Multispecies Plasma Research Articles

A new generalized formulation of dielectric tensor for multi-species plasma with anisotropic drift product-bi-kappa distribution

It is well established that space plasmas often contain particle components with high-energy tails that approximately follow a power-law distribution in velocity space. Such superthermal distributions, particularly those with an excess of fast particles, are more accurately described by generalized Kappa (Lorentzian) distributions rather than Maxwellian distributions. We propose the product-bi-kappa (PBK) distribution as an alternative to the kappa-Maxwellian (KM) and bi-Maxwellian (BM) distributions, leading to a new linear transformation form of the dielectric tensor for multi-component plasmas. This method utilizes the rational form and multi-pole expansion of the plasma dispersion function to convert the dielectric tensor of multi-component PBK plasmas into a linear eigenvalue system in conjunction with Maxwell's equations. Our approach transforms the traditional numerical iteration process for solving the finite roots of the dielectric tensor from initial values into an eigenvalue problem within a new, complete linear system, thus enabling the simultaneous determination of all principal eigenvalues. Constructing the eigenvalue system for multi-component plasmas is crucial for developing new, comprehensive oblique propagation solvers for multi-species anisotropic drift plasmas, including PBK, KM, and BM plasmas. The detailed construction of the linear eigenvalue system is extensively discussed in this work.

BO-KM: A comprehensive solver for dispersion relation of obliquely propagating waves in magnetized multi-species plasma with anisotropic drift kappa-Maxwellian distribution

The observation of superthermal plasma distributions in space reveals a multitude of distributions with high-energy tails, and the kappa-Maxwellian distribution is a type of non-Maxwellian distribution that exhibits this characteristic. However, accurately determining the multiple roots of the dispersion relation for superthermal plasma waves propagating obliquely presents a challenge. To tackle this issue, we have developed a comprehensive solver, BO-KM, utilizing an innovative numerical algorithm that eliminates the need for initial value iteration. The solver offers an efficient approach to simultaneously compute the roots of the kinetic dispersion equation for oblique propagation in magnetized plasmas. It can be applied to magnetized superthermal plasma with multi-species, characterized by anisotropic drifting kappa-Maxwellian, bi-Maxwellian distributions, or a combination of the two. The rational and J-pole Padé expansions of the dispersion relation are equivalent to solving a linear system's matrix eigenvalue problem. This study presents the numerical findings for kappa-Maxwellian plasmas, bi-Maxwellian plasmas, and their combination, demonstrating the solver's outstanding performance through benchmark analyses. Program summaryProgram Title: BO-KMCPC Library link to program files:https://doi.org/10.17632/pr9cvjrvfv.1Licensing provisions: BSD 3-clauseProgramming language: MatlabNature of problem: To efficiently solve for multiple roots of the kinetic dispersion relation in superthermal plasma distributions with high-energy tails observed in space, we have developed BO-KM, a novel and comprehensive solver that employs a unified framework for computing uprathermal (or thermal) waves and instabilities. This solver is applicable to magnetized multi-species collisionless plasmas with anisotropic drift kappa-Maxwellian, bi-Maxwellian distributions, or a combination of both. Furthermore, BO-KM incorporates a submodule dedicated to the perpendicular propagation dispersion relation of bi-Kappa plasmas, thereby significantly improving computational efficiency at high κ values.Solution method: The method converts the kinetic plasma dispersion relation based on rational expansion (for the kappa-Maxwellian model) and J-pole Padé expansion (for the bi-Maxwellian model) into an equivalent linear eigenvalue system. This transformation effectively turns the root-finding task into an eigenvalue problem, enabling the simultaneous determination of roots using standard eigenvalue libraries.Additional comments including restrictions and unusual features: Kinetic relativistic effects are not included in the present version yet.

Electron Influence on the Parallel Proton Firehose Instability in 10-moment, Multifluid Simulations

Instabilities driven by pressure anisotropy play a critical role in modulating the energy transfer in space and astrophysical plasmas. For the first time, we simulate the evolution and saturation of the parallel proton firehose instability using a multifluid model without adding artificial viscosity. These simulations are performed using a 10-moment, multifluid model with local and gradient relaxation heat-flux closures in high-β proton–electron plasmas. When these higher-order moments are included and pressure anisotropy is permitted to develop in all species, we find that the electrons have a significant impact on the saturation of the parallel proton firehose instability, modulating the proton pressure anisotropy as the instability saturates. Even for lower β's more relevant to heliospheric plasmas, we observe a pronounced electron energization in simulations using the gradient relaxation closure. Our results indicate that resolving the electron pressure anisotropy is important to correctly describe the behavior of multispecies plasma systems.

On acoustic solitary waves in a multispecies degenerate relativistic magnetized plasma using physics informed neural networks

In this paper, we investigate the nonlinear electrostatic wave propagation in a two-dimensional magnetized plasma. The plasma consists of electron and positron components with relativistic degeneracy and stationary ions for neutralizing its background. Using the basic equations for this type of plasma in combination with the reductive perturbation method, we derived the Zakharov–Kuznetsov equation using the Lorentz transformation stretching method (LT). For the first time, we compared the results of the Galilean transformation stretching method (GT) and the LT method to investigate the effect of plasma parameters, such as the relativistic degeneracy parameter of electron particles (re0), the density ratio of ion to electrons (δ), and the normalized electron cyclotron (Ωe), on the amplitude and width of the wave solutions. The plasma parameters used in this research are representative of compact astrophysical objects. Numerical results showed that the amplitude of wave solutions obtained by the LT method is smaller than the GT method, but the width is greater. We provide a physical explanation for these differences. Furthermore, we present a physics-informed neural network (PINN) approach to directly recover the intrinsic nonlinear dynamics from spatiotemporal data. The PINN model uses a deep neural network constrained by the governing equations to learn the optimal parameters, with the aim of enhancing the predictive capabilities of the system. The results of this study provide valuable insight into the propagation of nonlinear waves in white dwarfs, where relativistic effects are significant. These findings could substantially advance the development of emerging machine learning applications in astrophysics.

TECXY simulations of the power exhaust in the multi-impurity plasma of DTT reactor

Reduction of the heat load to plasma-facing components is a crucial problem for future fusion reactors like Divertor Test Tokamak (DTT). Mitigation of the power load via increased plasma radiation with the use of puffed ions of impurities would be one way to mitigate power in the scrape-off layer. This paper presents a numerical investigation of the impact of seeded impurities on the radiation pattern and the power load to the divertor plates of the high-field DTT reactor in the single null (SN) configuration. The simulations have been done with the use of the TECXY code, which solves multi-species plasma transport equations for multiple impurity species simultaneously and all associated ionization stages in a two-dimensional poloidal geometry. TECXY represents the model of plasma transport in the scrape-off layer region by a classical set of transport equations of multi-species plasma derived by Braginskii. The paper aims to compare the mitigation capabilities of neon and argon impurities seeded in the plasma of the DTT device and to obtain a significant energy flux reduction to the target plate at the smallest possible impurity concentration. Performed investigations showed the effects of neon and argon impurities seeding separately for constant electron density at the separatrix. It has been found that the decrease in electron temperature on the divertor plates up to 3 eV at the outer and the inner divertor plates and the peak power load below 15 MW m−2 at the outer divertor plate can be achieved with argon seeding and much lower impurity concentration than that in the case of neon impurity seeding. Studies have shown the complexity of the effect of neon and argon impurities on the boundary plasma. It was found that the reduction of temperature and the power on both divertor plates was the most effective for the high upstream plasma densities. The results show also that diffusive perpendicular transport strongly affects impurity radiation and thus plasma condition at divertor plates.

Numerical Simulation of Radiatively Driven Transonic Relativistic Jets

We perform the numerical simulations of axisymmetric, relativistic, optically thin jets under the influence of the radiation field of an accretion disk. We show that starting from a very low injection velocity at the base, jets can be accelerated to relativistic terminal speeds when traveling through the radiation field. The jet gains momentum through the interaction with the radiation field. We use a relativistic equation of state for multispecies plasma, which self-consistently calculates the adiabatic index for the jet material. All the jet solutions obtained are transonic in nature. In addition to the acceleration of the jet to relativistic speeds, our results show that the radiation field also acts as a collimating agent. The jets remain well collimated under the effect of radiation pressure. We also show that if the jet starts with a rotational velocity, the radiation field will reduce the angular momentum of the jet beam.

Complex shock structure in multi-species dusty plasma with nonextensive electrons and two-temperature nonthermal ions

A theoretical investigation has been made to explore the behavior of nonplanar (cylindrical and spherical) electrostatic shock waves in a dusty plasma system that consists of arbitarily charged dust particles, negatively charged heavy ions following Cairn’s distribution, positively charged ions with two different temperatures, and nonextensive electrons. The reductive perturbation technique is used to derive a modified Burgers equation analytically. Analytical analysis shows that the characteristics of the nonplanar shock waves, including their polarity, amplitude, width, and phase speed, undergo significant alterations due to factors such as the charges on dust particles, the number density of particles, the temperatures of heavy and light ions, nonextensive electron behavior, and dust kinematic viscosity. Furthermore, this study found shock structures with either a positive or negative potential, depending on the critical value of the proportion of ions to the density of dust particles. The findings maybe useful in understanding the characteristics of shock waves both in space plasma environments and laboratory plasmas.

A reduced kinetic method for investigating non-local ion heat transport in ideal multi-species plasmas

A reduced kinetic method (RKM) with a first-principles collision operator is introduced in a 1D2V planar geometry and implemented in a computationally inexpensive code to investigate non-local ion heat transport in multi-species plasmas. The RKM successfully reproduces local results for multi-species ion systems and the important features expected to arise due to non-local effects on the heat flux are captured. In addition to this, novel features associated with multi-species, as opposed to single species, cases are found. Effects of non-locality on the heat flux are investigated in mass and charge symmetric and asymmetric ion mixtures with temperature, pressure, and concentration gradients. In particular, the enthalpy flux associated with diffusion is found to be insensitive to sharp pressure and concentration gradients, increasing its significance in comparison to the conductive heat flux driven by temperature gradients in non-local scenarios. The RKM code can be used for investigating other kinetic and non-local effects in a broader plasma physics context. Due to its relatively low computational cost it can also serve as a practical non-local ion heat flux closure in hydrodynamic simulations or as a training tool for machine learning surrogates.

Anomalous transport of multi-species edge plasma with the generalized Hasegawa–Wakatani model and the FLR effects

Anomalous transport of multi-species edge plasma with the generalized Hasegawa–Wakatani model and the FLR effects

On anomalous transport of multi-species plasma associated with the resistive ballooning and resistive drift waves driven turbulence

Anomalous transport of multi-species plasma related to the resistive ballooning and resistive drift wave turbulence is considered in a “cold” ion approximation. It is found that similar to the resistive drift wave turbulence [see A. R. Knyazev and S. I. Krasheninnikov, Phys. Plasmas 31, 012502 (2024); and S. I. Krasheninnikov and R. D. Smirnov, Phys. Plasmas (to be published)] the addition of the ballooning drive does not change the main features of anomalous transport of the multi-species plasma: (i) The transport of all ion species is described as a transport of the passive scalars in the turbulent field of the electrostatic potential and electron density perturbation; (ii) the density of ion species with a larger ratio of the mass to charge has the tendency to the accumulation/depletion in the vortices of plasma flow; and (iii) the cross-field transport of all plasma species (including electrons and ions) is described by the same anomalous transport coefficient.

Resistive drift wave turbulence and anomalous transport of multi-species plasma

Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.

Electrostatic solitary waves in a bi-ion plasma with two suprathermal electron populations – application to Saturn’s magnetosphere

ABSTRACT Non-thermal particle distributions characterized by a high-energy tail are ubiquitous in space plasmas. They are usually described by a kappa distribution function, that has been shown to be an excellent fit in most real circumstances. Among other space missions, Cassini and Voyager have both recorded evidence of a coexistence of non-thermal electron populations (with different characteristics) in Saturn’s magnetosphere, and subsequent studies showed that these are well-described by using different tailor-fit realizations of the (parametrized) kappa distribution. Motivated by these observations we have formulated a multifluid plasma model incorporating two types of (positive) ions and two distinct kappa-distributed electron populations, in order to study electrostatic solitary waves (ESWs) in Saturn’s magnetosphere from first principles. Our analysis reveals that the spectral index (in fact, the κ parameter value related to the cold electron population mainly) is vital in explaining the difference among different types of non-linear structures. A comparison with spacecraft observations suggests that our theoretical model provides an efficient framework for the interpretation of ESW observations in Saturn’s magnetosphere. Our qualitative predictions may also apply to other planetary magnetospheres, where a similar multispecies plasma composition may be present.

Supervised machine learning-based multivariate regression of parallel closures for a high-collisionality deuterium-carbon plasma

Many plasmas of interest in laboratory experiments and space consist of multiple ion species. In tokamak edge plasmas, for instance, ionized impurities expelled from the vessel wall influence plasma transport. When describing multi-species plasmas using fluid equations, we need accurate closure relations to close the set of fluid equations. In this study, we introduce the development of fitting formulas for parallel closures using supervised machine learning, in conjunction with the recent closure theory [J.-Y. Ji, Plasma Phys. Controlled Fusion 65, 075014 (2023)], considering multi-ion collisions and arbitrary ion temperatures. We apply this approach to a high-collisionality deuterium-carbon plasma and demonstrate its effectiveness. The machine learning-based method for developing practical and accurate closures can be extended to a wider range of plasmas.

Analytical soliton solutions and wave profiles of the (3+1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation

In this research paper, the improved generalized Riccati equation mapping (IGREM) method is employed to get analytical soliton solutions of (3+1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV-ZK) equation. By giving appropriate parametric values, we obtain soliton solutions of various types, such as kink soliton, singular soliton, and periodic-singular soliton. The description provided in physical variables allows for the study of genuine multispecies plasmas, plasma models, and frequency regimes. These solutions are essential in illuminating several physical phenomena in engineering and other applied sciences. In addition, 3D and 2D graphs of some selected solutions are sketched for the best physical characterization of the obtained results. This method can also be implemented in many non-linear equations in contemporary research areas. Comparison with previous studies shows that the discovery of singular soliton is novel. Therefore, our research represents a significant advancement in the field and contributes to expanding the knowledge regarding soliton behavior. The applications of this study include electron and ion-acoustic modes in regular plasmas with hot Boltzmann electron species, as well as ion and dust-acoustic modes, depending on the specific modeling of the heavier components.

Dynamics of ion-acoustic waves in multi-species quantum plasmas with arbitrary degeneracy

Dynamics of ion-acoustic waves in multi-species quantum plasmas with arbitrary degeneracy

Collisional effects on the process of phase mixing of electron–positron oscillations in multispecies plasmas

Collisional effects on the process of phase mixing of electron–positron oscillations in multispecies plasmas

The Morphology and Dynamics of Relativistic Jets with Relativistic Equation of State

We study the effect of plasma composition on the dynamics and morphology of relativistic astrophysical jets. Our work is based on a relativistic total variation diminishing simulation code. We use a relativistic equation of state in the simulation code that accounts for the thermodynamics of a multispecies plasma, which is a mixture of electrons, positrons, and protons. To study the effect of plasma composition, we consider various jet models. These models are characterized by the same injection parameters, same jet kinetic luminosity, and the same Mach numbers. The evolution of these models shows that the plasma composition affects the propagation speed of the jet head, the structure of the jet head, and the morphology, despite fixing the initial parameters. We conclude that electron-positron jets are the slowest and show more pronounced turbulent structures in comparison to other plasma compositions. The area and locations of the hot-spots also depend on the composition of the jet plasma. Our results also show that boosting mechanisms are an important aspect of multi-dimensional simulations, which are also influenced by the change in composition.

The competing effects of wave amplitude and collisions on multi-ion species suppression of stimulated Brillouin scattering in inertial confinement fusion Hohlraums

Reduction in stimulated Brillouin scattering (SBS) from National Ignition Facility Hohlraums has been predicted through the use of multi-ion species materials on Hohlraum walls. This approach to controlling SBS is based upon introducing a lighter ion species to the heavier ion species Hohlraum wall in order to greatly increase the ion Landau damping of ion acoustic waves (IAWs). In a collisionless plasma, if the IAWs driven by SBS reach sufficient amplitudes, this increased damping is reduced or even eliminated by ion trapping in the IAWs. Here, the nonlinear behavior of IAWs is simulated with a multi-ion species Vlasov code, including interspecies ion–ion collisions, self-collisions, and electron–ion pitch-angle collisions. The effect of collisions on the trapping of ions and electrons in a large-amplitude IAW is studied in a regime of relevance to current Inertial Confinement Fusion experiments. Our simulations show that collisions can scatter trapped particles out of resonance with the IAW, suppressing trapping and helping to maintain an effective Landau damping of the IAW. The IAW amplitude required to trap particles in the presence of strong collisions is estimated analytically. These estimates are tested for strongly damped IAWs in tantalum oxide and pure helium plasmas. Our simulations show that, above a threshold amplitude, the damping is reduced by an amount inversely proportional to the wave amplitude. Thus, the success of controlling SBS using a multispecies plasma may depend sensitively on laser power and pulse length.

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.

Head-on collision between two-counter-propagating electron acoustic soliton and double layer in an unmagnetized plasma

The head-on collision between two-counter-propagating electron acoustic solitons and double layers (DLs) in an unmagnetized collisionless multi-species plasma consisting of inertial cold electron fluid and (α, q)-distributed hot electrons and positrons has been analyzed with the stationary background of massive positive ions. For nonlinear analysis of colliding wave phenomena, the coupled Korteweg–de Vries equation (KdVE), modified KdVE (mKdVE), and standard Gardner equation have been derived by adopting the extended Poincaré–Lighthill–Kuo technique. The effect of non-dimensional parameters on the collisional KdV, mKdV, and Gardner solitons (GSs) and DLs has been examined in detail by considering the limiting cases of (α, q)-distributions. It is found that the plasma model supports (i) the compressive and rarefactive collisional KdV solitons and GSs, (ii) only compressive mKdV solitons, and (iii) only rarefactive collisional DLs. The rarefactive collisional solitons are more affected by nonextensivity and the increase of the temperature of electrons than their compressive counterpart, whereas the rarefactive collisional DLs only existed in the presence of nonthermality.