Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation

Abstract

One of the most important advances in magnetically confined fusion plasma physics has been the discovery of high confinement regimes, where at sufficiently high heating power, the plasma self-organizes to produce internal transport barriers (ITB's). A possible explanation for the existence of such barriers is that they represent constrained minimum energy states, where the plasma within the barrier satisfies ideal MHD, and the plasma between barriers is in a Taylor relaxed state. In this work we develop a multiple interface variational formulation, comprising multiple Taylor-relaxed plasma regions, each of which are separated by an ideal MHD barrier. Application to a plasma cylinder is a generalization of the analysis of the treatment of Kaiser and Uecker, Q. Jl. Mech. Appl. Math.,57(1), 2004, who treated the single interface in cylindrical geometry. Expressions for the equilibrium field are generated, and equilibrium states computed. Unlike other Taylor relaxed equilibria, for the equilibria investigated here, only the plasma core necessarily has reverse magnetic shear. We show the existence of tokamak like equilibria, with increasing safety factor and stepped-pressure profiles.

Multi-region relaxed magnetohydrodynamics with flow

“…(15). The plasma equations (12)- (14) have been obtained previously by Woltjer 6 and Finn and Antonsen 7 in the context of single relaxed-region models. The derivation is essentially unchanged when considering the case of a finite number of nested relaxed-regions, which is the case considered here.…”

Relaxation models for single helical reversed field pinch plasmas

“…those actually observed in experiments. The presence of a reconnecting layer, on the other hand, produces a discontinuity that has to be handled in some way [5,6,7]. Although maybe too simplistic, the model presented here is a possible (and physically reasonable ) way to deal with this important issue avoiding complicate formalisms [5].…”

Multi-region relaxed magnetohydrodynamics with anisotropy and flow

“…The model we present in this paper is an extension of the MRxMHD model introduced previously 2, [15][16][17] . Briefly, the MRxMHD model consists of N nested plasma regions R i separated by ideal MHD barriers I i (see Fig.…”