Absence of complete finite-Larmor-radius stabilization in extended MHD

The dominant finite-Larmour-radius (FLR) stabilization effects on interchange instability can be retained by taking into account the ion gyroviscosity or the generalized Ohm's law in an extended MHD model. However, recent simulations and theoretical calculations indicate that complete FLR stabilization of the interchange mode may not be attainable by ion gyroviscosity or the two-fluid effect alone in the framework of extended MHD. For a class of plasma equilibria in certain finite-beta or nonisentropic regimes, the critical wave number for complete FLR stabilization tends toward infinity.     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metriplectic framework for dissipative magneto-hydrodynamics

The metriplectic framework, which allows for the formulation of an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The result is obtained by extending the HD symmetric bracket and free energy to include magnetic field dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identified with the total thermodynamic entropy of the plasma. The metriplectic framework of MHD is shown to be invariant under the Galileo Group. The metriplectic structure also permits us to obtain the asymptotic equilibria toward which the dynamics of the system evolves. This scheme is finally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications.     

On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow

While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.     

Magnetic propulsion of intense lithium streams in a tokamak magnetic field

This paper describes the effect and gives the theory of magnetic propulsion which allows driving free surface plasma facing liquid lithium streams in tokamaks. In the approximation of a thin flowing layer the MHD equations are reduced to one integrodifferential equation which takes into account the propulsion effect, viscosity, and the drag force due to magnetic pumping and other interactions with the magnetic field. A stability criterion is obtained for stabilization of the "sausage" instability of the streams by centrifugal force.     

Solving the 3D MHD equilibrium equations in toroidal geometry by Newton’s method

We describe a novel form of Newton’s method for computing 3D MHD equilibria. The method has been implemented as an extension to the hybrid spectral/finite-difference Princeton Iterative Equilibrium Solver (PIES) which normally uses Picard iteration on the full nonlinear MHD equilibrium equations. Computing the Newton functional derivative numerically is not feasible in a code of this type but we are able to do the calculation analytically in magnetic coordinates by considering the response of the plasma’s Pfirsch–Schlüter currents to small changes in the magnetic field. Results demonstrate a significant advantage over Picard iteration in many cases, including simple finite-β stellarator equilibria. The method shows promise in cases that are difficult for Picard iteration, although it is sensitive to resolution and imperfections in the magnetic coordinates, and further work is required to adapt it to the presence of magnetic islands and stochastic regions.     

Solitonlike solutions of the Grad-Shafranov equation

A new class of solitonlike solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schr?dinger equation for nonlinear wave propagation forms the basis to derive the new class of solutions. The solitonlike solutions are considered for their possible relevance to astrophysics and solar physics problems. We discuss how a solitonlike solution can be generated by a repetitive process of magnetic arcade stretching and plasmoid formation induced by the differential rotation of the solar photosphere or of an accretion disk.     

Magnetogravitational Instability of Anisotropic Plasma with Finite Ion Larmor and Generalized Polytrope Law

The effect of finite ion Larmor radius corrections on the propagation of small perturbations through self gravitating, anisotropic system with generalized polytrope law is investigated. The polytrope laws are considered for the pressure components in parallel and perpendicular directions to the magnetic field. The polytrope model proposed by Abraham-Shranuer can be reduced to CGL equations with double adiabatic equations of state and MHD set of equations with isothermal equation of state. The effects of FLR and polytrope indices are discussed on the gravitational, firehose and mirror instability. The critical Jeans wave numbers are found to depend on polytropic indices and derived for CGL and MHD cases. The FLR corrections are found effective in shorter wave length region and produce stabilizing influence. The condition of mirror instability is uninfluenced by FLR but dependent on polytropic indices.     

On the behavior and stability of a liquid metal in quasi-planar electric contacts

The contacts between conductors formed under relatively low pressures can be treated as quasi-planar. Melting of the material of such contacts upon the passage of electric current is used in some technological processes, but the behavior of liquid in these conditions has not been analyzed. In this study, such an estimate was obtained for specific conditions appearing under electric-pulse compacting (briquetting) of metal shavings. Analysis of derived relations shows that this estimate is valid for any quasi-2D contacts upon passage of a pulsed current of duration from microseconds to milliseconds. It is shown that the spacing between contact surfaces decreases, the liquid metal is extruded in the lateral directions, and the area of the contact and its conductivity increase. Sausage-type magnetohydrodynamic (MHD) instability and overheating instability do not evolve in these conditions because the instability wavelength is larger than the rated thickness of the molten layer; screw MHD instability can appear in slower processes.     

Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations

Ideal magnetohydrodynamic (MHD) equations consist of a set of nonlinear hyperbolic conservation laws, with a divergence-free constraint on the magnetic field. Neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions. In our recent work [F. Li, L. Xu, S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, Journal of Computational Physics 230 (2011) 4828–4847], second and third order exactly divergence-free central discontinuous Galerkin methods were proposed for ideal MHD equations. In this paper, we further develop such methods with higher order accuracy. The novelty here is that the well-established H(div)-conforming finite element spaces are used in the constrained transport type framework, and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence-free magnetic field. The overall algorithm is local, and it can be of arbitrary order of accuracy. Numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate.     

非圆截面等离子体MHD不稳定性的研究

本文采用阶跃电流模型研究了非圆截面环电流器等离子体的MHD不稳定性,使札哈洛夫(Zakharov)的工作推广到非圆截面,得到了新的稳定性判据。它指出了椭圆形变,三角形变,电流梯度以及q值(所谓的安全因子)对等离子体的β值的影响。为了得到最大的β值,本文给出了最佳q值公式。对等离子体的不同参数计算了临界β值,并与由局部模判据和气球模的数值计算所得到的结果进行了比较。文中指出,电流梯度的存在是对等离子体β值影响的重要因素;非圆截面等离子体比圆截面等离子体可能得到更高的β值。     

Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations

The lattice Boltzmann equation is commonly used to simulate fluids with isothermal equations of state in a weakly compressible limit, and intended to approximate solutions of the incompressible Navier–Stokes equations. Due to symmetry requirements there are usually more degrees of freedom in the equilibrium distributions than there are constraints imposed by the need to recover the Navier–Stokes equations in a slowly varying limit. We construct equilibria for general barotropic fluids, where pressure depends only upon density, using the two-dimensional, nine velocity (D2Q9) and one-dimensional, five velocity (D1Q5) lattices, showing that one otherwise arbitrary function in the equilibria must be chosen to suppress instability.     

Viscoresistive MHD configurations of plasma in accretion disks

We present a discussion of two-dimensional magneto-hydrodynamics (MHD) configurations, concerning the equilibria of accretion disks of a strongly magnetized astrophysical object. We set up a viscoresistive scenario which generalizes previous two-dimensional analyses by reconciling the ideal MHD coupling of the vertical and the radial equilibria within the disk with the standard mechanism of the angular momentum transport, relying on dissipative properties of the plasma configuration. The linear features of the considered model are analytically developed and the non-linear configuration problem is addressed, by fixing the entire disk profile at the same order of approximation. Indeed, the azimuthal and electron force balance equations are no longer automatically satisfied when poloidal currents and matter fluxes are included in the problem. These additional components of the equilibrium configuration induce a different morphology of the magnetic flux surface, with respect to the ideal and simply rotating disk.     

热电子等离子体的低频交换不稳定性

本文用磁流体理论,导出了包含导电端板“线结”效应的热电子等离子体低频交换模的色散关系,分析了热电子环的稳定作用,求出了稳定性判据。“线结”效应能大大降低交换模的增长率。取热电子密度为零,就得到简单流体等离子体的结果。     

A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics

We present a high-order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme, which has been successfully applied to hydrodynamic problems. The WENO scheme follows the same idea of an essentially non-oscillatory (ENO) scheme with an advantage of achieving higher-order accuracy with fewer computations. Both ENO and WENO can be easily applied to two and three spatial dimensions by evaluating the fluxes dimension-by-dimension. Details of the WENO scheme as well as the construction of a suitable eigen-system, which can properly decompose various families of MHD waves and handle the degenerate situations, are presented. Numerical results are shown to perform well for the one-dimensional Brio–Wu Riemann problems, the two-dimensional Kelvin–Helmholtz instability problems, and the two-dimensional Orszag–Tang MHD vortex system. They also demonstrate the importance of maintaining the divergence free condition for the magnetic field in achieving numerical stability. The tests also show the advantages of using the higher-order scheme. The new 5th-order WENO MHD code can attain an accuracy comparable with that of the second-order schemes with many fewer grid points.     

Point-vortex cluster formation in the plane and on the sphere: an energy bifurcation condition

The dynamics of a system of point vortices is considered in the plane and on the sphere. Particular attention is given to the formation of vortex clusters and to global vortex dynamics, especially in the spherical case. For integrable systems and systems with given symmetries, we show the existence of a critical energy above or below which (depending on the geometry of the surface) the system splits into clusters and vortex dynamics is confined to a particular region. The case of nonidentical vortices is of particular interest since we observe quite different global dynamics depending on the energy and the initial conditions. Furthermore we identify all the relative equilibria configurations as critical points of the reduced energy and we give an instability criterion to deduce instability for certain configurations.     

On the interaction between a charged drop and an external acoustic field

An interaction between capillary oscillations of a charged drop and an external acoustic field is investigated under conditions in which nonlinear components of the acoustic pressure on the drop surface may be neglected. It is shown that equations describing the temporal evolution of modes of the capillary waves in this case may be either the Mathieu-Hill equations or ordinary inhomogeneous equations of the second order describing forced oscillations. In both cases, the drop instability (of a parametric or resonance type) may result in its disintegration due to deformation caused by the acoustic field at its own drop charge, subcritical in the sense of the Rayleigh criterion.     

磁场中电弧等离子体柱的螺旋不稳定性

讨论了具有抛物互形电流分布的电弧等离子体柱在磁场中的不稳定性问题，从磁流体力学方程组出发，推导出电弧柱扰动满足的方程与边界条件，求得了这些方程的解析解，进而导出了在趋中心电流分布情形下电弧运动所满足的微分方程，由此给出了稳定性判据。将所得结果与均匀电流分布情形做了比较，稳定区域增宽，与实验结果相符。     

Nonequilibrium MHD plasma flow in a high-interaction disk generator

Nonequilibrium MHD plasma flow in a high-interaction disk-type MHD generator is examined by numerical simulations based on the two-temperature model equations. The simulations are performed for the generators driven by working gases: He-Cs and He-K. Homogeneous and inhomogeneous plasma behavior is observed with change of the load resistance, and it is found that the structures of the inhomogeneous plasma differ for different seed materials. The plasma structures associated with both the partial ionization instability and the magnetoacoustic instability are discussed for both plasmas