Facility pressure effects on a Hall thruster with an external cathode, II: theoretical model of the thrust and the significance of azimuthal asymmetries in the cathode plasma

Abstract

A theoretical model of the thrust produced by a Hall thruster has been developed to provide insight into the longstanding problem of performance dependence on facility pressure. Inputs to the model have been provided by 2D (r–z) axisymmetric simulations that were guided by measurements of the ion velocity field from laser induced fluorescence diagnostics. The combined analyses yield very good agreement with thrust measurements from ground tests of the SPT-140, a Hall thruster operating with an external cathode, and suggest two new findings. First, at intermediate pressures (∼9–15 μTorr) the rise of the thrust with increasing pressure is largely due to fast atoms produced by charge exchange collisions with beam ions. The acceleration region remains spatially invariant and the thrust rise is linear with pressure. As the pressure increases further, displacements of the acceleration region towards the anode become sizeable and reduce the rate of increase in thrust. Second, the thrust increase from vacuum to the lower values of pressure (≲9 μTorr) is driven largely by transport of electrons along magnetic lines, from the cathode to the near-plume of the thruster, which explains why the rise is nonlinear with pressure. It is argued based on first-principles that this higher rate of thrust variation observed at the lowest pressures may be strongly linked to the highly asymmetric distribution of the external-cathode electrons around the discharge. This would explain the insensitivity of performance in thrusters with centrally-mounted cathodes as well as the longstanding challenges 2D axisymmetric simulations have had in uncovering the source of the thrust dependence on facility pressure.