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

Reza, Maryam; Farbod, Faraji,; Knoll, Aaron

doi:10.2139/ssrn.4216635

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…It is evident from the time evolution plots in figure 14 that the E z signal becomes increasingly more complex with the increasing total ion current density. As it has been seen in our previous works [18,24] as well as in the literature [25,26], the higher complexity of the E z signal at higher J values roots in the presence of underlying nonlinear and transient processes at these values of J, such as the development of the electron drift instability and its transition to the ion acoustic waves. Nevertheless, the linear models from the OPT-DMD are observed to provide reasonable predictions of the groundtruth data evolution, especially at lower ion current densities of 50 and 100 Am −2 , where the OPT-DMD-predicted traces follow the ground-truth very closely.…”

Section: Axial-azimuthal Configurationsupporting

confidence: 62%

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

Faraji,

Reza,

Knoll

et al. 2023

J. Phys. D: Appl. Phys.

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In part I of the article, we demonstrated that a variant of the dynamic mode decomposition (DMD) algorithm based on variable projection optimization, called optimized DMD (OPT-DMD), enables a robust identification of the dominant spatiotemporally coherent modes underlying the data across various test cases representing different physical parameters in an E × B simulation configuration. We emphasized that the OPT-DMD significantly improves the analysis of complex plasma processes, revealing information that cannot be derived using conventionally employed analyses such as the fast Fourier transform. As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case. The predictive capacity of the OPT-DMD ROM is assessed primarily in terms of short-term dynamics forecast or, in other words, for large ratios of training-to-test data. However, the utility of the ROM for long-term dynamics forecasting is also presented for an example case in the radial-azimuthal configuration. The model’s predictive performance is heterogeneous across various test cases. Nonetheless, a remarkable predictiveness is observed in the test cases that do not exhibit highly transient behaviors. Moreover, in all investigated cases, the error between the ground-truth and the reconstructed data from the OPT-DMD ROM remains bounded over time within both the training and the test window. As a result, despite its limitation in terms of generalized applicability to all plasma conditions, the OPT-DMD is proven as a reliable method to develop low computational cost and highly predictive data-driven ROMs in systems with a quasi-periodic global evolution of the plasma state.

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Section: Axial-azimuthal Configurationsupporting

confidence: 62%

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

Faraji,

Reza,

Knoll

et al. 2023

J. Phys. D: Appl. Phys.

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“…We have observed that not only the same results reported in that article can be faithfully reproduced but also the improvements in the formulation of the reduced-order PIC scheme, discussed in this work, have notably augmented the predictive capability of the scheme in this low-computational-cost limit, enabling the approach to recover more accurately the results from the reference full-2D PIC simulations in several conditions. Interested readers are kindly referred to [29] where the detailed results of the verification of the generalized reduced-order PIC scheme at the low-order approximation limit are available.…”

Section: Discussionmentioning

confidence: 99%

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

Reza

Farbod

Knoll

2023

J. Phys. D: Appl. Phys.

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Reduced-order particle-in-cell (PIC) scheme is a novel modeling approach that enables computationally efficient electrostatic kinetic simulations of plasma. In our previous publications, we demonstrated that a proof-of-concept implementation of this novel PIC scheme resolves the multi-dimensional plasma processes and their interactions in a Hall thruster in a manner close to traditional electrostatic PIC codes. In this work, we extend our efforts on this topic and present a mathematically mature formulation for the dimensionality reduction of Poisson's equation in the Vlasov-Poisson system, which enables the generalized reduced-order "quasi-multi-dimensional" PIC scheme. The applicability of the dimensionality-reduction approach to solve general 2D Poisson problems is numerically verified. Next, we present several reduced-order quasi-2D simulations of a well-defined axial-azimuthal simulation case from the literature using approximation orders of the 2D problem whose computational costs are 2-15 % of a full-2D simulation. It is shown that these reduced-order simulations allow us to recover the same characteristics, behaviors and effects reported in the literature regarding the azimuthal instabilities in Hall thrusters. Moreover, in terms of the time-averaged plasma properties, it was found that, when increasing the approximation order, the error associated with the quasi-2D simulations’ predictions decreases from 15 to 4 % for the electric field and from 20 to 2 % for the ion number density. We have additionally discussed a series of sensitivity analysis results, including the influence of the initial number of macroparticles per cell on the predictions of the quasi-2D simulations. According to the detailed results and analyses presented, we conclude that the generalized reduced-order PIC scheme serves as a rigorous foundation for eventual cost-effective and comprehensive three-dimensional kinetic studies of the physics in Hall thrusters and similar electrostatic plasma technologies.

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Influence of the magnetic field curvature on the radial–azimuthal dynamics of a Hall thruster plasma discharge with different propellants

Reza,

Faraji,

Knoll

2023

Journal of Applied Physics

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The topology of the applied magnetic field is an important design aspect of Hall thrusters. For modern Hall thrusters, the magnetic field topology most often features curved lines with a concave (negative) curvature upstream of the field's peak and a convex (positive) curvature downstream. Additionally, the advent of the magnetic shielding technique has resulted in Hall thruster designs with non-conventional field topologies that exhibit high degrees of concavity upstream of the field's peak. In this article, a detailed study is carried out on the effects that the magnetic field curvature has on the plasma discharge in a 2D configuration representative of a Hall thruster's radial–azimuthal cross section. The analyses are performed for discharges of three propellants of high applied interest: xenon, krypton, and argon. For each propellant, high-fidelity electrostatic reduced-order particle-in-cell (PIC) simulations are performed with various degrees of positive and negative curvatures of the magnetic field. Corresponding 1D radial PIC simulations are also performed for xenon to compare the observations against the 2D results. Most notably, it is observed that the instability spectra in the positive-curvature cases are mostly dominated by electron cyclotron drift instability, whereas the modified two stream instability is dominant in the negative-curvature cases. The distributions of electron and ion temperatures, in particular, as well as the contribution of various mechanisms to electrons’ cross-field transport show notable variations between the positive and negative curvature values. Finally, the field curvature is observed to majorly influence the ion beam divergence along the radial and azimuthal coordinates.

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

Cited by 8 publications

References 14 publications

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

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

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

Influence of the magnetic field curvature on the radial–azimuthal dynamics of a Hall thruster plasma discharge with different propellants

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