Adiabatic relaxation to ID MHD pressure equilibrium. EQUIL: a Fortran module and test program

A numerical method is described by which a 1D MHD non-linear lagrangian system may be relaxed adiabatically to pressure equilibrium by an iterative process. The method is appropriate for problems involving a slow passage through a sequence of quasi-equilibrium states, and although described here in the context of the cylindrical plasma pinch it should be equally appropriate in other contexts, e.g. stellar evolution. The rate of convergence of the iterations can be given a simple physical interpretation and is very rapid: it corresponds to squaring the residual error at every iteration step. Results of numerical tests in double precision are given. Program EQUIL described in this paper represents one module of a larger plasma equilibrium and diffusion code ATHENE 1 which will be published in full elsewhere. As a demonstration of programe construction and documentation methods, the module has been developed and tested using an on-line utility, and a listing of the code is given together with a discussion of the programming techniques that have been found useful. The Fortran listing is reproduced in parallel with a version of the code in ordinary mathematical notation which is easier to follow. It is believed that this documentation technique could have many applications. (Auth.)