Abstract
The evolution of MHD equilibria toward high β is modeled by magnetic flux conservation with a given q(ψ) and by single fluid particle and energy balances which determine p(ψ, t). These one-dimensional flux surface averaged equations, written with magnetic flux ψ as the independent variable, are coupled to the two-dimensional MHD equilibrium equation through ψ, p(ψ, t), and q(ψ). The location and evolution of the plasma cross section boundary are precisely specified through the use of a fixed boundary equilibrium technique. In moving boundary studies (e.g., plasma compression) the resulting system of equations is advanced in time from an initial state by a procedure which utilizes two nested predictor-corrector loops together with an implicit time-stepping technique. The inner predictor-corrector loop advances the transport equations subject to a given equilibrium configuration while the outer loop evolves the equilibrium. For fixed plasma boundaries this procedure is modified for greater computational speed. These techniques provide satisfactory numerical convergence together with complete consistency between the coupled one-dimensional system of equations and the two-dimensional equilibrium. This method can be applied to the study of equilibrium evolution involving dramatic changes of plasma position, shape, and profiles while prescribing the evolution of the plasma boundary. As such, it can serve as a useful tool in the design of poloidal field systems or as a source of equilibria in high-β MHD stability studies. As an example, the compressional scaling laws of Furth and Yoshikawa are found to be modified for small aspect ratio.