Enhancing one-dimensional particle-in-cell simulations to self-consistently resolve instability-induced electron transport in Hall thrusters

Abstract

The advent of high-power Hall thrusters and the increasing interest toward their use as a primary propulsion system for various missions have given a new boost to the efforts aiming at self-consistent predictive modeling of this thruster technology. In this article, we present a novel approach, which allows enhancing the predictive capability of one-dimensional particle-in-cell (PIC) simulations to self-consistently capture the wave-induced electron transport due to the azimuthal instabilities in Hall thrusters. The so-called “pseudo-2D” PIC scheme resulting from this approach is extensively tested in several operating conditions. The results are compared against a well-established 2D3V axial–azimuthal reference case in terms of the axial profiles of the time-averaged plasma properties, the azimuthal electric field fluctuations and their dispersion features, and the contributions of the force terms in the electron azimuthal momentum equation to the cross-field mobility. We have demonstrated that the pseudo-2D PIC provides a prediction of the above aspects that compares very closely in almost all conditions with those from the full-2D simulation. In addition, the sensitivity of the pseudo-2D simulation results to the numerical parameters associated with our approach is assessed in detail. The outcomes of these analyses have casted light on the next steps to further improve the approach.

Generalized Reduced-Order Particle-in-Cell Scheme for Hall Thruster Modeling: Concept and In-Depth Verification in the Axial-Azimuthal Configuration

“…This result is consistent with what has been observed in the 2D reference simulations [15][18]. Nonetheless, this feature had not been observed in our previous work [10] where the preliminary "pseudo-2D" simulations showed temperatures in the near-plume region that were higher than the electrons' injection temperature from the cathode. This difference is now believed to be mostly caused by the adoption of the current-equality cathode boundary condition in the pseudo-2D simulations [10].…”

“…Nonetheless, this feature had not been observed in our previous work [10] where the preliminary "pseudo-2D" simulations showed temperatures in the near-plume region that were higher than the electrons' injection temperature from the cathode. This difference is now believed to be mostly caused by the adoption of the current-equality cathode boundary condition in the pseudo-2D simulations [10]. Noting this point, and as mentioned earlier in Section 1, the sensitivity of the reduced-order quasi-2D simulations to the model used for the electrons' injection from the cathode boundary is further discussed in Section 6.1.…”

“…[28], and the mathematical definition of each of the constituent terms in this equation is provided in Ref. [10].…”

“…In this respect, noting the necessity of 3D kinetic simulations to thoroughly study plasma dynamics in Hall thrusters, and to address the issue of enormous computational cost associated with conventional multi-dimensional kinetic simulations that renders them impractical for real-size Hall devices [9], we introduced the reduced-order "pseudo-2D" electrostatic particle-in-cell (PIC) scheme in a prior publication [10]. In essence, our reduced-order PIC scheme relies on a dimensionality-reduction technique to decompose the multi-dimensional Poisson's equation in the Vlasov-Poisson system into several one-dimensional components along the involved simulation directions.…”

“…In our previous works [10] [11], we presented a preliminary formulation to split the 2D Poisson's equation into a set of decoupled 1D Ordinary Differential Equations (ODE), which yielded the "pseudo-2D" PIC scheme. We studied the feasibility of the concept of reduced-order PIC scheme through performing several pseudo-2D kinetic simulations along various coordinates of a Hall thruster, i.e., axial-azimuthal, azimuthal-radial and axial-radial, comparing the results against the observations in full-2D reference cases.…”