Fluid and hybrid simulations of the ionization instabilities in Hall thruster

Abstract

Low-frequency axial oscillations in the range of 5–50 kHz stand out as a pervasive feature observed in many types of Hall thrusters. While it is widely recognized that the ionization effects play the central role in this mode, as manifested via the large-scale oscillations of neutral and plasma density, the exact mechanism(s) of the instabilities remain unclear. To gain further insight into the physics of the breathing mode and evaluate the role of kinetic effects, a one-dimensional time-dependent full nonlinear low-frequency model describing neutral atoms, ions, and electrons is developed in full fluid formulation and compared to the hybrid model in which the ions and neutrals are kinetic. Both models are quasi-neutral and share the same electron fluid equations that include the electron diffusion, mobility across the magnetic field, and the electron energy evolution. The ionization models are also similar in both approaches. The predictions of fluid and hybrid simulations are compared for different test cases. Two main regimes are identified in both models: one with pure low-frequency behavior and the other one, where the low-frequency oscillations coexist with high-frequency oscillations in the range of 100–200 kHz, with the characteristic time scale of the ion channel fly-by time, 100–200 kHz. The other test case demonstrates the effect of a finite temperature of injected neutral atoms, which has a substantial suppression effect on the oscillation amplitude.

Time-dependent axial fluid model of the Hall thruster discharge and its plume

“…In a time-dependent model, a relation I d (V d ) must be added to the set of differential equations. The common way to do it is by integrating equation ( 5) from N to A [11,12,14]. First, we rewrite that equation as…”

“…Models neglecting azimuthal inertia have u ′ ye = 0, and those ending the discharge at N with a surface cathode, have ι z = 1 [11,14]. Equation ( 21) is added to the set of differential equations in the numerical integration scheme.…”

“…When more physics is accounted for, it has been observed [14,15] that the ionization instability is more easily damped. This is also observed with our models: going from Model 1 to 5, with α ′ w = 0, figure 8 shows the time evolution of I d for different models and ℓ m1 = 1.383 cm, all of them launched with the same initial conditions.…”

“…In contrast, the intrinsic time-resolving capabilities of an axial transient model allow to study the non-linear evolution of instabilities. With this regard, axial-time dependent models have been extensively used to study the longitudinal, low-frequency oscillations of the discharge current caused by ionization instabilities [11][12][13][14][15][16], usually called the breathing mode.…”

“…Finally, the electron azimuthal inertia is retained and the plume past the cathode is included in the domain, which was done for the stationary case [7] but has never been done in previous time-dependent axial models [11][12][13][14][15][16][17].…”