Plasma Simulation Research Articles

Three-dimensional boundary turbulence simulations of a RFX-mod plasma in the presence of voltage biasing

Abstract Three-dimensional turbulence simulations of a RFX-mod diverted plasma are performed in the presence of a biasing electrode. The simulations show a strong suppression of turbulent transport caused by the induced E × B flow shear, which leads to the formation of an edge transport barrier with a pedestal-like structure, in qualitative agreement with RFX-mod experiments. The strong E × B flow shear turbulence suppression with edge voltage biasing is also observed in the proximity of the density limit crossing, suggesting that edge voltage biasing may allow for larger maximum achievable density values. By leveraging the simulation results, the theoretical scaling law of the edge pressure gradient length derived in Giacomin & Ricci (2020) J. Plasma Phys. 86(5) is extended here to account for the E × B flow shear turbulence suppression caused by voltage biasing. The improved theoretical scaling with typical RFX-mod shearing rate values predicts a factor of two increase of the pressure gradient at the separatrix, which is comparable to RFX-mod experiments in the presence of voltage biasing. The implications of the flow shear turbulence suppression due to voltage biasing on the density limit in RFX-mod are also discussed.

Applications of multi-GPU computing in large-scale fully kinetic particle-in-cell simulations of space plasma

The rapid development of an emerging computing device, the graphical processing unit (GPU), has significantly enhanced our ability to conduct full kinetic particle-in-cell (PIC) simulations in space physics. In this paper, we propose an approach that leverages multiple GPUs to facilitate large-scale PIC simulations. This method can effectively reduce data transmission frequency and latency during the computing process. The data communication between GPU devices is optimized through a combination of Message Passing Interface (MPI)-NVIDIA Collective Communications Library (NCCL) running pattern. Our implementation surpasses the expected linear acceleration, achieving superior computing performance and operational efficiency. The instances of large-scale PIC simulations are presented based on physical models of magnetic reconnection, plasma turbulence, and quasi-perpendicular shock. The importance of large-scale simulations is demonstrated in terms of grid resolution, macroparticles used per cell, and the mass ratio between ions and electrons. The multi-GPU enabled fully kinetic PIC simulation demonstrates its capability to efficiently handle large-scale PIC simulations as a crucial requirement for the study of space plasma physics.

Kinetic simulations of nuclear burning plasmas in inertial confinement fusions taking into account the large-angle collisions

Although ignition had been achieved at the National Ignition Facility (NIF), recent observations of the experiments indicate novel physics that beyond theoretical predictions emerge, e.g., the neutron analysis of experiments has revealed deviations from the Maxwellian distributions in ion relative kinetic energies of burning plasmas, with the surprising emergence of supra-thermal deuterium and tritium (DT) ions that fall outside the predictions of macroscopic statistical hydrodynamic models. Via our newly developed hybrid-particle-in-cell code, incorporating the newly-proposed model of large-angle collisions, we infer that that this could be attributed to the increased significance of large-angle collisions among DT ions and α-particles in the burning plasma. Extensive and unprecedented kinetic investigations into the implications of large-angle collisions in the burning plasma have yielded several key findings, including an ignition moment promotion by ∼10ps, the presence of supra-thermal ions below an energy threshold, and approximately twice the expected deposition of α-particles densities. The rationality of our findings is confirmed through the congruency between the neutron spectral moment analyses conducted by the NIF and our kinetic simulations, both highlighting progressively widening disparities between neutron spectral moment analyses and hydrodynamics predictions, which becomes more pronounced as the yield increases. Our kinetic simulations with large-angle collisions not only provide novel insights for experiment interpretation but also open new research opportunities for the largely unexplored regime of the nuclear burning plasmas, which are distinguished by their exceptionally high energy densities and hold immense potential for illuminating the intricate physics that underpins the evolution of the early universe.

The Vlasiator 5.2 ionosphere – coupling a magnetospheric hybrid-Vlasov simulation with a height-integrated ionosphere model

Abstract. Simulations of the coupled ionosphere–magnetosphere system are a key tool to understand geospace and its response to space weather. For the most part, they are based on fluid descriptions of plasma (magnetohydrodynamics, MHD) formalism, coupled to an electrostatic ionosphere. Kinetic approaches to modeling the global magnetosphere with a coupled ionosphere system are still a rarity. We present an ionospheric boundary model for the global near-Earth plasma simulation system Vlasiator. It complements the magnetospheric hybrid-Vlasov simulations with an inner boundary condition that solves the ionospheric potential based on field-aligned current and plasma quantities from the magnetospheric domain. This new ionospheric module solves the ionospheric potential in a height-integrated approach on an unstructured grid and couples back to the hybrid-kinetic simulation by mapping the resulting electric field to the magnetosphere's inner boundary. The solver is benchmarked against a set of well-established analytic reference cases, and we discuss the benefits of a spherical Fibonacci mesh for use in ionospheric modeling. Preliminary results from coupled global magnetospheric–ionospheric simulations are presented, showing formation of both Region 1 and Region 2 current systems.

Characterization of uncertainties in electron-argon collision cross sections

Abstract The predictive capability of a plasma discharge model depends on accurate representations of electron-impact collision cross sections, which determine the corresponding reaction rates and electron transport properties. The values of cross sections can be known only approximately either through experiments or simulations and are thus subject to uncertainties. Quantifying the uncertainties in plasma simulations allows us to assess the reliability of simulations and to provide a basis for interpreting discrepancies between simulations and experiments. For such uncertainty quantification of plasma simulations, it is essential to quantify the uncertainties of the underlying cross sections. Although much effort has been committed to calibrate the cross section values, their uncertainties are not well investigated. We characterize uncertainties in electron-argon atom collision cross sections using a Bayesian framework. Six collision processes—elastic momentum transfer, ionization, and four excitations—are characterized with semi-empirical models, which effectively capture the features important to the macroscopic properties of the plasma. A probability model for the uncertain parameters of these semi-empirical models is developed. Specifically, a Gaussian-process likelihood model is proposed to capture discrepancies among data sets, as well as the model-form inadequacies of the semiempirical models. Two other likelihood models are compared with the proposed Gaussian-process model, to illustrate the importance of the choice of the likelihood model. The cross section models are calibrated using the electron-beam experiments and ab-inito quantum simulations. The resulting calibrated uncertainties capture well the scattering among the data sets. The calibrated cross section models are further validated against swarm-parameter experiments and zero-dimensional Boltzmann equation simulations of widely used cross section datasets.

SOLEDGE3X full vessel plasma boundary simulations of ITER non-active phase plasmas

Abstract The onset of detachment in the ITER machine is analyzed in this work through the help of 2D-axisymmetric boundary plasma simulations with the SOLEDGE3X-EIRENE code, which features a numerical domain for the plasma solver extending up to the first wall. The plasma boundary is computed in scenarios from the first non-active phase of ITER, in pure H and at 20 MW. This set of simulations is used in two aspects: first, to study the plasma detachment in the divertor, and second, the plasma conditions, fluxes, and beryllium erosion at the first wall. Here, the code results are also compared to those obtained with the well-established SOLPS-ITER code, which includes a plasma numerical domain only covering the main SOL. Results show an increase in the SOL width $\lambda_q$ with increasing density, and a detailed analysis is carried out, for the first time, on each of the different plasma-neutral interactions in the code's physics model in EIRENE. The gross beryllium erosion rates of first wall panels are estimated from 2D simulations, with the aim of assessing their sensitivity to two parameters: the divertor density regime, and the presence of density shoulders in the far-SOL formed by enhanced perpendicular transport at this location. The erosion contributions from neutrals and ions are considered in each case, and the charge-exchange atoms fluxes and energy distributions are provided, highlighting the two atom populations (cold and charge-exchange).

Simulation of a pulsed CO2 plasma based on a six-temperature energy approach

Abstract Recent time-resolved measurements of gas and vibrational temperatures in pulsed glow discharges have fostered the development and validation of detailed kinetic models to understand the underlying heating dynamics. The models published so far have been successful in identifying the fundamental processes underlying vibrational and gas heating in pure CO2 discharges; however, this has come at the cost of including vibrational kinetics with thousands of reactions. This makes these models not compatible with self-consistent computational fluid dynamics (CFDs) codes, which are needed to develop new plasma reactors operating at high pressures or with complex flow patterns and capture the relevant dynamics in multi-dimension. In this work, we solve separate energy balance equations for the asymmetric and symmetric vibrational modes of CO2, as well as for the vibrational modes of CO and O2, the gas temperature, and the electron temperature, making it a six-temperature (6 T) plasma model. This eliminates the need to include a vast array of vibrational levels as separate species, drastically reducing the number of reactions in the model. The model is compared with experimental measurements conducted in a pulsed CO2 glow discharge at 6.7 mbar. Excellent agreement is observed for the temporal evolution of the vibrational and gas temperatures, confirming that our approach is suitable for modeling systems under significant non-equilibrium conditions, paving the way for coupling detailed CO2/CO/O2/O kinetics with CFD codes.

Analyzing the potential of ion chambers to measure laser-induced ionization rates.

We demonstrate and analyze the use of an ion chamber for measuring laser-induced ionization in cesium gas for the first time, which is of recent interest due to research in diode pumped alkali lasers (DPALs). In this report, the viability of an ion chamber diagnostic with high plasma density and ionization localized to a laser beam is investigated. A simulation of the laser-induced plasma in the ion chamber, based on the Thomson model with diffusion, is developed and will be shown to display similar qualitative behavior to measurements, and bound test results within model uncertainty. The analysis will show that complex processes occur: (1) space-charge limited ion drift, (2) Debye shielding preventing the electric field from penetrating a bulk plasma region, and (3) ambipolar diffusion across the bulk with possibly elevated electron temperature. However, these processes are well understood and do not limit the accuracy of an ion chamber diagnostic for laser-induced ionization rate measurement.

Predictive nonlinear MHD simulations of quiescent H-mode plasma in the HL-3 tokamak

Predictive nonlinear MHD simulations of quiescent H-mode plasma in the HL-3 tokamak

Step-by-step verification of particle-in-cell Monte Carlo collision codes

The particle-in-cell (PIC) method with Monte Carlo collisions (MCC) is widely used in the simulation of non-equilibrium plasmas for electric propulsion and laboratory applications. Due to the simplicity of the basic PIC algorithm and the specific modeling needs of the different research groups, many codes have been independently developed. Verification of these codes, i.e., ensuring that the computational code correctly implements the intended mathematical models and algorithms, is of fundamental importance. Different benchmark cases, such as one from Turner et al. [Phys. Plasmas 20, 013507 (2013)], Charoy et al. [Plasma Sources Sci. Technol. 28, 105010 (2019)], and Villafana et al. [Plasma Sources Sci. Technol. 30, 075002 (2021)], have been published in recent years. These have consisted of a complex physical setup, in which many computation modules interact to yield the final result. Although this approach has the advantage of testing the code in a realistic case, it may hide some implementation errors. Moreover, in the case of disagreement, the previous works do not provide an easy way to identify the faulty code modules. In this work, we propose a step-by-step approach for the verification of PIC-MCC codes in a 2D-3V electrostatic setup. The criteria for the test cases are (i) they should highlight possible implementation errors by testing the modules separately, whenever possible (ii) they should be free from physical instabilities to avoid chaotic behavior, and (iii) the numerical result should be accompanied by analytical calculations, for confirmation purposes. The seven test cases identified all show excellent agreement between the authors' codes.

Interplay among various cavity modes in a microwave plasma system with well-defined cavity geometry

In an experimental microwave ion source plasma system with a well-defined cavity geometry, multiple cavity resonant mode excitations have been observed. The interactions among these modes can influence microwave coupling to the plasma, enhance plasma uniformity, and affect plasma oscillations. The superposition of closely spaced cavity resonant modes leads to a temporal modulation of the plasma due to the beating effect between pairs of modes. As a result, a new range of plasma oscillations is recorded at the same modulation frequency. This modulation is confirmed by the experimentally measured frequency emission spectra and the accumulation of hot electrons within the plasma-filled cavity. The plasma's resonance with the modulated wave contributes to an increase in the hot electron population. Additionally, the phenomenon of parametric decay (PD) can help explain the rise in hot electron populations in over-dense plasma. The frequency emission spectra show evidence of ion acoustic waves, whose daughter electrostatic waves are resulting from the PD. These appear as two sideband frequency peaks around each excited cavity mode frequency, adhering to the frequency and k-vector selection rules. The observed daughter wave peaks are identified as ion acoustic waves. All experimental findings have been further supported by analytical calculations and microwave plasma simulations conducted using the Finite Element Method in COMSOL Multiphysics software. This paper highlights the temporal phase modulation and the PD phenomena induced by the excitation of different closely spaced cavity modes around the broadly launched microwave frequency of approximately 200 MHz at 2.45 GHz and their interactions.

Simulation of plasma and neutral transport in PISCES-RF using SOLPS-ITER*

Abstract In this research, the fluid plasma transport code SOLPS-ITER is applied and validated against experimental data from the plasma interaction surface component experimental station (PISCES)-RF linear plasma device to establish a physics basis for plasma and neutral transport in its two magnetic field (B-field) geometry setups-(1)the cusp and (2) non-cusp or linear B-field. The main focus of this study is to understand (1) radial plasma transport (2) heat and particle loads on the upstream dump and downstream target plate, and (3) the physics of plasma-neutral interactions in PISCES-RF. The simulation setup adheres to typical PISCES-RF experimental conditions, with a 2D helicon power deposition profile as an input heating source. SOLPS-ITER simulations reproduce experimental conditions with the Bohm diffusion model for both B-field configurations of the PISCES-RF experiment. Major energy loss channels include neutral radiation and power deposited on the wall and dump plate, with only 1 % of the input power reaching the target. The ionization front is well confined near the dump plate due to the heating and puffing regions. Additionally, SOLPS-ITER simulation results are also found to be in very good agreement with the particle-in-cell calculations using the code-PICOS++ which supports the validity of SOLPS in low collisionality regime.

Collision Frequency and Energy Transfer Rate in e–He Scattering

Using the optical interaction potential between an electron and a helium atom, we have calculated the momentum-transfer cross-section, collision frequency, and energy transfer rate during elastic electron–helium scattering, focusing on energies up to the ionization threshold of helium (24.6 eV). The interaction potential includes static, polarization, and exchange contributions, accurately representing the scattering process in this range. The optical potential method is well-suited for this analysis, as it effectively reduces the complexity of multiparticle interactions while maintaining the essential physics of elastic scattering. The calculated collision frequency as a function of energy exhibits a distinct maximum near 5 eV, consistent with experimental observations, which has not been captured in earlier theoretical studies. The energy transfer rate, derived using the effective collision frequency, demonstrates efficient energy exchange at low electron energies, with a gradual decline as the energy approaches the ionization threshold. These findings offer critical insights into plasma processes in the diverter region of tokamaks, where helium atoms play a significant role, and contribute to modeling energy transport properties such as electron mobility and temperature equilibrium. The results can serve as a valuable reference for plasma simulations and fusion research applications.

EMC3-EIRENE simulations of edge plasma and impurity transport by toroidally localized argon seeding on CFETR X-divertor

Abstract Three-dimensional (3D) Edge Monte Carlo transport code EMC3-EIRENE has been employed to study edge plasma and impurity transport with toroidally localized argon seeding on Chinese fusion engineering testing reactor (CFETR) X-divertor configuration. The argon impurity seeded at different poloidal locations has been investigated to evaluate the varied profile of the main plasma in the scrape-off layer (SOL) and on the divertor targets, which shows a strong dependence on the poloidal position of argon gas puffing. The argon impurity seeded at the upstream SOL regions can result in a toroidally asymmetric distribution of electron density and temperature, while a toroidally symmetric distribution is obtained for argon seeded at the strike point regions. The deposition pattern of electron density and temperature shows the several lobe-like and island-like structures on the 3D divertor targets of CFETR with upstream argon injections, whereas the perturbed profile is achieved for argon seeding at the strike point regions. In order to verify the toroidal asymmetry of heat loads distribution, the argon impurity seeded at different poloidal locations has been investigated to estimate its influence on toroidal heat loads on divertor plates. The argon injected at the strike point regions gives rise to a toroidal asymmetry of heat loads distribution on divertor targets, while a toroidal symmetry of heat loads distribution is gained for argon injected at the upstream SOL locations.

Mechanism Analysis of Bubble Discharge Within Silicone Gels Under Pulsed Electric Field.

Silicone gel, used in the packaging of high-voltage, high-power semiconductor devices, generates bubbles during the packaging process, which accelerates the degradation of its insulation properties. This paper establishes a testing platform for electrical treeing in silicone gel under pulsed electric fields, investigating the effect of pulse voltage amplitude on bubble development and studying the initiation and growth of electrical treeing in a silicone gel with different pulse edge times. The relationship between bubbles and electrical treeing in silicone gel materials is discussed. A two-dimensional plasma simulation model for bubble discharge in silicone gel under pulsed electric fields is developed, analyzing the internal electric field distortion caused by the response times of different ions and electrons. Additionally, the discharge current and its effects on silicone gel under pulsed electric fields are examined. By studying the influence of different pulse edge times, repetition frequencies, and temperatures on discharge current magnitude and ozone generation rates, the impact of electrical breakdown and chemical corrosion on the degradation of organic silicone gel under various operating conditions is analyzed. This study explores the macroscopic and microscopic mechanisms of dielectric performance degradation in organic silicone gel under pulsed electric fields, providing a basis for research on high-performance packaging materials and the development of high-voltage, high-power semiconductor devices.

Plasma and Flow Simulation of the Ion Wind in a Surface Barrier Discharge Used for Gas Conversion Benchmarked by Schlieren Imaging

Surface dielectric barrier discharges (sDBD) are efficient and scalable plasma sources for plasma-based gas conversion. One prominent feature of an sDBD is the generation of an ion wind, which exerts a force on the neutrals, thus leading to an efficient mixing of plasma and a passing gas stream. This becomes apparent by the creation of upstream and downstream vortices in the vicinity of the plasma. In this study, these vortices are generated by high voltage burst pulses consisting of two half cycles of an almost sinusoidal voltage shape. The vortices are monitored by Schlieren imaging diagnostic to benchmark and connect two simulations of the sDBD: a plasma model simulating a streamer for 25 ns starting from the electrode and propagating along a dielectric surface followed by a decay. The streamer is the source of electrical charges accelerated as ion wind by the applied electric field from the sDBD power supply. A second flow simulation models this ion wind as a time-averaged thrust acting on the passing gas stream. The conversion of the time-resolved forces from the nanosecond plasma simulation into the steady state thrust in the flow simulation indicates that the force from the plasma lasts much longer than the actual streamer propagation phase. This is explained by the fact that the charges in the streamer channel remain present for almost 100 ns, and the voltage from the power supply lasts for a few microseconds being applied to the electrode so that ions in the streamer channel are still accelerated even after a streamer stops to propagate after a few ns. The thrust generated during the streamer phase, including the relaxation phase, agrees well with predictions from flow simulation. Additionally, properly converting the time-resolved forces from the plasma simulation into a time-averaged thrust for the flow simulation yields exactly the synthetic Schlieren images as measured in the experiments.

Latent space dynamics learning for stiff collisional-radiative models

Abstract In this work, we propose a data-driven method to discover the latent space and learn the
corresponding latent dynamics for a collisional-radiative (CR) model in radiative plasma
simulations. The CR model, consisting of high-dimensional stiff ordinary differential
equations (ODEs), must be solved at each grid point in the configuration space, leading
to significant computational costs in plasma simulations. Our method employs a physicsassisted
autoencoder to extract a low-dimensional latent representation of the original CR
system. A flow map neural network is then used to learn the latent dynamics. Once trained,
the reduced surrogate model predicts the entire latent dynamics given only the initial condition
by iteratively applying the flow map. The radiative power loss is then reconstructed
using a decoder. Numerical experiments demonstrate that the proposed architecture can
accurately predict both the full-order CR dynamics and the radiative power loss rate.

Simulations of divertor designs that spatially separate power and particle exhaust using mid-leg divertor particle pumping

Simulations of divertor designs that spatially separate power and particle exhaust using mid-leg divertor particle pumping

Laboratory Simulations of Plasma Generated Around the Atmospheric Reentry Spacecraft

In this paper, plasma will be generated in a laboratory as a simulation of what happens to spacecraft when they enter the atmosphere of Earth. Parameters of plasma generation were determined in terms of pressures of 0.1, 0.2, 0.3, 0.4, and 0.5 mbar and generation energy 200 W. The parameters of the generated plasma were calculated using the optical emission spectroscopy two intensity ratio method, and the electron temperature, electron density, Debye length, and plasma frequency were calculated. Compare the results with the actual results, electron temperatures were 2.26–1.71 eV and plasma frequency 8.09 x1011-6.7x1011 at 0.1-0.5 mbar pressure.

Data-driven inference of high-dimensional spatiotemporal state of plasma systems

Many plasma systems and technologies, such as Hall thrusters for spacecraft propulsion, exhibit complex underlying physics that affect the global operation. When characterizing such systems in an experiment, obtaining full spatiotemporal maps of the involved state variables can be, thus, highly informative. However, this goal is not practically realizable because of various experimental limitations, e.g., finite spatial resolution of the diagnostics and geometrical accessibility constraints. Therefore, having the capability to reconstruct the full high-dimensional states of plasma systems from low-dimensional time-history measurements is greatly desirable. Compressed sensing is a signal processing technique that can answer this crucial need. However, existing compressed sensing approaches have several limitations that restrict their effectiveness for complex physical systems like plasma technologies. These include the need for abundant sensor measurements and a principled sensor placement. In this paper, we demonstrate the capabilities of Shallow Recurrent Decoder (SHRED) architecture for compressed sensing. We show in several plasma test cases that SHRED can robustly infer full high-dimensional spatiotemporal state vectors of these systems (i.e., all macroscopic plasma properties) from minimal system information. This minimal information can consist of three finite time-history measurements of either local values of a plasma property or the global plasma properties (spatially averaged or performance parameters). An application of SHRED's inference capability in the numerical plasma simulation context is “super-resolution” enhancement. We will discuss this application by presenting how SHRED can effectively establish mappings between a low-resolution and a high-resolution simulation, recovering detailed spatial plasma features that are below the simulation's grid size.