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

N. M. Zubarev^ab, S. A. Chaikovskii<sup>b

a</sup> P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia
^b Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

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.

Received: 26.08.2022
Revised: 13.09.2022
Accepted: 13.09.2022

DOI: 10.21883/PJTF.2022.21.53706.19349

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