Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow

Abstract

The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.

Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM

“…In China, professor Qiu, Huang, and Jian [56][57][58] from the Southwestern Institute of Physics studied theoretically the stabilization of sheared axial flow, finite Larmor radius, and viscosity on the MRT instability in Z pinches. Based on their work, we investigated the coupling effects of compressibility, viscosity and a sheared axial flow [59][60][61][62][63].…”

Effects of compressibility on the finite Larmor radius stabilized Rayleigh–Taylor instability in Z-pinch implosions

“…8 Therefore, k ʈ can be set to be vanished and k Ќ = k. That is, the perturbation can be assumed to be Moreover, the modes with k parallel to the equilibrium magnetic field cannot grow, since nonsymmetric modes ͑at least partially͒ are stabilized by the bending of magnetic field ͑B 0 ͒ lines.…”

“…2,3 However, this instability is often called the magneto-Rayleigh-Taylor instability to distinguish the fluid acceleration producing Rayleigh-Taylor instability. In the previous paper, 8 we employed FLR MHD theory to consider the Rayleigh-Taylor instability in an annular plasma implosion with sheared axial flow ͑SAF͒. Surface perturbations may occur at a density discontinuity, such as a transition between two different fluids or plasma-vacuum interface, but then these issues are left behind to investigate henceforth.…”

“…9 Therefore, it is instructive to investigate the influence of plasma compressibility on the RT instability in Z-pinch implosions in which equilibrium SAF and/or FLR effects are included. 5,7,8 In this paper we will study the effect of compressibility on the finite Larmor radius stabilized Rayleigh-Taylor instability, because of a lot of studies ͑see, e.g., Refs. The influence of compressibility on the RT instability mode in the case when no magnetic field was present has been studied by Bernstein and Book 10 for a discontinuity between two exponentially stratified fluids; also, several analytical solutions have been presented by Book.…”

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

“…All these problems and also related stability issues were attacked, theoretically, numerically and experimentally, by many researchers amongst many others, such as Refs. [16][17][18][19][20][21][22][23][24][25][26]. However, all of these results are either numerical or analytical-numerical.…”