Kinetic Plasma Research Articles

Identification and characterization of current sheets in collisionless plasmas turbulence

Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets.

Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes

This paper contributes new insights into discretizing Coulomb collisions in kinetic plasma models. Building on the previous works (Carrillo et al 2020 J. Comput. Phys. X 7 100066; Hirvijoki and Burby 2020 Phys. Plasmas 27 082307), I propose deterministic discrete-time energy- and positivity-preserving, entropy-dissipating marker-particle schemes for the standard Landau collision operator and the electrostatic gyrokinetic Landau operator. In the case of the standard Landau operator, the scheme preserves also the discrete-time kinetic momentum. The improvements, the extensions of the structure-preserving discretizations by Carrillo et al (2020 J. Comput. Phys. X 7 100066) and Hirvijoki and Burby (2020 Phys. Plasmas 27 082307) to discrete time, are made possible by exploiting the underlying metriplectic structure of the collision operators involved and the so-called discrete-gradient integrators.

The effects of density inhomogeneities on the radio wave emission in electron beam plasmas

Type III radio bursts are radio emissions associated with solar flares. They are considered to be caused by electron beams travelling from the solar corona to the solar wind. Magnetic reconnection is a possible accelerator of electron beams in the course of solar flares since it causes unstable distribution functions and density inhomogeneities (cavities). The properties of radio emission by electron beams in an inhomogeneous environment are still poorly understood. We capture the nonlinear kinetic plasma processes of the generation of beam-related radio emissions in inhomogeneous plasmas by utilizing fully kinetic particle-in-cell code numerical simulations. Our model takes into account initial electron velocity distribution functions (EVDFs) as they are supposed to be created by magnetic reconnection. We focus our analysis on low-density regions with strong magnetic fields. The assumed EVDFs allow two distinct mechanisms of radio wave emissions: plasma emission due to wave–wave interactions and so-called electron cyclotron maser emission (ECME) due to direct wave–particle interactions. We investigate the effects of density inhomogeneities on the conversion of free energy from the electron beams into the energy of electrostatic and electromagnetic waves via plasma emission and ECME, as well as the frequency shift of electron resonances caused by perpendicular gradients in the beam EVDFs. Our most important finding is that the number of harmonics of Langmuir waves increases due to the presence of density inhomogeneities. The additional harmonics of Langmuir waves are generated by a coalescence of beam-generated Langmuir waves and their harmonics.

Harmonic Electron Cyclotron Maser Emission Excited by Energetic Electrons Traveling inside a Coronal Loop

Abstract A complete understanding of solar radio bursts requires developing numerical techniques that can connect large-scale activities with kinetic plasma processes. As a starting point, this study presents a numerical scheme combining three different techniques: (1) extrapolation of the magnetic field overlying a specific active region in order to derive the background field, (2) guiding-center simulation of the dynamics of millions of particles within a selected loop to reveal the integral velocity distribution function (VDF) around certain sections of the loop, and (3) particle-in-cell simulation of kinetic instabilities driven by energetic electrons initiated by the obtained distributions. Scattering effects at various levels (weak, moderate, and strong) due to wave turbulence-particle interaction are considered using prescribed timescales of scattering. It was found that the obtained VDFs contain strip-like and loss-cone features with positive gradient, and both features are capable of driving electron cyclotron maser emission, which is a viable radiation mechanism for some solar radio bursts, in particular, solar radio spikes. The strip-like feature is important in driving the harmonic X mode, while the loss-cone feature can be important in driving the fundamental X mode. In the weak-scattering case, the rate of energy conversion from energetic electrons to X2 can reach up to , where is the initial kinetic energy of energetic electrons. The study demonstrates a novel way of exciting the X2 mode in the corona during solar flares and provides new sight into how escaping radiation can be generated within a coronal loop.

Mirror Instabilities in the Inner Magnetosphere and Their Potential for Localized ULF Wave Generation.

Results from the NASA Van Allen Probes mission indicate extensive observations of mirror/drift‐mirror (M/D‐M hereafter) unstable plasma regions in the night‐side inner magnetosphere. Said plasmas lie on the threshold between the kinetic and frozen‐in plasma regimes and have favorable conditions for the formation of M/D‐M modes and subsequent ultralow frequency (ULF) wave signatures in the surrounding plasma. We present the results of a climatological analysis of plasma‐γ (anisotropy measure) and total plasma‐β (ratio of particle to magnetic field pressure) in regard to the satisfaction of instability conditions on said M/D‐M modes under bi‐Maxwellian distribution assumption, and ascertain the most likely region for such plasmas to occur. Our results indicate a strong preference for the premidnight sector of the night‐side magnetosphere, with events ranging in time scales from half a minute (roughly 200 km in scale size) to several hours (multiple Earth radii). The statistical distribution of these plasma regions explicitly identifies the source region of “storm time Pc5 ULF waves” and suggests an alternative mechanism for their generation in the night‐side inner magnetosphere.

Kinetic Model of Large-amplitude Oscillations in Neutron Star Pair Cascades

Abstract Electron–positron pair cascades developed in the extreme electromagnetic fields of neutron star polar caps are considered a key source of magnetospheric plasma in these objects. We use a simplified model that maps the quantum electrodynamics processes governing pair cascades to analytically and numerically model these cascades, and show that large-amplitude oscillations of the electric field are inductively driven by the resulting plasma. A plasma instability arises in these oscillations, and particles accelerated in growing electric field perturbations can drive secondary pair bursts that damp the large-amplitude oscillations. An analytical model is proposed to describe this interplay between the pair production and kinetic collective plasma processes. All analytical results are shown to be in excellent agreement with particle-in-cell simulations.

Plasma physics and astrophysics: retrospects, state-of-the art, and prospects

Within the special issue “Classical and quantum plasmas: matter under extreme conditions” a series of papers are included that were presented at the international workshop “Plasma Physics and Astrophysics up to 2020 and beyond”. This meeting was held on October 7th–8th 2019 at the Physics Department of the Universita della Calabria in Rende (Italy) and was organised by the Physics Department “Astrophysics, Geophysics and Plasma Group” in connection with the celebration of Pierluigi Veltri’s 70th birthday. The goal of this interdisciplinary workshop was to review some of the main achievements in plasma physics in the last five decades from laboratory to space and astrophysical plasmas and to discuss future developments. It was attended by experimentalists, theoreticians and by scientists involved in numerical plasma modelling with the aim of promoting the exchange of ideas and collaborations between different communities working on plasma physics in different contexts. The participants discussed fundamental physics aspects of fluid and plasma turbulence, of magnetic field line reconnection, of shock wave dynamics and of kinetic and nonlinear plasma phenomena highlighting new results and novel approaches, as well as exchanging ideas between different branches of plasma physics.

Fast hybrid particle-in-cell technique for pulsed-power accelerators

Hybrid-implicit particle-in-cell (PIC) algorithms permit the simulation of complex problems involving both kinetic and fluid plasma regimes over large spatial and temporal scales. Fluid electrons can be computationally fast where and when fluid assumptions are valid. Additional flexibility is obtained if discrete PIC macroparticles, with velocities advanced by either fluid or kinetic equations, are permitted to dynamically migrate between the two descriptions based on phase space criteria. Ideally, these migrations result in energetic particles treated kinetically and dense thermal plasma particles as a fluid. With an energy-conserving particle advance, resolution of the plasma Debye length is not required for numerical accuracy or stability. For pulsed-power applications, the simulation time step is usually constrained by the electron cyclotron frequency, not the more restrictive plasma frequency. A new implicit technique permits accurate particle orbits even at highly underresolved cyclotron frequencies. Thus, greater temporal and spatial scales can be accurately modeled relative to conventional PIC techniques. In this paper, we describe the hybrid PIC technique and fully electromagnetic, hybrid simulations of plasma evolution and current shunting in an idealized accelerator designed for driving a $Z$-pinch load. The dynamics of electrode heating, electron transport, and surface contaminant evolution are studied in a series of relativistic hybrid-implicit PIC simulations. These dynamics can lead to the shunting of current before reaching the $Z$-pinch load, thus degrading load performance. Examining two previously published power flow problems, we compare results from fully kinetic, multifluid, and hybrid kinetic-fluid simulations and discuss the computational performance of these three options. The key thrust of the work is to identify possible computational acceleration, through hybrid methods, required for accelerator understanding and design.

Plasma Double Layers at the Boundary Between Venus and the Solar Wind.

The solar wind is slowed, deflected, and heated as it encounters Venus's induced magnetosphere. The importance of kinetic plasma processes to these interactions has not been examined in detail, due to a lack of constraining observations. In this study, kinetic‐scale electric field structures are identified in the Venusian magnetosheath, including plasma double layers. The double layers may be driven by currents or mixing of inhomogeneous plasmas near the edge of the magnetosheath. Estimated double‐layer spatial scales are consistent with those reported at Earth. Estimated potential drops are similar to electron temperature gradients across the bow shock. Many double layers are found in few high cadence data captures, suggesting that their amplitudes are high relative to other magnetosheath plasma waves. These are the first direct observations of plasma double layers beyond near‐Earth space, supporting the idea that kinetic plasma processes are active in many space plasma environments.

Bridging kinetic plasma descriptions and single-fluid models

The purpose of this paper is to bridge kinetic plasma descriptions and low-frequency single-fluid models. More specifically, the asymptotics leading to magnetohydrodynamic regimes starting from the Vlasov–Maxwell system are investigated. The analogy with the derivation, from the Vlasov–Poisson system, of a fluid representation for ions coupled to the Boltzmann relation for electrons is also outlined. The aim is to identify asymptotic parameters explaining the transitions from one microscopic description to a macroscopic low-frequency model. These investigations provide groundwork for the derivation of multi-scale numerical methods, model coupling or physics-based preconditioning.

Space-filter techniques for quasi-neutral hybrid-kinetic models

The space-filter approach has been proved as a fundamental tool in studying turbulence in neutral fluids, providing the ability to analyze scale-to-scale energy transfer in configuration space. It is well known that turbulence in plasma presents challenges different from neutral fluids, especially when the scale of interest includes kinetic effects. The space-filter approach is still largely unexplored for kinetic plasma. Here, we derive the space-filtered (or equivalently “coarse-grained”) equations in configuration space for a quasi-neutral hybrid-kinetic plasma model, in which ions are fully kinetic and electrons are a neutralizing fluid. Different models and closures for the electron fluid are considered, including finite electron-inertia effects and full electrons' pressure-tensor dynamics. Implications for the cascade of turbulent fluctuations in real space depending on different approximations are discussed.

Exploring the Acceleration Mechanisms for Particle Injection and Power-law Formation during Transrelativistic Magnetic Reconnection

Abstract Magnetic reconnection in the relativistic and transrelativistic regimes is able to accelerate particles to hard power-law energy spectra f ∝ γ −p (approaching p = 1). The underlying acceleration mechanism that determines the spectral shape is currently a topic of intense investigation. By means of fully kinetic plasma simulations, we carry out a study of particle acceleration during magnetic reconnection in the transrelativistic regime of a proton–electron plasma. While earlier work in this parameter regime has focused on the effects of electric field parallel to the local magnetic field on the particle injection (from thermal energy to the lower-energy bound of the power-law spectrum), here we examine the roles of both parallel and perpendicular electric fields to gain a more complete understanding on the injection process and further development of a power-law spectrum. We show that the parallel electric field does contribute significantly to particle injection, and is more important in the initial phase of magnetic reconnection. However, as the simulation proceeds, the acceleration by the perpendicular electric field becomes more important for particle injection and completely dominates the acceleration responsible for the high-energy power-law spectrum. This holds robustly, in particular for longer reconnection times and larger systems, i.e., in simulations that are more indicative of the processes in astrophysical sources.

A relativistic particle pusher for ultra-strong electromagnetic fields

Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above$\gamma \approx 10^3$–$10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to$10^{15}$or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

Variational integrators for stochastic dissipative Hamiltonian systems

Abstract Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian, which approximates a type-II stochastic generating function for the stochastic flow of the Hamiltonian system. The generating function is obtained by introducing an appropriate stochastic action functional and considering a stochastic generalization of the deterministic Lagrange–d’Alembert principle. Our approach presents a general methodology to derive new structure-preserving numerical schemes. The resulting integrators satisfy a discrete version of the stochastic Lagrange–d’Alembert principle, and in the presence of symmetries, they also satisfy a discrete counterpart of Noether’s theorem. Furthermore, mean-square and weak Lagrange–d’Alembert Runge–Kutta methods are proposed and tested numerically to demonstrate their superior long-time numerical stability and energy behaviour compared to nongeometric methods. The Vlasov–Fokker–Planck equation is considered as one of the numerical test cases, and a new geometric approach to collisional kinetic plasmas is presented.

Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

We present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker–Planck collision operators. These operators arise in many fields of physics, and our particular application is for kinetic plasma simulations. In particular, we focus on an operator often known as the ‘Lenard–Bernstein’ or ‘Dougherty’ operator. Several novel algorithmic innovations, based on the concept of weak equality, are reported. These weak equalities are used to define weak operators that compute primitive moments, and are also used to determine a reconstruction procedure that allows an efficient and accurate discretization of the diffusion term. We show that when two integrations by parts are used to construct the discrete weak form, and finite velocity-space extents are accounted for, a scheme that conserves density, momentum and energy exactly is obtained. One novel feature is that the requirements of momentum and energy conservation lead to unique formulas to compute primitive moments. Careful definition of discretized moments also ensure that energy is conserved in the piecewise linear case, even though the kinetic-energy term, $v^{2}$ is not included in the basis set used in the discretization. A series of benchmark problems is presented and shows that the scheme conserves momentum and energy to machine precision. Empirical evidence also indicates that entropy is a non-decreasing function. The collision terms are combined with the Vlasov equation to study collisional Landau damping and plasma heating via magnetic pumping.

Plasma simulation to analyze velocity distribution characteristics of pseudospark-sourced electron beam**Project supported by the Sichuan Science and Technology Program, China (Grant No. 2019YJ0188) and the National Natural Science Foundation of China (Grant Nos. 61671116 and 11905026).

Pseudospark-sourced electron beam is a promising candidate for driving vacuum electronic devices to generate millimeter wave and terahertz wave radiation as it has a very high combined beam current density. However, the inherent velocity spread of the beam, which is difficult to measure in experiment, has a great influence on the operating frequency and efficiency of the vacuum electronic device. In this paper, the velocity distribution characteristics of the electron beam produced by a single-gap hollow cathode electron gun are numerically studied and a three-dimensional kinetic plasma simulation model of a single-gap hollow cathode electron gun is built by using particle in cell and Monte Carlo collision methods in Vorpal. Based on the simulation model, the time-dependent evolution of the plasma formation inside the hollow cathode and electron beam generation process are observed. It is demonstrated that the pseudospark-sourced electron beam has a relatively large velocity spread. The time-dependent velocity distribution of the beam is analyzed, and the dependence of the beam velocity distribution under various operating conditions such as anode–cathode potential difference, gas pressure, and cathode aperture size are also studied.

Origin of Pulsar Radio Emission

Since pulsars were discovered as emitters of bright coherent radio emission more than half a century ago, the cause of the emission has remained a mystery. In this Letter we demonstrate that coherent radiation can be directly generated in nonstationary pair plasma discharges which are responsible for filling the pulsar magnetosphere with plasma. By means of large-scale two-dimensional kinetic plasma simulations, we show that if pair creation is nonuniform across magnetic field lines, the screening of electric field by freshly produced pair plasma is accompanied by the emission of waves which are electromagnetic in nature. Using localized simulations of the screening process, we identify these waves as superluminal ordinary (O) modes, which should freely escape from the magnetosphere as the plasma density drops along the wave path. The spectrum of the waves is broadband and the frequency range is comparable to that of observed pulsar radio emission.

Schur Complement and Continuous Spectrum in a Kinetic Plasma Model

The goal of this paper is spectral analysis of an evolutionary semigroup generator describing the dynamics of a rarefied two-component plasma subjected to a self-consistent electromagnetic field. For the problem in question, the spectrum is given in terms of the dispersion relationship and an effective approach to the calculation of the instability index is developed.

Dependence of kinetic plasma waves on ion-to-electron mass ratio and light-to-Alfvén speed ratio

ABSTRACT The magnetization |Ωe|/ωe is an important parameter in plasma astrophysics, where Ωe and ωe are the electron gyro-frequency and electron plasma frequency, respectively. It depends only on the mass ratio mi/me and the light-to-Alfvén speed ratio c/vAi, where mi (me) is the ion (electron) mass, c is the speed of light, and vAi is the ion Alfvén speed. Non-linear numerical plasma models such as particle-in-cell simulations must often assume unrealistic values for mi/me and for c/vAi. Because linear theory yields exact results for parametric scalings of wave properties at small amplitudes, we use linear theory to investigate the dispersion relations of Alfvén/ion-cyclotron and fast-magnetosonic/whistler waves as prime examples for collective plasma behaviour depending on mi/me and c/vAi. We analyse their dependence on mi/me and c/vAi in quasi-parallel and quasi-perpendicular directions of propagation with respect to the background magnetic field for a plasma with βj ∼ 1, where βj is the ratio of the thermal to magnetic pressure for species j. Although their dispersion relations are largely independent of c/vAi for c/vAi ≳ 10, the mass ratio mi/me has a strong effect at scales smaller than the ion inertial length. Moreover, we study the impact of relativistic electron effects on the dispersion relations. Based on our results, we recommend aiming for a more realistic value of mi/me than for a more realistic value of c/vAi in non-relativistic plasma simulations if such a choice is necessary, although relativistic and sub-Debye-length effects may require an additional adjustment of c/vAi.

Macroscopic and parametric study of a kinetic plasma expansion in a paraxial magnetic nozzle

A kinetic paraxial model of a collisionless plasma stationary expansion in a convergent-divergent magnetic nozzle (MN) is analyzed. Monoenergetic and Maxwellian velocity distribution functions of upstream ions are compared, leading to differences in the expansion only on second and higher-order velocity moments. Individual and collective magnetic mirror effects are analyzed. Collective ones are small on the electron population since only a weak temperature anisotropy develops, but they are significant on the ions all over the nozzle. Momentum and energy equations for ions and electrons are assessed based on the kinetic solution. The ion response is different in the hot and cold limits, with the anisotropic pressure tensor being relevant in the first case. Heat fluxes of parallel and perpendicular energies have a dominant role in the electron energy equations. They do not fulfill a Fourier-type law; they are large even when electrons are near isothermal. A crude electron fluid closure based on a constant diffusion-to-convective thermal energy ratio is shown equivalent to the much invoked polytropic law. Analytical dimensionless parameter laws are derived for the nozzle total electric potential fall and the downstream residual electron temperature. Electron confinement and related current control by a thin Debye sheath and a semi-infinite divergent MN are compared.