THE POLARITY DEPENDENT EFFECT OF GYROVISCOSITY ON THE FLOW SHEAR STABILIZED RAYLEIGH-TAYLOR INSTABILITY

The general linear dispersion relation is reviewed for incompressible fluid modes with wave numbers transverse to the magnetic field in a magnetically accelerated finite Larmor radius plasma where the unperturbed density and fluid velocity in the wave number direction vary in the direction of acceleration. Stability criteria are derived and unstable growth rate diagrams plotted for the combined Rayleigh-Taylor/Kevin-Helmholtz modes for various two and three region piecewise uniform cases. The effect of gyroviscosity on large wave number stability is shown to differ if the direction of the magnetic field is reversed, all else being equal, being either stabilizing or destabilizing depending on this direction. This implies an electrode polarity dependence for magnetically accelerated plasmas with sheared flow, such as is found in plasma foci. This mechanism is suggested as a possible reason why the plasma focus has superior performance when the center conductor is the anode. Given a central anode, a maximum Bt product is derived for stable large wave numbers for given current waveform, where B is the driving magnetic field magnitude and t is the current rise timescale. This implies critical constraints on energy and power scaling, though strategies for mitigating the constraints are discussed, such as applying an exponentially increasing current waveform. Ultimately, this may lead to higher performance for plasma foci and related devices such as flow shear stabilized z-pinches