Toroidal plasma reactor with a low external magnetic field

Abstract

The Lyapunov conditions for plasma stability are shown to be met in a toroidal pinch configuration with the safety factor q<0.5, decreasing from the centre to the periphery without field reversal. This magnetic configuration is capable of containing high pressure plasma with only a small external toroidal magnetic field. Stable configurations are found with average beta near 15% and with the magnetic field associated mainly with the plasma current. The beta value calculated with the external magnetic field can be >100%. Fast charged particles produced by fusion reactions are asymmetrically confined by the poloidal magnetic field (owing to the lack of a strong toroidal field). They thus generate a current in the non-central part of the plasma volume, which reinforces the poloidal field. This current drive can sustain the monotonic decrease of q with radius. The plasma stability is studied by constructing the Lyapunov functional and investigating its extrema both analytically and numerically. This can be justified by either a qualitative argument about the hierarchy of the relaxation processes or a straightforward search for equilibria that are stable against non-linear perturbations. The results of the Lyapunov approach lead to an additional restriction on the equilibria as compared to the conventional linear theory, namely that a stable equilibrium should correspond to an extremum of an integral of motion. This restriction can be expressed as an additional equation involving the arbitrary functions of the Grad-Shafranov equilibrium