Hall-Driven Effects in Electron-Magnetohydrodynamic Z-Pinch--Like Implosions

In previous work,\footnote{A. S. Richardson, et al., Physics of Plasmas, 23(5), 2016} it has been shown that density gradients give rise to Hall-driven magnetic field penetration in electron-magnetohydrodynamics (EMHD). Here, we examine the effect of geometry on this Hall-driven penetration. It is found that in z-pinch--like geometries, the implosion velocity of a Hall-driven magnetic pinch depends on its distance from the axis, moving faster as it approaches the axis. We compare analytical and numerical results for the z-pinch geometry to previous results for a rectangular slab geometry. Similar effects are found in both geometries, including electron-inertia driven nonlinearities, a Kelvin-Helmoltz like instability, and the generation of vortices. The electric field in the vortices is also examined, to determine how much charge separation occurs. If the electric field becomes large enough, it could accelerate the background ions to very high energies.