Forced van der Pol oscillator modeling of Hall-thruster's externally modulated breathing mode*

Signatures of entrainment, frequency, and wavenumber pulling, excitation thresholds, and particle transport, all associated with observed patterns of self-organizing dynamics of instabilities are examined in the archived data from PPPL's cylindrical Hall-Thruster. The objective is explaining spatio-temporal plasma behavior of "spokes" observed in modulated breathing oscillations in E×B plasma discharges using a combination of forced van der Pol oscillator equations, electrostatic gradient drift instabilities, the modified Simon-Hoh instability, and the influence of ionization instability. These signatures, yet to be fully explained, resemble limit-cycle behavior, thoroughly characterized in other discharge plasmas and electronic nonlinear-oscillator circuits, so the anticipated validation of an improved model of spoke frequency scaling with the pressure and magnetic field for Xenon and other gases is underway. Archived evidence includes time-resolved laser-induced-fluorescence measurements that were performed in the two identified thruster-response regimes: linear and nonlinear. In linear regime, the ion velocity distribution function was observed in all phases of the discharge and, with this methodology, precise kinetic evidence of ion sloshing during the evolution of the discharge current was acquired. A key gap issue is the theory of Modified Simon-Ho instability does not explain the observed pressure and magnetic field effects even though the suppression of spoke rotation frequency with the pressure correlates with the condition E is approximately zero (seemingly in agreement with MSHI). Furthermore, the observed spoke frequency scaling is different from known scaling for conventional sputtering E×B magnetron discharges and thrusters.