Collisionless Space Plasmas Research Articles

Model of a Thin Current Sheet in the Earth’s Magnetotail with a Kinetic Description of Magnetized Electrons

Steady-state two-dimensional thin current sheets (TCSs) in collisionless space plasma, similar to the current sheet of the near-Earth magnetotail, are considered. The magnetic field of the sheet is orthogonal to the current and has a nonzero normal component, the electrons are magnetized, and the ions are unmagnetized. To solve the problem of kinetic description of electrons in such current sheets in a general form, they are described by the Vlasov equation in the drift approximation, the general solution to which is found in the form of a function of three independent integrals of the system of drift motion equations. An important case is considered in which the electron guiding centers obey a Maxwell–Boltzmann distribution in a stationary electromagnetic field. The obtained results make it possible to create one- and two-dimensional numerical− analytical models of current sheets in which unmagnetized ions are described by the Vlasov equation, which should be solved numerically, whereas the contribution of magnetized electrons is taken into account analytically. To numerically solve the time-independent Vlasov equation, a new method is proposed that allows one to perform the bulk of computations by using graphic processors. On the basis of the new theory, a one-dimensional numerical−analytical model of a steady-state TCS in the near-Earth magnetotail is presented, TCS configurations are calculated, and the role of electrostatic effects and electron pressure anisotropy is analyzed.

Direct measurements of two-way wave-particle energy transfer in a collisionless space plasma

Particle acceleration by plasma waves and spontaneous wave generation are fundamental energy and momentum exchange processes in collisionless plasmas. Such wave-particle interactions occur ubiquitously in space. We present ultrafast measurements in Earth's magnetosphere by the Magnetospheric Multiscale spacecraft that enabled quantitative evaluation of energy transfer in interactions associated with electromagnetic ion cyclotron waves. The observed ion distributions are not symmetric around the magnetic field direction but are in phase with the plasma wave fields. The wave-ion phase relations demonstrate that a cyclotron resonance transferred energy from hot protons to waves, which in turn nonresonantly accelerated cold He+ to energies up to ~2 kilo-electron volts. These observations provide direct quantitative evidence for collisionless energy transfer in plasmas between distinct particle populations via wave-particle interactions.

Magnetic Reconnection as a Driver for a Sub-ion-scale Cascade in Plasma Turbulence

Abstract A new path for the generation of a sub-ion-scale cascade in collisionless space and astrophysical plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidence that the development of power-law energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simulations, the reconnection-mediated small-scale energy spectrum of parallel magnetic fluctuations exhibits a very stable spectral slope of , whether or not a large-scale turbulent cascade has already fully developed. Once a quasi-stationary turbulent state is achieved, the spectrum of the total magnetic fluctuations settles toward a spectral index of in the MHD range and of at sub-ion scales.

Kinetics of sub‐ion scale magnetic holes in the near‐Earth plasma sheet

AbstractIn collisionless space plasmas, the energy cascade from larger to smaller scales requires effective interactions between ions and electrons. These interactions are organized by sub‐ion scale plasma structures in which strong electric fields connect demagnetized ions to magnetized electrons. We consider one such structure, magnetic holes, observed by THEMIS spacecraft in the dipolarized hot plasma sheet. Magnetic holes are localized depressions of the magnetic field with strong currents at their boundaries. Taking advantage of slow plasma convection (∼10–20 km/s), we reconstruct the electron velocity distribution within magnetic holes and demonstrate that the current at their boundaries is predominantly carried by magnetized thermal electrons. The motion of these electrons is the combination of diamagnetic drift and E × B drift in a Hall electric field. Magnetic holes can effectively modulate the intensity of electron cyclotron harmonic waves, and thus the spatial distribution of thermal electron precipitation. They may also contain field‐aligned currents with magnitudes of ∼5 nA/m2 (1 order of magnitude smaller than the cross‐field current density). Therefore, sub‐ion scale magnetic holes can be important for ionosphere‐magnetosphere coupling.

System of kinetic equations describing large-scale processes in collisionless space plasma

A system of kinetic equations describing relatively slow large-scale processes in collisionless magnetoplasma structures with a spatial resolution of about the characteristic gyroradius is derived. Plasma is assumed to be quasineutral, while the magnetic and electric fields are determined by the instantaneous distributions of the particle and current densities and the stress tensor of all plasma components in the longrange instantaneous interaction approximation. A special version of equations is derived for the case of magnetized electrons described by the Vlasov equation in the drift approximation. The obtained system of equations can be used to develop a global numerical kinetic model of the Earth’s magnetosphere with a spatial resolution of about 100 km, as well as local models of certain regions of the Earth’s magnetosphere with a higher resolution.

LEOPARD: A grid‐based dispersion relation solver for arbitrary gyrotropic distributions

AbstractParticle velocity distributions measured in collisionless space plasmas often show strong deviations from idealized model distributions. Despite this observational evidence, linear wave analysis in space plasma environments such as the solar wind or Earth's magnetosphere is still mainly carried out using dispersion relation solvers based on Maxwellians or other parametric models. To enable a more realistic analysis, we present the new grid‐based kinetic dispersion relation solver LEOPARD (Linear Electromagnetic Oscillations in Plasmas with Arbitrary Rotationally‐symmetric Distributions) which no longer requires prescribed model distributions but allows for arbitrary gyrotropic distribution functions. In this work, we discuss the underlying numerical scheme of the code and we show a few exemplary benchmarks. Furthermore, we demonstrate a first application of LEOPARD to ion distribution data obtained from hybrid simulations. In particular, we show that in the saturation stage of the parallel fire hose instability, the deformation of the initial bi‐Maxwellian distribution invalidates the use of standard dispersion relation solvers. A linear solver based on bi‐Maxwellians predicts further growth even after saturation, while LEOPARD correctly indicates vanishing growth rates. We also discuss how this complies with former studies on the validity of quasilinear theory for the resonant fire hose. In the end, we briefly comment on the role of LEOPARD in directly analyzing spacecraft data, and we refer to an upcoming paper which demonstrates a first application of that kind.

Sub-grid-scale description of turbulent magnetic reconnection in magnetohydrodynamics

Magnetic reconnection requires, at least locally, a non-ideal plasma response. In collisionless space and astrophysical plasmas, turbulence could transport energy from large to small scales where binary particle collisions are rare. We have investigated the influence of small scale magnetohydrodynamics (MHD) turbulence on the reconnection rate in the framework of a compressible MHD approach including sub-grid-scale (SGS) turbulence. For this sake, we considered Harris-type and force-free current sheets with finite guide magnetic fields directed out of the reconnection plane. The goal is to find out whether unresolved by conventional simulations MHD turbulence can enhance the reconnection process in high-Reynolds-number astrophysical plasmas. Together with the MHD equations, we solve evolution equations for the SGS energy and cross-helicity due to turbulence according to a Reynolds-averaged turbulence model. The SGS turbulence is self-generated and -sustained through the inhomogeneities of the mean fields. By this way, the feedback of the unresolved turbulence into the MHD reconnection process is taken into account. It is shown that the turbulence controls the regimes of reconnection by its characteristic timescale τt. The dependence on resistivity was investigated for large-Reynolds-number plasmas for Harris-type as well as force-free current sheets with guide field. We found that magnetic reconnection depends on the relation between the molecular and apparent effective turbulent resistivity. We found that the turbulence timescale τt decides whether fast reconnection takes place or whether the stored energy is just diffused away to small scale turbulence. If the amount of energy transferred from large to small scales is enhanced, fast reconnection can take place. Energy spectra allowed us to characterize the different regimes of reconnection. It was found that reconnection is even faster for larger Reynolds numbers controlled by the molecular resistivity η, as long as the initial level of turbulence is not too large. This implies that turbulence plays an important role to reach the limit of fast reconnection in large Reynolds number plasmas even for smaller amounts of turbulence.

TURBULENCE-GENERATED PROTON-SCALE STRUCTURES IN THE TERRESTRIAL MAGNETOSHEATH

ABSTRACT Recent results of numerical magnetohydrodynamic simulations suggest that in collisionless space plasmas, turbulence can spontaneously generate thin current sheets. These coherent structures can partially explain the intermittency and the non-homogenous distribution of localized plasma heating in turbulence. In this Letter, Cluster multi-point observations are used to investigate the distribution of magnetic field discontinuities and the associated small-scale current sheets in the terrestrial magnetosheath downstream of a quasi-parallel bow shock. It is shown experimentally, for the first time, that the strongest turbulence-generated current sheets occupy the long tails of probability distribution functions associated with extremal values of magnetic field partial derivatives. During the analyzed one-hour time interval, about a hundred strong discontinuities, possibly proton-scale current sheets, were observed.

Kappa and q Indices: Dependence on the Degrees of Freedom

The kappa distributions, or their equivalent, the q-exponential distributions, are the natural generalization of the classical Boltzmann-Maxwell distributions, applied to the study of the particle populations in collisionless space plasmas. A huge step in the development of the theory of kappa distributions and their applications in space plasma physics has been achieved with the discovery that the observed kappa distributions are connected with the solid statistical background of non-extensive statistical mechanics. Now that the statistical framework has been identified, it is straightforward to improve our understanding of the nature of the kappa index (or the entropic q-index) that governs these distributions. One critical topic is the dependence of the kappa index on the degrees of freedom. In this paper, we first show how this specific dependence is naturally emerged, using the formalism of the N-particle kappa distribution of velocities. Then, the result is extended in the presence of potential energies. It is shown that the kappa index is simply related to the kinetic and potential degrees of freedom. In addition, it is shown that various problems of non-extensive statistical mechanics, such as (i) the correlation dependence on the total number of particles; and (ii) the normalization divergence for finite kappa indices, are resolved considering the kappa index dependence on the degrees of freedom.

MHD instabilities of collisionless space plasma with heat fluxes

Properties of instabilities in a collisionless plasma are considered based on 16-moment MHD equations with allowance for differences between the heat fluxes along the magnetic field due to longitudinal and transverse thermal ion motions. It is shown that the increments and thresholds appreciably depend on these two heat fluxes for all compressible instabilities arising in the MHD approach (second compressible fire-hose, mirror, and thermal instabilities).

Role of Z-pinches in magnetic reconnection in space plasmas

A widely accepted scenario of magnetic reconnection in collisionless space plasmas is the breakage of magnetic field lines in X-points. In laboratory, reconnection is commonly studied in pinches, current channels embedded into twisted magnetic fields. No model of magnetic reconnection in space plasmas considers both null-points and pinches as peers. We have performed a particle-in-cell simulation of magnetic reconnection in a three-dimensional configuration where null-points are present initially, and Z-pinches are formed during the simulation along the lines of spiral null-points. The non-spiral null-points are more stable than spiral ones, and no substantial energy dissipation is associated with them. On the contrary, turbulent magnetic reconnection in the pinches causes the magnetic energy to decay at a rate of ~1.5% per ion gyro period. Dissipation in similar structures is a likely scenario in space plasmas with large fraction of spiral null-points.

Superdiffusion revisited in view of collisionless reconnection

Abstract. The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail during reconnection is reexamined making use of the division of particle orbits into waiting orbits and break-outs into ballistic motion lying at the bottom, for instance, of Lévy flights. The rms average displacement in this case increases with time, describing superdiffusion, though faster than classical, is still a weak process, being however strong enough to support fast reconnection. Referring to two kinds of numerical particle-in-cell simulations we determine the anomalous diffusion coefficient, the anomalous collision frequency on which the diffusion process is based, and construct a relation between the diffusion coefficients and the resistive scale. The anomalous collision frequency from electron pseudo-viscosity in reconnection turns out to be of the order of the lower-hybrid frequency with the latter providing a lower limit, thus making similar assumptions physically meaningful. Tentative though not completely justified use of the κ distribution yields κ ≈ 6 in the reconnection diffusion region and, for the anomalous diffusion coefficient, the order of several times Bohm diffusivity.

In situ observations of high-Mach number collisionless shocks in space plasmas

Shock waves are widespread in collisionless space plasmas throughout the Universe. How particles are accelerated at these shocks has been the subject of much research attention. The dominant source of the high-energy particles that pervade our Galaxy (cosmic rays) is thought to be the high-Mach number collisionless shocks that form around young supernova remnants, but it is unclear how much the lower Mach number collisionless shock waves frequently encountered by spacecraft in Solar System space plasmas can tell us about particle acceleration in the higher Mach number regime. Here we review recent studies of the shock wave that stands in the solar wind in front of the planet Saturn (Saturn's bow shock), based on Cassini spacecraft observations. This review represents a new direction of shock physics research, with the potential to bridge the gap between Solar System and astrophysical shocks. These studies have confirmed that Saturn's bow shock is one of the strongest shocks in the Solar System, and a recent discovery indicates that electron acceleration at high-Mach numbers may occur irrespective of the upstream magnetic field geometry. This is important because astrophysical shocks can often only be studied remotely via emissions associated with accelerated electrons. We discuss possible future directions of this emerging sub-field of collisionless space plasma shock physics.

Dynamical-systems approach to relativistic nonlinear wave-particle interaction in collisionless plasmas

In this report, we present a dynamical systems approach to study the exact nonlinear wave-particle interaction in relativistic regime. We give particular attention to the effect of wave obliquity on the dynamics of the orbits by studying the specific cases of parallel (θ = 0) and perpendicular (θ = -π/2) propagations in comparison to the general case of oblique propagation θ =]-π/2,0[. We found that the fixed points of the system correspond to Landau resonance and that the dynamics can evolve from trapping to surfatron acceleration for propagation angles obeying a Hopf bifurcations condition. Cyclotron-resonant particles are also studied by the construction of a pseudo-potential structure in the Lorentz factor γ. We derived a condition for which Arnold diffusion results in relativistic stochastic acceleration. Hence, two general conclusions are drawn: (1) The propagation angle θ can significantly alter the dynamics of the orbits at both Landau and cyclotron-resonances. (2) Considering the short-time scales upon which the particles are accelerated, these two mechanisms for Landau and cyclotron resonant orbits could become potential candidates for problems of particle energization in collisionless space and cosmic plasmas.

Isotropic ion distribution functions triggered by consecutive solar wind bulk velocity jumps: a new equilibrium state

Context. Throughout the heliosphere, ion power spectra have been found in observations to exhibit suprathermal tails that follow power laws. Ion power-law spectra, though having a broad range of spectral indices 4.4 ≤ γv ≤ 6.6, perhaps favourably seem to have velocity power indices of γv � (−5), a phenomenon that can more or less ubiquitously be found in heliospheric space plasmas. This is probably indicative of an as yet unidentified quasi-equilibrium state of collisionless space plasmas. Aims. We develop the idea that these forms of ion spectra could be produced by a continuous back- and forth- shuffling of wind convected ions in consecutive jumps from fast to slow, and vice-versa, bulk velocity regimes. Methods. The appearance of a quasi-equilibrium state due to this shuffling and re-shuffling, as we show, naturally results in ion distribution functions that are superpositions of a series of weighted Maxwellians resulting into power laws beyond a critical velocity border. Spectral intensities thereby anticorrelate with bulk velocities, but power indices depend only slightly on bulk velocity. Results. The fully developed equilibrium state is shown here, however, to be characterized by a power law with power index γv = (−3), instead of 4.4 ≤ γv ≤ 6.6. These latter states, which generally show up in observations, thus may characterize an off-equilibrium state as we discuss in this paper.

Thin current sheets in collisionless plasma: Equilibrium structure, plasma instabilities, and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.

Nonlinear electromagnetic wave interactions in Hall–MHD plasmas

AbstractWe have developed a massively parallelized fully three-dimensional (3D) compressible Hall–magnetohydrodynamic (MHD) code to investigate inertial range electromagnetic wave cascades and dissipative processes in the regime, where characteristic length scales associated with plasma fluctuations are smaller than ion gyroradii. Such regime is ubiquitously present in the solar wind and many other collisionless space plasmas. Particularly, in the solar wind, the high time resolution databases depict a spectral break near the end of the 5/3 spectrum that corresponds to a high-frequency regime where the electromagnetic turbulent cascades cannot be explained by the usual MHD models. This refers to a second inertial range, where turbulent cascades follow a k−7/3 (where k is a wavenumber) spectrum in which the characteristic electromagnetic fluctuations evolve typically on kinetic Alfvén time scales. In this paper, we describe results from our 3D compressible Hall–MHD simulations that explain the observed k−7/3 spectrum in the solar wind plasma, energy cascade, anisotropy, and other spectral features.

Sixteen-moment approximation for a collisionless space plasma: Waves and instabilities

A study is carried out of waves and instabilities in an anisotropic collisionless plasma. In a strongly magnetized plasma, the velocity distributions along and across the magnetic field lines are different, which results in anisotropy of the total pressure and gives rise to an anisotropic heat flux. The fluid description of the plasma is based on the 16-moment integral transport equations, which are integral equations obtained from the Boltzmann-Vlasov kinetic equation. For small incompressible perturbations in a homogeneous plasma, the general dispersion relation implies that there are not only firehose modes, but also three additional modes, and that all four wave modes interact with each other if a heat flux is present. Heat fluxes do not change the properties of conventional firehose modes. The conditions for the onset of instabilities are investigated as functions of the parameters of the problems. Qualitative estimates for conditions typical of the solar corona are presented.

Tearing mode in thin current sheets of the Earth’s magnetosphere: A scenario of transition to unstable state

The results of numerical modeling of thinning process in the Earth’s magnetotail current sheet are compared with the model of an anisotropic current sheet in collisionless space plasma. Stability of the current sheet during its evolution is investigated. In the evolution one can distinguish three basic stages: 1) transformation of the initial two-dimensional “isotropic” equilibrium that is well described within the MHD-approximation into a relatively thin current structure; 2) further kinetic evolution, as a result of which the virtually one-dimensional, extremely thin current sheet is formed; 3) relaxation of the system into a new equilibrium that can be stable or unstable. A substorm scenario of transformation of the magnetospheric tail and its transition into the unstable state is suggested. The spontaneously appearing tearing disturbance favors a current sheet disruption. It is shown that the estimate of a tearing mode wavelength, obtained from the model, is in accordance with experimental observations during the explosive phase of substorms.

Mathematical and physical aspects of Kappa velocity distribution

One major characteristic associated with collisionless space plasmas is the development of non-Maxwellian velocity distribution that in many circumstances can be represented by the κ function characterized by the κ parameter. This paper discusses the mathematical character and physical origin of the κ function by first showing that the κ velocity function may be expressed in terms of exponential functions multiplied by the kinetic energy and its higher orders. The possible development of κ velocity distribution is illustrated by the problem of low-frequency waves and instabilities in uniform magnetized plasmas with bi-Maxwellian distribution. It is observed that the background and perturbed distribution functions bear the same forms as the zeroth- and higher-order terms of the κ function expanded in the limit of κ→∞. The consequence of assuming κ velocity distribution in inhomogeneous plasmas is illustrated by the Vlasov-Maxwell equilibrium problems that show the nonthermal equilibrium characteristic of nonuniform plasmas. A generalized Grad-Shafranov equation is proposed for two-dimensional Vlasov equilibria with κ velocity distribution.