Abstract
An integral equation method of finding equilibria of a z-pinch situated in an external magnetic multipole field, due to a number of symmetrically placed external current-carrying conductors (Extrap configuration), is developed. A perturbation technique has been used, where the influence of the external field is treated as a small correction to a zero external field z-pinch circular equilibrium. To first order, equilibria for various current profiles are explicitly calculated. It is found that profiles of skin type give the largest perturbations of the magnetic surfaces from circular shape, whereas the plasma is much less distorted for peaked current distributions. Furthermore, except for the skin current case, the displacement of the outermost plasma edge is found to be very little affected by the details of the current profile, and is determined essentially by the total plasma current only. Second order effects are also considered.
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