The polarity dependent effect of gyroviscosity on the flow shear stabilized Rayleigh–Taylor instability and an application to the plasma focus

Abstract

The linear dispersion relation is derived for modes of an isothermal finite Larmor radius incompressible plasma with an equilibrium density and horizontal fluid velocity varying with depth in a uniform gravitational field. The velocity and magnetic field are assumed parallel and transverse to the wave number, respectively. Stability criteria are derived and unstable growth rate diagrams plotted for the combined Rayleigh-Taylor/Kelvin-Helmholtz modes for two and three region piecewise uniform cases representing an accelerated plasma layer with sheared flow. The effect of gyroviscosity on wave numbers larger than a critical value is shown to differ if the direction of the magnetic field is reversed, all else being equal, being either stabilizing or destabilizing depending on direction. This implies an electrode polarity dependence for a magnetically accelerated plasma with sheared flow consistent with the observation that plasma foci generally have superior performance if the center conductor is the anode. Characteristic properties of the shocked plasma layer of a plasma focus during the accretion phase are inferred for use with the model. Given a plasma focus with a central anode, a maximum B 0 t product is derived for high wave number stability for a given current waveform, where B 0 is the driving magnetic field magnitude and t is the current risetime. When combined with a recognized empirical scaling law for neutron yield optimized D 2 plasma foci, a maximum current for high wave number stability is implied independent of t. For a linearly rising current, for example, this is 2 MA. Strategies for mitigating the constraints are discussed, such as applying an exponentially increasing current waveform. This and other parametric relationships of the model may lead to designs with higher performance than would otherwise be possible for plasma foci and other devices such as flow shear stabilized Z-pinches.

Finite Larmor radius magnetohydrodynamic analysis of the ballooning modes in tokamaks

“…In these calculations there is a common assumption that the parallel electric field perturbation E vanishes. [13] As we know, however, E may become finite when kinetic effects, such as finite Larmor radius effect (FLR effect, also referred to as the effect of gyroviscosity [14] ), Landau resonances, trapped particles, collisional effects etc, are included. Especially, in the high-n limit these kinetic effects can be significant.…”

“…However, in as early as the 1960s, attempts were made to use MHD theory instead of kinetic theory to study the system in which FLR effects became important: Roberts and Taylor, [20] and Braginskii [21] independently incorporated the FLR effects into the momentum equation of MHD theory via anisotropic ion (FLR) stress tensor, which is always referred to as finite Larmor radius magnetohydrodynamic (FLR MHD) theory. So far, however, all the subjects that the FLR MHD theory is employed to analyse concentrate on the Rayleigh-Taylor instability in different plasma configurations: Ruden [14] and Huba [22] used this theory to study independently the Rayleigh-Taylor instability in the plasma configuration of two-dimensional geometry. Recently, Qiu et al [23] and Huang et al [24] have used the FLR MHD theory to investigate the Rayleigh-Taylor instability in Z-pinch incompressible plasma with a sheared axial flow and compressible plasma without sheared axial flow.…”

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

“…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.…”