Double Adiabatic Relaxation and Stability

Phys. Fluids 30, 770 (1987)https://ireap.umd.edu/10.1063/1.8663271987Journal ArticlePlasma, Accelerator, and Nuclear Physics

A relaxation model employing double adiabatic magnetohydrodynamics (MHD) is introduced. In this model the neglect of heat flux in the Chew–Goldberger–Low (CGL) equations is treated by considering a very special class of the entropy invariants. The equilibria have uniform temperatures T_⊥ and T_∥, nearly uniform λ≡j_∥/B=μ/σ, where σ is the local firehose parameter, and p=p(B). The density profile is not uniform (unless T_⊥=T_∥), in qualitative agreement with experiments. The equilibria are shown to be linearly stable, in spite of ‘‘bad’’ curvature, if the firehose and mirror parameters are positive and if the parallel current is not too large. A nonlinear stability criterion involving modified firehose and mirror parameters, and based upon the so‐called energy‐Casimir method, is also derived.