Plasma Solver Research Articles

Pressure Based Compressible Solver for Electric Arc-plasma Simulation

The electric arc discharge in a liquid medium is used in several applications such as the sterilization of the liquid by UV radiation, the fracturing of rocks by shock wave, the circuit breakers in oil bath or the forming of mechanical parts. Thus, describing the physics of the arc in a liquid and in particular its interaction with a liquid interface is an important issue to better characterize this type of configuration. However, such a challenging task requires to couple high-fidelity solver for compressible two-phase flows with liquid phase change and a plasma solver to describe the plasma and its interaction with the bubble. To study this type of medium, we use a compressible formulation of the fluid equations. For this purpose, a pressure based solver has been developed for the computation of the energy conservation equation. Moreover, our numerical model uses the immersed boundary method to simulate the solid electrodes. The numerical model is briefly described in this paper and the first results of the electric arc discharge in steam water are presented. To our knowledge this pressure based model has never been used to describe plasmas and electric arc discharge.

Numerical modeling of plasma assisted ignition of CH4/O2/He mixture by the nanosecond repetitive pulsed surface dielectric barrier discharge

A nanosecond repetitive pulsed surface dielectric barrier discharge (NRP-SDBD) is a promising method for generation of non-equilibrium plasma with more kinetic activity. This paper presents numerical studies on the effects of pulse repetition frequency (PRF) on low temperature ignition of lean and stoichiometric CH4/O2/He mixture in NRP-SDBD plasma. A skeletal plasma kinetics mechanism is primary developed and calibrated, to mitigate the computationalloads of modeling SDBD discharge by the two-dimensional plasma solver PASSKEy coupled with Poisson's equation. The discharge current was well predicted, meanwhile the sequential and spatial reduced electric field (E/N) is revealed as the ionization wave propagates forward. Special attention is placed on time-evolution of electric field strength used as inputs in simulation of plasma assisted ignition (PAI) conducted by zero-dimensional ZDPlasKin-CHEMKIN code. The principle of PAI on lean and stoichiometric CH4/O2/He mixture via varied PRF is analyzed in details from view of plasma kinetics and chemical kinetics. Ultimately, the important role of plasma active species O, O(1D), O2(a1Δg) on promoting ignition chain reactions is highlighted. It is also concluded that high PRF is beneficial for the accumulation of short lifetime species such as CH4(v13) and O(1D), which participate in the formation of important intermediate CH3.

The Effects of Nonequilibrium Velocity Distributions on Alfvén Ion-cyclotron Waves in the Solar Wind

In this work, we investigate how the complex structure found in solar wind proton velocity distribution functions (VDFs), rather than the commonly assumed two-component bi-Maxwellian structure, affects the onset and evolution of parallel-propagating microinstabilities. We use the Arbitrary Linear Plasma Solver, a numerical dispersion solver, to find the real frequencies and growth/damping rates of the Alfvén modes calculated for proton VDFs extracted from Wind spacecraft observations of the solar wind. We compare this wave behavior to that obtained by applying the same procedure to core-and-beam bi-Maxwellian fits of the Wind proton VDFs. We find several significant differences in the plasma waves obtained for the extracted data and bi-Maxwellian fits, including a strong dependence of the growth/damping rate on the shape of the VDF. By applying the quasilinear diffusion operator to these VDFs, we pinpoint resonantly interacting regions in velocity space where differences in VDF structure significantly affect the wave growth and damping rates. This demonstration of the sensitive dependence of Alfvén mode behavior on VDF structure may explain why the Alfvén ion-cyclotron instability thresholds predicted by linear theory for bi-Maxwellian models of solar wind proton background VDFs do not entirely constrain spacecraft observations of solar wind proton VDFs, such as those made by the Wind spacecraft.

Electron-scale current sheets and energy dissipation in 3D kinetic-scale plasma turbulence with low electron beta

Abstract 3D kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is βe = 0.1 for electrons and βi = 1 for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth’s magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (SPS) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure-strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20% of the total volume. Some of the current sheets corresponding to the largest pressure-strain interaction are found to be associated with Alfvénic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about 1% of all the current sheets identified.

Numerical investigation of the spark discharge process in a crossflow

The present study numerically investigates the spark discharge process under crossflow conditions using a thermal equilibrium plasma solver that fully couples the electromagnetic physics and fluid dynamics in a computational framework. Numerical results are validated by the comparison with experimental data. The spark discharge experiment is performed in a constant volume vessel using an inductive coil ignition system for automotive applications, and the evolution of the spark channel is measured using high-speed imaging. The crossflow in the gap between the spark-plug electrodes is generated by a rotating fan with two different fan speeds, and the flow velocity across the gap is characterized by particle image velocimetry (PIV) measurement. A computational fluid dynamics (CFD) solver is employed to simulate the crossflow and provide the flow field variables (velocity, pressure, temperature) to the plasma solver. The crossflow velocity predicted in the flow simulation agrees well with the PIV data in that the non-uniform velocity profiles at monitoring points are reproduced by the CFD code. With the crossflow initialization in the plasma solver, the simulated spark discharge process from the breakdown to spark discharge matches the experimental data, including the voltage and circuit waveforms and the high-speed images of the spark channel evolution. The stretch of spark channel captured by plasma simulations agrees with the measured data. The plasma simulation reveals that the mean temperature of the spark channel is maintained at 5000 K during the discharge phase, and the temperature varies along the spark channel so that the highest value is obtained at the spark root on the center electrode. Overall, the results presented in this paper are meant to provide valuable information about the properties of the plasma generated by the spark discharge.

Whistler Waves as a Signature of Converging Magnetic Holes in Space Plasmas

Magnetic holes are plasma structures that trap a large number of particles in a magnetic field that is weaker than the field in its surroundings. The unprecedented high time-resolution observations by NASA’s Magnetospheric Multiscale Mission enable us to study the particle dynamics in magnetic holes in the Earth’s magnetosheath in great detail. We reveal the local generation mechanism of whistler waves by a combination of Landau-resonant and cyclotron-resonant wave–particle interactions of electrons in response to the large-scale evolution of a magnetic hole. As the magnetic hole converges, a pair of counter-streaming electron beams form near the hole’s center as a consequence of the combined action of betatron and Fermi effects. The beams trigger the generation of slightly oblique whistler waves. Our conceptual prediction is supported by a remarkable agreement between our observations and numerical predictions from the Arbitrary Linear Plasma Solver. Our study shows that wave–particle interactions are fundamental to the evolution of magnetic holes in space and astrophysical plasmas.

SOLEDGE3X full vessel plasma simulations for computation of ITER first‐wall fluxes

AbstractITER Pre‐Fusion Power Operation 1 (PFPO‐1) phase low‐power plasmas are simulated with the SOLEDGE3X‐EIRENE code, a multi‐fluid edge plasma solver that can describe plasma conditions up to the machine's first wall, including a kinetic description of neutrals. Here, SOLEDGE3X is used in 2D mean‐field mode. A throughput scan is performed, reproducing a similar scan from the ITER SOLPS simulations database. The physics assumptions for these simulations are presented, in particular the plasma–neutral interaction model where molecule charge‐exchange and ion‐molecule elastic collisions have newly been added. Challenges encountered in such up‐to‐the‐wall simulations are discussed, along with remaining open questions. Results are presented with two foci: on targets, and on the rest of the first wall. On targets, conditions transition from attached to partially detached as expected, and toroidally symmetric heat fluxes (i.e. without 3D effects) remain below 5 MW/m2, within the divertor design limits. An increase in the parallel heat flux decay length λq with throughput is also observed. On the rest of the first wall, increasing puff rate does not only spread power deposited on the target but also increases heat load on the first wall. These fluxes remain however small (<100 kW/m2).

Modeling Nanosecond-Pulsed Spark Discharge and Flame Kernel Evolution

Abstract Dilute combustion, either using exhaust gas recirculation or with excess air, is considered a promising strategy to improve the thermal efficiency of internal combustion engines. However, the dilute air-fuel mixture, especially under intensified turbulence and high-pressure conditions, poses significant challenges for ignitability and combustion stability, which may limit the attainable efficiency benefits. In-depth knowledge of the flame kernel evolution to stabilize ignition and combustion in a challenging environment is crucial for effective engine development and optimization. To date, a comprehensive understanding of ignition processes that result in the development of fully predictive ignition models usable by the automotive industry does not yet exist. Spark-ignition consists of a wide range of physics that includes electrical discharge, plasma evolution, joule-heating of gas, and flame kernel initiation and growth into a self-sustainable flame. In this study, an advanced approach is proposed to model spark-ignition energy deposition and flame kernel growth. To decouple the flame kernel growth from the electrical discharge, a nanosecond-pulsed high-voltage discharge is used to trigger spark-ignition in an optically accessible small ignition test vessel with a quiescent mixture of air and methane. Initial conditions for the flame kernel, including its thermodynamic state and species composition, are derived from a plasma-chemical equilibrium calculation. The geometric shape and dimension of the kernel are characterized using a multi-dimensional thermal plasma solver. The proposed modeling approach is evaluated using a high-fidelity computational fluid dynamics procedure to compare the simulated flame kernel evolution against flame boundaries from companion Schlieren images.

Plasma edge simulations including realistic wall geometry with SOLPS-ITER

Abstract In plasma edge simulations using the SOLPS-ITER code, the simulated Scrape-Off Layer plasma domain has historically been restricted to magnetic flux surfaces contacting divertor targets at both ends. We present here a newly developed numerical solver for the B2.5 plasma solver in SOLPS-ITER, allowing the numerical grid to be extended to the true vessel boundaries. The new, unstructured Finite Volume scheme can deal with arbitrary grids and magnetic topologies in the 2D poloidal plane. It includes a correct numerical treatment of possibly misaligned faces and cells w.r.t. the magnetic field to cope with, for example, strong divertor target shaping. The solver combines the benefits of an accurate numerical separation of fast parallel and slow radial transport, with a realistic description of the wall geometry, and the possibility of local grid refinement to capture sharp features in the Scrape-Off Layer flows. Generalized sheath boundary conditions are presented that can be imposed at all vessel boundaries, removing an important modeling uncertainty related to the specification of ad hoc decay length boundary conditions at the outer flux surfaces. The resulting model is applied to an AUG single-null case, a standard benchmark case for SOLPS-ITER. We analyze in particular the impact of the extended plasma model on upstream and divertor plasma conditions, and the improved predictions of heat and particle loads to the main chamber wall. The extended solver also allows for a much improved qualitative agreement between fluid and kinetic neutral simulations, because the fluid neutral solution, which is obtained on the plasma grid, now also extends to the true main chamber and divertor vessel boundaries.

Implicit and coupled fluid plasma solver with adaptive Cartesian mesh and its applications to non-equilibrium gas discharges

We present a new fluid plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (nonlinear, implicit) scheme for non-equilibrium gas discharge plasma. The electrons and ions are described using drift–diffusion approximation coupled to Poisson equation for the electric field. The electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperature and could also depend on electron density (important for plasma stratification). The ion and gas temperature are kept constant. The transport equations are discretized using a non-isothermal Scharfetter–Gummel scheme to resolve possible large temperature gradients in the sheaths. We demonstrate the new solver for simulations of direct current (DC) and radiofrequency (RF) discharges. The implicit treatment of the coupled equations allows using large time steps. The full-Newton method (FNM) enables fast nonlinear convergence at each time step, offering significantly improved simulation efficiency. We discuss the selection of time steps for solving different plasma problems. The new solver enables solving several problems we could not solve before with existing software: two- and three-dimensional structures of the entire DC discharges including cathode and anode regions, electric field reversals and double-layer formation, the normal cathode spot and an anode ring, moving striations in diffuse and constricted DC discharges, and standing striations in RF discharges. The developed FNM-ACM technique offers many benefits for tackling the disparity of gas discharge plasma systems' time scales and nonlinearity.

The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov–Maxwell equations

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov–Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge–Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

Numerical modeling of an inductively coupled plasma torch using OpenFOAM

A customized code using the free and fully open-source CFD software package OpenFOAM was developed to simulate a two-dimensional axisymmetric model of an inductively coupled plasma torch. To efficiently calculate the high-frequency magnetic fields generated by the inductive coil, a technique based on the vector potential formulation of Maxwell’s equations was implemented using the block coupled matrix solver provided by the foam-extend toolbox. While the fluid equations for the inner torch region are solved under the assumption of a laminar flowing argon plasma under atmospheric pressure and local thermodynamic equilibrium conditions, the electromagnetic equations are solved on an overlapping mesh extended far outside the torch. Moreover, a novel technique for initializing the plasma solver by separately precomputing the velocity and temperature fields is presented. Using this approach our plasma solver can run in both steady-state and transient modes. The implementation has been validated by means of analytical methods, and the simulation results of the Tekna-PL50 plasma torch have been compared against literature data. The results obtained using the OpenFOAM code are in good agreement with those of the commercial CFD codes.

Numerical Model of a Helicon Plasma Thruster

This article is devoted to the presentation of a numerical model of a Helicon Plasma Thruster (HPT) which relies on: 1) the 3-D adVanced fluId dRifT diffUsion plaSma solver (3D-VIRTUS) for the simulation of the plasma source and 2) an analytical model of the plume for the solution of the plasma acceleration and detachment, and in turn for the preliminary estimation of the propulsive performances (e.g., thrust and specific impulse). The results of the numerical model have been compared against experimental measurements performed with a thrust stand in order to evaluate the reliability of the code when dealing with real-life prototypes. Specifically, a dedicated combined numerical–experimental campaign has been conducted on a low power (50-W range) HPT prototype operated with argon propellant.

Active Flow Control of Flapping Airfoil Using Openfoam

ABSTRACTThe concept of the fixed wing Micro Air Vehicles (MAVs) has received increasing interest over the past few decades, with the principal aim of carrying out the surveillance missions. The design of the flapping wing MAVs still is in infancy stage. On the other hand, there has been increasing interest over the flow control using plasma actuators in worldwide. The aim of this research is to study the flow control of a flapping airfoil with and without plasma actuation in OpenFOAM. The OpenFOAM CFD platform has been used to develop our own plasma solver. For the plasma induced turbulence in the flow regime, k-ε turbulence model was adopted to address the interaction between plasma and fluid flows. For the plasma-fluid interaction, we use reduced-order modelling to solve the plasma induced electric force. A two dimensional NACA0012 flapping airfoil without plasma actuation study has been benchmarked with previous published literature. We have not only focused on the active flow control but also analyzed the important parameter reduced frequency at different values, those are 0.1, 0.05 and 0.025. Reduced frequency (κ) is very important parameter of an airfoil in the unsteady motion. Our major contribution is testing the several reduced frequencies with the plasma actuation. The positive and beneficial effects of the plasma actuator for all cases have been observed. From the observed results, the flapping with plasma actuation at reduced frequency of 0.1 showed the 14.285 percent lift improvement and the 16.19 percent drag reduction than the flapping without plasma actuation at the respective dynamic stall angles. The maximum lift coefficient is increased with the increase in reduced frequency. In overall, plasma actuators are effective in the flow control of a flapping airfoil. In future, the combination of the flapping with plasma actuators will be a promising application to boast the maneuverability of MAVs.

Advances in simulations of moving striations in DC discharges of noble gases

We describe the results of two-dimensional self-consistent simulations of moving striations in DC discharges of noble gases for both diffuse and constricted plasma regimes. We use a fluid plasma model capturing key physics and change only one control parameter (volume recombination rate) to describe both the diffuse and constricted plasma. The newly developed implicit coupled plasma solver with an adaptive Cartesian mesh enables us to obtain for the first time the two-dimensional structure of the entire cathode-to-anode discharge and self-excited nonlinear ionization waves in the constricted plasmas. The results are in agreement with the previously developed linear theory of striations in constricted discharges.

3D-VIRTUS: Equilibrium condition solver of radio-frequency magnetized plasma discharges for space applications

We present 3D-VIRTUS (3-Dimensional adVanced fluId dRifT diffUsion plaSma solver), a numerical tool conceived for the evaluation of the equilibrium conditions of Helicon plasma sources, that consists of the Electro-Magnetic Module, and the FLUID Module. The first evaluates the power deposited into the plasma by the antenna that drives the discharge, and it is based on a solid numerical tool (i.e., ADAMANT). The power deposition is used by the second module to solve for the macroscopic transport of charged and neutral species by means of a fluid approach, and assuming valid the Drift-Diffusion approximation. The set of continuity, momentum, energy, and Poisson equations are solved numerically through the Finite Volume Method, and are implemented in OpenFOAM. The two modules are iterated until a converged solution is obtained. This approach allows the self-consistent evaluation of the local plasma parameters (e.g., plasma density) at equilibrium in Helicon sources that feature (i) arbitrary-shaped plasma regions, and antennas, (ii) realistic magneto-static fields generated by electromagnets or permanent magnets. The numerical accuracy of the FLUID Module has been assessed as a function of the time, and space discretization. The FLUID Module, and the 3D-VIRTUS code have been independently validated against other well-established numerical approaches and experimental measurements. Finally, 3D-VIRTUS has been exploited to investigate Helicon plasma discharges for space propulsion applications for magneto-static field values from 0 G up to 750 G.

나노세컨드 펄스 DBD 플라즈마의 멀티스케일 모델링을 위한 비평형 플라즈마 유동 해석 및 검증

In a nanosecond pulse discharge, the computational cost is high because of the characteristic time difference between the plasma and the flow. In order to reduce the computational cost, multi-scale modeling study of nanosecond pulse discharge plasma is needed. In this study, we developed and verified a non-equilibrium plasma solver for nanosecond-pulse Dielectric Barrier Discharge(NS-DBD) multi-scale modeling study. To simulate the non-equilibrium phenomena, 17 chemical species / 54 chemistry reaction models were used. The governing equations included chemical species continuity equations, a electrical potential equation, and Navier-Stokes equations. Numerical results show that streamer velocity and micro shock wave speed are comparable to those of other experimental results. This study is expected to contribute to the future study of NS-DBD multi-scale modeling.

High-order two-fluid plasma solver for direct numerical simulations of plasma flows with full transport phenomena

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating terms, have been implemented in the CFDNS code and solved by using sixth-order non-dissipative compact finite differences for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales, while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. Non-dimensional analysis of the two-fluid plasma equations shows that, by varying the characteristic/background number density, length scale, temperature, and magnetic strength, the corresponding Hall, resistive, and ideal magnetohydrodynamic equations can be recovered as limiting cases. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows in different regimes have been validated against four canonical problems: Alfven and whistler dispersion relations, electromagnetic plasma shock, and magnetic reconnection. For all test cases, by using physical dissipation and diffusion, with negligible numerical dissipation/diffusion, fully converged Direct Numerical Simulation (DNS)-like solutions are obtained when the ion Reynolds number based on the grid size is smaller than a threshold value which is about 2.3 in this study. For the magnetic reconnection problem, the results show that the magnetic flux saturation time and value converge when the ion and magnetic Reynolds numbers are large enough. Thus, the DNS-like results become relevant to practical problems with much larger Reynolds numbers.

Implementation of a 9-point stencil in SOLPS-ITER and implications for Alcator C-Mod divertor plasma simulations

The SOLPS-ITER code suite is used worldwide for plasma edge modeling, the interpretation of experiments, as well as for the design of the ITER divertor. The numerical scheme of the plasma solver of the code, B2.5, is based on the assumption of perfectly orthogonal grids in the poloidal plane, aligned with the magnetic field, while in practice grids are often strongly distorted to match divertor target shapes. Neglecting these grid distortion leads to qualitatively and quantitatively incorrect results for fluid neutral simulations, and may affect results in cold (detached) divertors even when using kinetic neutral simulations. In this contribution, we present the first results of a newly implemented 9-point stencil in B2.5 to properly handle misaligned grids. The new scheme is then applied to fluid neutral simulations of a well-diagnosed and previously modeled Alcator C-Mod discharge. Results are compared with the original 5-point scheme neglecting grid distortion effects, as well as with simulations including a full kinetic neutral model. We conclude that the 9-point stencil is essential to correctly model the transport of fluid neutrals on distorted grids, and to capture the effects of divertor closure on the fluid neutral behavior.

Sensitivity analysis of plasma edge code parameters through algorithmic differentiation

Anomalous radial transport coefficients, boundary conditions and reaction rates are among the main sources of uncertainty within plasma edge modeling. In principle, an analysis to determine the sensitivity of code results to changes in uncertain model parameters can be easily implemented through finite differences. However, this incurs in error accumulations and allows scanning only one parameter at a time, requiring a huge computational effort. Algorithmic Differentiation (AD) is a possible alternative to finite differences already applied to several transport codes in different research domains but not yet in plasma edge modeling. AD tools preprocess the source code, identifying elementary operations for which the differential form is well known, and producing a new version of the code that contains the additional derivative information. In this paper, the feasibility of applying AD to plasma edge codes is demonstrated using the TAPENADE tool on the SOLPS-ITER code. As a first preliminary step, the AD tool is applied in the so-called “forward” mode on the B2.5 plasma solver, adopting a fluid neutral approximation to obtain the sensitivities of the calculated quantities of interest on selected code parameters. The proof of principle is carried out by comparing the AD results with those evaluated with finite differences on an ITER H-only case. The sensitivities of the target peak heat load and maximum electron temperature with respect to anomalous radial transport coefficients and core input power are assessed. The comparison with finite differences results in a relative error lower than 10−6. This proves that, in a next step, AD can be exploited for an efficient and accurate sensitivity analysis in the framework of plasma edge simulations.