arXiv subjects

Aaron Knoll

Publications and source records attributed to Aaron Knoll.

At least 19 recordsLinked to original sources

arXiv2025

Benchmark for two-dimensional large scale coherent structures in partially magnetized ExB plasmas -- Community collaboration & lessons learned

Low-temperature plasmas are essential to both fundamental scientific research and critical industrial applications. As in many areas of science, numerical simulations have become a vital tool for uncovering new physical phenomena and guiding technological development. Code benchmarking remains crucial for verifying implementations and evaluating performance. This work continues the Landmark benchmark initiative, a series specifically designed to support the verification of low-temperature plasma codes. In this study, seventeen simulation codes from a collaborative community of nineteen international institutions modeled a partially magnetized ExB Penning discharge. The emergence of large scale coherent structures, or rotating plasma spokes, endows this configuration with an enormous range of time scales, making it particularly challenging to simulate. The codes showed excellent agreement on the rotation frequency of the spoke as well as key plasma properties, including time-averaged ion density, plasma potential, and electron temperature profiles. Achieving this level of agreement came with challenges, and we share lessons learned on how to conduct future benchmarking campaigns. Comparing code implementations, computational hardware, and simulation runtimes also revealed interesting trends, which are summarized with the aim of guiding future plasma simulation software development.

physics.plasm-ph↗

arXiv2025

Investigation of the influence of electrostatic excitation on instabilities and electron transport in ExB plasma configurations

Partially magnetized plasmas in ExB configurations - where the electric and magnetic fields are mutually perpendicular - exhibit a cross-field transport behavior, which is widely believed to be dominantly governed by complex instability-driven mechanisms. This phenomenon plays a crucial role in a variety of plasma technologies, including Hall thrusters, where azimuthal instabilities significantly influence electron confinement and, hence, device performance. While the impact of prominent plasma instabilities, such as the electron cyclotron drift instability (ECDI) and the modified two-stream instability (MTSI) on cross-field transport of electron species is well recognized and widely studied, strategies for actively manipulating these dynamics remain underexplored. In this study, we investigate the effect of targeted wave excitation on instability evolution and electron transport using one- and two-dimensional particle-in-cell simulations of representative plasma discharge configurations. A time-varying electric field is applied axially to modulate the spectral energy distribution of the instabilities across a range of forcing frequencies and amplitudes. Our results reveal that the so-called "unsteady forcing" can both suppress and amplify instability modes depending on excitation parameters. In particular, across both 1D and 2D simulation configurations, forcing near 40 MHz effectively reduces ECDI amplitude and decreases axial electron transport by about 30%, while high-frequency excitation near the electron cyclotron frequency induces spectral broadening, inverse energy cascades, and enhanced transport. These findings point to the role of nonlinear frequency locking and energy pathway disruption as mechanisms for modifying instability-driven transport. Our results offer insights into potential pathways to enhance plasma confinement and control in next-generation ExB devices.

physics.plasm-ph↗

arXiv2024

Latest progress on the reduced-order particle-in-cell scheme: I. refining the underlying formulation

The particle-in-cell (PIC) method is a well-established and widely used kinetic plasma modelling approach that provides a hybrid Lagrangian-Eulerian approach to solve the plasma kinetic equation. Despite its power in capturing details of the underlying physics of plasmas, conventional PIC implementations are associated with a significant computational cost, rendering their applications for real-world plasma science and engineering challenges impractical. The acceleration of the PIC method has thus become a topic of high interest, with several approaches having been pursued to this end. Among these, the concept of reduced-order (RO) PIC simulations, first introduced in 2023, provides a uniquely flexible and computationally efficient framework for kinetic plasma modelling - characteristics verified extensively in various plasma configurations. In this two-part article, we report the latest progress achieved on RO-PIC. Part I article revisits the original RO-PIC formulation and introduces refinements that substantially enhance the cost-efficiency and accuracy of the method. We discuss these refinements in comparison against the original formulation, illustrating the progression to a "first-order" implementation from the baseline "zeroth-order" one. In a detailed step-by-step verification, we first test the newly updated reduced-dimension Poisson solver (RDPS) in the first-order RO-PIC against its zeroth-order counterpart using test-case Poisson problems. Next, comparing against the zeroth-order version, we examine the performance of the complete first-order RO-PIC code in two-dimensional plasma problems. The detailed verifications demonstrate that the improvements in the RO-PIC formulation enable the approach to provide full-2D-equivalent results at a substantially lower (up to an order of magnitude) computational cost compared to the zeroth-order RO-PIC.

physics.plasm-ph↗

arXiv2024

Latest progress on the reduced-order particle-in-cell scheme: II. Quasi-3D implementation and verification

Across many plasma applications, the underlying phenomena and interactions among the involved processes are known to exhibit three-dimensional characteristics. Furthermore, the global properties and evolution of plasma systems are often determined by a process called inverse energy cascade, where kinetic plasma processes at the microscopic scale interact and lead to macroscopic coherent structures. These structures can have a major impact on the stability of plasma discharges, with detrimental effects on the operation and performance of plasma technologies. Kinetic particle-in-cell (PIC) methods offer a sufficient level of fidelity to capture these processes and behaviors. However, three-dimensional PIC simulations that can cost-effectively overcome the curse of dimensionality and enable full-scale simulations of real-world time significance have remained elusive. Tackling the enormous computational cost issue associated with conventional PIC schemes, the computationally efficient reduced-order (RO) PIC approach provides a viable path to 3D simulations of real-size plasma systems. This part II paper builds upon the improvements to the RO-PIC's underpinning formulation discussed in part I and extends the novel "first-order" RO-PIC formulation to 3D. The resulting Quasi-3D (Q3D) implementation is rigorously verified in this paper, both at the module level of the Q3D reduced-dimension Poisson solver (RDPS) and at the global PIC code level. The plasma test cases employed correspond to 3D versions of the 2D configurations studied in Part I, including a 3D extension to the Diocotron instability problem. The detailed verifications of the Q3D RO-PIC confirm that it maintains the expected levels of cost-efficiency and accuracy, demonstrating the ability of the approach to indistinguishably reproduce full-3D simulation results at a fraction of the computational cost.

physics.plasm-ph↗

arXiv2024

Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics

Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design, exhaustive exploration and physical understanding. Plasma simulations, in particular those applied to the study of ${\bf E}\times {\bf B}$ plasma discharges and technologies, such as Hall thrusters, require substantial computational resources in order to resolve the multidimentional dynamics that span across wide spatial and temporal scales. Although high-fidelity computational tools are available to simulate such systems over limited conditions and in highly simplified geometries, simulations of full-size systems and/or extensive parametric studies over many geometric configurations and under different physical conditions are computationally intractable with conventional numerical tools. Thus, scientific studies and industrially oriented modeling of plasma systems, including the important ${\bf E}\times {\bf B}$ technologies, stand to significantly benefit from reduced order modeling algorithms. We develop a model reduction scheme based upon a {\em Shallow REcurrent Decoder} (SHRED) architecture. The scheme uses a neural network for encoding limited sensor measurements in time (sequence-to-sequence encoding) to full state-space reconstructions via a decoder network. Based upon the theory of separation of variables, the SHRED architecture is capable of (i) reconstructing full spatio-temporal fields with as little as three point sensors, even the fields that are not measured with sensor feeds but that are in dynamic coupling with the measured field, and (ii) forecasting the future state of the system using neural network roll-outs from the trained time encoding model.

physics.plasm-ph↗

arXiv2024

Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verifications

Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to facilitate scientific research and expedite the development of plasma technologies. In line with the advancements in computational power and data-driven methods, we introduce the "Phi Method" in this two-part article. Part I presents this novel algorithm, which employs constrained regression on a candidate term library informed by numerical discretization schemes to discover discretized systems of differential equations. We demonstrate Phi Method's efficacy in deriving reliable and robust reduced-order models (ROMs) for three test cases: the Lorenz attractor, flow past a cylinder, and a 1D Hall-thruster-representative plasma. Part II will delve into the method's application for parametric dynamics discovery. Our results show that ROMs derived from the Phi Method provide remarkably accurate predictions of systems' behavior, whether derived from steady-state or transient-state data. This underscores the method's potential for transforming plasma system modeling.

physics.plasm-ph↗

arXiv2024

Data-driven local operator finding for reduced-order modelling of plasma systems: II. Application to parametric dynamics

Real-world systems often exhibit dynamics influenced by various parameters, either inherent or externally controllable, necessitating models capable of reliably capturing these parametric behaviors. Plasma technologies exemplify such systems. For example, phenomena governing global dynamics in Hall thrusters (a spacecraft propulsion technology) vary with various parameters, such as the "self-sustained electric field". In this Part II, following on the introduction of our novel data-driven local operator finding algorithm, Phi Method, in Part I, we showcase the method's effectiveness in learning parametric dynamics to predict system behavior across unseen parameter spaces. We present two adaptations: the "parametric Phi Method" and the "ensemble Phi Method", which are demonstrated through 2D fluid-flow-past-a-cylinder and 1D Hall-thruster-plasma-discharge problems. Comparative evaluation against parametric OPT-DMD in the fluid case demonstrates superior predictive performance of the parametric Phi Method. Across both test cases, parametric and ensemble Phi Method reliably recover governing parametric PDEs and offer accurate predictions over test parameters. Ensemble ROM analysis underscores Phi Method's robust learning of dominant dynamic coefficients with high confidence.

physics.plasm-ph↗

arXiv2023

Effects of the applied fields' strength on the plasma behavior and processes in ExB plasma discharges of various propellants: I. Electric field

We present, in this two-part article, an extensive study on the influence that the magnitudes of the applied electric (E) and magnetic (B) fields have on a collisionless plasma discharge of xenon, krypton, and argon in a 2D radial-azimuthal configuration with perpendicular orientation of the fields. The dependency of the behavior and the underlying processes of ExB discharges on the strength of electromagnetic field and ion mass has not yet been studied in depth and in a manner that can distinguish the role of each individual factor. This has been, on the one hand, due to the significant computational cost of conventional high-fidelity particle-in-cell (PIC) codes that do not allow for extensive simulations over a broad parameter space within practical timeframes. On the other hand, the experimental efforts have been limited, in part, by the measurements' spatial and temporal resolution. In this sense, the notably reduced computational cost of the reduced-order PIC scheme enables to numerically cast light on the parametric variations in various aspects of the physics of ExB discharges, such as high resolution spatial-temporal mappings of the plasma instabilities. In part I of the article, we focus on the effects of the E-field intensity. We demonstrate that the intensity of the field determines two distinct plasma regimes, which are characterized by different dominant instability campaigns. At relatively low E-field magnitudes, the Modified Two Stream Instability (MTSI) is dominant, whereas, at relatively high E-field magnitudes, the MTSI is mitigated, and the Electron Cyclotron Drift Instability (ECDI) becomes dominant. These two regimes are identified for all studied propellants. Consequent to the change in the plasma regime, the radial distribution of the axial electron current density and the electron temperature anisotropy vary.

physics.plasm-ph↗

arXiv2023

Effects of the applied fields' strength on the plasma behavior and processes in ExB plasma discharges of various propellants: II. Magnetic field

We present in this part II the effects of the magnetic field intensity on the properties of the plasma discharge and the underlying phenomena for different propellant's ion mass. The plasma setup represents a perpendicular configuration of the electric and magnetic fields, with the electric field along the axial direction and the magnetic field along the radial direction. The magnetic field intensity is changed from 5 to 30 mT, with 5 mT increments. The propellant gases are xenon, krypton, and argon. The simulations are carried out using a particle-in-cell (PIC) code based on the computationally efficient reduced-order PIC scheme. Similar to the observations in part I, we show that, across all propellants, the variation in the intensity of the magnetic field yields two distinct regimes of the plasma, where either the Modified Two Stream Instability (MTSI) or the Electron Cyclotron Drift Instability (ECDI) are present. Nonetheless, a third plasma regime is also observed for cases with moderate values of the magnetic field intensity (15 and 20 mT), in which the ECDI and the MTSI co-exist with comparable amplitudes. This described change in the plasma regime becomes clearly reflected in the radial distribution of the axial electron current density and the electron temperature anisotropy. Contrary to the effect of the electric field magnitude in part I, we observed here that the MTSI is absent at the relatively low magnetic field intensities (5 and 10 mT). At the relatively high magnitudes of the magnetic field (25 and 30 mT), the MTSI becomes strongly present, a long-wavelength wave mode develops, and the ECDI does not excite. An exception to this latter observation was noticed for xenon, for which the ECDI's presence persists up to the magnetic field peak value of 25 mT.

physics.plasm-ph↗

arXiv2023

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

The topology of the applied magnetic field is an important design aspect of Hall thrusters. For modern Hall thrusters, the field topology most often features curved lines with a concave (negative) curvature upstream of the field peak and a convex (positive) curvature downstream. Additionally, the advent of the magnetic shielding technique has resulted in the design of Hall thrusters with non-conventional magnetic fields that exhibit high degrees of concavity upstream of the field's peak. We carry out a rigorous and detailed study of the effects that the magnetic field's curvature has on the plasma properties and the underlying processes in a 2D configuration representative of a Hall thruster's radial-azimuthal cross-section. The analyses are performed for plasma discharges of three propellants: xenon, krypton, and argon. For each propellant, we have carried out high-fidelity reduced-order particle-in-cell (PIC) simulations with various degrees of positive and negative curvatures of the magnetic field. Corresponding 1D radial PIC simulations were also performed for xenon to compare the observations between 1D and 2D simulations. We observed that there are distinct differences in the plasma phenomena between the cases with positive and negative field curvatures. The instability spectra in the cases of positive curvature is mostly dominated by the Electron Cyclotron Drift Instability, whereas the Modified Two Stream Instability is dominant in the negative-curvature cases. The distribution of the plasma properties, particularly the electron and ion temperatures, and the contribution of various mechanisms to electrons' cross-field transport showed notable variations with the field's curvature, especially between the positive and the negative values. Finally, the magnetic field curvature was observed to majorly influence the ion beam divergence along the radial and azimuthal coordinates.

physics.plasm-ph↗

arXiv2023

Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns

In this two-part article, we evaluate the utility and the generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations. The DMD algorithm is an interpretable data-driven method that finds a best-fit linear model describing the time evolution of spatiotemporally coherent structures (patterns) in data. We have applied the DMD to extensive high-fidelity datasets generated using a particle-in-cell (PIC) code based on a cost-efficient reduced-order PIC scheme. In this part, we first provide an overview of the concept of DMD and its underpinning Proper Orthogonal and Singular Value Decomposition methods. Two of the main DMD variants are next introduced. We then present and discuss the results of the DMD application in terms of the identification and extraction of the dominant spatiotemporal modes from high-fidelity data over a range of simulation conditions. We demonstrate that the DMD variant based on variable projection optimization (OPT-DMD) outperforms the basic DMD method in identification of the modes underlying the data, leading to notably more reliable reconstruction of the ground-truth. Furthermore, we show in multiple test cases that the discrete frequency spectrum of OPT-DMD-extracted modes is consistent with the temporal spectrum from the Fast Fourier Transform of the data. This observation implies that the OPT-DMD augments the conventional spectral analyses by being able to uniquely reveal the spatial structure of the dominant modes in the frequency spectra, thus, yielding more accessible, comprehensive information on the spatiotemporal characteristics of the plasma phenomena.

physics.plasm-ph↗

arXiv2023

Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting

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 ExB simulation configuration. 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 reduced-order models in systems with a quasi-periodic global evolution of the plasma state.

physics.plasm-ph↗

arXiv2023

Reduced-order particle-in-cell simulations of a high-power magnetically shielded Hall thruster

High-power magnetically shielded Hall thrusters have recently emerged to meet the needs of the next-generation space missions. Even though a few such thrusters are currently undergoing their late-stage development campaigns, many unanswered questions yet exist concerning the behavior and evolution of the plasma in these large-size thrusters that feature an unconventional magnetic field topology. Noting the complex, multi-dimensional nature of plasma processes in Hall thrusters, high-fidelity particle-in-cell simulations are optimal tools to study the intricate plasma behavior. Nonetheless, the significant computational cost of traditional PIC schemes renders simulating high-power thrusters without any physics-altering speed-up factors unfeasible. Thus, in this article, we demonstrate the applicability of the novel reduced-order PIC scheme for a cost-efficient, self-consistent study of the high-power Hall thrusters by performing simulations of a 20 kW magnetically shielded Hall thruster along the axial-azimuthal and radial-azimuthal coordinates. The axial-azimuthal simulations are performed for three operating conditions in a rather simplified representation of the thruster's inherently 3D configuration. Nevertheless, we resolved self-consistently an unprecedented 650 us of the discharge evolution without any ad-hoc electron mobility model, capturing several breathing cycles and approximating the experimental performance parameters with an accuracy of 70 to 80 % across the operating conditions. The radial-azimuthal simulations casted further light on the evolution of the azimuthal instabilities and the resulting variations in the electrons' cross-field mobility and the plasma-wall interactions. Particularly, we observed the development of a long-wavelength, relatively low-frequency wave mode near the exit plane of the thruster's channel that induces a notable electron transport.

physics.plasm-ph↗

arXiv2023

Effects of the neutral dynamics model on the particle-in-cell simulations of a Hall thruster plasma discharge

The dynamics of the neutral atoms in Hall thrusters affect several plasma processes, from the ionization to the electrons' mobility. In the context of Hall thruster's particle-in-cell (PIC) modeling, the neutrals are often treated kinetically, similar to the plasma species, and their interactions with themselves and the ions are resolved using the Direct-Simulation Monte-Carlo (DSMC) algorithm. However, the DSMC approach is computationally resource demanding. Therefore, modeling the neutrals as a 1D fluid has been also pursued in simulations that do not involve the radial coordinate and, hence, do not resolve the neutrals' radial expansion. In this article, we present an extensive study on the sensitivity of the PIC simulations of Hall thruster discharge to the model used for the neutral dynamics. We carried out 1D axial PIC simulations with various fluid and kinetic models of the neutrals as well as self-consistent quasi-2D axial-azimuthal simulations with different neutrals' fluid descriptions. Our results show that the predictions of the simulations in either 1D or 2D configurations are highly sensitive to the neutrals' model, and that different treatments of the neutrals change the spatiotemporal evolution of the discharge. Moreover, we observed that considering the ion-neutral collisions causes a significant variation in the neutral temperature, thus requiring that the neutrals' energy equation to be included as well in their fluid system of equations. Finally, the self-consistent axial-azimuthal simulations highlighted that a neutrals' model based on the continuity conservation equation only is not an appropriate choice and leads to physically unexpected high-frequency global discharge oscillations.

physics.plasm-ph↗

arXiv2022

Effects of magnetic field gradient and secondary electron emission on instabilities and transport in an ExB plasma configuration

Today, partially magnetized low-temperature plasmas (LTP) in an ExB configuration, where the applied magnetic field is perpendicular to the self-consistent electric field, have important industrial applications. Hall thrusters, a type of electrostatic plasma propulsion, are one of the main LTP technologies whose advancement is hindered by the not-fully-understood underlying physics of operation, particularly, with respect to the plasma instabilities and the associated electron cross-field transport. The development of Hall thrusters with unconventional magnetic field topologies has imposed further questions regarding the instabilities' characteristics and the electrons' dynamics in these modern cross-field configurations. Accordingly, we present in this effort a series of studies on the influence of four factors on the plasma processes in the radial-azimuthal coordinates of a Hall thruster, namely, the magnetic field gradient, Secondary Electron Emission, electron-neutral collisions, and plasma number density. The studies are carried out using the reduced-order particle-in-cell (PIC) code developed by the authors. The setup of the radial-azimuthal simulations largely follows a well-defined benchmark case from the literature in which the magnetic field is oriented along the radius and a constant axial electric field is applied perpendicular to the simulation plane. The salient finding from our investigations is that, in the studied cases corresponding to elevated plasma densities, an inverse energy cascade leads to the formation of a long-wavelength, high-frequency azimuthal mode. Moreover, in the presence of strong magnetic field gradients, this mode is fully developed and induces a significant electron cross-field transport as well as a notable heating of the ion population.

physics.plasm-ph↗

arXiv2022

Verification of the generalized reduced-order particle-in-cell scheme in a radial-azimuthal ExB plasma configuration

In this article, we present an in-depth verification of the generalized electrostatic reduced-order particle-in-cell (PIC) scheme in a cross electric and magnetic field configuration representative of a radial-azimuthal section of a Hall thruster. The setup of the simulations follows a well-established benchmark case. The main purpose of this effort is to demonstrate that our novel PIC scheme can reliably resolve the complex two-dimensional dynamics and interactions of the plasma instabilities in the radial-azimuthal coordinates of a Hall thruster at a fraction of the computational cost compared to full-2D PIC codes. To this end, we first present the benchmarking of our newly developed full-2D PIC code. Next, we provide an overview of the reduced-order PIC scheme and the resulting "quasi-2D" code, specifying that the degree of order reduction in the quasi-2D PIC is defined in terms of the number of "regions" along the simulation's directions used to divide the computational domain. We compare the predictions of the quasi-2D simulation in various approximation degrees of the 2D problem against our full-2D simulation results. We show that, by increasing the number of regions in the Q2D simulations, the quasi-2D results converge to the 2D ones. Nonetheless, we also highlight that a quasi-2D simulation that provides a factor of 5 reduction in the computational cost resolves the underlying physical processes in an almost indistinguishable manner with respect to the full-2D simulation and incurs a maximum error of only about 10 % in the ion number density and about 5 % in the electron temperature.

physics.plasm-ph↗

arXiv2022

Generalized reduced-order particle-in-cell scheme for Hall thruster modeling: concept and in-depth verification in the axial-azimuthal configuration

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 the potentials of a preliminary implementation of this PIC scheme to resolve the multi-dimensional plasma processes in a Hall thruster in a manner close to traditional multi-dimensional PIC simulations. In this work, we first introduce a mathematically mature formulation for the dimensionality reduction of Poisson's equation, which enables the generalized "quasi-multi-dimensional" PIC scheme. We present the proof that the dimensionally reduced Poisson's equation converges to the multi-dimensional one in the limit. A reduced-dimension Poisson solver incorporating the dimensionality-reduction formulation is then verified for general 2D Poisson problems. Next, we present the results of several quasi-2D axial-azimuthal simulations performed using the generalized reduced-order electrostatic PIC scheme. We show that the improvements in the formulation of the reduced-order PIC notably augments its predictive capability, enabling the approach to reproduce quite accurately the results from reference full-2D PIC simulations in several conditions using low-order approximations of the 2D problem. Moreover, higher order approximations allow us to recover the same characteristics and behaviors reported in the literature regarding the azimuthal instabilities in Hall thrusters with simulations offering several factors reduction in computational cost. Finally, we discuss a series of sensitivity analyses, including the influence of the cathode boundary condition and the azimuthal domain length on the quasi-2D simulations' predictions. Accordingly, we outline in the conclusions the ongoing activities on the reduced-order scheme toward cost-effective three-dimensional studies of Hall thrusters' physics.

physics.plasm-ph↗

arXiv2022

Dimensionality reduction of Poisson's equation with application to particle-in-cell simulations of Hall thrusters

In this article, we introduce a novel dimensionality reduction formulation for the Poisson's equation in the Vlasov-Poisson system that yields a reduced-order particle-in-cell scheme. This scheme allows a remarkable reduction in the computational cost of self-consistent kinetic simulations of Hall thrusters. The formulation of the dimensionality reduction approach, together with its verification for a general Poisson's problem, is presented. Moreover, we show the results of several "quasi-2D" axial-azimuthal simulations we performed with the conditions of a well-established 2D3V reference case. Comparison between the results of the quasi-2D simulations and the reference case revealed that our method is able to resolve accurately the axial distributions of the intensive plasma parameters. In addition, the characteristics of the azimuthal instabilities observed from the quasi-2D simulation are shown to be closely in line with those reported in the literature. Accordingly, the reduced-order PIC scheme is verified as a viable, low-computational-cost alternative to the traditional multi-dimensional particle-in-cell simulations of Hall thrusters.

physics.comp-ph↗