Limits on steady diffuse mode operation of the cathode in magnetoplasmadynamic thrusters

Electrode erosion in magnetoplasmadynamic thrusters is significantly dependent on whether the mode of operation is diffuse (i.e., the net current density is distributed over the electrode surface) or via spots. Since spot mode erosion rates are typically much higher than the diffuse mode erosion rates, the latter is more desirable from the standpoint of sustained steady-state operation. In this paper, the steady-state thermal response of the cathode in a magnetoplasmadynamic thruster is analyzed in order to determine the limits of diffuse mode operation. An energy balance at the cathode surface along with current conservation serve to simultaneously determine the surface temperature and the total sheath voltage drop at a given location on the electrode. It is found that two different limits to steady-state diffuse mode operation exist. One limit corresponds to an unsteady thermal runaway caused by excessive electron bombardment, in which regenerative heating leads to local melting of the electrode surface. The other limit corresponds to an operating regime where a steady state cannot exist because of increased ion bombardment. In this regime, a small increase in the net plasma current density results in a large sheath voltage drop. This causes an increase in local surface heating through ion bombardment, until a new state is reached, which is inherently unsteady and accompanied by plasma oscillations. These two limits found here may correspond to transitions from diffuse to prespot modes of electrode operation. These operating limits are also found to be influenced strongly by electrode and discharge parameters, as well as by external cooling.