The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show here that the electrons are still globally accelerated by the wave packet, and, in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and, therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, this leads to an effective defocussing effect which we quantify, and which we compare to the self-focussing induced by wave front bowing.
Numerical studies implementing different versions of the collisionless Ohm's law have shown a reconnection rate insensitive to the nature of the non-ideal mechanism occuring at the X line, as soon as the Hall effect is operating. Consequently, the dissipation mechanism occurring in the vicinity of the reconnection site in collisionless systems is usually thought not to have a dynamical role beyond the violation of the frozen-in condition. The interpretation of recent studies have however led to the opposite conclusion that the electron scale dissipative processes play an important dynamical ro…
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.
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…
Parallel permittivity elements are derived for radio frequency waves in an axisymmetric D-shaped tokamak with Soloviev type equilibrium under arbitrary aspect ratio, arbitrary elongation and moderate triangularity. The drift-kinetic equation is solved separately for untrapped (passing or circulating) and three groups of trapped particles as a boundary-value problem, accounting for the transit-time and bounce resonances, respectively. It is shown that the new two groups of trapped particles can appear only in tokamaks with large elongation and large central beta. Our dielectric characteristics …
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.
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.
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…
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…
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…
A simplified model of particle transport at a quasiparallel one-dimensional collisionless shock is suggested. In this model the MHD-turbulence behind the shock is dominated by a circularly polarized, large amplitude Alfvén wave originated upstream from the turbulence excited by particles leaking from the downstream medium. It is argued that such a wave having significantly increased its magnetic field during the transmission through the shock interface can effectively trap thermal ions, regulating their leakage upstream. Together with a background turbulence this wave also plays a fundamental …
Electron dynamics and energization are one of the key components of magnetic field dissipation in collisionless reconnection. In 2D numerical simulations of magnetic reconnection, the main mechanism that limits the current density and provides an effective dissipation is most probably the electron pressure tensor term, that has been shown to break the frozen-in condition at the x-point. In addition, the electron-meandering-orbit scale controls the width of the electron dissipation region, where the electron temperature has been observed to increase both in recent Magnetospheric Multiple-Scale …
Collisionless dissipation of macroscopic energy into heat is an unsolved problem of space and astrophysical plasmas, e.g., solar wind and Earth's magnetosheath. The most viable process under consideration is the turbulent-cascade of macroscopic energy to kinetic-scales where collisionless-plasma-processes dissipate the energy. Space observations and numerical simulations show the formation of kinetic scale current sheets in turbulent plasmas. Instabilities in these CS can provide collisionless dissipation and influence the turbulence. Spatial gradients of physical quantities and non-Maxwellian…
In the presence of wave dissipation, phase-space structures emerge in nonlinear Vlasov dynamics. Their dynamics can lead to a nonlinear continuous shifting of the wave frequency (chirping). This report summarizes my personal contribution to these topics in the fiscal year 2012. The effects of collisions on chirping characteristics were investigated, with a one-dimensional beam-plasma kinetic model. The long-time nonlinear evolution was systematically categorized as damped, steady-state, periodic, chaotic and chirping. The chirping regime was sub-categorized as periodic, chaotic, bursty, and in…
The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure-strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure-strain interaction. The…
A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges by using a two-fluid model for cold ions and electrons. Explosive growth of the tearing mode enabled by electron inertia is analytically estimated by using an energy principle with a nonlinear displacement map. Decrease of the potential energy in the nonlinear regime (where the island width exceeds the electron skin depth) is found to be steeper than in the linear regime, resulting in accelerated reconnection. Release of potential energy by such a fluid displa…
The debate surrounding fast magnetic energy dissipation by magnetic reconnection has remained a fundamental topic in the plasma universe, not only in the Earth's magnetosphere but in astrophysical objects such as pulsar magnetospheres and magnetars, for more than half a century. Recently, nonthermal particle acceleration and plasma heating during reconnection have been extensively studied, and it has been argued that rapid energy dissipation can occur for a collisionless "thin" current sheet, the thickness of which is of the order of the particle gyro-radius. However, it is an intriguing enigm…
In contrast to hydrodynamic vortices, vortices in plasma contain an electric current circulating around the center of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices, and plasma waves. Two major contributors to the energy damping of double vortex system, namely, magneti…
The dissipation mechanism of the magnetic energy in turbulent collisionless space and astrophysical plasmas is still not well understood. Its investigation requires efficient kinetic simulations of the energy transfer in collisionless plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions are treated as particles and electrons as an inertial fluid, have begun to attract a significant interest recently. Hybrid-kinetic models describe both ion- and electron scale processes by ignoring electron kinetic effects so that they are computationally much less demanding compared to…
We examine the effect of an external guide field and current sheet thickness on the growth rates and nature of three dimensional unstable modes of an electron current sheet driven by electron shear flow. The growth rate of the fastest growing mode drops rapidly with current sheet thickness but increases slowly with the strength of the guide field. The fastest growing mode is tearing type only for thin current sheets (half thickness $\approx d_e$, where $d_e=c/ω_{pe}$ is electron inertial length) and zero guide field. For finite guide field or thicker current sheets, fastest growing mode is non…
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the fi…
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 existence of low frequency waveguide modes of ion acoustic waves is demonstrated in magnetized plasmas for electron temperature striated along the magnetic field lines. At higher frequencies, in a band between the ion cyclotron and the ion plasma frequency, radiative modes develop and propagate obliquely to the field away from the striation. Arguments for the subsequent formation and propagation of electrostatic shock are presented and demonstrated numerically. For such plasma conditions, the dissipation mechanism is the "leakage" of the harmonics generated by the wave steepening.
We present the first quantified measure of the rate of energy dissipated per unit volume by high frequency electromagnetic waves in the transition region of the Earth's collisionless bow shock using data from the THEMIS spacecraft. Every THEMIS shock crossing examined with available wave burst data showed both low frequency (< 10 Hz) magnetosonic-whistler waves and high frequency (> 10 Hz) electromagnetic and electrostatic waves throughout the entire transition region and into the magnetosheath. The waves in both frequency ranges had large amplitudes, but the higher frequency waves, which are …
By means of a fully kinetic simulation of freely decaying plasma turbulence, we study the spectral properties and the energy exchanges characterizing the turbulent cascade in the kinetic range. We find that the magnetic field spectrum follows the ${k^{-α}\,exp(-λ\, k)}$ law at kinetic scales with $α\!\simeq\!2.73$ and $λ\!\simeq\!ρ_e$ (where ${ρ_e}$ is the electron gyroradius). The same law with $α\!\simeq\!0.94$ and an exponential decay characterized by $λ\!\simeq\!0.87ρ_e$ is observed in the electron velocity spectrum but not in the ion velocity spectrum that drops like a steep power law $\s…
The magnetic energy of nonlinear Alfven waves in compressible plasmas may be ponderomotively coupled only to ion-acoustic quasi-modes which modulate the wave phase velocity and cause wave-front steepening. In the collisionless plasma with $β\not=0$, the dynamics of nonlinear Alfven wave is also affected by the resonant particle-wave interactions. Upon relatively rapid evolution (compared to the particle bounce time), the quasi-stationary wave structures, identical to the so called (Alfvenic) Rotational Discontinuities, form, the emergence and dynamics of which has not been previously understoo…
We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms -- the ``combinatorial'' form related to the logarithm of the number of microstates per macrostate and the ``continuous'' form related to $f \ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collis…
Turbulence is ubiquitously observed in nearly collisionless heliospheric plasmas, including the solar wind and corona and the Earth's magnetosphere. Understanding the collisionless mechanisms responsible for the energy transfer from the turbulent fluctuations to the particles is a frontier in kinetic turbulence research. Collisionless energy transfer from the turbulence to the particles can take place reversibly, resulting in non-thermal energy in the particle velocity distribution functions (VDFs) before eventual collisional thermalization is realized. Exploiting the information contained in …
Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $δn/n_0 \gtrsim 2/β$ (where $β\gg{1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves' otherwise potent collis…
Shocks waves are a ubiquitous feature of many astrophysical plasma systems, and an important process for energy dissipation and transfer. The physics of these shock waves are frequently treated/modeled as a collisional, fluid MHD discontinuity, despite the fact that many shocks occur in the collisionless regime. In light of this, using fully kinetic, 3D simulations of non-relativistic, parallel propagating collisionless shocks comprised of electron-positron plasma, we detail the deviation of collisionless shocks form MHD predictions for varying magnetization/Alfvénic Mach numbers, with particu…
Turbulence is thought to play a role in the heating of the solar wind plasma, though many questions remain to be solved regarding the exact nature of the mechanisms driving this process in the heliosphere. In particular, the physics of the collisionless interactions between particles and turbulent electromagnetic fields in the kinetic dissipation range of the turbulent cascade remains incompletely understood. A recent analysis of an interval of Magnetosphere Multiscale (MMS) observations has used the field-particle correlation technique to demonstrate that electron Landau damping is involved i…
A pair of nonlinear diffusion equations in Fourier space} is used to study the dynamics of strong Alfvén-wave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is …
Heliospheric plasma turbulence plays a key role in transferring the energy of large-scale magnetic field and plasma flow fluctuations to smaller scales where the energy can be dissipated, ultimately leading to plasma heating. High-quality measurements of electromagnetic fields and electron velocity distributions by the Magnetospheric Multiscale (MMS) mission in Earth's magnetosheath present a unique opportunity to characterize plasma turbulence and to determine the mechanisms responsible for its dissipation. We apply the field-particle correlation technique to a set of twenty MMS magnetosheath…
Previous studies of phase mixing of ion cyclotron (IC), Alfvénic, waves in the collisionless regime have established the generation of parallel electric field and hence acceleration of electrons in the regions of transverse density inhomogeneity. However, outstanding issues were left open. Here we use 2.5D, relativistic, fully electromagnetic PIC (Particle-In-Cell) code and an analytic MHD (Magnetohydrodynamic) formulation, to establish the following points: (i) Using the generalised Ohm's law we find that the parallel electric field is supported mostly by the electron pressure tensor, with a …
This paper addresses the linear and nonlinear three-dimensional propagation of an electron wave in a collisionless plasma that may be inhomogeneous, nonstationary, anisotropic and even weakly magnetized. The wave amplitude, together with any hydrodynamic quantity characterizing the plasma (density, temperature,...) are supposed to vary very little within one wavelength or one wave period. Hence, the geometrical optics limit is assumed, and the wave propagation is described by a first order differential equation. This equation explicitly accounts for three-dimensional effects, plasma inhomogene…
Dissipation and particle acceleration in astrophysical jets with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink Instabilities
We present two-dimensional kinetic simulations, with a broad range of initial guide fields, that isolate the role of parallel electric fields ($E_\parallel$) in energetic electron production during collisionless magnetic reconnection. In the strong guide field regime, $E_\parallel$ drives essentially all of the electron energy gain, yet fails to generate an energetic component. We suggest that this is due to the weak energy scaling of particle acceleration from $E_\parallel$ compared to that of a Fermi-type mechanism responsible for energetic electron production in the weak guide-field regime.…
The zeroth law is one of the oldest conjecture in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a new dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscou…
In hydrodynamic turbulence, it is well established that the length of the dissipation scale depends on the energy cascade rate, i.e., the larger the energy input rate per unit mass, the more the turbulent fluctuations need to be driven to increasingly smaller scales to dissipate the larger energy flux. Observations of magnetic spectral energy densities indicate that this intuitive picture is not valid in solar wind turbulence. Dissipation seems to set in at the same length scale for different solar wind conditions independently of the energy flux. To investigate this difference in more detail,…
The dissipation mechanism by which the magnetic field reconnects in the presence of an external (guide) magnetic field in the direction of the main current is not well understood. In thin electron current sheets (ECS) (thickness ~ an electron inertial length) formed in collisionless magnetic reconnection, electron shear flow instabilities (ESFI) are potential candidates for providing an anomalous dissipation mechanism which can break the frozen-in condition of the magnetic field affecting the structure and rate of reconnection. We investigate the evolution of ESFI in guide field magnetic recon…
Dissipation and particle acceleration at intermittent structures with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink instabilities
Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas
University of California, Berkeley（加州大学伯克利分校）；Space Sciences Laboratory, University of California, Berkeley（加州大学伯克利分校空间科学实验室）；Department of Physics & Astronomy, University of New Hampshire（新罕布什尔大学物理与天文学系）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学月球与行星实验室）；The Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室）
We perform 2.5D hybrid simulations with massless fluid electrons and kinetic particle-in-cell ions to study the temporal evolution of ion temperatures, temperature anisotropies and velocity distribution functions in relation to the dissipation and turbulent evolution of a broad-band spectrum of parallel and obliquely propagating Alfvén-cyclotron waves. The purpose of this paper is to study the relative role of parallel versus oblique Alfvén-cyclotron waves in the observed heating and acceleration of minor ions in the fast solar wind. We consider collisionless homogeneous multi-species plasma, …
Whether turbulence induced anomalous resistivity (AR) can facilitate a fast magnetic reconnection in collisionless plasma is a subject of active debate for decades. Recent space observations suggest that the reconnection rate can be higher than the Hall-reconnection rate and turbulent dissipation is required. In this paper, using particle-in-cell simulations, we present a case study of how AR produced by Buneman instability accelerates magnetic reconnection. We first show that the AR/drag produced by Buneman instability in a thin electron current layer 1) can dissipate magnetic energy stored i…
A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic…
