has been demonstrated in which the Lorentz force is used to propel an electrolytic solution along a microchannel etched in silicon. This micropump has no moving parts, produces a continuous (not pulsatile) flow, and is compatible with solutions containing biological specimens. micropump, using the Lorentz force as the pumping mechanism for biological analysis. The AC Magnetohydrodynamic (MHD) micropump investigated produces a continuous flow and allows for complex microchannel design.
Dislocations in magnetohydrodynamic waves in a stellar atmosphere.
López Ariste, A; Collados, M; Khomenko, E
2013-08-23
We describe the presence of wave front dislocations in magnetohydrodynamic waves in stratified stellar atmospheres. Scalar dislocations such as edges and vortices can appear in Alfvén waves, as well as in general magnetoacoustic waves. We detect those dislocations in observations of magnetohydrodynamic waves in sunspots in the solar chromosphere. Through the measured charge of all the dislocations observed, we can give for the first time estimates of the modal contribution in the waves propagating along magnetic fields in solar sunspots.
Government research and development summaries: Magnetohydrodynamic project briefs. Irregular
1995-03-01
Magnetohydrodynamic Project Briefs describe the status of all R and D programs submitted to the Power Information Center by the government sponsors in energy conversion involving the magnetohydrodynamic (MHD) interaction between electromagnetic fields and electrically conducting fields, including fuels, materials, plasma dynamics, and combustion. The document is not to be reproduced, in whole or in part, for dissemination outside your own organization nor may it be reproduced for advertising or sales promotion purposes.
Magnetohydrodynamic Augmentation of Pulse Detonation Rocket Engines (Preprint)
2010-09-28
system will either be over- or under-expanded for the majority of the cycle , with en- ergy being used without maximum gain. Magnetohydrodynamic ( MHD ...to their potentially superior performance over constant pressure cycle engines. Yet due to its unsteady chamber pressure, the PDE system will either...be over- or under-expanded for the majority of the cycle , with energy being used without maximum gain. Magnetohydrodynamic ( MHD ) augmentation offers
Government research and development summaries: Magnetohydrodynamic project briefs. Irregular
Not Available
1994-01-01
Magnetohydrodynamic Project Briefs describe the status of all R and D programs submitted to the Power Information Center by the government sponsors in energy conversion involving the magnetohydrodynamic (MHD) interaction between electromagnetic fields and electrically conducting fields, including fuels, materials, plasma dynamics, and combustion. The document is not to be reproduced, in whole or in part, for dissemination outside your own organization nor may it be reproduced for advertising or sales promotion purposes.
Analysis of Kelvin Helmholtz Instabilities of Plasma Jets
NASA Technical Reports Server (NTRS)
Friedman, Mark J.; Hollingsworth, Blane J.
1999-01-01
Ulysses data indicates density fluctuations which axe theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.
Analysis of Kelvin Helmholtz Instabilities of Plasma Jets
NASA Technical Reports Server (NTRS)
Friedman, Mark J.; Hollingsworth, Blane J.
1999-01-01
Ulysses data indicates density fluctuations which are theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.
Kingfish striations and the Kelvin-Helmholtz instability. Part 1
Hunter, J.H. Jr.
1985-10-01
The role of the Kelvin-Helmholtz instability in initiating the formation of the density striations observed in the Kingfish fireball is examined. Two idealized models are proposed for the velocity shear layer on the sides of the fireball, each of which includes essential characteristics of the Kingfish event insofar as the development of Kelvin-Helmholtz instabilities is concerned. A complete linear analysis is presented for each model.
Nonlinear instability of elementary stratified flows at large Richardson number.
Majda, Andrew J.; Shefter, Michael G.
2000-03-01
Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.
Gravitational instability of filamentary molecular clouds, including ambipolar diffusion
NASA Astrophysics Data System (ADS)
Hosseinirad, Mohammad; Naficy, Kazem; Abbassi, Shahram; Roshan, Mahmood
2017-02-01
The gravitational instability of a filamentary molecular cloud in non-ideal magnetohydrodynamics is investigated. The filament is assumed to be in hydrostatic equilibrium. We add the effect of ambipolar diffusion to the filament which is threaded by an initial uniform axial magnetic field along its axis. We write down the fluid equations in cylindrical coordinates and perform linear perturbation analysis. We integrate the resultant differential equations and then derive the numerical dispersion relation. We find that a more efficient ambipolar diffusion leads to an enhancement of the growth of the most unstable mode, and to the increase of the fragmentation scale of the filament.
Instability of a water-spout flow
NASA Astrophysics Data System (ADS)
Carrión, Luis; Herrada, Miguel A.; Shtern, Vladimir N.
2016-03-01
The paper studies the linear stability of a steady axisymmetric air-water motion in a vertical sealed cylinder, driven by the rotating top disk, motivated by possible applications in aerial bioreactors. As the flow strength Re increases, a vortex breakdown bubble (VBB) emerges near the bottom center and expands toward the interface. Regions of clockwise meridional circulation of air and water become separated by a thin anticlockwise circulation layer (TCL) adjacent to the interface in water. This study reveals that instability develops for larger Re than those at which VBB and TCL emerge. The instability focuses in the air region being typically of shear-layer type. The instability is centrifugal if the air volume fraction is small.
Crack instabilities of a heated glass strip
NASA Astrophysics Data System (ADS)
Adda-Bedia, Mokhtar; Pomeau, Yves
1995-10-01
Recently, Yuse and Sano [Nature (London) 362, 329 (1993)] have observed that a crack traveling in a glass strip submitted to a nonuniform thermal diffusion field undergoes numerous instabilities. We study two cases of quasistatic crack propagation. The crack extension condition in straight propagation is determined. An asymptotic analysis of the elastic free energy is introduced and scaling laws are derived. A linear stability analysis of the straight propagation is performed, based on the assumption that the crack tip propagation deviates from the centered straight one as soon as it is submitted to a ``physical'' singular shear stress. It is shown that a straight propagation can become unstable after which a wavy instability appears. The condition for instability as well as the selected wavelength is calculated quantitatively. The results are compared with experiments and the agreement is favorable.
Tuning graphene properties by shear
NASA Astrophysics Data System (ADS)
Concha, Andres; Cheng, Shengfeng; Covaci, Lucian; Mahadevan, L.
2014-03-01
Graphene being the thinnest possible membrane made out of carbon atoms is prone to deformations under slight external forcing. Here, we take advantage of this proneness to deformations to manipulate transport properties of graphene ribbons. We analyze the effect on conductance and LDOS of the spontaneous pattern produced when a wide ribbon is subject to shear. The deformation of the ribbon produces pseudo-magnetic fields, scalar potentials, and Fermi velocity renormalization resulting in the modification of transmission properties without the need of an external gate potential. Our proposal paves the way for producing electronic waveguides by using an elastic instability that spans from the nano to macro-scales. AC was partially supported by Conicyt PAI 79112004 and Fondecyt iniciacion 11130075. LC acknowledges individual support from FWO-Vlaanderen.
Electron heat flux instability
NASA Astrophysics Data System (ADS)
Saeed, Sundas; Sarfraz, M.; Yoon, P. H.; Lazar, M.; Qureshi, M. N. S.
2017-02-01
The heat flux instability is an electromagnetic mode excited by a relative drift between the protons and two-component core-halo electrons. The most prominent application may be in association with the solar wind where drifting electron velocity distributions are observed. The heat flux instability is somewhat analogous to the electrostatic Buneman or ion-acoustic instability driven by the net drift between the protons and bulk electrons, except that the heat flux instability operates in magnetized plasmas and possesses transverse electromagnetic polarization. The heat flux instability is also distinct from the electrostatic counterpart in that it requires two electron species with relative drifts with each other. In the literature, the heat flux instability is often called the 'whistler' heat flux instability, but it is actually polarized in the opposite sense to the whistler wave. This paper elucidates all of these fundamental plasma physical properties associated with the heat flux instability starting from a simple model, and gradually building up more complexity towards a solar wind-like distribution functions. It is found that the essential properties of the instability are already present in the cold counter-streaming electron model, and that the instability is absent if the protons are ignored. These instability characteristics are highly reminiscent of the electron firehose instability driven by excessive parallel temperature anisotropy, propagating in parallel direction with respect to the ambient magnetic field, except that the free energy source for the heat flux instability resides in the effective parallel pressure provided by the counter-streaming electrons.
A Reduced Model for the Magnetorotational Instability
NASA Astrophysics Data System (ADS)
Jamroz, Ben; Julien, Keith; Knobloch, Edgar
2008-11-01
The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.
Instabilities in nonlinear internal waves on the Washington continental shelf
NASA Astrophysics Data System (ADS)
Zhang, Shuang; Alford, Matthew H.
2015-07-01
Previous studies have identified two primary mechanisms (shear instability and convective instability) by which nonlinear internal waves (NLIWs) induce mixing on continental shelves. To determine the relative importance of these and their dependence on background flow conditions, we examine a much longer (6 month) data set from a moored ADCP/thermistor chain with 2 m vertical spacing in which over 600 NLIWs are detected. Turbulent properties of the 318 waves with detectable overturning instabilities are documented using Thorpe scales. The 130 waves detected while an ADCP was functioning are classified based on a Froude number criterion (Fr =
Turbine instabilities: Case histories
NASA Technical Reports Server (NTRS)
Laws, C. W.
1985-01-01
Several possible causes of turbine rotor instability are discussed and the related design features of a wide range of turbomachinery types and sizes are considered. The instrumentation options available for detecting rotor instability and assessing its severity are also discussed.
Kinesics of Affective Instability.
ERIC Educational Resources Information Center
Dil, Nasim
1979-01-01
Discusses the rationale of studying kinesics of affective instability, describes the phenonmenon of affective instability, examines the role of kinesics in the overall process of communication, and presents three case studies. (Author/AM)
A Global Magnetohydrodynamic Model of Jovian Magnetosphere
NASA Technical Reports Server (NTRS)
Walker, Raymond J.; Sharber, James (Technical Monitor)
2001-01-01
The goal of this project was to develop a new global magnetohydrodynamic model of the interaction of the Jovian magnetosphere with the solar wind. Observations from 28 orbits of Jupiter by Galileo along with those from previous spacecraft at Jupiter, Pioneer 10 and 11, Voyager I and 2 and Ulysses, have revealed that the Jovian magnetosphere is a vast, complicated system. The Jovian aurora also has been monitored for several years. Like auroral observations at Earth, these measurements provide us with a global picture of magnetospheric dynamics. Despite this wide range of observations, we have limited quantitative understanding of the Jovian magnetosphere and how it interacts with the solar wind. For the past several years we have been working toward a quantitative understanding of the Jovian magnetosphere and its interaction with the solar wind by employing global magnetohydrodynamic simulations to model the magnetosphere. Our model has been an explicit MHD code (previously used to model the Earth's magnetosphere) to study Jupiter's magnetosphere. We continue to obtain important insights with this code, but it suffers from some severe limitations. In particular with this code we are limited to considering the region outside of 15RJ, with cell sizes of about 1.5R(sub J). The problem arises because of the presence of widely separated time scales throughout the magnetosphere. The numerical stability criterion for explicit MHD codes is the CFL limit and is given by C(sub max)(Delta)t/(Delta)x less than 1 where C(sub max) is the maximum group velocity in a given cell, (Delta)x is the grid spacing and (Delta)t is the time step. If the maximum wave velocity is C(sub w) and the flow speed is C(sub f), C(sub max) = C(sub w) + C(sub f). Near Jupiter the Alfven wave speed becomes very large (it approaches the speed of light at one Jovian radius). Operating with this time step makes the calculation essentially intractable. Therefore under this funding we have been designing a
Converging cylindrical shocks in ideal magnetohydrodynamics
Pullin, D. I.; Mostert, W.; Wheatley, V.; Samtaney, R.
2014-09-15
We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R=√(μ{sub 0}/p{sub 0}) I/(2 π) where I is the current, μ{sub 0} is the permeability, and p{sub 0} is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The
Converging cylindrical shocks in ideal magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Pullin, D. I.; Mostert, W.; Wheatley, V.; Samtaney, R.
2014-09-01
We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R=sqrt{μ _0/p_0} I/(2 π ) where I is the current, μ0 is the permeability, and p0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field
A study of shear banding in polymer solutions
NASA Astrophysics Data System (ADS)
Cromer, Michael; Fredrickson, Glenn H.; Leal, L. Gary
2014-06-01
In a recent letter [M. Cromer, M. C. Villet, G. H. Fredrickson, and L. G. Leal, "Shear banding in polymer solutions," Phys. Fluids 25, 051703 (2013)], we showed the existence of a steady shear-banded velocity profile for a model polymer solution with an underlying monotonic constitutive curve. The driving mechanism is the coupling of the polymer stress to an inhomogeneous concentration profile. To further understand this phenomenon, in this paper we investigate the underlying linear instability as well as probe the model parameters and their effect on transient and steady state solutions. The linear stability analysis of the steady, base homogeneous model shows that, in opposition to diffusion, the polymer concentration moves up stress gradients in a shear flow creating a critical balance such that, for a range of parameters, an instability occurs that drives the system away from homogeneity. The simulation of the full nonlinear equations in planar one-dimensional shear reveals a window within which the linear instability manifests itself as a shear-banded flow. Unlike the case for a nonmonotonic constitutive curve for which two bands are predicted, there is no apparent selection process for a monotonic curve that sets the number of bands in planar shear. Thus, we find the possibility of greater than two bands, the number of which is determined by the ratio of the polymer correlation length to the channel width. In addition to steady shear banding, transient phenomena are also probed revealing a complicated band transition (i.e., number of bands changing in time) as well as elastic recoil in a Taylor-Couette cell, each of which have been observed in experiment. Finally, as we showed in our letter, a nonlinear subcritical instability exists resulting in multiple steady states depending upon the wall ramp speed. Here, we show that this phenomenon can occur for realistic parameter values, in particular those obtained for a particular polymer solution that has shown
THE THERMAL INSTABILITY OF SOLAR PROMINENCE THREADS
Soler, R.; Goossens, M.; Ballester, J. L.
2011-04-10
The fine structure of solar prominences and filaments appears as thin and long threads in high-resolution images. In H{alpha} observations of filaments, some threads can be observed for only 5-20 minutes before they seem to fade and eventually disappear, suggesting that these threads may have very short lifetimes. The presence of an instability might be the cause of this quick disappearance. Here, we study the thermal instability of prominence threads as an explanation of their sudden disappearance from H{alpha} observations. We model a prominence thread as a magnetic tube with prominence conditions embedded in a coronal environment. We assume a variation of the physical properties in the transverse direction so that the temperature and density continuously change from internal to external values in an inhomogeneous transitional layer representing the particular prominence-corona transition region (PCTR) of the thread. We use the nonadiabatic and resistive magnetohydrodynamic equations, which include terms due to thermal conduction parallel and perpendicular to the magnetic field, radiative losses, heating, and magnetic diffusion. We combine both analytical and numerical methods to study linear perturbations from the equilibrium state, focusing on unstable thermal solutions. We find that thermal modes are unstable in the PCTR for temperatures higher than 80,000 K, approximately. These modes are related to temperature disturbances that can lead to changes in the equilibrium due to rapid plasma heating or cooling. For typical prominence parameters, the instability timescale is of the order of a few minutes and is independent of the form of the temperature profile within the PCTR of the thread. This result indicates that thermal instability may play an important role for the short lifetimes of threads in the observations.
Center for Extended Magnetohydrodynamics Modeling - Final Technical Report
Parker, Scott
2016-02-14
This project funding supported approximately 74 percent of a Ph.D. graduate student, not including costs of travel and supplies. We had a highly successful research project including the development of a second-order implicit electromagnetic kinetic ion hybrid model [Cheng 2013, Sturdevant 2016], direct comparisons with the extended MHD NIMROD code and kinetic simulation [Schnack 2013], modeling of slab tearing modes using the fully kinetic ion hybrid model and finally, modeling global tearing modes in cylindrical geometry using gyrokinetic simulation [Chen 2015, Chen 2016]. We developed an electromagnetic second-order implicit kinetic ion fluid electron hybrid model [Cheng 2013]. As a first step, we assumed isothermal electrons, but have included drift-kinetic electrons in similar models [Chen 2011]. We used this simulation to study the nonlinear evolution of the tearing mode in slab geometry, including nonlinear evolution and saturation [Cheng 2013]. Later, we compared this model directly to extended MHD calculations using the NIMROD code [Schnack 2013]. In this study, we investigated the ion-temperature-gradient instability with an extended MHD code for the first time and got reasonable agreement with the kinetic calculation in terms of linear frequency, growth rate and mode structure. We then extended this model to include orbit averaging and sub-cycling of the ions and compared directly to gyrokinetic theory [Sturdevant 2016]. This work was highlighted in an Invited Talk at the International Conference on the Numerical Simulation of Plasmas in 2015. The orbit averaging sub-cycling multi-scale algorithm is amenable to hybrid architectures with GPUS or math co-processors. Additionally, our participation in the Center for Extend Magnetohydrodynamics motivated our research on developing the capability for gyrokinetic simulation to model a global tearing mode. We did this in cylindrical geometry where the results could be benchmarked with existing eigenmode
Absolute and Convective Instability of a Liquid Jet
NASA Technical Reports Server (NTRS)
Lin, S. P.; Hudman, M.; Chen, J. N.
1999-01-01
The existence of absolute instability in a liquid jet has been predicted for some time. The disturbance grows in time and propagates both upstream and downstream in an absolutely unstable liquid jet. The image of absolute instability is captured in the NASA 2.2 sec drop tower and reported here. The transition from convective to absolute instability is observed experimentally. The experimental results are compared with the theoretical predictions on the transition Weber number as functions of the Reynolds number. The role of interfacial shear relative to all other relevant forces which cause the onset of jet breakup is explained.
Liang, Edison; Smith, Ian; Boettcher, Markus E-mail: iansmith@rice.edu
2013-04-01
Using particle-in-cell simulations, we study the kinetic physics of relativistic shear flow in collisionless electron-positron (e+e-) plasmas. We find efficient magnetic field generation and particle energization at the shear boundary, driven by streaming instabilities across the shear interface and sustained by the shear flow. Nonthermal, anisotropic high-energy particles are accelerated across field lines to produce a power-law tail turning over just below the shear Lorentz factor. These results have important implications for the dissipation and radiation of jets in blazars and gamma-ray bursts.
Stabilization of ballooning modes with sheared toroidal rotation
Miller, R.L.; Waelbroeck, F.L.; Hassam, A.B.; Waltz, R.E.
1995-10-01
Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfven wave, and an initial value code solves the resulting equations. The {ital s}{minus}{alpha} diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency ({ital d}{Omega}/{ital dq}, where {Omega} is the angular toroidal velocity and {ital 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 direct stable access to the second stability regime occurs when this frequency is approximately one-quarter to one-half the Alfven frequency, {omega}{sub A}={ital V}{sub A}/{ital qR}. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Global magnetohydrodynamic simulations of the magnetosphere
Walker, R.J.; Ogino, T.
1989-04-01
Global magnetohydrodynamic (MHD) simulations of the interaction between the solar wind and a planetary magnetosphere enable us to calculate self-consistently the time-dependent three-dimensional configuration of the magnetosphere. To demonstrate the application of a global MHD model to the magnetosphere, the authors have calculated the dependence of the magnetospheric configuration and polar-cap structure on the north-south component of the interplanetary magnetic field (IMF). First, they modeled the magnetosphere in the absence of an IMF and found a slowly evolving system in which steady convection leads to slow reconnection in the plasma sheet. When a uniform northward IMF was initially imposed throughout the system the plasma sheet thickened in a small region near the noon-midnight meridian and extended into the tail lobes. When viewed from the polar cap, this appears as a narrow finger of closed field lines extending into the polar cap. The plasma sheet thickening is caused by reconnection on the nightside magnetopause. This plasma sheet extension becomes less pronounced when the northward IMF enters the simulation box with the solar wind. For both cases the convection near midnight is toward the sun, and region-1-type field-aligned currents appear on both sides of the plasma sheet extension. For northward IMF the resulting magnetospheric configuration approached a quasi-steady state in which stable magnetospheric convection was maintained. The simulation results indicate that the presence of a northward B in the plasma sheet stabilizes the tail.
Imbalanced relativistic force-free magnetohydrodynamic turbulence
Cho, Jungyeon; Lazarian, A.
2014-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfvénic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper, we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., b{sub +}{sup 2}/b{sub −}{sup 2}∝(ϵ{sub +}/ϵ{sub −}){sup n} with n > 2). These results are consistent with those obtained for imbalanced non-relativistic Alfvénic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.
Large-scale quasi-geostrophic magnetohydrodynamics
Balk, Alexander M.
2014-12-01
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the 'shallow water' beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra (adiabatic-type) invariant. Its presence implies energy accumulation in the 30° sector around zonal direction. With some special energy input, the extra invariant can lead to the accumulation of energy in zonal magnetic field; this happens if the input of the extra invariant is small, while the energy input is considerable.
Global invariants in ideal magnetohydrodynamic turbulence
Shebalin, John V.
2013-10-15
Magnetohydrodynamic (MHD) turbulence is an important though incompletely understood factor affecting the dynamics of many astrophysical, geophysical, and technological plasmas. As an approximation, viscosity and resistivity may be ignored, and ideal MHD turbulence may be investigated by statistical methods. Incompressibility is also assumed and finite Fourier series are used to represent the turbulent velocity and magnetic field. The resulting model dynamical system consists of a set of independent Fourier coefficients that form a canonical ensemble described by a Gaussian probability density function (PDF). This PDF is similar in form to that of Boltzmann, except that its argument may contain not just the energy multiplied by an inverse temperature, but also two other invariant integrals, the cross helicity and magnetic helicity, each multiplied by its own inverse temperature. However, the cross and magnetic helicities, as usually defined, are not invariant in the presence of overall rotation or a mean magnetic field, respectively. Although the generalized form of the magnetic helicity is known, a generalized cross helicity may also be found, by adding terms that are linear in the mean magnetic field and angular rotation vectors, respectively. These general forms are invariant even in the presence of overall rotation and a mean magnetic field. We derive these general forms, explore their properties, examine how they extend the statistical theory of ideal MHD turbulence, and discuss how our results may be affected by dissipation and forcing.