Theoretical prediction of β and τE in a hard core Z pinch

Abstract

The energy confinement time and maximum achievable pressure are critical figures of merit for any proposed magnetic fusion concept. The present work focuses on these issues for a hard core Z pinch, which is the cylindrical limit of a large aspect ratio levitated dipole configuration. An analysis is presented that theoretically predicts both τE and β for this configuration. The model makes the optimistic assumption that transport is purely classical in the region of the profile that is magnetohydrodynamically (MHD) stable against interchange modes. In the interchange-unstable region use is made of the quasilinear theory described in the accompanying paper [A. Kouznetsov, J. Freidberg, and J. Kesner, Phys. Plasmas 14, 102501 (2007)] which shows that the plasma pressure relaxes to the MHD marginally stable profile while the density evolves to n∝[∮dl∕B]−1. Analytic and numerical calculations lead to explicit scaling relations for τE and β which can be tested in future LDX experiments.