First-order toroidal correction to the minimum energy state of a cylindrical plasma column of finite β

A first-order toroidal correction to the minimum energy equilibrium state of a cylindrical plasma column of finite β, embedded in a vacuum region, is constructed. The use of this correction improves the comparison between the theoretical model, set up for a rotationally symmetric straight cylinder, and the toroidal pinch experiments. The comparison demands the numerical evaluation of an integral with an apparent singularity at the plasma axis, and matching of four parameters to appropriate boundary conditions