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Recently the shallow water magnetohydrodynamic (SMHD) equations have been proposed for describing the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two-dimensional (2D) with magnetohydrostatic equilibrium in the third direction. In the present paper the properties of the SMHD equations as a nonlinear system of hyperbolic conservation laws are described. Characteristics and Riemann invariants are studied for 1D unsteady and 2D steady flow. Simple wave solutions are derived, and the nonlinear character of the wave modes is investigated. The ∇·(h B)=0 constraint and its role in obtaining a regularized Galilean invariant conservation law form of the SMHD equations is discussed. Solutions of the Rankine-Hugoniot relations are classified and their properties are investigated. The derived properties of the wave modes are illustrated by 1D numerical simulation results of SMHD Riemann problems. A Roe-type linearization of the SMHD equations is given which can serve as a building block for accurate shock-capturing numerical schemes. The SMHD equations are presently being used in the study of the dynamics of layers in the solar interior, but they may also be applicable to problems involving the free surface flow of conducting fluids in laboratory and industrial environments. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Magnetic fields are an essential component of a plasma. In many astrophysical, solar, magnetospheric, and laboratory situations the magnetic field in the plasma can be very dynamic and form highly complex structures. One approach to unraveling these structures is to determine the magnetic skeleton of the field, a set of topological features that divide the magnetic field into topologically distinct domains. In general, the features of the magnetic skeleton are difficult to locate, in particular those given by numerical experiments. In this paper, we propose a new set of tools to find the skeleton of general magnetic fields including null points, spines, separatrix surfaces, and separators. This set of tools is found to be considerably better at finding the skeleton than the currently favored methods used in magnetohydrodynamics. [ABSTRACT FROM AUTHOR]

The paper investigates the role of relative motion between the fluid components of a plasma model, which is simulated by concatenation of two anisotropic magnetohydrodynamic (MHD) fluids, on the propagation of low-frequency waves and instabilities. The gyrotropic pressure of both the MHD components is given by generalized polytropic laws that allow the system to reduce to a variety of states. The linearized analysis is carried out and dispersion relation is derived using the normal mode technique. The dispersion relation, which gives numerous earlier results as special cases, is discussed both analytically as well as numerically for parameters appropriate for the space plasma. It is found that the relative motion between the two components, besides modifying the condition for fire-hose instability, causes the concatenated system to exhibit different kinds of relative ordering of the magnitudes of phase speeds of the various MHD modes in the directions parallel and antiparallel to the magnetic field. The relative motion between the components also influences the phase relationship between density and magnetic field fluctuations for the various compressive modes in the background ambient plasma. [ABSTRACT FROM AUTHOR]

The reversal mechanism of a dipole magnetic field generated by dynamo action in a rotating spherical shell is investigated by a three-dimensional nonlinear magnetohydrodynamic simulation as well as a linear stability analysis. The emphasis of the study is on understanding the relationship between dipole reversal and the symmetry properties of the dynamo solution. As a result, first, it is found that there is a threshold of the magnetic Prandtl number, below which the dipole field is never reversed, and above which the reversal occurs at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of a dipole field (called “a-dynamo” in this paper) consists only of the antimirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo grow only during the polarity reversal events and quickly decay afterwards. This indicates that the dipole field reversal and the loss of equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by numerical analyses that the a-dynamo process is linearly unstable for the perturbation of opposite symmetry when the magnetic Prandtl number exceeds the threshold for dipole reversal. Mode coupling between the longitudinal Fourier components plays a crucial role in creating the instability. Based on the above results, it is proposed that symmetry-breaking instability could be the mechanism for dipole field reversal in the geodynamo process. The energy conversion between components of different symmetry is also analyzed in the quasistable polarity phase and in the polarity reversal phase, respectively. [ABSTRACT FROM AUTHOR]

The energy confinement time and maximum achievable pressure are critical figures of merit for any proposed magnetic fusion concept. The present work focuses on these issues for a hard core Z pinch, which is the cylindrical limit of a large aspect ratio levitated dipole configuration. An analysis is presented that theoretically predicts both τE and β for this configuration. The model makes the optimistic assumption that transport is purely classical in the region of the profile that is magnetohydrodynamically (MHD) stable against interchange modes. In the interchange-unstable region use is made of the quasilinear theory described in the accompanying paper [A. Kouznetsov, J. Freidberg, and J. Kesner, Phys. Plasmas 14, 102501 (2007)] which shows that the plasma pressure relaxes to the MHD marginally stable profile while the density evolves to n∝[∮dl/B]-1. Analytic and numerical calculations lead to explicit scaling relations for τE and β which can be tested in future LDX experiments. [ABSTRACT FROM AUTHOR]

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied with a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable and may peak around m=mpeak∼10. In this paper, it is first demonstrated that this result agrees with existing linear theory for DTMs. Based on this theory, a semiempirical formula for the dependence of mpeak on the system parameters is proposed. Second, with the use of nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, where small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant to the understanding of the magnetohydrodynamic activity near the minimum of q and may thus be of interest for studies on stability and confinement of advanced tokamaks. [ABSTRACT FROM AUTHOR]

This paper presents the experimental characterization of pedestal parameters, edge localized mode (ELM) energy, and particle losses from the main plasma and the corresponding ELM energy fluxes on plasma facing components for a series of dedicated experiments in the Joint European Torus (JET). From these experiments, it is demonstrated that the simple hypothesis relating the peeling-ballooning linear instability to ELM energy losses is not valid. Contrary to previous observations at lower triangularities, small energy losses at low collisionality have been obtained in regimes at high plasma triangularity and q95∼4.5, indicating that the edge plasma magnetohydrodynamic stability is linked with the transport mechanisms that lead to the loss of energy by conduction during type I ELMs. Measurements of the ELM energy fluxes on the divertor target show that their time scale is linked to the ion transport along the field and the formation of a high energy sheath, in agreement with kinetic modeling of ELMs. Higher density ELMs, of a convective nature, lead to overall much longer time scales for the ELM energy flux, with more than 80% of the ELM energy flux arriving after the surface divertor temperature has reached its maximum value. On the contrary, for low density ELMs, of a conductive nature, up to 40% of the energy flux arrives at the divertor target before the surface divertor temperature has reached its maximum value. These large and more conductive ELMs may lead to up to ∼50% of the ELM energy reaching the main wall plasma facing components instead of the divertor target. The extrapolation to the International Thermonuclear Experimental Reactor of the obtained results is described and the main uncertainties discussed. [ABSTRACT FROM AUTHOR]

The 3D instability of the spontaneous fast magnetic reconnection process is studied with magnetohydrodynamics (MHD) simulations, where the 2D model of the spontaneous fast magnetic reconnection is destabilized in three dimension. As well known in many 2D numerical MHD studies, when a 1D current sheet is destabilized with the current-driven anomalous resistivity, the 2D Petschek type fast magnetic reconnection is established. This paper shows that the 2D Petschek type fast magnetic reconnection can be destabilized in three dimension by an initial resistive disturbance which includes a weak fluctuation in the sheet current direction, i.e., along the magnetic neutral line. The resulting 3D fast magnetic reconnection finally becomes intermittent and random through a 3D instability. In addition, it is also shown that the 3D instability is suppressed by the uniform resistivity. It suggests that the 3D instability is caused in the Petschek-type reconnection process which is characterized by a strongly localized magnetic diffusion region and the slow shock acceleration of the plasma jets and is suppressed in the Sweet-Parker type reconnection process. [ABSTRACT FROM AUTHOR]

The dynamics of ablated plasmas of wire-array Z-pinches are studied numerically in (r,θ) geometry by using the magnetohydrodynamic (MHD) simulation model in which the mass injection boundary conditions are presented, and two-dimensional spatio-temporal distributions of magnetic field and precursor current during the ablation phase are obtained. The ablated-plasma dynamics contains four processes: drifting toward the axis, arriving at the axis and forming the precursor column, and contraction and expansion of the precursor column. The relationship among the maximum inward velocity of ablated plasma streams and the initial wire array parameters is analyzed and it is found that this velocity is relatively sensitive to the change of inter-wire separation but weakly depends on the original array radius. The results are in reasonable agreement with the experiments on MAGPIE facility. The origin of the current flow in the precursor plasmas is analyzed from the point of view of the B-field convection in (r,θ) plane. The dynamics of ablation streams determine the distribution of magnetic field and the current density Jz inside the wire array. The precursor current can be approximately calculated by the integral of Jz inside the region of a radius near to the column. In this model, the fraction of precursor current is less than 10% of the total current, which is close to the experimental results. When the current waveform is fixed, the increase of the inter-wire gap or decrease of the initial radius will lead to the increase of the precursor current. [ABSTRACT FROM AUTHOR]

Numerical studies of magnetohydrodynamic (MHD) instabilities with feedback control in reversed field pinches (RFPs) are presented. Specifically, investigations are performed of the stability of m=1 modes in RFPs with control based on sensing the normal and tangential magnetic fields at the resistive wall and applying two-parameter feedback proportional to these fields. The control scheme is based on that of [J. M. Finn, Phys. Plasmas 13, 082504 (2006)], which is here modified to use a more realistic plasma model. The plasma model now uses full resistive MHD rather than reduced MHD, and it uses three realistic classes of equilibrium parallel current density profiles appropriate to RFPs. Results with these modifications are in qualitative agreement with [J. M. Finn, Phys. Plasmas 13, 082504 (2006)]: the feedback can stabilize tearing modes (with resistive or ideal-wall) and resistive wall ideal modes. The limit for stabilization is again found to be near the threshold for ideal modes with an ideal-wall. In addition to confirming these predictions, the nature of the instabilities limiting the range of feedback stabilization near the ideal-wall ideal-plasma threshold are studied, and the effects of viscosity, resistive wall time, and plasma resistivity are reported. [ABSTRACT FROM AUTHOR]

Two-dimensional stationary nontearing inertial scale electron magnetohydrodynamic (EMHD) instability is described. The physical mechanism of the instability is illustrated. Analytical asymptotic estimate of the growth rate is provided and verified with a numerical calculation of the instability, also describing the characteristic structure of the eigenmode. Natural occurrence of the instability is demonstrated in a nonlinear EMHD simulation of a system undergoing magnetic reconnection, where the instability manifests itself on the outflow side of the magnetic field separatrix and may affect the self-determined length of the layer. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic instabilities of high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation for stability. The jointed European torus-like equilibria of H-mode discharges are generated numerically using the VMEC code. It is found that, when the bootstrap current is taken into account, a safety-factor reversal or plateau can be generated near plasma edge. This confirms previous results of numerical equilibrium reconstructions using other types of codes. The n = 1 magnetohydrodynamic instabilities, where n is toroidal mode number, are investigated numerically in this type of equilibria using the AEGIS code. It is found that the infernal type harmonic can prevail at safety-factor reversal or plateau region. The toroidal plasma rotation effect with low Mach number is investigated. The numerical results show that the mode frequency is close to the rotation frequency at pedestal top, when the value of safety factor at plateau is slightly above a rational number. This mode frequency range seems to coincide with the experimentally observed frequencies of n = 1 edge harmonic oscillations (or outer modes) at the quiescent H-mode discharges. [ABSTRACT FROM AUTHOR]

Discrete relaxation events in reversed-field pinch relevant configurations are investigated numerically with nonlinear extended magnetohydrodynamic (MHD) modeling, including the Hall term in Ohm's law and first-order ion finite Larmor radius effects. Results show variability among relaxation events, where the Hall dynamo effect may help or impede the MHD dynamo effect in relaxing the parallel current density profile. The competitive behavior arises from multi-helicity conditions where the dominant magnetic fluctuation is relatively small. The resulting changes in parallel current density and parallel flow are aligned in the core, consistent with experimental observations. The analysis of simulation results also confirms that the force density from fluctuation-induced Reynolds stress arises subsequent to the drive from the fluctuation-induced Lorentz force density. Transport of the momentum density is found to be dominated by the fluctuation-induced Maxwell stress over most of the cross section with viscous and gyroviscous contributions being large in the edge region. The findings resolve a discrepancy with respect to the relative orientation of current density and flow relaxation, which had not been realized or investigated in King et al. [Phys. Plasmas 19, 055905 (2012)], where only the magnitude of flow relaxation is actually consistent with experimental results. [ABSTRACT FROM AUTHOR]

The Magnetized Plasma Fusion Reactor concept is proposed as a magneto-inertial fusion approach based on the target plasma created through the collision merging of two oppositely translating field reversed configuration plasmas, which is then compressed by the imploding liner driven by the pulsed-power driver. The target creation process is described by a two-dimensional magnetohydrodynamics model, resulting in the typical target parameters. The implosion process and the fusion reaction are modeled by a simple zero-dimensional model, taking into account the alpha particle heating and the bremsstrahlung radiation loss. The compression on the target can be 2D cylindrical or 2.4D with the additive axial contraction taken into account. The dynamics of the liner compression and fusion burning are simulated and the optimum fusion gain and the associated target parameters are predicted. The scientific breakeven could be achieved at the optimized conditions. [ABSTRACT FROM AUTHOR]

An instability observed in whole-device, resistive magnetohydrodynamic simulations of the driven phase of coaxial helicity injection in the National Spherical Torus eXperiment is identified as a current-driven resistive mode in an unusual geometry that transiently generates a current sheet. The mode consists of plasma flow velocity and magnetic field eddies in a tube aligned with the magnetic field at the surface of the injected magnetic flux. At low plasma temperatures (∼10–20 eV), the mode is benign, but at high temperatures (∼100 eV) its amplitude undergoes relaxation oscillations, broadening the layer of injected current and flow at the surface of the injected toroidal flux and background plasma. The poloidal-field structure is affected and the magnetic surface closure is generally prevented while the mode undergoes relaxation oscillations during injection. This study describes the mode and uses linearized numerical computations and an analytic slab model to identify the unstable mode. [ABSTRACT FROM AUTHOR]

Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidalMHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τR/τV ≫ 1, where τR and τV represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τR/τV ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large. [ABSTRACT FROM AUTHOR]

Bow shock structures are important to various hydrodynamics and magnetohydrodynamics (MHD) phenomena in geophysics and astrophysics. The formation and propagation of bow shocks around the lightning return stroke channel are investigated based on the self-similar motion theory and simulated with a two-dimensional Eulerian finite volume resistive radiation MHD code. In this framework, as verification of theoretical models, the evolving structures of many quantities, such as the plasma density, temperature, pressure, shock velocity, and magnetic field, can be obtained, which present all the characteristics of bow shocks in the lightning return stroke processes. The evolution characteristics and the configuration of the curved return stroke channels, e.g., the non-ideal effects and the scaling laws, are discussed in detail. The results may have applications for some observed features of the return stroke channels and other phenomena in the lightning discharge plasmas. [ABSTRACT FROM AUTHOR]

Effects of poloidal rotation profile on tearing and Kelvin-Helmholtz (KH) instabilities in a cylindrical plasma are investigated by using a reduced magnetohydrodynamic model. Since the poloidal rotation has different effects on the tearing and KH modes in different rotation regimes, four unstable domains are numerically identified, i.e., the destabilized tearing mode domain, stabilized tearing mode domain, stable-window domain, and unstable KH mode domain. It is also found that when the rotation layer is in the outer region of the rational surface, the stabilizing role of the rotation can be enhanced so significantly that the stable window domain is enlarged. Moreover, Alfven resonances can be induced by the tearing and KH modes in such rotating plasmas. Radially wide profiles of current and vorticity perturbations can be formed when multiple current sheets on different resonance positions are coupled together. [ABSTRACT FROM AUTHOR]

Hall effects on local structures in homogeneous, isotropic, and incompressible magnetohydrodynamic turbulence are studied numerically. The transition of vortices from sheet-like to tubular structures induced by the Hall term is found, while the kinetic energy spectrum does not distinguish the two types of structures. It is shown by the use of the sharp low-pass filter that the transition occurs not only in the scales smaller than the ion skin depth but also in a larger scale. The transition is related with the forward energy transfer in the spectral space. Analyses by the use of the sharp low-pass filter show that the nonlinear energy transfer associated with the Hall term is dominated by the forward transfer and relatively local in the wave number space. A projection of the simulation data to a Smagorinsky-type sub-grid-scale model shows that the high wave number component of the Hall term may possibly be replaced by the model effectively. [ABSTRACT FROM AUTHOR]

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does not contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects. [ABSTRACT FROM AUTHOR]

Alfvén eigenmodes in up-down asymmetric tokamak equilibria are studied by a new magnetohydrodynamic eigenvalue code. The code is verified with the NOVA code for the Solovév equilibrium and then is used to study Alfvén eigenmodes in a up-down asymmetric equilibrium of the Experimental Advanced Superconducting Tokamak. The frequency and mode structure of toroidicity-induced Alfvén eigenmodes are calculated. It is demonstrated numerically that up-down asymmetry induces phase variation in the eigenfunction across the major radius on the midplane. [ABSTRACT FROM AUTHOR]

A numerical study of magnetic reconnection in two-dimensional resistive magnetohydrodynamics for marginally unstable Sweet-Parker current sheets that are subject to plasmoid formation is carried out. Despite the procedure used to form the primary Sweet-Parker-like current layer, that is different with respect to previous studies, the reconnection layer is unstable to the plasmoid instability for a Lundquist number greater than the expected critical value Sc≈104. For Lundquist numbers S>=Sc, the instability exhibits a quasi-periodic behaviour consisting of formation, rapid growth, and evacuation of a moving magnetic island. The so called 'plasmoid' breaks up the primary current layer and significantly enhances the maximum current density over the value expected from Sweet-Parker theory. This local enhancement spatially coincides with the downstream X-point of the magnetic island and is associated with the formation of a pair of slow-mode Petschek-like shocks bounding the outflowing plasma. These results suggest that the inter-plasmoid current layers forming in high-Lundquist-number plasmas (S>Sc) could not be simply described as marginally stable Sweet-Parker current sheets. [ABSTRACT FROM AUTHOR]

The statistical study of magnetic reconnection events in two-dimensional turbulence has been performed by comparing numerical simulations of magnetohydrodynamics (MHD) and Hall magnetohydrodynamics (HMHD). The analysis reveals that the Hall term plays an important role in turbulence, in which magnetic islands simultaneously reconnect in a complex way. In particular, an increase of the Hall parameter, the ratio of ion skin depth to system size, broadens the distribution of reconnection rates relative to the MHD case. Moreover, in HMHD the local geometry of the reconnection region changes, manifesting bifurcated current sheets and quadrupolar magnetic field structures in analogy to laminar studies, leading locally to faster reconnection processes in this case of reconnection embedded in turbulence. This study supports the idea that the global rate of energy dissipation is controlled by the large scale turbulence, but suggests that the distribution of the reconnection rates within the turbulent system is sensitive to the microphysics at the reconnection sites. [ABSTRACT FROM AUTHOR]

The effects of the initial upstream plasma β on the plasmoid instability are studied via two-dimensional resistive magnetohydrodynamic simulations. For cases with nonuniform β dependent initial plasma mass density and uniform temperature, our numerical results indicate that the critical Lundquist number for onset of the plasmoid instability depends on the initial plasma β. The critical Lundquist number is approximately 2000-3000 for β=50 and is 8000-10 000 for β=0.2. The higher the β, the smaller the critical Lundquist number is. Similar to previous studies of high-β systems, the average reconnection rate in low β systems is found to become weakly dependent on the Lundquist number in the plasmoid-unstable regime. However, the average reconnection rate, normalized to the asymptotic value of upstream BVA, is lower in a low β system than that in a high β system. The magnetic energy spectral index, which characterizes fragmentation of the reconnection layer, is approximately two and is insensitive to β in the high-Lunquist number regime. It is also found that the magnetic reconnection rate becomes similar for different β cases, if the initial force-balance is provided by temperature gradient instead of density gradient. Therefore, it is concluded that the β-dependence mentioned above may be largely attributed to the density variation. [ABSTRACT FROM AUTHOR]

The implosion dynamics of wire-array Z-pinches are investigated numerically in 2D (r, θ) geometry by using a resistive MHD code. It is assumed that the wires have expanded to plasmas with diameter d0, which is used as the initial condition for the consequent implosion process. In fact, the explosion process of individual wires is not included. By changing d0, the effects of the wire expansion degree on the implosion dynamics are analyzed. When d0 is larger, the current density is more concentrated at the outer side of the wires and the fraction of current flow around the wire plasmas is nearly in proportion to d0. As a result, the ablation rate of wires is increased and the implosion phase starts earlier. This conclusion agrees with the simulation works of other authors [Chittenden et al., Phys. Plasmas 11(3), 1118 (2004)]. When the array radius and initial wire plasma diameter are fixed, the increase of wire number leads to the azimuthal merge of wires during implosion. When the wires number exceed a critical value, which is related to d0, wire plasmas can merge to a continuous shell with an azimuthal perturbation in density, which depends on the initial wires number. [ABSTRACT FROM AUTHOR]

We present a numerical study of the 2.5D Kelvin-Helmholtz instability and its vortices, where an initial plasma configuration appropriate for the situation around unmagnetized planets is assumed. We solve the set of ideal magnetohydrodynamic equations numerically with the total variation diminishing Lax-Friedrichs algorithm. Our density profile is such that the mass density increases toward the planet. A high density leads to smaller growth rates of the instability and, thus, has a stabilizing effect for the boundary layer. Moreover, we include source terms in the equations, enabling us to study the influence of gravity. Our results show that gravity affects the evolution of the Kelvin-Helmholtz instability. However, the effect is not very significant. We thus conclude that the density increase toward the planet stabilizes the boundary layer around Venus more than gravity does. [ABSTRACT FROM AUTHOR]

We analytically and numerically study the analogue of the Parker (magnetic buoyancy) instability in a uniformly rotating plasma screw pinch confined in a cylinder. Uniform plasma rotation is imposed to create a centrifugal acceleration, which mimics the gravity required for the classical Parker instability. The goal of this study is to determine how the Parker instability could be unambiguously identified in a weakly magnetized, rapidly rotating screw pinch, in which the rotation provides an effective gravity and a radially varying azimuthal field is controlled to give conditions for which the plasma is magnetically buoyant to inward motion. We show that an axial magnetic field is also required to circumvent conventional current driven magnetohydrodynamic (MHD) instabilities such as the sausage and kink modes that would obscure the Parker instability. These conditions can be realized in the Madison plasma Couette experiment (MPCX). Simulations are performed using the extended MHD code NIMROD for an isothermal compressible plasma model. Both linear and nonlinear regimes of the instability are studied, and the results obtained for the linear regime are compared with analytical results from a slab geometry. Based on this comparison, it is found that in a cylindrical pinch, the magnetic buoyancy mechanism dominates at relatively large Mach numbers (M > 5), while at low Mach numbers (M < 1), the instability is due to the curvature of magnetic field lines. At intermediate values of Mach number (1 < M < 5), the Coriolis force has a strong stabilizing effect on the plasma. A possible scenario for experimental demonstration of the Parker instability in MPCX is discussed. [ABSTRACT FROM AUTHOR]

The scale locality of energy fluxes for magnetohydrodynamics (MHD) is investigated numerically for stationary states of turbulence. Two types of forces are used to drive turbulence, a kinetic force that acts only on the velocity field and a kinetic-inductive force, which acts on the velocity and magnetic fields alike. The analysis is performed in spectral space, which is decomposed into a series of shells following a power law for the boundaries. The triadic transfers occurring among these shells are computed, and the fluxes and locality functions are obtained by partial summation over the relevant shells. Employing Kraichnan locality functions, values of 1/3 and 2/3 for the scaling exponents of the four MHD energy fluxes are found. These values are smaller than the value of 4/3 found for hydrodynamic turbulence. To better understand these results, an in depth analysis is performed on the total energy flux. [ABSTRACT FROM AUTHOR]

Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an extended version of hybrid magnetohydrodynamics gyrokinetic code (XHMGC) to study thermal ion kinetic effects on Alfvénic modes driven by energetic particles, such as kinetic beta induced Alfvén eigenmodes in tokamak fusion plasmas. The XHMGC nonlinear model can be used to address a number of problems, where kinetic treatments of both thermal and supra-thermal plasma components are necessary, as theoretically predicted, or where it is desirable to investigate the phenomena connected with the presence of two supra-thermal particle species with different radial profiles and velocity space distributions. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic evolution of the double tearing mode (DTM) with a guiding magnetic field (By0) is investigated by magnetohydrodynamical numerical simulation. The dynamic process of DTM depends weakly on the guiding field in the weak guiding field regime (By0≤1), but is suppressed by a strong guiding field (By0>2). During the explosive nonlinear phase, the maximum reconnection rate (γmax) increases weakly with the increase of the resistivity as γmax~η0.06 for By0≤1, but for By0>2, γmax is nearly independent of the resistivity. The maximum reconnection rate in the explosive growth phase increases with increase of the initial current sheet separation. A secondary tearing instability is observed at moderate current sheet separation. A strong guiding field suppresses the formation of a secondary island. Based on the simulation results, it is found that the secondary tearing instability occurs only when the length-to-thickness aspect ratio of the reconnection region exceeds about 20. [ABSTRACT FROM AUTHOR]

The linear and nonlinear evolution of a single-helicity tearing mode in a cylindrical, force-free pinch are investigated using a fluid model with first-order finite-Larmor-radius corrections. Linear results computed with the nimrod [nonideal magnetohydrodynamics (MHD) with rotation, open discussion] code [Sovinec et al., J. Comput. Phys. 195, 355 (2004)] produce a regime at small ρs where the growth rate is reduced relative to resistive MHD, though the Hall term is not significant. The leading order contributions from ion gyroviscosity may be expressed as a drift associated with ∇B0 and poloidal curvature for experimentally relevant β=0.1, S~105-106 force-free equilibria. The heuristic analytical dispersion relation, γ4(γ-iω*gv)=γMHD5 where ω*gv is the gyroviscous drift frequency, confirms numerical results. The behavior of our cylindrical computations at large ρs corroborates previous analytic slab studies where an enhanced growth rate and radially localized Hall dynamo are predicted. Similar to previous drift-tearing results, nonlinear computations with cold ions demonstrate that the Hall dynamo is small when the island width is large in comparison with the scale for electron-ion coupling. The saturation is then determined by the resistive MHD physics. However, with warm ions the gyroviscous stress supplements the nonlinear Lorentz force, and the saturated island width is reduced. [ABSTRACT FROM AUTHOR]

Within the framework of a reduced collisionless magnetohydrodynamics (MHD) model containing the effects of electron inertia and electron pressure gradient, scaling laws of the strongly coupled collisionless q=2 triple tearing instabilities with broad linear spectra in a tokamak plasma are studied numerically. It is found that as the poloidal mode number m increases, the scaling power laws of the linear growth rate of triple tearing modes (TTMs) on SHp, de, and ρs change gradually from the strongly coupled tearing mode scalings to the standard single tearing mode (STM) scalings, where SHp is the magnetic Reynolds number, de is the electron inertial skin depth, and ρs is the ion sound gyroradius. For example, de-scaling of the linear growth rate γ~deαd changes gradually from γ~de1 to γ~de3 as the m number increases in the case of ρse, while ρs-scaling γ~deαρ shifts gradually from γ~ρs2/3 to γ~ρs1 as m increases in the case of de<ρs. Furthermore, it is observed that the increase of ρs gradually weakens the dependence on de in both large and small Δ' regimes, such as, ~de1→~de1/3 in the large Δ' regime, where Δ' is the linear instability parameter of tearing modes. The numerical results about the scaling laws are validated by the previous relevant analytical theories in terms of the similarity of physical characteristics in the same Δ' regime. In addition, the effects of de and ρs on the spectrum structures of the unstable TTMs are discussed. Finally, the spatial characteristics of the eigenmode structures for different mode numbers are analyzed in detail. It is interestingly found that the structure of the most unstable eigenmode of the TTMs is quite similar to the eigenmode structure of a standard double tearing mode (DTM). [ABSTRACT FROM AUTHOR]

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential. [ABSTRACT FROM AUTHOR]

Phenomenological theories of strong incompressible magnetohydrodynamic (MHD) turbulence derived by Goldreich and Sridhar (GS) in 1995 and by Boldyrev in 2006 are only applicable to turbulence with vanishing cross-helicity. In this study, these two theories are generalized to treat turbulence with nonvanishing cross-helicity in such a way that the relation (w+/w-)2=([variant_greek_epsilon]+/[variant_greek_epsilon]-)2 observed in numerical simulations is satisfied. The average energy (second order structure function) in the generalized GS theory is E(r⊥)=[lowercase_phi_synonym]1(σc)([variant_greek_epsilon]r⊥)2/3 and that in the generalized Boldyrev theory is E(r⊥)=[lowercase_phi_synonym]2(σc)(vA[variant_greek_epsilon]r⊥)1/2, where the function [lowercase_phi_synonym](σc) describes the dependence on the normalized cross-helicity σc. The form of the function [lowercase_phi_synonym](σc) is derived through a renormalization of the variable σc that yields a one parameter family of solutions. The theory derived by Lithwick, Goldreich, and Sridhar (LGS) in 2007 is a special case of the generalized GS theory derived here; however, other generalizations of the GS theory are obtained that have a different cross-helicity dependence than the LGS theory. This new class of solutions and similar generalizations of Boldyrev's theory are investigated to see how the energy cascade rate [variant_greek_epsilon] changes as a function of σc when the energy at a given scale is held fixed. The generalization of Boldyrev's theory derived here is applicable to homogeneous MHD turbulence in the solar wind, for example, and can be used to obtain the turbulent dissipation rate [variant_greek_epsilon] from measurements of the energy spectrum and the normalized cross-helicity. [ABSTRACT FROM AUTHOR]

The spatial and temporal evolution of the electric and magnetic fields in a current-carrying plasma is investigated in the nonlinear regime. Using the magnetohydrodynamic equations, a nonlinear diffusion equation for the magnetic field in the plasma is obtained. This nonlinear equation is numerically solved and the spatiotemporal evolution of the electric and magnetic fields and the electron density distribution are plotted. It is shown that as the time passes, the profile of the electric and magnetic fields changes from a sinusoidal shape to a saw-tooth one and the electron density distribution becomes very steepened. Also, the mechanism of the filament formation is then discussed. Furthermore, the effects of the thermal motion, collisions, and ion mass on growth rate of filaments as well as the saturation time are argued. Finally, it is found that the energy dissipation is associated with the aforementioned effects and strong plasma density gradient. [ABSTRACT FROM AUTHOR]

In this work we numerically test a model of Hall magnetohydrodynamics in the presence of a strong mean magnetic field: the reduced Hall magnetohydrodynamic model (RHMHD) derived by [Gomez et al., Phys. Plasmas 15, 102303 (2008)] with the addition of weak compressible effects. The main advantage of this model lies in the reduction of computational cost. Nevertheless, up until now the degree of agreement with the original Hall MHD system and the range of validity in a regime of turbulence were not established. In this work direct numerical simulations of three-dimensional Hall MHD turbulence in the presence of a strong mean magnetic field are compared with simulations of the weak compressible RHMHD model. The results show that the degree of agreement is very high (when the different assumptions of RHMHD, such as spectral anisotropy, are satisfied). Nevertheless, when the initial conditions are isotropic but the mean magnetic field is maintained strong, the results differ at the beginning but asymptotically reach a good agreement at relatively short times. We also found evidence that the compressibility still plays a role in the dynamics of these systems, and the weak compressible RHMHD model is able to capture these effects. In conclusion the weak compressible RHMHD model is a valid approximation of the Hall MHD turbulence in the relevant physical context. [ABSTRACT FROM AUTHOR]

Analyses of plasma behavior often begin with a description of the ideal magnetohydrodynamic equilibrium, this being the simplest model capable of approximating macroscopic force balance. Ideal force balance is when the pressure gradient is supported by the Lorentz force, ∇p=j×B. We discuss the implications of allowing for a chaotic magnetic field on the solutions to this equation. We argue that the solutions are pathological and not suitable for numerical calculations. If the pressure and magnetic field are continuous, the only nontrivial solutions have an uncountable infinity of discontinuities in the pressure gradient and current. The problems arise from the arbitrarily small length scales in the structure of the field, and the consequence of ideal force balance that the pressure is constant along the field-lines, B·∇p=0. A simple method to ameliorate the singularities is to include a small but finite perpendicular diffusion. A self-consistent set of equilibrium equations is described, and some algorithmic approaches aimed at solving these equations are discussed. [ABSTRACT FROM AUTHOR]

The coupling of low-frequency Alfvénic modes with acoustic oscillations due to curvature of the background magnetic field is considered for stellarator plasmas with low shear. Magnetohydrodynamic (MHD) analysis demonstrates that the interaction between these branches can generate gaps in the continua with a width proportional to beta as well as the magnitude of the Fourier harmonics of the magnetic field strength which cause the coupling. The gaps can provide a habitat for beta-induced Alfvén-acoustic eigenmodes (BAAEs). Using the causality principle, a technique is developed to resolve the singular behavior of the MHD BAAE eigenmode equation at the points of resonance with the acoustic continuum. Alternatively, the singularities arising in the reduced MHD description can be resolved by accounting for the finite parallel electrical field. Both approaches yield consistent continuum damping rate, which proves to be small. Numerical calculations for analytically fitted experimental profiles of electron-dominated plasma in Helically Symmetric eXperiment (HSX) facility yield two weakly damped BAAE modes with different frequencies: one is close to the maximum of the lower-frequency Alfvén-acoustic continuum, and the other is located well within the BAAE gap. The numerically found BAAEs have frequencies in the same range as the experimentally observed electromagnetic modes in HSX, even when the finite diamagnetic frequency effects are considered. [ABSTRACT FROM AUTHOR]

Homogeneous electron magnetohydrodynamic turbulence is investigated under the presence of an imposed magnetic field. It is shown that this situation is well described in physical space by a divergence relation, which expresses the statistical conservation of magnetic energy flux through the inertial range. The ansatz is made that the development of anisotropy implies a foliation of space correlation with an algebraic relation between the axial and radial components of the separation vector r. A direct consequence is the possibility to derive a new universal law for the third-order moments, which is parametrized by the intensity of anisotropy. The so-called critical balance condition is used to fix this parameter and find a unique vectorial expression. [ABSTRACT FROM AUTHOR]

An analytic expression for the stability threshold of linear tearing modes is derived. The magnetized plasma is described in terms of a standard viscoresistive magnetohydrodynamic model. The analytic derivation requires an extension of the standard layer equation that represents an approximation of the full model in the vicinity of the reconnecting layer. The analytic result is checked against numerical simulations, showing excellent agreement. [ABSTRACT FROM AUTHOR]

The conceptual development and implementation of a scalable nonlinear solver for the time-dependent three-dimensional (3D) compressible resistive magnetohydrodynamics model (MHD) is discussed. The approach is based on Jacobian-free Newton–Krylov technology, preconditioned with multigrid methods for algorithmic scalability. The key to the approach is the reformulation of the hyperbolic MHD system into a parabolic one, which is amenable to multigrid techniques. Such reformulation (parabolization) aims to render the modified system block diagonally dominant (unlike the original MHD system, which is diagonally submissive for implicit time steps Δt larger than the explicit Courant–Friedrichs–Lewy time step). The algorithm has been tested on a variety of 2D and 3D configurations which demonstrate its excellent algorithmic scalability properties. In particular, it is shown that, serially, the CPU time for a given simulation scales linearly with the number of unknowns, and that large CPU gains (∼30) are attainable with respect to an explicit approach even for moderate grids (256×256). In parallel, the algorithm features excellent scalability properties up to thousands of processors (4096) and millions of unknowns (∼1.3×108). [ABSTRACT FROM AUTHOR]

Nonlinear simulations based on the magnetohydrodynamic model have been executed to reveal the dynamics of the ballooning mode in the spherical tokamak plasma. The simulation results have reproduced the characteristic features of the edge-localized mode crash phase, where the filamentary structures are formed along the magnetic field in the edge region, and separated from the core plasma. Moreover, the finite Larmor radius effect is addressed. [ABSTRACT FROM AUTHOR]

Rotating magnetic fields (RMF) have been employed to both form and sustain currents in field reversed configurations (FRC). A major concern about this method has been the fear of opening up magnetic field lines with even small ratios of vacuum RMF Bω to external confinement field Be. A recently proposed innovation was to use an antisymmetric arrangement of RMF, but vacuum calculations with full RMF penetration showed that very low values of Bω/Be would still be required to provide field-line closure. Recent comparisons of symmetric and antisymmetric RMF drive on the translation, confinement, and sustainment (TCS) facility [A. L. Hoffman, H. Y. Guo, J. T. Slough et al., Fusion Sci. Technol. 41, 92 (2002)] have shown strong improvements in the basic confinement properties of the FRCs when using antisymmetric drive, even with ratios of Bω/Be as high as 0.3. This is due to normal standard operation with only partial penetration of the RMF beyond the FRC separatrix. The uniform transverse RMF in vacuum is shielded by the conducting plasma, resulting in a mostly azimuthal field near the FRC separatrix with a very small radial component. Simple numerical calculations using analytical solutions for the partially penetrated antisymmetric RMF, superimposed on Grad–Shafranov solutions for the poloidal FRC fields, show good field-line closure for the TCS experimental conditions. The antisymmetric arrangement also leads to more efficient current drive and improved stabilization of rotational modes. [ABSTRACT FROM AUTHOR]

Four types of magnetohydrodynamic modes determine the overall stability of centrifugally confined plasmas: flute interchanges and the Kelvin-Helmholtz instability, in a low β system, and the magnetorotational instability (MRI) and the Parker instability, in a high β system. Analytic calculations and numerical simulations of velocity shear stabilization of flute interchanges are reviewed. The results showed strong evidence of stabilization. The Kelvin-Helmholtz instability is ideally stable if the generalized Rayleigh's inflexion criterion is satisfied. The physical mechanisms of both the MRI and the Parker instability are examined and an explanation of why the MRI mechanism is insufficient to destabilize the system while the Parker instability could occur is given. Numerical simulations of the nonlinear behavior of the Parker instability are presented. It is shown that clumping from the Parker instability could reinforce centrifugal confinement. [ABSTRACT FROM AUTHOR]

A wall confined plasma in an inverse-pinch configuration holds potential as a plasma target for Magnetized Target Fusion (MTF) as well as a simple geometry to study wall-confined plasma. An experiment is planned to study the inverse-pinch configuration using the Zebra Z pinch [B. S. Bauer et at, AlP Conference Proceedings Vol. 409 (American Institute of Physics, Melville, 1997), p. 153] of the Nevada Terawatt Facility at the University of Nevada, Reno (UNR). The dynamics of the discharge formation have been analyzed using analytic models and numerical methods. Strong heating occurs by thermalization of directed energy when an outward moving current sheet (the inverse pinch effect) collides with the outer wall of the experimental chamber. Two-dimensional magnetohydrodynamic simulations show Rayleigh-Taylor and Richtmyer-Meshkov like modes of instability, as expected because of the shock acceleration during plasma formation phase. The instabilities are not disruptive, hut give rise to a mild level of turbulence. The conclusion from this work is that an interesting experiment relevant to wall confinement for MTF could be done using existing equipment at UNR. [ABSTRACT FROM AUTHOR]