Analysis of the Liner Stability in Various Experiments

The main problem occurring at cylindrical liner acceleration by azimuthal magnetic field is its motion distortion caused by the combination of Rayleigh-Taylor and sausage instabilities, which, in principle, can lead to a complete liner destruction. The strength of the material can inhibit the development of such instabilities; however, as far as the melted liner-section thickness increases due to Ohmic heating, the instabilities start to develop fast. The experiments have shown that even similar acceleration conditions may result in significantly different states of liners with different degrees of their distortion. Thus, in similar conditions of the liner demonstration series (LD), hydro-features series (HF), and near term liner experiments series (NTLX) experiments, the X-ray images for the HF and NTLX experiments showed the liners' homogeneity, suggesting that their motion was comparatively stable, whereas the X-ray images made for the LD experiments showed that the liners' external surfaces were seriously distorted due to the perturbation growth. In this paper, 2D MHD computations are presented for the liner LD, HF, and NTLX implosions with consideration of the perturbation growth. Initial perturbations are assumed as random with characteristic values determined by the resolution of used computational grid. Computation results have shown that, in fact, the conditions of the HF and NTLX experiments lead to a smaller perturbation growth, than those of the LD experiments, if the value of the perturbation growth is determined over the perturbation development on the internal surface. A comparison of the computed shape of the external surface for the HF and LD shows that in the computations, as well as in the experiments, the HF liner remains weakly perturbed, whereas the LD liner is significantly distorted. However, for the LD and NTLX, the external surfaces of the liners remain qualitatively similar and rather perturbed even at extremely refined grid. Hence, the issue of greater perturbation development in the LD experiments may be considered as explainable to some extent by the 2D computations, but the degree of computation and experimental-data agreement requires additional improvement. The 2D computation results for the liners driven by a 40-cm-diameter 15-module disk explosive magnetic generator (DEMG) show that in these conditions, the perturbation growth can be significant for the liners with an aspect ratio higher than 20, and therefore, it is necessary to study the liner stability for the liner DEMG experiments' designing.

I. Introduction

Applications of condensed liners [1]–[7] in high-energy-density physics need the liners' velocities of about 1 and more. To achieve such velocities, the megagauss-range magnetic fields are needed, which cause melting and even evaporation and transition to plasma of some part of the liner (the skin layer) [8] and, consequently, to the loss of strength in this part of the liner and the development of Rayleigh–Taylor (RT) and sausage instabilities. As a result, in this part, the conditions for RT and sausage instabilities are provided. This instability development may result in inhomogeneous state of the liner, spoiling the conditions of its utilization or even leading to its destruction.