Resolving multi-dimensional plasma phenomena in Hall thrusters using the reduced-order particle-in-cell scheme

Abstract

Plasma in Hall thrusters exhibits a complex behavior, characterized by the interplay between various dominant processes in each of the thruster’s coordinates. The emergence of high-power Hall thrusters in the recent years and the design modifications intended to extend the lifetime of these devices have further amplified the three-dimensional nature of the plasma behavior. In this regard, the novel reduced-order particle-in-cell (PIC) scheme provides the possibility to resolve the multi-dimensional interactions in a Hall thruster at a computational cost up to two orders of magnitude lower than current multi-dimensional PIC simulations. To demonstrate this point, we present in this article the results from a series of pseudo-two-dimensional simulations we performed in three configurations: axial-azimuthal, azimuthal-radial, and axial-radial. We show that, in each configuration, the pseudo-2D PIC scheme provides a significantly improved picture of the involved physics compared to a one-dimensional PIC simulation and captures self-consistently the coupling between the plasma processes in different directions, notably similar to the observations from full-2D kinetic simulations.

Concept of the generalized reduced-order particle-in-cell scheme and verification in an axial-azimuthal Hall thruster configuration

“…The same converging behavior of the solution is observed for the Poisson problem in Case 3 (figure 5). Indeed, from the right-hand-side plot of figure 5, which shows the distribution of the error, as defined by equation (11), between the approximate solution at M = N = 100 (figure 5 (left)) and the full-2D solution, the maximum error is found to be ±1.2%, which is in the same order of the error corresponding to the full-2D solver itself, The convergence characteristic of the RDPS and the decrease in error between the approximate and the groundtruth solutions when increasing the number of regions can be better understood by looking at the plots of figure 6, which present the evolution of the root-mean-square (RMS) error (equation ( 12)) for different Poisson problems,…”

“…Underlying this PIC scheme was a preliminary formulation to split the 2D Poisson's equation into a set of decoupled 1D ordinary differential equations (ODEs). We demonstrated in [10,11] that this splitting of Poisson's equation allows us to remarkably reduce the required number of computational cells and the total number of macroparticles, hence, gaining significant computational advantage over traditional PIC codes. We performed proof-of-concept studies on the pseudo-2D kinetic simulation along various coordinates of a Hall thruster, i.e.…”

“…We performed proof-of-concept studies on the pseudo-2D kinetic simulation 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 [10,11]. In this respect, despite the rather simple dimensionality-reduction formulation that were used in the 'pseudo-2D' simulations, the essential capability of the approach to resolve the main physics and interactions among plasma phenomena in different 2D configurations was demonstrated [10,11].…”

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: I. Extraction of spatiotemporally coherent patterns

“…To provide a brief overview, the reduced-order quasi-2D simulations [21][22][23] of the radial-azimuthal plasma configuration were carried out in a domain corresponding to a 2D x − z Cartesian plane which is illustrated in figure 1.…”

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: II. Dynamics forecasting

“…The high-fidelity ground-truth data used to derive and test the OPT-DMD models are obtained from the reduced-order quasi-two-dimensional particle-in-cell (PIC) simulations of the test cases that will be overviewed in section 2. Developed at Imperial Plasma Propulsion Laboratory (IPPL), the computationally efficient reduced-order PIC code [17][18][19] plays an enabling role in our research toward DD predictive plasma modeling. This is because of the proven capability of this PIC scheme to provide large sets of high-fidelity data over extended parameter spaces and time windows at a significantly reduced computational resource compared to traditional multidimensional PIC codes [17,20,21].…”