The magnetohydrodynamic variational principle is employed to calculate equilibrium
and stability of toroidal plasmas without two-dimensional symmetry. Differential
equations are solved in a conservation form that describes force balance correctly
across islands that are treated as discontinuities. The method is applied to both
stellarators and tokamaks, and comparison with observations is favorable in both
cases. Sometimes the solution of the equations turns out not to be unique,
and there exist bifurcated equilibria that are nonlinearly stable when other
theories predict linear instability. The calculations are consistent with recent
measurements of high values of the pressure in stellarators. For tokamaks we compute
three-dimensionally asymmetric solutions that are subject to axially symmetric
boundary conditions.
Keywords
magnetic fusion, plasma physics, equilibrium and stability
