Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation
M. J. HOLE a1, S. R. HUDSON a2andR. L. DEWAR a1 a1 Research School of Physical Science and Engineering, Australian National University, ACT 0200, Australia a2 Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USA
We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions separated by ideal magnetohydrodynamic (MHD) barriers. A principal motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically three-dimensional equilibria, with non-zero internal pressure. A second application is the description of transport barriers as constrained minimum energy states. As a first example, we calculate the plasma solution in a periodic cylinder, generalizing the analysis of the treatment of Kaiser and Uecker (2004 Q.
Math.57, 1–17), 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.
(Received August 14 2005) (Accepted March 15 2006)