Mode transitions in a magnetically shielded Hall thruster. II. Stability criterion

A stability criterion is derived for mode transitions in the discharge current oscillations of a magnetically shielded Hall thruster. The two-equation model evaluated in Paper I for these large-amplitude (>100% background), low-frequency (<25 kHz) current oscillations is generalized and then validated with measurements from a 9 kW class test article. It is shown that the model can re-create quantitatively trends in both oscillation amplitude and frequency with discharge voltage and current. The validated model is non-dimensionalized and applied to derive an analytical stability criterion for the onset of large-amplitude oscillations. The resulting expression depends on several properties, including discharge current, discharge voltage, neutral transit time in the channel, length of the acceleration zone, magnetic field strength, and channel area. The criterion is leveraged to inform two mitigation strategies—changing magnetic field strength and controlling anode temperature— for adjusting the stability margin of the thruster. The criterion is also employed to motivate a physical explanation for why mode transitions occur and, in turn, why the stability margin differs between shielded and unshielded thrusters.