Dynamics of high β tokamaks

The reduced nonlinear low β tokamak magnetohydrodynamic equations are extended to the case of high β. A large aspect ratio ordering is used. The dynamics can be described using only three variables: the stream functions for the poloidal magnetic field and velocity, and the pressure. The equations are solved numerically to find two-dimensional equilibria. These equilibria can be unstable to ballooning modes, which tend to grow to large amplitude in nonlinear, three-dimensional computations.