Magnetic implosion of liners is usually accompanied by the development of the Rayleigh–Taylor instability, which makes it hard to achieve high energy densities. However, the liners, which are thin compared with their skin layer (let us call them resistive), can also experience a different kind of instability, when parallel currents in different liner parts are attracted and draw these parts together dividing the liner into layers and filaments (filamentation or the tearing instability). We consider the problem of perturbation development in an infinitely thin resistive liner accounting for the distribution of the magnetic field, spread of currents, and flow of matter assuming that the perturbations are linear. Considering potential applications for different liner configurations (Z- and $\Theta $ -pinch liners and flat flyers) and the fact that the most destructive instabilities develop from the shortest wavelengths, we restrict our analysis to a planar case, which ignores the curvature of the liner and magnetic field lines. We find that the instability develops from any perturbation wavelengths, similar to the case of a perfectly conducting liner, with the instability growth rate for all the wavenumbers $k$ being of the order of $\sqrt {kg} $ ( $g$ is the liner acceleration), but always less than $\sqrt {kg} $ , and with the maximum growth rates for any directions of the wave vector k being greater than the growth rates of the perfectly conducting liner. One can often treat wire-array liners as resistive and, hence, use the results obtained for the description of instability development after the phase of merging the plasmas produced by individual wires.

中文翻译：

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线性近似中薄电阻衬垫的不稳定性

衬垫的磁内爆通常伴随着瑞利-泰勒不稳定性的发展，这使得很难达到高能量密度。然而，与表层相比较薄的衬垫（我们称其为电阻性）也会经历不同类型的不稳定性，当不同衬垫部分中的平行电流被吸引并将这些部分拉到一起时，将衬垫分成层和层。细丝（细丝化或撕裂不稳定）。假设扰动是线性的，我们考虑考虑磁场分布、电流传播和物质流动的无限薄电阻衬垫中的扰动发展问题。考虑不同衬管配置（Z- 和 $\Theta $ -夹线和扁平传单）以及最具破坏性的不稳定性从最短波长发展的事实，我们将我们的分析限制在平面情况下，忽略了线和磁场线的曲率。我们发现不稳定性从任何扰动波长发展，类似于完美导电的衬里的情况，所有波数的不稳定性增长率 $千$ 属于 $\sqrt {公斤} $ ( $g$ 是线性加速度），但总是小于 $\sqrt {公斤} $ ，并且波矢量 k 的任何方向的最大增长率都大于完美导电衬垫的增长率。人们通常可以将线阵列衬垫视为电阻性的，因此，可以使用所获得的结果来描述由单个线产生的等离子体合并阶段之后的不稳定性发展。