Theoretical investigation of resistivity on the magneto-Rayleigh–Taylor instability in Z-pinch plasmas

In this paper, the effect of finite resistivity on the magneto-Rayleigh–Taylor (MRT) instability in linear development stage is theoretically investigated. Based on the incompressible approximation and the resistive magnetohydrodynamics equations, a three-region slab model is used to derive the dispersion relation of MRT in cases of k⋅B0II=0 and k⋅B0II≠0 in the plasma shell, respectively. By analytical investigations and numerical calculations, the quantitative effect of plasma resistivity on the MRT instability in several typical profiles of magnetic field in Z-pinch implosions are discussed. It is shown that for the case only with the driving magnetic field B0y in the vacuum region, inclusion of plasma resistivity will destabilize the MRT instability. The normalized growth rate of MRT perturbations increases from 2−1 to 1.25−0.5 as the plasma resistivity is increased from zero to infinity in the limit of zero wavenumber. The corresponding normalized cutoff wavenumber, above which linear MRT is completely stabilized, will increase from 1/2 to 1. For cases with the axial magnetic field B0z in the vacuum region or in the plasma shell and with the driving magnetic field B0y in the vacuum region, the normalized cutoff wavenumber will increase from B0y/B0z2/2 to B0y/B0z2. However, for the case of uniform B0z in three regions, the growth rate will be increased to 1.0 in the case of infinite resistivity, indicating there is no stabilizing effect of external axial magnetic field on the MRT instability.