Equilibrium and stability of an axially symmetric plasma with anisotropic pressure

Abstract

The stability of axially symmetric plasma with anisotropic pressure is studied by extending the method used in a preceding paper [Nuclear Fusion 1 (1960) 47]. The necessary condition for stability, previously found for a scalar pressure, is generalized; two additional conditions appear which are always satisfied for a scalar pressure.

On axisymmetric double adiabatic MHD equilibria with plasma flow

“…The isotropic pressure and adiabatic flow axisymmetric equilibria are described when σ − vanishes and γ = 5/3 (Morozov and Solovev 1980, Hameiri 1983, Maschke and Perrin 1984, Kerner and Tokuda 1987. The equations for axisymmetric plasmas with pure toroidal flow and anisotropic pressure are recovered when F vanishes (Mercier and Cotsaftis 1961, Clemente 1993, 1994. Isotropic pressure equilibria with pure toroidal rotation are described when F = σ − = 0 (Maschke and Perrin 1980, Clemente and Farengo 1984, Viana et al 1997.…”

On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear

“…where F(A) is some arbitrary function of the magnetic flux (Mercier and Cotsaftis 1961). Secondly, we recover a Grad-Shafranov type equation analogous to 2:…”

“…We now consider a formulation that uses the flux function A and the modulus of its gradient (B p = |∇ A|, the magnitude of the magnetic field in the x-z-plane) instead of A and B as in previous papers (e.g. Mercier and Cotsaftis 1961). Throughout this paper we will be using Cartesian coordinates with invariant direction y, i.e.…”

“…The theory of MHD equilibria with anisotropic pressure seems to have also developed relatively independently in the laboratory plasma community (e.g. Mercier and Cotsaftis 1961, Taylor 1963, Grad 1967, Spies and Nelson 1974, Hall and McNamara 1975, Sestero and Taroni 1977, Nelson et al 1978, Clemente 1993, 1994, Clemente et al 1995, Clemente and Viana 1999, Zwingmann et al 2001, Shi et al 2006, Clemente and Sterzo 2009, Pustovitov 2010, Asahi et al 2011, Asahi et al 2013, Lepikhin and Pustovitov 2013. Hence, a number of different formulations of the MHD equilibrium theory with anisotropic pressure exist, which apart from the specific application the authors had in mind, can depend on the symmetry assumptions made, the inclusion of plasma flows or external forces, the use of particular equations of state, the use of a relativistic formulation of MHD for certain astrophysical systems, or a combination of several of these points.…”

“…Often, further assumptions are made about the relationship between the shear component of the magnetic field (also referred to as a guide field) and the anisotropy parameter (basically the difference between the parallel and perpendicular pressure), leading to, for example, the magnetic shear field component being constant on flux surfaces as in the isotropic case (e.g Mercier and Cotsaftis 1961, Clemente 1993, Shi et al 2006. While this simplifies the equilibrium equation and makes it more similar to the isotropic Grad-Shafranov equation, it also leads to a restriction in the functional forms allowed for the magnetic pressure tensor.…”