Kinetic Plasma Model Research Articles

Kinetic model of a three-component plasma

In this work, a system of kinetic equations is constructed to study the processes in a three-component plasma. It is an analogue of the Krook model, which is widely used in the dy-namics of rarefied gases. The model is supposed to be used to study the processes in the channels of rocket electric thrusters.

Modeling of ion transport from ionization region to entrance of mass spectrometer in HiPIMS argon/Cr target

Plasma global kinetic model coupled with the Monte Carlo method is used to study the ion transport in HiPIMS Ar/Cr target. The plasma kinetic global model is developed to study the time evolution of neutral, ion, and electron species created in the ionization region. To analyze the ion temporal spectra at the entrance of the mass spectrometer, a simple model based on the Monte Carlo technique is developed to track the ion trajectories from the ionization region to the mass spectrometer. The ion temporal spectra obtained by the global kinetic model in the ionization region are introduced in the Monte Carlo model as input data. The simulation results reveal a temporal shift of the ion spectra as well as their spreading in comparison with those obtained in the ionization region. Such temporal shapes of the ion spectra are more sensitive to the ion temperatures in the ionization region, and the position of the mass spectrometer is connected to the reactor. A satisfactory agreement between simulated ion temporal spectra and those measured by the mass spectrometer is obtained when we have represented the ion population energies by two Maxwellian distributions, where the first one corresponds to the low temperature and the second to the high temperature.

Kinetic Model of a Three-Component Plasma

Kinetic Model of a Three-Component Plasma

Fully relativistic distorted wave calculations of electron impact excitation of gallium atom: Cross sections relevant for plasma kinetic modeling

Electron impact excitation cross sections of neutral Ga are calculated using the relativistic distorted wave approximation with the aid of multiconfigurational Dirac-Fock wavefunctions. The cross sections are calculated from the fine structure resolved levels of the 4s24p manifold, i.e., from the ground 2P1/2 and the first excited state 2P3/2, to the fine structure resolved levels of the manifolds 4s24pdf, 4s4p2(4P1/2,4P3/2, and 4P5/2), 4s25spdf, 4s26spdf, 4s27spdf, and 4s28spdf for incident electron energies ranging from threshold to 500 eV. Where available, a comparison of the calculated oscillator strengths, transition probabilities, and cross sections with the previously reported results has been performed. The cross sections for the excitation from 4s24p2P1/2 to 4s24f, 4s4p2(4P1/2,4P3/2, and 4P5/2), 4s25f, 4s26f, 4s27df, and 4s28spdf and all the excitation cross sections from 4s24p2P3/2 are calculated and reported for the first time for a wide range of electron energies. Furthermore, the rate coefficients are also calculated using the present cross sections for an electron temperature varying from 0.5 to 5 eV. An analytic fitting of the calculated rate coefficients is provided to facilitate their inclusion in various plasma kinetic models.

RAM‐SCB Runs on Request at CCMC

AbstractThe Ring current–Atmosphere interactions Model (RAM) with Self‐Consistent magnetic (B) field (SCB) combines a large‐scale kinetic model of ring current plasma with a three‐dimensional (3‐D) force‐balanced model of the terrestrial magnetic field. RAM‐SCB simulates the evolution of major ion species (H+, O+, and He+ by default) and electrons as a function of azimuth, radial distance, energy, and pitch angle. Simulation outputs include the Dst index, and pressure and differential flux of the modeled species, thus providing benefit as a science code and to inform surface charging hazard within the model domain. Version 2.2 of this open‐source simulation code has now—as of 8 August 2023—been made available for Runs‐On‐Request via the Community Coordinated Modeling Center.

The Gamma-Ray Pulsar Phenomenology in View of 3D Kinetic Global Magnetosphere Models

We develop kinetic plasma models of pulsar magnetospheres with magnetic-field-line-dependent plasma injection that reveal the importance of various magnetosphere regions in regulating the γ-ray emission. We set different particle injection rates for the so-called open, closed, and separatrix zones. Moderate particle injection rates in open and closed zones ensure a global field structure close to the force-free structure, while the dissipation occurs mainly in and around the equatorial current sheet. The particles that are injected into the separatrix zone affect the particle populations that enter the equatorial current sheet region, and therefore the corresponding accelerating electric fields, particle energies, the spectral cutoff energy, and γ-ray efficiency. The separatrix zone models reproduce the recently discovered fundamental plane of γ-ray pulsars consistent with curvature radiation emission, the γ-ray light-curve shapes, and the radio-lag versus peak-separation correlation reported in the Fermi second pulsar catalog. The model beaming factors indicate that the pulsar total γ-ray luminosities listed in the Fermi catalogs are overestimations of the actual ones. We find that the radiation reaction limited regime starts ceasing to govern the high-energy emission for . Our results also indicate that toward high magnetic inclination angles, the Y point around the rotational equator migrates well inside the light cylinder, sparking additional peaks in the γ-ray pulse profiles. We find that an equivalent enhanced particle injection beyond the Y point strengthens these features, making the model γ-ray light curves inconsistent with those observed.

(Invited) Electrifying Nitrogen Transformations: Decarbonizing Ammonia Using Plasma Catalysis and Electrochemical Reduction of Nitrate in Wastewaters

Nitrogen fixation in fertilizers forms the basis of modern agriculture and mediates global food insecurity. Energy-dense nitrogen-based compounds also represent promising carbon-free alternative fuels when synthesized using sustainable energy and materials. However, conventional thermally-activated nitrogen conversion processes consume substantial amounts of fossil fuels as materials and energy inputs, leading to an unsustainable energy and carbon footprint. Therefore, electron-driven approaches are needed to establish fossil-free nitrogen interconversions. Electrochemical and plasma-activated reactions operate under mild conditions, enabling facile coupling to intermittent renewable energy sources to reduce CO2 emissions and reactive nitrogen pollution, facilitating storage and transportation of renewable energy in nitrogen-based fuels.Non-thermal plasma has been used to synthesize ammonia under mild conditions, but the dearth of fundamental understanding of plasma catalytic reactions handicaps the development of efficient plasma catalytic N2 conversion. Therefore, an in situ FTIR reactor was employed in combination with steady-state flow reactor experiments and plasma kinetic modeling to elucidate the surface reaction mechanisms and plasma-catalyst interactions. Ammonia yield can be influenced by plasma-derived intermediates and their interactions with catalyst surfaces, which lead to different reaction pathways. Furthermore, techno-economic analysis was employed to reveal the threshold efficiency required for a plasma process to become environmentally and economically competitive.Beyond electrification of N2 fixation for ammonia synthesis, existing waste streams containing fixed nitrogen as nitrate may be mined for fertilizer or carbon-free renewable energy storage while avoiding the need for H2 as a reagent, via selective nitrate electroreduction to ammonium. Nitrate electrochemical reduction can eliminate the production of concentrated waste streams while avoiding the addition of reductant or hole scavenger chemicals. However, major challenges for nitrate removal from water via electrochemical conversion involve reducing the use of expensive precious metal electrocatalysts while also improving the reaction activity and selectivity, stability, and mass transport of nitrate to electrocatalyst active sites. Therefore, electrochemical membranes were employed as porous flow-through electrodes to address these challenges based on improved mass transport and altered kinetics under flow conditions within membrane pores.Conductive electrified membranes, fabricated using inexpensive materials and green synthesis methods, showed significantly higher nitrate removal efficiency during electrified filtration compared to flow-by mode. The small pore sizes in the membrane reduced the diffusional boundary layer by several orders of magnitude with respect to flow-by mode, overcoming diffusional mass transport limitations. During electro-filtration, the nitrate conversion activity was easily controlled by tuning the permeate flow rate, regardless of applied potential. These multifunctional electrified membranes for reduction of nitrate in wastewaters have the potential to partially displace carbon-intensive industrially synthesized ammonia while simultaneously accomplishing water decontamination.

Adaptive symplectic model order reduction of parametric particle-based Vlasov–Poisson equation

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of parameters. In this work, we derive reduced order models for the semi-discrete Hamiltonian system resulting from a geometric particle-in-cell approximation of the parametric Vlasov–Poisson equations. Since the problem’s nondissipative and highly nonlinear nature makes it reducible only locally in time, we adopt a nonlinear reduced basis approach where the reduced phase space evolves in time. This strategy allows a significant reduction in the number of simulated particles, but the evaluation of the nonlinear operators associated with the Vlasov–Poisson coupling remains computationally expensive. We propose a novel reduction of the nonlinear terms that combines adaptive parameter sampling and hyper-reduction techniques to address this. The proposed approach allows decoupling the operations having a cost dependent on the number of particles from those that depend on the instances of the required parameters. In particular, in each time step, the electric potential is approximated via dynamic mode decomposition (DMD) and the particle-to-grid map via a discrete empirical interpolation method (DEIM). These approximations are constructed from data obtained from a past temporal window at a few selected values of the parameters to guarantee a computationally efficient adaptation. The resulting DMD-DEIM reduced dynamical system retains the Hamiltonian structure of the full model, provides good approximations of the solution, and can be solved at a reduced computational cost.

Solar-wind electron precipitation on weakly magnetized bodies: The planet Mercury

Rocky objects in the Solar System (such as planets, asteroids, moons, and comets) undergo a complex interaction with the flow of magnetized, supersonic plasma emitted from the Sun called solar wind. We address the interaction of such a flow with the planet Mercury, considered here as the archetype of a weakly magnetized, airless, telluric body immersed in the solar wind. Due to the lack of dense atmosphere, a considerable fraction of solar-wind particles precipitate on Mercury. The interaction processes between precipitating electrons and other nonionized parts of the system remain poorly understood. Shading light on such processes is the goal of this work. Using a 3D fully kinetic self-consistent plasma model, we show for the first time that solar-wind electron precipitation drives (i) efficient ionization of multiple neutral exosphere species and (ii) emission of X-rays from the surface of the planet. We conclude that, compared to photoionization, electron-impact ionization should not be considered a secondary process for the H, He, O, and Mn exosphere. Moreover, we provide the first, independent evidence of X-ray aurora-like emission on Mercury using a numerical approach.

Effect of electron temperature on formation of travelling waves in plasma: Kinetic and hydrodynamic models

Abstract The kinetic formulation of the model problem of plasma waves excitation by a powerful short laser pulse is numerically studied for the first time. Kinetic and simplest hydrodynamic plasma models are also compared for the problem under consideration. It is shown that the considered hydrodynamic models do not provide good approximations to the solution to the Vlasov kinetic equation, namely, one leads to discontinuous solutions and the other has a significant qualitative distinction. At a low plasma temperature, the effect of non-isothermicity of the process is small, but it can lead to significant distortions of the solution during further heating. The results obtained here imply that the first two moments of the distribution function are not enough to describe the plasma hydrodynamics; higher-order moments should be used.

Computationally efficient high-fidelity plasma simulations by coupling multi-species kinetic and multi-fluid models on decomposed domains

A numerical method is developed for coupling a multi-species kinetic plasma model with a 5N-moment multi-fluid plasma model. The simulation domain is decomposed such that the local conditions satisfy the corresponding plasma model's region of validity. The method allows for hybrid simulations by formulating each model as a set of conservation laws and using a continuum numerical method to solve each model's governing equations in the subdomains of the decomposed domain. The models are coupled through fluxes across subdomain interfaces. Two methods are explored for the formulation of the fluxes that can be self-consistently represented by both plasma models. One method allows for flux calculations consistent with the 5N-moment multi-fluid plasma model and assumes thermodynamic equilibrium within each species of the kinetic plasma model. The second method ensures conservation of the distribution function as well as mass, momentum, and energy by formulating the fluxes using a composite underlying distribution function at the subdomain interfaces. The methods are compared in 1D1V simulations of a double rarefaction wave and a plasma sheath using the WARPXM framework, which solves each model using the discontinuous Galerkin finite element method. Both methods for formulating the fluxes perform well as the subdomain interface distribution function approaches a Maxwellian, with the consistent method being more robust to larger deviations. A simulation of the magnetized Kelvin-Helmholtz instability in 2D2V is also performed using the consistent method, which demonstrates the potential of the domain-decomposed hybrid method in facilitating speedup and reduction in required computational resources for high-fidelity plasma simulations, allowing for the investigation of problems that are beyond current capabilities.

Combustion Characteristics of Hydrogen/Air Mixtures in a Plasma-Assisted Micro Combustor

This work performs an analysis of plasma-assisted non-premixed H2-air flames in Y-shaped micro combustors in the presence of field emission dielectric barrier discharge (FE-DBD) plasma actuators. The combustion, flow, and heat transfer characteristics are numerically investigated, and the effect of sinusoidal plasma discharges on combustion performance is examined at various equivalence ratios (φ). A coupled plasma and chemical kinetic model is implemented, using a zero-dimensional model based on the solution of the Boltzmann equation and the ZDPlasKin toolbox to compute net charges and radical generation rates. The estimated body forces, radical production rates, and power densities in the plasma regions are then coupled with hydrogen combustion in the microchannel. Plasma-assisted combustion reveals improvements in flame length and maximum gas temperature. The results demonstrate that FE-DBDs can enhance mixing and complete the combustion of unreacted fuel, preventing flame extinction. It is shown that even in cases of radical and thermal quenching, these plasma actuators are essential for stabilizing the flame.

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. The plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

Ammonia decomposition in a dielectric barrier discharge plasma: Insights from experiments and kinetic modeling

Utilizing ammonia as a storage medium for hydrogen is currently receiving increased attention. A possible method to retrieve the hydrogen is by plasma-catalytic decomposition. In this work, we combined an experimental study, using a dielectric barrier discharge plasma reactor, with a plasma kinetic model, to get insights into the decomposition mechanism. The experimental results revealed a similar effect on the ammonia conversion when changing the flow rate and power, where increasing the specific energy input (higher power or lower flow rate) gave an increased conversion. A conversion as high as 82 % was achieved at a specific energy input of 18 kJ/Nl. Furthermore, when changing the discharge volume from 31 to 10 cm3, a change in the plasma distribution factor from 0.2 to 0.1 was needed in the model to best describe the conversions of the experiments. This means that a smaller plasma volume caused a higher transfer of energy through micro-discharges (non-uniform plasma), which was found to promote the decomposition of ammonia. These results indicate that it is the collisions between NH3 and the high-energy electrons that initiate the decomposition. Moreover, the rate of ammonia destruction was found by the model to be in the order of 1022 molecules/(cm3 s) during the micro-discharges, which is 5 to 6 orders of magnitude higher than in the afterglows. A considerable re-formation of ammonia was found to take place in the afterglows, limiting the overall conversion. In addition, the model revealed that implementation of packing material in the plasma introduced high concentrations of surface-bound hydrogen atoms, which introduced an additional ammonia re-formation pathway through an Eley-Rideal reaction with gas phase NH2. Furthermore, a more uniform plasma is predicted in the presence of MgAl2O4, which leads to a lower average electron energy during micro-discharges and a lower conversion (37 %) at a comparable residence time for the plasma alone (51 %).

Plasma-catalytic ammonia synthesis in a dielectric barrier discharge reactor: A combined experimental study and kinetic modeling

Plasma-catalytic ammonia synthesis in a dielectric barrier discharge reactor has emerged as a possible route for electrification of nitrogen fixation. In this study, we use a combination of experiments and a plasma kinetic model to investigate the ammonia synthesis from N2 and H2, both with and without a solid packing material in the plasma zone. The effect of plasma power, feed flow rate, N2:H2 feed ratio, gas residence time, temperature, and packing material (MgAl2O4 alone or impregnated with Co or Ru) on the ammonia synthesis rate were examined in the experiments. The kinetic model was employed to improve our understanding of the ammonia formation pathways and identify possible changes in these pathways when altering the N2:H2 feed ratio. A higher NH3 synthesis rate was achieved when increasing the feed flow rate, as well as when increasing the gas temperature from 100 to 200 °C when a packing material was present in the plasma. At the elevated temperature of 200 °C, an optimum in the NH3 synthesis rate was observed at an equimolar feed ratio (N2:H2 = 1:1) for the plasma alone and MgAl2O4, while a N2-rich feed was favored for Ru/MgAl2O4 and Co/MgAl2O4. The optimum in the synthesis rate with the N2-rich feed, where high energy electrons are more likely to collide with N2, suggests that the rate-limiting step is the dissociation of N2 in the gas phase. This is supported by the kinetic model when packing material was used. However, for the plasma alone, the model found that the N2 dissociation is only rate limiting in H2-rich feeds, whereas the limited access to H in N2-rich feeds makes the hydrogenation of N species limiting.

Editorial: Numerical simulations of plasma thrusters and/or related technologies

In the last few decades, electric propulsion has become in high demand on modern spacecrafts, from 8 very small nano-satellites to large communications orbital platforms. The difficulty of experimentally 9 characterizing the plasma discharge channels and the operative in-space conditions of plasma thrusters make 10 simulations a real game changer in this advanced technology/research field. In this respect, the rapid growth 11 of high-performance computing and esa-scale flops of modern architecture supercomputers has enabled 12 tackling more and more complex and computationally costly scenarios. With the use of different numerical 13 approaches, typically based on kinetic, hybrid or fluid plasma models, a large number of applications 14 can be covered: thruster physics and performance estimation, plasma thruster plume interaction with the 15 spacecraft, synthetic simulations of plasma diagnostic tools, etc.This research topic aimed to investigate, from a numerical point of view, plasma propulsion applications 17 or physical phenomena. When possible, in order to validate and/or tune the numerical tools, simulation

Nonequilibrium plasma in water vapor

A kinetic model of a non-equilibrium water vapor plasma created by a nanosecond pulsed discharge at elevated temperatures and at low pressure is presented. The model includes equations for electron, vibrational and gas temperatures combined with equations for neutral, charged, electronically and vibrationally excited species. Simulation results are compared with the available experimental data and show good agreement in dynamics of the plasma decay and electron drift velocities. It is shown that the plasma decay in pure water vapor is controlled by the dissociative recombination. Under the conditions simulated, the concentration of electronically excited species is low, but we observe a formation of vibrationally excited species. A significant decrease in the electrical conductivity of water plasma with time, which depends on the level of initial ionization, is shown.

Landau damping of ion‐acoustic waves with simultaneous effects of non‐extensivity and non‐thermality in the presence of hybrid Cairns‐Tsallis distributed electrons

AbstractThe dispersion properties and Landau damping rate of ion‐acoustic waves (IAWs) with the hybrid Cairns‐Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov‐Poisson's equations. For both super‐extensive (q < 1) and sub‐extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θi, e (ion‐to‐electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super‐extensive and sub‐extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non‐thermal parameter α and non‐extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θe, i (electron‐to‐ion temperature ratio), on decreasing the values of the non‐extensive parameter and increasing values of the non‐thermal parameter, the weak damping rate is observed (vice versa) in super‐extensive or super‐thermal plasma, although the trend of the damping rate in sub‐thermal plasma is similar (as in the case of super‐thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non‐thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.

Low-temperature plasma simulation based on physics-informed neural networks: Frameworks and preliminary applications

Plasma simulation is an important, and sometimes the only, approach to investigating plasma behavior. In this work, we propose two general artificial-intelligence-driven frameworks for low-temperature plasma simulation: Coefficient-Subnet Physics-Informed Neural Network (CS-PINN) and Runge–Kutta Physics-Informed Neural Network (RK-PINN). CS-PINN uses either a neural network or an interpolation function (e.g., spline function) as the subnet to approximate solution-dependent coefficients (e.g., electron-impact cross sections, thermodynamic properties, transport coefficients, etc.) in plasma equations. Based on this, RK-PINN incorporates the implicit Runge–Kutta formalism in neural networks to achieve a large-time step prediction of transient plasmas. Both CS-PINN and RK-PINN learn the complex non-linear relationship mapping from spatiotemporal space to the equation's solution. Based on these two frameworks, we demonstrate preliminary applications in four cases covering plasma kinetic and fluid modeling. The results verify that both CS-PINN and RK-PINN have good performance in solving plasma equations. Moreover, RK-PINN has the ability to yield a good solution for transient plasma simulation with not only large time steps but also limited noisy sensing data.

Mechanism study on gliding arc (GA) plasma reforming: A combination approach of experiment and modeling

AbstractAiming at a deep understanding of the reaction kinetics of gliding arc (GA) plasma reforming, a new approach to combining simulation and experiment is reported. By adding thermodynamic module and conservation equations of mass and energy into the conventional 0D plasma kinetics model, an effective link between experimental diagnostics and reaction kinetics simulation is established for dry reforming of CH4 in GA plasma. The GA plasma parameters are diagnosed experimentally as electron density of 1.4 × 1014 cm−3, electron temperature of 1.5 eV, and arc gas temperature of 2500 K. The kinetics simulation is implemented based on the obtained plasma parameters and verified by the online analysis of gaseous products. Consequently, the reaction mechanism is revealed by the reliable model.