A Basic Predator‐Prey Type Model for Low Frequency Discharge Oscilations in Hall Thrusters

Abstract

The mechanism of low frequency oscillations in Hall thrusters is usually explained using the predator-prey type model, but the reasonable boundary conditions for the model have not been given. Analyses on thrusters' model equations show that besides the processes of neutral replenishment and ionization avalanche, the effects of dynamic electric field are also necessary for low frequency oscillations. The dynamic electric field reflects the interaction of ionization zone with acceleration zone, and is embodied in boundary conditions of the predatorprey type model. Furthermore, a basic predator-prey type model with reasonable boundary conditions and complete physical mechanism is proposed. And the effects of electric field on low frequency oscillations are verified by experiment.

Numerical study of low-frequency discharge oscillations in a 5 kW Hall thruster

“…Subsequently, the low-frequency oscillations have been well reproduced by numerous time-dependent numerical models [8][9][10]. Recently, Barral, Yu, Wei, and Wang et al have conducted considerable research [11][12][13][14][15][16][17][18][19][20][21][22][23] on the influencing factors, physical mechanisms, and stability of low-frequency oscillations.…”

Searching for Chaotic Behavior in the Ion Current Waveforms of a Hall Effect Thruster

“…The most common type of oscillations, so-called breathing mode (BM), appears within the range of 10 -60 kHz. The mechanism of these large amplitude low frequency volumetric oscillations has been investigated with simple analytical models of prey-predator type for the neutral gas ionization (0D model) [11][12][13][14], as well as with more sophisticated theories [15][16][17]. The BM appears in numerical simulations even within 1D description [16,18,19] and are unambiguously reproduced by 2D models, e. g. [20].…”

On the mechanism of ionization oscillations in Hall thrusters

“…Fig. 7a shows the family of the ion velocity profiles, constructed in a similar manner (by a parabola) but keeping the back-flow length the same (1 cm) and varying v i (L) = (14,18,22,26) km/s. The resulting frequency for all these profiles was found to be close to 10 kHz, Fig.…”

“…It was, however, noted that for the constant ion and neutral velocities, the model is stable and does not predict any instability 13 so the conditions for the excitation of the ionization oscillations are not clear. Additional effects and modifications 13,14 were proposed for the predator-prey model to make it unstable but it remains unclear to what degree the 0-D models are capable to predict the breathing mode oscillations (discussed in section II).…”