Effects induced by the finite number $N$ of particles on the evolution of a monochromatic electrostatic perturbation in a collisionless plasma are investigated. For growth as well as damping of a single wave, discrete particle numerical simulations show a $N$-dependent long time behavior which differs from the numerical errors incurred by vlasovian approaches and follows from the pulsating separatrix crossing dynamics of individual particles.
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.
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…
A new fully kinetic system is proposed for modeling collisionless magnetic reconnection. The formulation relies on fundamental principles in Lagrangian dynamics, in which the inertia of the electron mean flow is neglected in the expression of the Lagrangian, rather then enforcing a zero electron mass in the equations of motion. This is done upon splitting the electron velocity into its mean and fluctuating parts, so that the latter naturally produce the corresponding pressure tensor. The model exhibits a new Coriolis force term, which emerges from a change of frame in the electron dynamics. Th…
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 possibility of fast dynamo action by collisionless kinetic Alfven Wave turbulence is demonstrated. The irreversibility necessary to lock in the generated field is provided by electron Landau damping, so the induced electric field does not vanish with resistivity. Mechanisms for self-regulation of the system and the relation of these results to the theory of alpha quenching are discussed. The dynamo-generated fields have symmetry like to that of zonal flows, and thus are termed zonal fields.
The collisionless expansion of spherical plasmas composed of cold ions and hot electrons is analyzed using a novel kinetic model, with special emphasis on the influence of the electron dynamics. Simple, general laws are found, relating the relevant expansion features to the initial conditions of the plasma, determined from a single dimensionless parameter. A transition is identified in the behavior of the ion energy spectrum, which is monotonic only for high electron temperatures, otherwise exhibiting a local peak far from the cutoff energy.
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.
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…
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…
A fully kinetic Vlasov simulation of the Geospace Environment Modeling (GEM) Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions $f_k$ ($k=i,e$) are discretised on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm's law are compar…
For low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the nonMaxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equatio…
We investigate the formation of collisionless magnetized shocks triggered by the interaction between magnetized plasma flows and miniature-sized (order of plasma kinetic-scales) magnetic obstacles resorting to massively parallel, full particle-in-cell simulations, including the electron kinetics. The critical obstacle size to generate a compressed plasma region ahead of these objects is determined by independently varying the magnitude of the dipolar magnetic moment and the plasma magnetization. We find that the effective size of the obstacle depends on the relative orientation between the dip…
Magnetic reconnection can explosively release magnetic energy when opposing magnetic fields merge and annihilate through a current sheet, driving plasma jets and accelerating non-thermal particle populations to high energy, in plasmas ranging from space and astrophysical to laboratory scales. Through laboratory experiments and spacecraft observations, significant experimental progress has been made in demonstrating how fast dissipation and reconnection occurs in narrow, kinetic-scale current sheets. However, a challenge has been to demonstrate what triggers reconnection and how it proceeds rap…
We report the results of a direct comparison between different kinetic models of collisionless plasma turbulence in two spatial dimensions. The models considered include a first principles fully-kinetic (FK) description, two widely used reduced models [gyrokinetic (GK) and hybrid-kinetic (HK) with fluid electrons], and a novel reduced gyrokinetic approach (KREHM). Two different ion beta ($β_i$) regimes are considered: 0.1 and 0.5. For $β_i=0.5$, good agreement between the GK and FK models is found at scales ranging from the ion to the electron gyroradius, thus providing firm evidence for a kin…
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 …
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…
A theoretical treatment is presented of kinetic equilibria in accretion discs around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axi-symmetric and to be acted on by gravitational and electromagnetic fields; in this paper, the particular case is considered where the magnetic field admits a family of toroidal magnetic surfaces, which are locally mutually-nested and closed. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by primarily to…
Although turbulence has been conjectured to be important for magnetic reconnection, still very little is known about its role in collisionless plasmas. Previous attempts to quantify the effect of turbulence on reconnection usually prescribed Alfvénic or other low-frequency fluctuations or investigated collisionless kinetic effects in just two-dimensional configurations and antiparallel magnetic fields. In view of this, we analyzed the kinetic turbulence self-generated by three-dimensional guide-field reconnection through force-free current sheets in frequency and wavenumber spaces, utilizing 3…
The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for a Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle ($θ$) with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes ($θ\neq 0$). We find th…
A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively-inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow colli…
Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, volume 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (PRL, volume 64, 1990, 3019). Here, their approach is analyzed on the basis of heat flux data from a Vlasov s…
Recent laboratory experiments with laser-produced plasmas have observed and studied a number of fundamental physical processes relevant to magnetized astrophysical plasmas, including magnetic reconnection, collisionless shocks, and magnetic field generation by Weibel instability, opening up new experimental platforms for laboratory astrophysics. We develop a fully kinetic simulation model for first-principles simulation of these systems including the dynamics of magnetic fields---magnetic field generation by the Biermann battery effect or Weibel instability; advection by the ion flow, Hall eff…
Collisionless shocks occur in various fields of physics. In the context of space and astrophysics they have been investigated for many decades. However, a thorough understanding of shock formation and particle acceleration is still missing. Collisionless shocks can be distinguished into electromagnetic and electrostatic shocks. Electromagnetic shocks are of importance mainly in astrophysical environments and they are mediated by the Weibel or filamentation instability. In such shocks, charged particles gain energy by diffusive shock acceleration. Electrostatic shocks are characterized by a str…
A largely unsolved theoretical issue in controlled fusion research is the consistent \textit{kinetic} treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchalleged to date. The goal…
Nonlinear dynamics of collisionless non-neutral plasma in an external electrical trapping field is considered. Time-dependent solution of the nonlinear Vlasov-Poisson equations are obtained. The influence of initial conditions on the dynamics of charged layer is discussed.
It has recently been proposed (Loureiro & Boldyrev 2017; Mallet et al. 2017) that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so that the MHD approximation is not applicable to turbulence at small scales. In this Letter, we propose the extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring …
We present two-dimensional particle-in-cell (PIC) simulations of the fully kinetic collisionless magnetorotational instability (MRI) in weakly magnetized (high $β$) pair plasma. The central result of this numerical analysis is the emergence of a self-induced turbulent regime in the saturation state of the collisionless MRI, which can only be captured for large enough simulation domains. One of the underlying mechanisms for the development of this turbulent state is the drift-kink instability (DKI) of the current sheets resulting from the nonlinear evolution of the channel modes. The onset of t…
Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed matter physics, atomic physics, and quantum chemistry. DFT establishes that a system of $N$ interacting electrons can be described uniquely by its single-particle density $n(\boldsymbol{r})$, instead of the $N$-body wave function, yielding an enormous gain in terms of computational speed and memory storage space. Here, we use time-dependent DFT to show that a classical collisionless plasma can always, in principle, be described by a set of fluid equations for the single-…
Quantum Calculation of Classical Kinetic Equations: A Novel Approach for Numerical Analysis of 6D Boltzmann-Maxwell Equations in Collisionless Plasmas Using Quantum Computing
We present results from three-dimensional hybrid-kinetic simulations of Alfvénic turbulence in a high-beta, collisionless plasma. The key feature of such turbulence is the interplay between local wave--wave interactions between the fluctuations in the cascade and the non-local wave-particle interactions associated with kinetic micro-instabilities driven by anisotropy in the thermal pressure (namely, firehose, mirror, and ion-cyclotron). We present theoretical estimates for, and calculate directly from the simulations, the effective collisionality and plasma viscosity in pressure-anisotropic hi…
When a steady-state cylindrical plasma discharge is centrally fuelled, the collisionless radial electron flux is canonically coupled to an axial current. The identification and analysis of this transport driven current, previously reported in collisionless simulations [W. J. Nunan and J. M. Dawson, Phys. Rev. Lett. $\mathbf{73}$, 1628 (1994)], is addressed analytically and extended to the collisional regime by means of first-principles kinetic models. Collisionless radial transport is described with the standard quasilinear model and collisional velocity anisotropy relaxation with the Landau k…
A high energy density plasma embedded in a neutral gas is able to launch an outward-propagating nonlinear electrostatic ionization wave that traps energetic electrons. The trapping maintains a strong sheath electric field, enabling rapid and long-lasting wave propagation aided by field ionization. Using 1D3V kinetic simulations, we examine the propagation of the ionization wave in the presence of a transverse MG-level magnetic field with the objective to identify qualitative changes in a regime where the initial thermal pressure of the plasma exceeds the pressure of the magnetic field ($β>1$).…
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 …
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…
The evolution of a linearly-polarized, long-wavelength Alfvén wave --propagating in a collisionless magnetized plasma with a sheared parallel-directed velocity flow-- is here studied by means of two-dimensional hybrid Vlasov-Maxwell (HVM) simulations. The unperturbed sheared flow has been represented by an exact solution of the HVM set of equations (Malara {\it et al.}, Phys. Rev. E 97, 053212), this avoiding spurious oscillations that would arise from the non-stationary initial state and inevitably affect the dynamics of the system. We have considered the evolution of both a small and a moder…
Plasma Mixing Driven by the Collisionless Kelvin-Helmholtz Instability: Insights from fully kinetic simulation and density-based diagnostics
KU Leuven（荷语鲁汶大学）；Royal Belgian Institute for Space Aeronomy（比利时皇家空间空气动力学研究所）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；National Research Council, CNR-ISTP（国家研究委员会等离子体科学与技术研究所）；Observatoire Côte d’Azur, Université Côte d’Azur（蔚蓝海岸天文台，蔚蓝海岸大学）；LPC2E, CNRS, Université d’Orléans（奥尔良大学CNRS LPC2E实验室）
The results of kinetic simulations of magnetic reconnection in Harris current sheets are analyzed. A range of guide fields is considered to study reconnection in plasmas characterized by different $β$ values, $β> m_e/m_i$. Both an implicit Particle-in-Cell (PIC) simulation method and a parallel explicit PIC code are used. Simulations with mass ratios up to the physical value are performed. The simulations show that the reconnection rate decreases with the guide field and depends weakly on the mass ratio. The off-diagonal components of the electron pressure tensor break the frozen-in condition,…
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 …
Optimised stellarators and other magnetic-confinement devices having the property that the average magnetic curvature is favourable for all particle orbits are called maximum-$J$ devices, and have recently been shown to be immune to trapped-particle instabilities driven by the density gradient. Gyrokinetic simulations reveal, however, that another instability can arise, which is also associated with particle trapping but causes less transport than typical trapped-electron modes. The nature of this instability is clarified here. It is shown to be similar to the "ubiquitous mode" in tokamaks, an…
The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal MHD theory. These stationary structures can represent plausible candidates for the modelling of coronal plasmas expected to arise in association with accretion discs. However, accretion disc coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can be determined also in the case of collisionless plas…
The full kinetic dynamics of a perpendicular collisionless shock is studied by means of a one-dimensional electromagnetic full particle simulation. The present simulation domain is taken in the shock rest frame in contrast to the previous full particle simulations of shocks. Preliminary results show that the downstream state falls into a unique cyclic reformation state for a given set of upstream parameters through the self-consistent kinetic processes.
Simulations of collisionless oblique propagating slow shocks have revealed the existence of a transition associated with a critical temperature anisotropy epsilon=1-mu_0(P_parallel-P_perpendicular)/ B^2 = 0.25 (Liu, Drake and Swisdak (2011)). An explanation for this phenomenon is proposed here based on anisotropic fluid theory, in particular the Anisotropic Derivative Nonlinear-Schrodinger-Burgers equation, with an intuitive model of the energy closure for the downstream counter-streaming ions. The anisotropy value of 0.25 is significant because it is closely related to the degeneracy point of…
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…
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…
In the vinicity of phase-space resonances for a given species of plasma, the particle distribution function is flattened as free energy is exchanged between the plasma and resonant electromagnetic waves. Here, we present action-angle variables which explicitly separate the adiabatic invariant from the contribution that arises from perturbation of the Hamiltonian over the course of a single orbit. Then, we perform similar analysis for the orbit period, allowing one to identify a generating function $ψ$ which modifies the zeroth order contribution to the orbit period (unperturbed orbit) in the c…
Using a kinetic model for the ions and adiabatic electrons, we solve a steady state, electron-repelling magnetic presheath in which a uniform magnetic field makes a small angle $α\ll 1$ (in radians) with the wall. The presheath characteristic thickness is the typical ion gyroradius $ρ_{\text{i}}$. The Debye length $λ_{\text{D}}$ and the collisional mean free path of an ion $λ_{\text{mfp}}$ satisfy the ordering $λ_{\text{D}} \ll ρ_{\text{i}} \ll αλ_{\text{mfp}}$, so a quasineutral and collisionless model is used. We assume that the electrostatic potential is a function only of distance from the…
