Collisionless Plasma Research Articles

A superstatistical measure of distance from canonical equilibrium

Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical frameworks such as superstatistics, which assumes that the inverse temperature β=1/(kBT) is an unknown quantity having some pre-established statistical distribution. The uncertainty in β is usually understood as the fluctuation of a physical observable, however, it has been previously proved (Davis and Gutiérrez 2018 Physica A 505 864–70) that β in a superstatistical model cannot be associated to an observable function B(Γ) of the microstates Γ. In this work, we provide an information-theoretical interpretation of this theorem by introducing a new quantity D , the mutual information between β and Γ. Our results show that D is also a measure of departure from canonical equilibrium, and reveal a minimum, non-zero uncertainty about β given Γ for every non-canonical superstatistical ensemble. The behavior of D is illustrated in the case of a collisionless plasma described by kappa distributions, revealing the precise sense in which the spectral index κ can be understood as a measure of distance from equilibrium.

Mathematical simulation of ionospheric plasma diagnostics by electric current measurements using an insulated probe system

The goal of this work is to theoretically substantiate the possibility of determining the charged particle density in the ionospheric plasma by separately measuring the electric currents of an insulated probe system in the electron saturation region. The ionospheric plasma composition is modeled by two ion species with significantly different masses and electrons to keep the plasma quasi-neutrality. The probe system, which is electrically insulated from the spacecraft structure, consists of cylindrical electrodes: a probe and a reference electrode. The reference electrode to probe current-collecting area ratio can be significantly less than required by the single cylindrical probe theory. The electrodes are oriented transversely to a supersonic flow of a collisionless plasma. In addition to the main plasma with two ion species, a model plasma with a single ion species is considered. The mass of the model ions is such that the ion saturation current to the cylinder is the same for both plasma models. Based on a previously obtained asymptotic solution for the electron saturation current in a plasma with a single ion species, computational formulas are found for determining the ion mass composition and the electron density by probe current measurements. The errors of the formulas are estimated numerically and analytically as a function of the probe system geometry, the bias potential of the probe relative to the reference electrode, and the accuracy of potential and current measurements. It is shown that a proper choice of the probe system settings and the accuracy of probe measurements assures a reliable determination of the charged particle densities in a plasma with two ion species. A priori estimates are presented for the effect of the current bias potential measurement errors on the reliability of determining the ion mass composition and the electron density of the ionospheric plasma.

Laboratory Study of Magnetic Reconnection in Lunar-relevant Mini-magnetospheres

Mini-magnetospheres are small ion-scale structures that are well suited to studying kinetic-scale physics of collisionless space plasmas. Such ion-scale magnetospheres can be found on local regions of the Moon, associated with the lunar crustal magnetic field. In this paper, we report on the laboratory experimental study of magnetic reconnection in laser-driven, lunar-like ion-scale magnetospheres on the Large Plasma Device at the University of California, Los Angeles. In the experiment, a high-repetition rate (1 Hz), nanosecond laser is used to drive a fast-moving, collisionless plasma that expands into the field generated by a pulsed magnetic dipole embedded into a background plasma and magnetic field. The high-repetition rate enables the acquisition of time-resolved volumetric data of the magnetic and electric fields to characterize magnetic reconnection and calculate the reconnection rate. We notably observe the formation of Hall fields associated with reconnection. Particle-in-cell simulations reproducing the experimental results were performed to study the microphysics of the interaction. By analyzing the generalized Ohm’s law terms, we find that the electron-only reconnection is driven by kinetic effects through the electron pressure anisotropy. These results are compared to recent satellite measurements that found evidence of magnetic reconnection near the lunar surface.

Fundamental difference between the mechanisms of electrostatic field screening in dense and thoroughly collisionless plasmas

When an external electric field appears in a homogeneous plasma, ions move into regions where their electrostatic energy is lower. Simultaneously, forces arise that counteract this effect, causing the plasma to reach equilibrium when the field disappears completely. In collisional plasma, the resulting charge inhomogeneities decrease both Coulomb energy and entropy. Randomly induced diffusion flows tend to hinder their growth, minimizing free energy at any point. Accordingly, in the Debye–Hückel theory, the external field strength decreases exponentially with distance within the plasma. In a collisionless plasma, an antiscreening mechanism operates differently. Each ion moves in a self-consistent field along distinct trajectories, following classical dynamics laws. An external field bends these trajectories, bringing ions into regions where their Coulomb energy is lower. The antiscreening mechanism occurs when ions accelerate into potential wells, increasing the distances between them along their trajectories and decreasing their number densities along these paths. The law of energy conservation for any single ion governs this principally nonlocal process, and the dependence of field strength on distance is not necessarily exponential. This paper demonstrates that the Debye–Hückel theory should not be used to describe the charge density distribution within an unrestricted stream of collisionless plasma, such as the solar wind. It also analyzes non-exponential solutions of the Poisson equation for plasma sheaths above flat surfaces, from which such a flow takes off and on which it falls, obtained in quadratures.

Numerical analysis of three-dimensional magnetopause-like reconnection properties by Hall MHD simulation for SPERF-AREX

The ground-based device, the Space Plasma Environment Research Facility (SPERF), is established for experimentally simulating magnetosphere plasma processes, with one of its major components, asymmetric reconnection experiment (AREX), for three-dimensional physics relevant to dayside asymmetric magnetopause reconnection. As an outstanding property of fast magnetic reconnection in collisionless plasmas, the Hall effect and its geometric features can be experimentally investigated in SPERF-AREX with various magnetic configurations related to different driven scenarios for simulating interplanetary magnetic field (IMF) conditions. In this work, the Hall effect and its geometric characteristics in such proposed experiments are numerically studied based on a Hall MHD model. The simulation results reveal that in the X-line geometry relevant to southward IMFs, the Hall field features in cross section perpendicular to the X-line are mostly analogous to typical two-dimensional Hall quadrupole structures, clearly an “anti-parallel reconnection” feature. In the separator (A-B null-line) geometry relevant to arbitrary IMF orientations, along the separator between magnetic nulls, the magnetic field configuration near a magnetic null also demonstrates the typical quadrupolar pattern. However, the pattern is distorted away (>10di, here di=c/ωpi is the ion inertial length) from the nulls, in a way similar to that in “component reconnection.” Furthermore, the Hall effect induces a dawn-dusk asymmetry for both the X-line and the separator geometries.

Plasma compressibility and the generation of electrostatic electron Kelvin–Helmholtz instability

This study explores the generation of electrostatic (ES) electron Kelvin–Helmholtz instability (EKHI) in collisionless plasma with a step-function electron velocity shear akin to that developed in the electron diffusion region in magnetic reconnection. In incompressible plasma, ES EKHI does not arise in any velocity shear profile due to the decoupling of the electric potential from the electron momentum equation. Instead, a fluid-like Kelvin–Helmholtz instability (KHI) can arise. However, in compressible plasma, the compressibility couples the electric potential with the electron dynamics, leading to the emergence of a new ES mode EKHI on Debye length λDe, accompanied by the co-generation of an electron acoustic-like wave. The minimum threshold of ES EKHI is ΔU>2cse, i.e., the electron velocity shear is larger than twice the electron acoustic speed cse. The corresponding growth rate is Im(ω)=((ΔU/cse)2−4)1/2ωpe, where ωpe is the electron plasma frequency.

The Response of the Magnetosphere to Changes in the Solar Wind Dynamic Pressure: 2. Ion and Electron Kappa Distribution Functions

AbstractThe Earth's magnetosphere is filled with a collisionless plasma that exhibits non‐Maxwellian particle distributions which are well described by Kappa functions. In contrast to the Maxwellian, the Kappa contains not only density and temperature but also the kappa index that allows us to characterize the energetic tails. In this study, we analyze the response of the ion and electron Kappa distributions, obtained by fitting ion and electron fluxes measured by the five THEMIS satellites, to changes of the solar wind dynamic pressure. It was found that the solar wind dynamic pressure strongly affects the values of the kappa index, and that its impact depends on the magnetic local time (MLT). In particular, there is a significant dawn‐dusk asymmetry for low PSW values which is enhanced in the night side. Further, we observe a narrow partial ring‐shaped structure at different azimuthal extension that divides the plasma into two clearly defined domains. The results obtained reflect the global reconfiguration of the magnetosphere caused by variations of the solar wind dynamic pressure. Kappa distribution parameters and their average values for different ranges of PSW and MLT are provided, which we believe will contribute as realistic inputs to the modeling of the magnetosphere.

Firehose instability in heat-conducting solar wind plasmas including FLR corrections and electrical resistivity

The effects of finite Larmor radius (FLR) corrections and heat-flux vector are studied on the pressure anisotropy-driven firehose instability in finitely conducting solar wind plasmas described by the double-adiabatic Chew, Goldberger and Low (CGL) fluid theory. The fluid description of collisionless plasmas is governed through modified adiabatic equations due to the heat-flux vector and finite ion Larmor radius corrections. The analytical dispersion relation of the firehose instability has been derived using the normal mode analysis and discussed in the solar wind plasmas. In the transverse mode, the dispersion relation of the Alfvénic mode is modified due to electrical resistivity and FLR corrections. In the longitudinal mode, the effects of the heat-flux parameter and electrical resistivity are observed separately. The dispersion relation of the firehose mode is modified due to the combined effects of FLR corrections and electrical resistivity. The graphical illustrations show that finite electrical resistivity and ion Larmor frequency destabilize the growth rate of the firehose instability. The results are useful for analyzing the solar mission data to study the firehose instability in the solar wind plasmas.

Derivation of dirac exchange interaction potential from quantum plasma kinetic theory

The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for real systems is worked out, in terms of temperature and density parameters. Within the region of applicability, the correlation potential energy is shown to be always smaller than the exchange contribution. From the moments of the quantum kinetic equations, macroscopic, hydrodynamic equations are found, for an electron-ion plasma. The Dirac exchange term is explicitly derived, in the case of a completely degenerate electron gas. These results show, within quantum kinetic theory for charged particle systems, a new view of the Dirac exchange interaction frequently used in density functional theory parametrization. Finally, a simpler form of the quantum plasma exchange kinetic theory is also found.

Landau Damping and Kinetic Instabilities

Landau’s method works out waves and damping in collisionless plasmas, and in particular his prescription for dealing with the singularities in the integrals. The physical consequences resulting from Landau damping are illustrate with restriction to high frequency oscillations, i.e. that only the electrons respond to the wave. Thus, around the wave-particle resonance , the particles just lagging behind the wave receive energy from the wave and those just overtaking it give up energy to wave. This process is therefore intrinsically of kinetic nature.

Dominance of polarization modes and external magnetic field on self-focusing of laser beams in collisionless magnetized plasma

Dominance of polarization modes and external magnetic field on self-focusing of laser beams in collisionless magnetized plasma

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence.

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equationfor the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

Quantized tensor networks for solving the Vlasov–Maxwell equations

The Vlasov–Maxwell equations provide an ab initio description of collisionless plasmas, but solving them is often impractical because of the wide range of spatial and temporal scales that must be resolved and the high dimensionality of the problem. In this work, we present a quantum-inspired semi-implicit Vlasov–Maxwell solver that uses the quantized tensor network (QTN) framework. With this QTN solver, the cost of grid-based numerical simulation of size $N$ is reduced from $O(N)$ to $O(\text {poly}(D))$ , where $D$ is the ‘rank’ or ‘bond dimension’ of the QTN and is typically set to be much smaller than $N$ . We find that for the five-dimensional test problems considered here, a modest $D=64$ appears to be sufficient for capturing the expected physics despite the simulations using a total of $N=2^{36}$ grid points, which would require $D=2^{18}$ for full-rank calculations. Additionally, we observe that a QTN time evolution scheme based on the Dirac–Frenkel variational principle allows one to use somewhat larger time steps than prescribed by the Courant–Friedrichs–Lewy constraint. As such, this work demonstrates that the QTN format is a promising means of approximately solving the Vlasov–Maxwell equations with significantly reduced cost.

Ponderomotive cross focusing and filamentation of two coaxial $$q$$-gaussian laser beams in collisionless plasmas

Ponderomotive cross focusing and filamentation of two coaxial $$q$$-gaussian laser beams in collisionless plasmas

Gyrofluid simulations of turbulence and reconnection in space plasmas

A Hamiltonian two-field gyrofluid model is used to investigate the dynamics of an electron-ion collisionless plasma subject to a strong ambient magnetic field, within a spectral range extending from the magnetohydrodynamic (MHD) scales to the electron skin depth. This model isolates Alfvén, Kinetic Alfvén and Inertial Kinetic Alfvén waves that play a central role in space plasmas, and extends standard reduced fluid models to broader ranges of the plasma parameters. Recent numerical results are reviewed, including (i) the reconnection-mediated MHD turbulence developing from the collision of counter-propagating Alfvén wave packets, (ii) the specific features of the cascade dynamics in strongly imbalanced turbulence, including a possible link between the existence of a spectral transition range and the presence of co-propagating wave interactions at sub-ion scales, for which new simulations are reported, (iii) the influence of the ion-to-electron temperature ratio in two-dimensional collisionless magnetic reconnection. The role of electron finite Larmor radius corrections is pointed out and the extension of the present model to a four-field gyrofluid model is discussed. Such an extended model accurately describes electron finite Larmor radius effects at small or moderate values of the electron beta parameter, and also retains the coupling to slow magnetosonic waves.

Destabilization of geodesic acoustic-like mode in the presence of poloidally inhomogeneous heat sources in tokamak plasmas

The effects of poloidally inhomogeneous heat sources are investigated through a gyrokinetic formula in collisionless toroidal plasmas. A gyrokinetic dispersion relation is newly derived under the assumption that equilibrium parallel heat flows are generated to remove the injected poloidally nonuniform heat source. The dispersion relation is numerically solved, considering both inboard and outboard heat source injections. In the case of the inboard source injection, both Stringer spin-up and geodesic acoustic mode (GAM) are excited. Conversely, outboard injection leads to the emergence of a heat source-driven GAM (referred to as Q-GAM), featuring a frequency around half that of the standard GAM. Various physical quantities of the Q-GAM, such as mode frequency and source threshold, are analyzed through parametric scans. The Q-GAM exhibits similarities with the energetic-particle-driven GAM (EGAM), particularly in its frequency range, and both belong to one of the strong Landau damped poles. Despite having distinct driving mechanisms and structural differences in parallel velocity and poloidal coordinates, the response function of the perturbed parallel pressure to the potential, mainly contributing to the destabilization of each mode around half of the GAM frequency, is derived to have a similar form for both the Q-GAM and EGAM cases.

Presheath-like structures and effusive particle losses for biased probes at and near I–V electron saturation

A theory for presheath-like structures near probes biased at and above the plasma potential is developed for collisionless plasmas with an electron-neutral mean free path on the order of the chamber scale. The theory predicts presheath-like perturbations to the plasma that result from the free streaming of electrons and an effusion loss process from the chamber at the electrode. For these situations, a loss-cone-like velocity distribution function for electrons is predicted where the loss angle of the depletion region corresponds to the angular size of the electrode at a specified distance. The angle of the loss cone becomes 180° at the sheath edge. In comparison with a previous collisional electron presheath model that required electrons satisfy a Bohm criterion at the sheath edge [Scheiner et al., Phys. Plasmas 22, 123520 (2015)], the present work suggests that no such condition is needed for collisionless low pressure plasmas in the ≲10 mTorr range. The theory predicts the generation of a density depletion of roughly 0.5ne and an electron velocity moment of tens of percent of the electron thermal speed by the sheath edge in a presheath with a potential drop of less than Ti/e. The range of this presheath perturbation is determined by the electrode geometry instead of the collisional mean free path. These predictions are tested against previously published particle in cell simulations and are found to be in good agreement.

Propagation of twisted laser carrying orbital angular momentum in magnetized plasma

The propagation of electromagnetic beams carrying orbital angular momentum l is investigated in a cold collisionless plasma where a static magnetic field is applied in the axial direction. The relativistic and ponderomotive nonlinearities are taken into consideration simultaneously. A stationary nonlinear Schrödinger equation is derived using the Wentzel–Kramers–Brillouin method and the slowly varying envelope approximation. The critical condition for the self-trapped mode is achieved as a function of orbital angular momentum (OAM), magnetic field, and initial laser intensity of the beam. The response of the medium to the two types of polarizations, i.e., left circular polarization (LCP) and right circular polarization (RCP), is compared, and it is observed that the RCP laser shows better focusing than the LCP laser and also requires a smaller beam radius for achieving the self-trapped mode. The effect of applied magnetic field and OAM of the laser is also studied on the beam width evolution. The laser is found to be focused earlier in the cases of a larger applied magnetic field. A Laguerre–Gaussian laser with higher OAM is observed to show efficient self-focusing. This study enables exploration in the fields of particle acceleration, electron bunch generation, x-ray sources, and more.

Dominance of polarization modes and absorption on self-focusing of laser beams in collisionless magnetized plasma

This work investigates the polarization modes i.e., Extraordinary (E-mode) and Ordinary (O-mode) on self-focusing of higher-order mode of elegant Hermite-cosh-Gaussian (EHChG) laser beams within collisionless magnetized plasma medium. In this study, the authors have taken transverse electromagnetic ([Formula: see text]) mode with mode indices (0, 4) and explored. The ponderomotive force is primarily responsible for the dielectric constant’s nonlinearity in this context. Also, WKB and paraxial approximations via the parabolic wave equation approach are used to establish the general form of differential equations for beam-width parameters in both transverse dimensions of the beam. In this paper, the authors have theoretically investigated the dominance of polarization modes and absorption coefficient on self-focusing. The final results show good enhancement of laser propagation through collisionless plasma medium.

Effect of mutual interaction of two cosh-Gaussian laser beams on upper hybrid wave excitation and subsequent electron acceleration

This paper presents the excitation of an upper hybrid wave by resonant excitation of two intense cosh-Gaussian laser beams of frequencies ω 1 and ω 2 in a collisionless plasma. The excited upper hybrid wave is used for electron acceleration which accelerates the electrons towards higher energy. The acceleration of electrons through an excited upper hybrid wave has also been studied. This study has been analysed using the Wentzel Kramers Brillouin (WKB) and paraxial-ray approximation, where relativistic and ponderomotive nonlinearities are employed together. Analytical expressions for the beam width/intensity of the cosh-Gaussian laser beams, the electric field/power of the excited upper hybrid wave and the electron acceleration have been derived, which have been solved numerically for an established set of laser and plasma parameters. The results are also compared to relativistic nonlinearity. It has been observed that the mutual interaction of two cosh-Gaussian laser beams at a difference frequency significantly affects the self-focusing of each beam, leading to an increase in the amplitude/power of the upper hybrid wave as well as energy gain by the electrons. The effect of the magnetic field (ωc) and decentered parameter (b) on the power of the excited upper hybrid wave and the energy gain by the electrons are also explored. The results show that the power of upper hybrid wave and the energy gain by the electrons increase at higher values ​​of b and ω c.