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. A two-equation model (presented in Part I) for the large amplitude (> 100% background), low frequency (10-50 kHz) oscillations in discharge current is generalized and then validated with measurements from a 9-kW class, magnetically-shielded Hall effect thruster. It is shown that the model can re-create quantitatively trends in both os- cillation amplitude and frequency with discharge voltage and current. The validated model is non-dimensionalized and leveraged to derive an analytical stability criterion for the onset of large-amplitude oscillations. This criterion is shown to depend on thruster beam utilization, length of the acceleration zone, neutral transit time, discharge voltage, and current density in the channel. This 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.