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 B0t product is derived for high wave number stability for a given current waveform, where B0 is the driving magnetic field magnitude and t is the current risetime. When combined with a recognized empirical scaling law for neutron yield optimized D2 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.