On the mechanism of ionization oscillations in Hall thrusters

Abstract

Low-frequency ionization oscillations involving plasma and neutral density (breathing modes) are the most violent perturbations in Hall thrusters for electric propulsion. Because of its simplicity, the zero-dimensional (0D) predator–prey model of two nonlinearly coupled ordinary differential equations for plasma and neutral density has often been used for the characterization of such oscillations and scaling estimates. We investigate the properties of its continuum analog, the one-dimensional (1D) system of two nonlinearly coupled equations in partial derivatives (PDEs) for plasma and neutral density. This is a more general model, of which the standard 0D predator–prey model is a special limit case. We show that the 1D model is stable and does not show any oscillations for the boundary conditions relevant to Hall thrusters and the uniform ion velocity. We then propose a reduced 1D model based on two coupled PDEs for plasma and neutral densities that is unstable and exhibit oscillations if the ion velocity profile with the near-the-anode back-flow (toward the anode) region is used. Comparisons of the reduced model with the predictions of the full model that takes into account the self-consistent plasma response show that the main properties of the breathing mode are well captured. In particular, it is shown that the frequency of the breathing mode oscillations is weakly dependent on the final ion velocity but shows a strong correlation with the width of the ion back-flow region.

Detection of the magnetic field parameters influence on discharge current fluctuations and optimal operation modes of the hall thruster

“…In them, the main attention is paid to the formal construction of mathematical models of fluctuations of plasma parameters in Hall thrusters and mathematical modeling without specific reference to the integral parameters of the thruster -thrust, specific impulse, efficiency. Well-known mathematical models [14][15][16] describe, as a rule, some specific physical mechanism of occurrence of discharge current fluctuations. At the same time, when conducting experimental studies, fluctuations of the discharge current of different character were found, the mechanisms of which may be different.…”

Two-dimensional effects on electrostatic instabilities in Hall thrusters. I. Insights from particle-in-cell simulations and two-point power spectral density reconstruction techniques

“…Several instabilities have been identified and studied in HTs. These instabilities cover a large range of frequencies, including: (1) the so-called Breathing Mode (BM) [17][18][19][20] at ≈ 10 kHz, (2) the Ion Transit-Time Instability (ITTI) [21][22][23][24] at ≈ 500 kHz, (3) the Modified Two-Streams Instability (MTSI) [25][26][27][28] at ≈ 1 MHz, (4) the Electron Cyclotron Drift Instability (ECDI) 6,8,15,25,[29][30][31][32][33] and (5) the evolution of the ECDI towards an Ion Acoustic Wave (IAW) 16,27,34 , at ≈ 8 MHz. However, the origin, the growth and the saturation mechanisms of some of the above instabilities remain unclear (see for instance the different theories proposed for the BM 18,19 , or the partial theoretical treatment of the IAW 16 or the ITTI 21 ).…”

Two-dimensional effects on electrostatic instabilities in Hall thrusters. II. Comparison of particle-in-cell simulation results with linear theory dispersion relations

“…Finally, in the low-frequency range (∼ 10 kHz), the Breathing Mode (BM) is found as a low-frequency ionization instability. Despite the origin of this instability not being fully understood 49,50 , it is commonly accepted that the BM should not be considered among electrostatic plasma instabilities.…”