It is well known that collisionless systems are dissipation free from the perspective of particle collision and thus conserve entropy. On the other hand, processes such as magnetic reconnection and turbulence appear to convert large-scale magnetic energy into heat. In this paper, we investigate the energization and heating of collisionless plasma. The dissipation process is discussed in terms of fluid entropy in both isotropic and gyrotropic forms. Evolution equations for the entropy are derived and they reveal mechanisms that lead to changes in fluid entropy. These equations are verified by a collisionless particle-in-cell simulation of multiple reconnecting current sheets. In addition to previous findings regarding the pressure tensor, we emphasize the role of heat flux in the dissipation process.
A new measure to identify a small-scale dissipation region in collisionless magnetic reconnection is proposed. The energy transfer from the electromagnetic field to plasmas in the electron's rest frame is formulated as a Lorentz-invariant scalar quantity. The measure is tested by two-dimensional particle-in-cell simulations in typical configurations: symmetric and asymmetric reconnection, with and without the guide field. The innermost region surrounding the reconnection site is accurately located in all cases. We further discuss implications for nonideal MHD dissipation.
A higher-order multiscale analysis of the dissipation range of collisionless plasma turbulence is presented using in-situ high-frequency magnetic field measurements from the Cluster spacecraft in a stationary interval of fast ambient solar wind. The observations, spanning five decades in temporal scales, show a crossover from multifractal intermittent turbulence in the inertial range to non-Gaussian monoscaling in the dissipation range. This presents a strong observational constraint on theories of dissipation mechanisms in turbulent collisionless plasmas.
Irreversibility and Entropy Exclusion in Collisionless Plasmas
Evgeni Kharadze Georgian National Astrophysical Observatory（叶夫根尼·哈拉泽格鲁吉亚国家天体物理观测台）；Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University（雅瓦希什维里第比利斯国立大学精确与自然科学学院）
We present the first study of the formation and dissipation of current sheets at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence simulation. We investigate the relative importance of dissipation associated with collisionless damping via resonant wave-particle interactions versus dissipation in small-scale current sheets in weakly collisional plasma turbulence. Current sheets form self-consistently from the wave-driven turbulence, and their filling fraction is well correlated to the electron heating rate. However, the weakly collisional nature of the simulation neces…
It was recently proposed that the electron-frame dissipation measure, the energy transfer from the electromagnetic field to plasmas in the electron's rest frame, identifies the dissipation region of collisionless magnetic reconnection [Zenitani et al. Phys. Rev. Lett. 106, 195003 (2011)]. The measure is further applied to the electron-scale structures of antiparallel reconnection, by using two-dimensional particle-in-cell (PIC) simulations. The size of the central dissipation region is controlled by the electron-ion mass ratio, suggesting that electron physics is essential. A narrow electron j…
The linear MHD Kelvin-Helmholtz instability (KHI) in an anisotropic plasma concerning the direction of an external magnetic field is examined in detail. For this purpose, the MHD equations are used to describe the motion of plasma as a fluid, which is derived from 16 moments of Boltzmann-Vlasov kinetic equations for collisionless plasma. In addition, the heat flux along the magnetic field is taken into account. The growing rates of KHI are calculated as functions of the anisotropic plasma properties for a shear flow along the magnetic field at supersonic velocities. On the other hand, the quas…
Particle in cell (PIC) simulations of collisionless magnetic reconnection are presented that demonstrate that the electron dissipation region develops a distinct two-scale structure along the outflow direction. The length of the electron current layer is found to decrease with decreasing electron mass, approaching the ion inertial length for a proton-electron plasma. A surprise, however, is that the electrons form a high-velocity outflow jet that remains decoupled from the magnetic field and extends large distances downstream from the x-line. The rate of reconnection remains fast in very large…
The kinetic evolution of the Orszag-Tang vortex is studied using collisionless hybrid simulations. In the magnetohydrodynamic regime this vortex leads rapidly to broadband turbulence. Significant differences from MHD arise at small scales, where the fluid scale energy dissipates into heat almost exclusively through the magnetic field because the protons are decoupled from the magnetic field. Although cyclotron resonance is absent, the protons heat preferentially in the plane perpendicular to the mean field, as in the corona and solar wind. Effective transport coefficients are calculated.
Particle condensates in general magnetic mirror geometries in high temperature plasma may be caused by a discrete resonance with thermal ion-acoustic background noise near mirror points. The resonance breaks the bounce symmetry, temporally locking the particles to the resonant wavelength. The relevant correlation lengths are the Debye length in parallel direction and the ion gyroradius in perpendicular direction.
Intermittency of heating in weakly collisional plasma turbulence is an active subject of research, with significant potential impact on understanding of the solar wind, solar corona and astrophysical plasmas. Recent studies suggest a role of vorticity in plasma heating. In magnetohydrodynamics small scale vorticity is generated near current sheets and this effect persists in kinetic plasma, as demonstrated here with hybrid and fully kinetic Particle-In-Cell (PIC) simulations. Furthermore, vorticity enhances local kinetic effects, with a generalized resonance condition selecting sign-dependent …
In a collisionless, magnetized plasma, particles may stream freely along magnetic-field lines, leading to phase "mixing" of their distribution function and consequently to smoothing out of any "compressive" fluctuations (of density, pressure, etc.,). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma-one of the most fundamental physical phenomena that make plasma different from a conventional fluid. Nevertheless, broad power-law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditi…
When two plasmas collide, their interaction can be mediated by collisionless plasma instabilities or binary collisions between particles of each shell. By comparing the maximum growth rate of the collisionless instabilities with the collision frequency between particles of the shells, we determine the critical density separating the collisionless formation from the collisional formation of the resulting shock waves. This critical density is also the density beyond which the shock downstream is field free, as plasma instabilities do not have time to develop electromagnetic patterns. We further …
We study the damping of collisionless Alfvénic turbulence by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude $δz_λ$) and linear Landau damping (whose efficiency is independent of $δz_λ$), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a n…
An innovative field-particle correlation technique is proposed that uses single-point measurements of the electromagnetic fields and particle velocity distribution functions to investigate the net transfer of energy from fields to particles associated with the collisionless damping of turbulent fluctuations in weakly collisional plasmas, such as the solar wind. In addition to providing a direct estimate of the local rate of energy transfer between fields and particles, it provides vital new information about the distribution of that energy transfer in velocity space. This velocity-space signat…
We study processes at the transition region between hot (rare) and cold (dense) plasma in the collisionless regime. We use a 3-dimensional electromagnetic particle-in-cell (3-D PIC) relativistic code. Motivated by the transition region in the solar atmosphere the temperature and density ratio of the plasmas is chosen as 100 and 0.01, respectively. For better understanding of studied processes we make two types of computations: a) without any interactions among plasma particles (free expansion) and b) with the full electromagnetic interactions. In both the cases we found that the flux of cold p…
A Landau fluid model for a collisionless electron-proton magnetized plasma, that accurately reproduces the dispersion relation and the Landau damping rate of all the magnetohydrodynamic waves, is presented. It is obtained by an accurate closure of the hydrodynamic hierarchy at the level of the fourth order moments, based on linear kinetic theory. It retains non-gyrotropic corrections to the pressure and heat flux tensors up to the second order in the ratio between the considered frequencies and the ion cyclotron frequency.
We show that an electronic beam passing through the collisionless plasma of the "cold" ions and the "hot" Boltzmann electrons can give rise to the propagation of the supersonic ion-acoustic rarefaction shock waves. These waves are analogous to those predicted by Zeldovich [5] in gasodynamics and complementary to the ion-acoustic compression shock waves in collisionless plasma described by Sagdeev [3].
Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly-polarized laser at normalized laser vector potential a0 that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on a0 and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-com…
We describe local shearing box simulations of turbulence driven by the magnetorotational instability (MRI) in a collisionless plasma. Collisionless effects may be important in radiatively inefficient accretion flows, such as near the black hole in the Galactic Center. The MHD version of ZEUS is modified to evolve an anisotropic pressure tensor. A fluid closure approximation is used to calculate heat conduction along magnetic field lines. The anisotropic pressure tensor provides a qualitatively new mechanism for transporting angular momentum in accretion flows (in addition to the Maxwell and Re…
During magnetically dominated relativistic reconnection, inflowing plasma depletes the initial relativistic pressure at the x-line and collisionless plasma heating inside the diffusion region is insufficient to overcome this loss. The resulting pressure drop causes a collapse at the x-line, essentially a localization mechanism of the diffusion region necessary for fast reconnection. The extension of this low-pressure region further explains the bursty nature of anti-parallel reconnection because a once opened outflow exhaust can also collapse, which repeatedly triggers secondary tearing island…
The research is aimed at the study of the properties of solutions for parallel MHD shock waves in collisionless plasma with heat fluxes, using 8-moment MHD approximation. Restrictions have been established on the upstream shock parameters preserving physical meaning of the downstream plasma parameters.
Here we present a commentary on the role of small-scale (e.g., few tens of meters) wave-particle interactions in large-scale (e.g., few tens of kilometers) processes and their capacity to accelerate particles from thermal to suprathermal or even to cosmic-ray energies. The purpose of this commentary is to provoke thought and further investigation into the relative importance of electromagnetic waves in the global dynamics of many macroscopic systems. We specifically focus on the terrestrial radiation belts and collisionless shock waves as examples.
Most plasmas have a very thin sheath compared with the plasma dimension. This necessitates separate calculations of the plasma and sheath. The Bohm criterion provides the boundary condition for calculation of plasma profiles. To calculate sheath properties a value of electric field at the plasma-sheath interface has to be specified in addition to the Bohm criterion. The value of the boundary electric field and robust procedure to approximately patch plasma and collisionless sheath with a very good accuracy are reported.
In collisional fluids, a number of key processes rely on the frequency of binary collisions. Collisions seem necessary to generate a shock wave when two fluids collide fast enough, to fulfill the Rankine-Hugoniot relations, to establish an equation of state or a Maxwellian distribution. Yet, these seemingly collisional features are routinely either observed or assumed, in relation with collision\emph{less} astrophysical plasmas. This article will review our current answers to the following questions: How do colliding collisionless plasmas end-up generating a shock as if they were fluids? To wh…
A model of global magnetic reconnection rate in relativistic collisionless plasmas is developed and validated by the fully kinetic simulation. Through considering the force balance at the upstream and downstream of the diffusion region, we show that the global rate is bounded by a value $\sim 0.3$ even when the local rate goes up to $\sim O(1)$ and the local inflow speed approaches the speed of light in strongly magnetized plasmas. The derived model is general and can be applied to magnetic reconnection under widely different circumstances.
We present two-dimensional hybrid kinetic/magnetohydrodynamic simulations of planned laser-ablation experiments in the Large Plasma Device (LAPD). Our results, based on parameters which have been validated in previous experiments, show that a parallel collisionless shock can begin forming within the available space. Carbon-debris ions that stream along the magnetic-field direction with a blow-off speed of four times the Alfven velocity excite strong magnetic fluctuations, eventually transfering part of their kinetic energy to the surrounding hydrogen ions. This acceleration and compression of …
A fundamental problem in plasma and astrophysics is the interaction between energetic particles and magnetized plasmas. In the current paper we focus on particle diffusion across the guide magnetic field. It is shown that the perpendicular diffusion coefficient depends only on the parallel diffusion coefficient and the Kubo number. Therefore, one can find four asymptotic limits depending on the values of these two parameters. These regimes are the quasilinear limit, the Kadomtsev & Pogutse limit, the scaling of Rechester & Rosenbluth, and the scaling found by Zybin & Istomin. In the current ar…
We investigate an efficient mechanism for generating magnetic fields in turbulent, collisionless plasmas. By using fully kinetic, particle-in-cell simulations of an initially non-magnetized plasma, we inspect the genesis of magnetization, in a nonlinear regime. The complex motion is initiated via a Taylor-Green vortex, and the plasma locally develops strong electron temperature anisotropy, due to the strain tensor of the turbulent flow. Subsequently, in a domino effect, the anisotropy triggers a Weibel instability, localized in space. In such active wave-particle interaction regions, the magne…
We present space- and time-resolved experimental data of head-on-merging, supersonic plasma jets (of an argon/impurity mixture) in an initially collisionless regime for counter-streaming ions. The merging begins with collisionless interpenetration followed by a transition to collisional stagnation. The transition occurs due to an experimentally inferred rising mean-ionization level, which rapidly reduces the counter-streaming ion-ion mean free path. The measurements demonstrate a specific mechanism by which a collisionless interaction transitions to a collisional one and constrain collisionali…
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
The first kinetic study of transient growth for a collisionless homogeneous Maxwellian plasma in a uniform magnetic field is presented. A system which is linearly stable may display transient growth if the linear operator describing its evolution is non-normal, so that its eigenvectors are non-orthogonal. In order to include plasma kinetic effects a Landau fluid model is employed. The linear operator of the model is shown to be non-normal and the results suggest that the nonnormality of a collisionless plasma is intrinsically related to its kinetic nature, with the transient growth being more …
Dissipative processes cause collisionless plasmas in many systems to develop nonthermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic simulations of systems with a variety of acceleration and trapping (or escape) mechanisms poses a deep mystery. We consider the possibility that such distributions can be modeled from maximum-entropy principles, when accounting for generalizations beyond the Boltzmann-Gibbs entropy. Using a dimensional representation of entropy (related to the Renyi and Tsallis …
Low-frequency mangnetosonic pulses in a two-ion-species plasma are studied theoretically and by simulation with a one-dimensional electromagnetic simulation code based on a three-fluid model, with particular attention to the dynamics of minority heavy ions. It is found that heavy ions can gain some energy from the pulses. Because of this energy transfer, the pulses are damped even if the plasma is collisionless and pulse propagation is perpendicular to the magnetic field.
Dynamics of the magnetospheric plasma configuration intrinsically features intermittent slow and fast phases. The fast transition is a nonlinear process, loss of equilibrium which ends up the slow quasi-static evolution. The process is analysed as a dynamical bifurcation. It appears when marginal stability state is reached in the course of that evolution, either for tearing mode or for ballooning mode disturbances. The resulting force imbalance leads to spontaneous formation of nonlinear kinetic thin current structures. Those are either a pair of slow collisionless shocks or a specific anisotr…
This paper presents Sweet-Parker type scaling arguments in the context of hyper-resistive Hall magnetohyrdodynamics (MHD). The predicted steady state scalings are consistent with those found by Chacón et al. [PRL 99, 235001 (2007)], though as with that study, no prediction of electron dissipation region \emph{length} is made. Numerical experiments confirm that both cusp-like and modestly more extended geometries are realizable. However, importantly, the length of the electron dissipation region, which is taken as a parameter by several recent studies, is found to depend explicitly on the level…
The collisionless interaction of an expanding high-energy plasma cloud with a magnetized background plasma in the presence of a dipole magnetic field is examined in the framework of a 2D3V hybrid (kinetic ions and massless fluid electrons) model. The retardation of the plasma cloud and the dynamics of the perturbed electromagnetic fields and the background plasma are studied for high Alfven-Mach numbers using the particle-in-cell method. It is shown that the plasma cloud expands excluding the ambient magnetic field and the background plasma to form a diamagnetic cavity which is accompanied by …
Collisionless shocks are common features in space and astrophysical systems where supersonic plasma flows interact, such as in the solar wind, the heliopause, and supernova remnants. Recent experimental capabilities and diagnostics allow detailed laboratory investigations of high-Mach-number shocks, which therefore can become a valuable way to understand shock dynamics in various astrophysical environments. Using 2D particle-in-cell simulations with a Coulomb binary collision operator, we demonstrate the mechanism for generation of energetic electrons and experimental requirements for detectin…
Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated using a novel fluid-kinetic model [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains non-isothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is $cE_{max}\approx 0.2v_AB_{y,0}$, whe…
The head-on collision of ion-acoustic solitary waves in a collisionless plasma with cold ions and Boltzmann electrons is studied. It is shown that solitary waves of sufficiently large amplitudes do not retain their identity after a collision. Their amplitudes decrease and their forms change. Dependences of amplitudes of the potential and densities of ions and electrons after a head-on collision of identical solitary waves on their initial amplitude are presented.
Attention is drawn to a fundamental difference between the physical mechanisms responsible for the magnetic field freezing-in effect in spatially isotropic (collisional) and strongly anisotropic (collisionless) plasmas. (The first case is characteristic of internal regions of the Sun and other stars; the second, for the solar corona, interplanetary and interstellar medium, planetary ionospheres and magnetospheres, cometary tails.) It is shown that particles of a collisionless plasma remain in the same field line during their motion because of the properties of electrodynamic drift which stem f…
Collisionless shocks follow the Rankine-Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent Particle-in-Cell simulations reveal a significant departure from magnetohydrodynamics behavior for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we …
A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $Δω$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $Δω\sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a loga…
The emergence of a density bump at the front of a collisionless electrostatic shock wave have been observed experimentally during the ablation of an aluminium foil by a femtosecond laser pulse. We have performed numerical simulations of the dynamics of this phenomena developing alongside the generation of a package of ion-acoustic waves, exposed to a continual flow of energetic electrons, in a collisionless plasma. We present the physical interpretation of the observed effects and show that the bump consists of transit particles, namely, the accelerated ions from the dense plasma layer, and th…
We present an approximation scheme for the dielectric response of thermal collisionless plasmas at arbitrary degeneracy. A T-fraction representation is obtained from the known expansions of the real part of the dielectric function for small and large arguments. The partial numerators and denominators of the continued fraction are generated by a modified Q-D algorithm. For several typical values of the degeneracy parameter $θ$, extensive tables for the expansion coefficients and the partial numerators and denominations are given allowing for an easy implementation of the fitting function. Also,…
A dust grain in a plasma has a fluctuating electric charge, and past work concludes that spherical grains in a stationary, collisionless plasma have an essentially Gaussian charge probability distribution. This paper extends that work to flowing plasmas and arbitrarily large spheres, deriving analytic charge probability distributions up to normalizing constants. We find that these distributions also have good Gaussian approximations, with analytic expressions for their mean and variance.
Among the fundamental and most challenging problems of laboratory, space, and astrophysical plasma physics is to understand the relaxation processes of nearly collisionless plasmas toward quasi-stationary states; and the resultant states of electromagnetic plasma turbulence. Recently, it has been argued that solar wind plasma $β$ and temperature anisotropy observations may be regulated by kinetic instabilities such as the ion-cyclotron, mirror, electron-cyclotron, and firehose instabilities; and that magnetic fluctuation observations are consistent with the predictions of the Fluctuation-Dissi…
The kinetic theory of collisionless electrostatic shocks resulting from the collision of plasma slabs with different temperatures and densities is presented. The theoretical results are confirmed by self-consistent particle-in-cell simulations, revealing the formation and stable propagation of electrostatic shocks with very high Mach numbers ($M \gg 10$), well above the predictions of the classical theories for electrostatic shocks.
A new class of exact electrostatic solutions of the Vlasov-Maxwell equations based on the Jeans's theorem is proposed for studying the evolution and properties of two-dimensional anisotropic plasmas that are far from thermodynamic equilibrium. In particular, the free expansion of a slab of electron-ion plasma into vacuum is investigated.
