Plasma Simulation Research Articles

Full-wave and plasma simulations of microstrip excited, high-frequency, atmospheric pressure argon microdischarges

Two-dimensional fully coupled electromagnetic (EM) wave-plasma simulations are used to study the formation, early transient and quasi-steady state of the argon plasma excited by a two-dimensional discontinuous microstrip line. The EM waves that normally propagate in the microstrip transmission line, radiate and scatter at the position of the gap and the electric field is enhanced primarily at the corner of the gap. The microdischarge is preferentially formed at this position of the EM field hotspot and in low frequencies propagates on the dielectric surface, much like a microwave surface streamer. In longer times, diffusion dominates and the whole gap is filled with plasma of maximum density in the order of 1020 while it occupies a volume larger than the gap. Cycle-averaged mean electron temperatures range from 2.8 to 3.9 eV, while the plasma reaches a quasi-static regime in approximately 2 µs having reconfigured the transmission and radiation patterns of the slitted microstrip line. The tunability of the microstrip due to plasma formation provides means for sustaining the discharge in a stable regime. For the same input EM power, the electron temperature increases with increasing excitation frequency while electron densities found to decrease. For the same wave frequency, a decrease of the electron densities with increasing gap is also found in addition to a restriction of the discharge expansion. Finally, thicker dielectrics result to higher electron densities and electron temperatures as well as absorbed power from the plasma. These findings are attributed to the dependence of absorbed EM power and skin depth on the EM wave angular frequency, the critical for shielding electron density as well as the restructuring of the S-parameters due to the changes in operational parameters.

Efficient numerical simulation of atmospheric pulsed discharges by introducing deep learning

Plasma simulation is an important but sometimes time-consuming approach to study the discharge behaviors of atmospheric pulsed discharges. In this work, an efficient simulation method is proposed by introducing deep learning to investigate the discharge characteristics driven by very short pulsed voltages. A loss function is designed and optimized to minimize the discrepancy between the Deep Neural Network (DNN) and the verified fluid model. The prediction data obtained via well-trained DNN can accurately and efficiently reveal the key discharge characteristics, such as the waveforms of discharge current and gap voltage, spatial profiles of charged particles density and electric field. The spatial distributions of charged particles density and electric field obtained from DNN are also given to unveil the underlying mechanisms. Additionally, the predictions from deep learning and the formula analysis both highlight that the breakdown voltage and current density can be effectively reduced by increasing repetition frequency, which quantitatively agrees well with the experimental observations. This study provides a great potential promise for vastly improving the simulation efficiency by introducing deep learning in the field of atmospheric plasmas computation.

Simulation of ion cyclotron resonance heating by using particle-in-cell method in MPS-LD linear plasma device

The auxiliary heating of electrons and ions in linear plasma devices (LPDs) is necessary to achieve the boundary plasma relevant environment of tokamaks, to investigate the boundary physics and plasma—material interactions. In this work, the simulation of ion cyclotron resonance heating (ICRH) in the LPD multiple plasma simulation linear device (MPS-LD) is carried out by using a 3D particle-in-cell method, and the wave—ion interaction mechanism based on a ‘beach-heating’ technique in the ion heating region is investigated. A left-handed, circularly polarized wave along the magnetic field lines is used to represent the electromagnetic wave in the model, after the analysis of the cold plasma dispersion relation. The mechanism of ion heating by collisionless damping absorption is demonstrated and explained by using the plasma current as the plasma response. The dependencies of the heating efficiency on the plasma density, magnetic field strength and magnetic field configuration are studied. The correlation between plasma density and magnetic field strength, which satisfies the heating efficiency, is found and it is in perfect agreement with the theoretical derivation. Finally, by using the designed parameters of MPS-LD provided by SOLPS-ITER, the prediction of ICRH is performed. The simulation result shows that the ion temperature can be heated higher than 40 eV and it satisfies the requirement for scrape-off layer/divertor simulation experimentally in MPS-LD.

Advances in the Implementation of the Exactly Energy Conserving Semi-Implicit (ECsim) Particle-in-Cell Method

The energy-conserving semi-implicit (ECsim) method presented by the author in 2017, is a particle-in-cell (PIC) algorithm for the simulation of plasmas. Energy conservation is achieved within a semi-implicit formulation that does not require any non-linear solver. A mass matrix is introduced to linearly express the particle-field coupling. With the mass matrix, the algorithm preserves energy conservation to machine precision. The construction of the mass matrix is the central nature of the method and also the main cost of the computational cycle. Here, three methods that modify the construction of the mass matrix are analyzed. First, the paper considers how the sub-cycling of the particle motion modifies the mass matrix. Second, a form of smoothing that reduces the noise while retaining exact energy conservation is introduced. Finally, an approximation of the mass matrix is discussed that transforms the ECsim scheme to the implicit moment method.

Decreasing ultrafast x-ray pulse durations with saturable absorption and resonant transitions.

Saturable absorption is a nonlinear effect where a material's ability to absorb light is frustrated due to a high influx of photons and the creation of electron vacancies. Experimentally induced saturable absorption in copper revealed a reduction in the temporal duration of transmitted x-ray laser pulses, but a detailed account of changes in opacity and emergence of resonances is still missing. In this computational work, we employ nonlocal thermodynamic equilibrium plasma simulations to study the interaction of femtosecond x rays and copper. Following the onset of frustrated absorption, we find that a K-M resonant transition occurring at highly charged states turns copper opaque again. The changes in absorption generate a transient transparent window responsible for the shortened transmission signal. We also propose using fluorescence induced by the incident beam as an alternative source to achieve shorter x-ray pulses. Intense femtosecond x rays are valuable to probe the structure and dynamics of biological samples or to reach extreme states of matter. Shortened pulses could be relevant for emerging imaging techniques.

Assessment of the electron-proton energy relaxation rates extracted from molecular dynamics simulations in weakly-coupled hydrogen plasmas.

Electron-proton energy relaxation rates are assessed using molecular dynamics (MD) simulations in weakly-coupled hydrogen plasmas. To this end, we use various approaches to extract the energy relaxation rate from MD-simulated temperatures, and we find that existing extracting approaches may yield results with a sizable discrepancy larger than the variance between analytical models, which is further verified by well-known case studies. Present results show that two of the extracting approaches can produce identical results, which is attributed to a proper treatment of relaxation evolution. To discriminate the use of various methods, an empirical criterion with respect to initial plasma temperatures is proposed, which can self-consistently explain the cases considered. In addition, for a transient electron-proton plasma, we show that it is possible to extrapolate the Coulomb logarithm from that derived by initial plasma parameters in a single MD calculation, which is reasonably consistent with previous MD data. Our results are helpful to obtain accurate MD-based energy relaxation rates.

High resolution finite volume method for kinetic equations with Poisson brackets

Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral relation for Poisson brackets to solve the Liouville equation, the most fundamental kinetic equation. The proposed scheme conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. Other types of kinetic equations may be also formulated in terms of Poisson brackets and solved with the proposed method including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance, since the high energy SEPs produce radiation hazards. The proposed scheme is demonstrated to be accurate and efficient, which makes it applicable to global simulation systems analyzing space weather.

Algorithm for computing the electron-positron yield from the linear Breit-Wheeler process in high-intensity laser-plasma interactions

High-intensity laser-plasma interactions have been shown to generate dense populations of gamma-rays, so these interactions are expected to generate electron-positron pairs via binary photon collisions (linear Breit-Wheeler process). However, particle-in-cell (PIC) codes that are used for studies of laser plasma interactions are not yet equipped to compute the yield from the linear Breit-Wheeler process. We present a post-processing algorithm that allows one to quickly calculate the yield of the linear Breit-Wheeler process inside a photon-emitting plasma using PIC simulation data. The algorithm splits the PIC computational domain into smaller sub-domains whose shape and size are determined based on a specific problem. The photons emitted within each sub-domain are grouped into collimated mono-energetic beams called beamlets. The algorithm computes the yield by evaluating beamlet-beamlet collisions without the spatial integration over the interaction region. Presented benchmarking shows that the computational time is reduced by two orders of magnitude compared to the direct approach that involves the spatial integration, while the resulting error in the total yield remains around 10%. We also show how the algorithm can be leveraged to compute the density of the pair-producing events and the positron momentum distribution at the time of their creation. The ability of our algorithm to quickly compute the pair yield makes it a useful tool for studies of high-intensity laser-plasma interactions. It can also be useful for testing future implementations of the linear Breit-Wheeler process into plasma simulation codes.

High-efficient particle-in-cell/Monte Carlo model for complex solution domain andsimulation of anode layer ion source

Plasma simulation is important in studying the plasma discharge systematically, especially the anode layer ion source which has the complex geometrical characteristics of the discharge structure. However, owing to the complex solution domain formed by the geometric profile of the anode and cathode, the traditional simulation models show extremely small computational efficiency and poor convergence. This work presents a separate simulation for the ion source structure and the plasma discharge, separately, where the cathode geometric parameters (including the size, the shape and the relative position of the inner and outer cathodes) are simplified into two magnetic mirror parameters (the magnetic mirror ratio <i>R</i><sub>m</sub> and the magnetic induction intensity in the center of the magnetic mirror <i> <b>B</b> </i><sub>0</sub>), and then a high-efficient particle-in-cell/Monte Carlo collision (PIC/MCC) model is established to improve the computational efficiency and stability of the plasma simulation later. As a result, the convergence time of the plasma simulation is shortened significantly from 1.00 μs to 0.45 μs, and by which the influences of the geometrical characteristics of the discharge structure on the plasma properties are systematically studied. The simulation results reveal that magnetic mirror with <i>R</i><sub>m</sub> = 2.50 and <i> <b>B</b> </i><sub>0</sub> = 36 mT can best confine the plasma in the central area between the inner cathode and outer cathode. When the discharge center of the plasmacoincides with the magnetic mirror center, the anode layer ion source presents both high density output of ion beam current and significantly reduced cathode etching, suggesting that the best balance is obtained between the output and cathode etching.

Cross section sets and transport parameters for Ar+ ions in CF4 gas

Understanding plasma distribution, characteristics and phenomena is important for the development and optimization of semiconductor device manufacturing plasma equipment, such as etching and deposition tools. For this reason, plasma simulation is currently being utilized at every stage of equipment design, development and improvement. The cross section sets obtained by applying Denpoh-Nanbu theory to Ar+ on CF4 collisions were found to be in general qualitative and in part quantitative agreement with data from the literature. The Monte Carlo technique was applied to perform calculations of transport parameters. Calculated cross sections can be used to obtain transport coefficients, specially drift velocity, characteristic energy, reduced mobility, longitudinal diffusion and rate coefficients for low and moderate reduced electric fields E/N (E-electric field strength; N-gas density) and accounting for the non-conservative collisions.

Collision rates estimated from exact N-body simulations of a one-dimensional plasma

In a plasma, the charged particles interact via long-range forces, and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible, while collective effects dominate the dynamics. In contrast, when g≈1 collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the two-stream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations.

Simulation of dense aluminum plasma under intense x-rays

We used the THERMOS code to calculate properties of hot dense aluminum plasma created and probed by ultrashort intense X-ray pulses generated by a free-electron laser at the LCLS facility. In our simulations we accented on taking into account the ionization potentials depression and considered both the stationary and non-stationary approaches. The calculation results reproduced the main experimental observations qualitatively and were in good agreement with other published simulations. As it turned out, despite the shortness of the X-ray impact, the non-stationary effects were rather negligible in contrast to those of the ionization potentials depression.

Grid-point requirements for direct kinetic simulation of weakly collisional plasma plume expansion

Direct kinetic solvers enable high-fidelity simulation of multiscale plasmas in a number of applications including space physics and propulsion, materials processing, astrophysics, and nuclear fusion. While they eliminate the statistical noise associated with particle-in-cell methods, they are associated with higher dimensionalities. Thus, a detailed understanding of grid-point requirements is required to design efficient meshes so that direct kinetic solvers can be feasibly employed in general settings without compromising on predictivity. The grid-point requirements of a direct kinetic solver employing the Vlasov-Poisson-BGK equations are characterized using an electrostatic and weakly collisional plasma plume expansion model problem, which is unsteady and spatially inhomogeneous with significant deviations from equilibrium. It is demonstrated that at least two to four points per the appropriate Debye length and thermal velocity are necessary to resolve macroscopic density gradients and thus the lowest-order macroscopic quantities, with more stringent requirements for higher-order quantities. Local charge separation and the distribution function itself require at least an additional order of magnitude in resolution for comparable accuracy, as they require the resolution of gradients in the distribution function. Collisions impede plume expansion and introduce secondary flow and field structures, but do not significantly relax the grid requirements despite their smoothing action in velocity space. While specific numerical requirements necessarily depend on the solver, plasma configuration, and collision model, trends in the variation of the elucidated grid-point requirements with the quantity of interest and plasma collisionality can be generalizable across problems with comparable physics. Knowledge of similarly derived trends can contribute to efficient direct kinetic simulation of unsteady and spatially inhomogeneous plasmas of a variety of configurations and collisionalities.

A phase-shift-periodic parallel boundary condition for low-magnetic-shear scenarios

We formulate a generalized periodic boundary condition as a limit of the standard twist-and-shift parallel boundary condition that is suitable for simulations of plasmas with low magnetic shear. This is done by applying a phase shift in the binormal direction when crossing the parallel boundary. While this phase shift can be set to zero without loss of generality in the local flux-tube limit when employing the twist-and-shift boundary condition, we show that this is not the most general case when employing periodic parallel boundaries, and may not even be the most desirable. A non-zero phase shift can be used to avoid the convective cells that plague simulations of the three-dimensional Hasegawa–Wakatani system, and is shown to have measurable effects in periodic low-magnetic-shear gyrokinetic simulations. We propose a numerical program where a sampling of periodic simulations at random pseudo-irrational flux surfaces are used to determine physical observables in a statistical sense. This approach can serve as an alternative to applying the twist-and-shift boundary condition to low-magnetic-shear scenarios, which, while more straightforward, can be computationally demanding.

On the curvature invariants of the massive Banados–Teitelboim–Zanelli black holes and their holographic pictures

In this paper, the curvature structure of a ([Formula: see text])-dimensional black hole in the massive-charged-Born–Infeld gravity is investigated. The metric that we consider is characterized by four degrees of freedom which are the mass and electric charge of the black hole, the mass of the graviton field, and a cosmological constant. For the charged and neutral cases separately, we present various constraints among scalar polynomial curvature invariants which could invariantly characterize our desired space–times. Specially, an appropriate scalar polynomial curvature invariant and a Cartan curvature invariant which together could detect the black hole horizon would be explicitly constructed. Using algorithms related to the focusing properties of a bundle of light rays on the horizon which are accounted for by the Raychaudhuri equation, a procedure for isolating the black hole parameters, as the algebraic combinations involving the curvature invariants, would be presented. It will be shown that this technique could specially be applied for black holes with zero electric charge, contrary to the cases of solutions of lower-dimensional nonmassive gravity. In addition, for the case of massive ([Formula: see text])-dimensional black hole, the irreducible mass, which quantifies the maximum amount of energy which could be extracted from a black hole would be derived. Therefore, we show that the Hawking temperatures of these black holes could be reduced to the pure curvature properties of the space–times. Finally, we comment on the relationship between our analysis and the novel roles it could play in numerical quark–gluon plasma simulations and other QCD models and also black hole information paradox where the holographic correspondence could be exploited.

New applications for the Boris Spectral Deferred Correction algorithm for plasma simulations

The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a particle pusher in an electrostatic particle-in-cell (PIC) code can, at least in the linear regime, improve simulation accuracy compared with the standard second order Boris method. In some instances, the higher order of Boris-SDC even allows a much larger time step, leading to modest computational gains. Second, we propose a modification of Boris-SDC for the relativistic regime. Based on an implementation of Boris-SDC in the RUNKO PIC code, we demonstrate for a relativistic Penning trap that Boris-SDC retains its high order of convergence for velocities ranging from 0.5c to >0.99c.

1D model of tokamak scrape-off layer and divertor plasmas: Dimensionless parameters and the results of numerical simulations

Solutions of a 1D model of the scrape-off layer and a divertor plasma in a tokamak are analyzed on the basis of dimensionless parameters governing the physics of both plasma and neutral transport and atomic physics processes. Numerical simulations based on fluid plasma and Monte Carlo neutral modeling confirm earlier results obtained with simplified analytic considerations and numerical simulations performed with fluid neutral description and demonstrate bifurcation of plasma parameters. These simulations also confirm that the major physical reasons for the rollover of the plasma flux to the target, which is the key feature of the phenomenon of divertor plasma detachment, are the impurity radiation loss and plasma recombination. It is suggested that simulations of the edge plasma based on dimensionless parameters provide a powerful tool for checking the consistency of the physics incorporated in existing complex 2D codes used for edge plasma modeling.

Ultra long turbulent eddies, magnetic topology, and the triggering of internal transport barriers in tokamaks

Local nonlinear gyrokinetic simulations of tokamak plasmas demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns when the magnetic shear is very small. By accurately modeling different field line topologies (e.g. low-order rational, almost rational, or irrational value of the safety factor), we show that the self-interaction of such ‘ultra long’ eddies can dramatically reduce heat transport. This extreme sensitivity of turbulent transport to the safety factor reveals novel strategies to improve confinement, constitutes experimentally testable predictions, and illuminates past observations of internal transport barriers.

Overview of initial negative triangularity plasma studies on the ASDEX Upgrade tokamak

An overview of results of negative triangularity (NT) studies from the ASDEX Upgrade tokamak (AUG) is given. Moderate values of the triangularity in the range of δ average ≈ −0.2 have been obtained. Results from both unfavorable and favorable magnetic configuration in terms of high-confinement mode (H-mode) access are presented. In unfavorable configuration, the ion grad B drift points away from the active x-point, which usually results in a factor of 2 higher power thresholds to enter H-mode. In unfavorable configuration, low-confinement mode (L-mode) operation is confirmed at high auxiliary heating input powers MW at low collisionality. Under these conditions, plasmas with positive triangularity (PT) are usually in H-mode. Highest plasma energies have been obtained using a combination of neutral beam injection, electron- and ion cyclotron resonance heating, where values of the plasma beta of β N ≈ 1.7 have been reached in L-mode. While discharges with mixed auxiliary heating power input show moderate confinement on L-mode levels, plasmas heated with electron cyclotron resonance heating show H-mode like confinement. Operation in favorable configuration, however, leads to H-mode with type-I edge localized modes (ELMs). The power required for the L–H transition is comparable to the typical L–H power threshold in PT cases ( MW), and good confinement of typical PT H-modes is obtained. The ELM frequency is demonstrated to reach 700 Hz. These results show a clear effect of the NT configuration on the ELM behavior in H-modes, and that on AUG, unfavorable configuration is an essential ingredient if H-mode operation is to be avoided in NT plasmas. So far, in all AUG NT plasmas, power degradation is observed. Initial gyrokinetic simulations of the edge plasma in unfavorable configuration reveal the ion-temperature gradient mode as the fastest growing mode with a subdominant trapped-electron-mode.

Benchmark of a self-consistent dynamic 1D divertor model DIV1D using the 2D SOLPS-ITER code

This paper presents DIV1D, a new 1D dynamic physics-based model of the divertor plasma under development to study and control the dynamics of detached plasmas. An innovative feature of DIV1D is that it mimics cross-field transport using an effective flux expansion and includes a neutral gas background outside the divertor leg. We outline a 1D mapping procedure for static 2D SOLPS-ITER simulations of divertor plasmas in the Tokamak á Configuration Variable, which can be used to benchmark 1D codes. For DIV1D good agreement is found for the most important divertor plasma quantities along the leg (e.g., densities temperature, heat flux, and velocity) both in a qualitative and quantitative sense. In addition, the comparison with SOLPS-ITER demonstrates that DIV1D self-consistently captures the evolution of divertor plasma quantities in the main heat flux channel as a function of the upstream plasma density in a scan from 2 to . The agreement is ascribed to the unique account of cross-field transport in DIV1D with an effective flux expansion and the interaction with an external neutral gas background.