Effects of parallel magnetic fields on sheaths near biased electrodes in a highly collisional Z-pinch plasma

Abstract

Sheath formation near biased electrodes in magnetic fields parallel to the wall is an understudied topic, especially within the context of Z-pinch fusion experiments. We perform 1X-2V Boltzmann-Poisson simulations of an axial cut at the pinch radius of a Z-pinch plasma between two biased electrodes with a magnetic field parallel to the wall. The collision frequencies are artificially increased to enhance thermalization of the plasma in the smaller simulation domain versus the actual experiment size; this increases the perpendicular mobility and partially de-magnetizes the ions resulting in non-monotonic sheath profiles with the potential increasing away from the wall to a peak before decaying. A classical sheath forms within an electron gyroradius from the wall not due to the natural thermal motion of the electrons, but due to the magnetized electrons gyrating into the wall; therefore, the sheath structure does not significantly change with bias potential or between electrodes. With increasing bias potential, a current is induced perpendicular to the wall due to changes in ion flow, differing from unmagnetized cases where current is induced by changes in electron flow. The magnetic field acts as a high resistivity with the perpendicular current density being three orders of magnitude lower than unmagnetized theoretical predictions. There is, however, significant flow parallel to the wall from the force balance between the pressure tensor and Lorentz force. These parallel flows induce a parallel current density three orders of magnitude larger than the perpendicular current density.