Exact two-dimensional solution for magnetic compression of a thin axisymmetric shell and neck formation in an X-pinch

Abstract

Exact two-dimensional solutions are constructed that describe the dynamics of magnetic compression of a hollow shell, which is a one-sheeted hyperboloid of revolution. The solutions are applicable for interpreting the results of experiments on the formation of necks in X-pinches. In particular, they make it possible to relate the main parameters of the problem: the axial scale of the neck, the time of its formation, and the geometric characteristics of the system. Keywords: X-pinch, neck formation, thin shell model.