Kappa distributions are ubiquitous in space and astrophysical poorly collisional plasmas, such as the solar wind, suggesting that microscopic and macroscopic properties of these non-equilibrium plasmas are highly conditioned by the wave-particle interactions. The present work addresses the evolution of anisotropic bi-Kappa (or bi-$κ$-)distributions of electrons triggering instabilities of electromagnetic electron-cyclotron (or whistler) modes. The new quasi-linear approach proposed here includes time variations of the $κ$ parameter during the relaxation of temperature anisotropy. Numerical results show that $κ$ may increase for short interval of times at the beginning, but then decreases towards a value lower than the initial one, while the plasma beta and temperature anisotropy indicate a systematic relaxation. Our results suggest that the electromagnetic turbulence plays an important role on the suprathermalization of the plasma, ultimately lowering the parameter $κ$. Even though the variation of $κ$ is in general negative ($Δκ<0$) this variation seems to depend of the initial conditions of anisotropic electrons, which can vary very much in the inner heliosphere.
The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long-wavelength, spatial mod…
Electron velocity distributions in the solar wind are known to have field-aligned skewness, which has been characterized by the presence of secondary populations such as the halo and strahl. Skewness may provide energy for the excitation of electromagnetic instabilities, such as the whistler heat-flux instability (WHFI), that may play an important role in regulating the electron heat-flux in the solar wind. Here we use kinetic theory to analyze the stability of the WHFI in a solar-wind-like plasma where solar wind core, halo and strahl electrons are described as a superposition of two distribu…
Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel propagating whistler that stop…
In the solar wind electron velocity distributions reveal two counter-moving populations which may induce electromagnetic (EM) beaming instabilities known as heat flux instabilities. Depending on plasma parameters two distinct branches of whistler and firehose instabilities can be excited. These instabilities are invoked in many scenarios, but their interplay is still poorly understood. An exact numerical analysis is performed to resolve the linear Vlasov-Maxwell dispersion and characterize these two instabilities, e.g., growth rates, wave frequencies and thresholds, enabling to identify their …
Kinetic instabilities in a dense plasma of a continuous ECR discharge in a mirror magnetic trap at the GISMO setup are studied. We experimentally define unstable regimes and corresponding plasma parameters, where the excitation of electromagnetic emission is observed, accompanied by the precipitation of energetic electrons from the magnetic trap. Comprehensive experimental study of the precipitating electron energy distribution and plasma electromagnetic emission spectra, together with theoretical estimates of the cyclotron instability increment proves that under the experimental conditions th…
The electron beam-plasma system is ubiquitous in the space plasma environment. Here, using a Darwin particle-in-cell method, the excitation of electrostatic and whistler instabilities by a gyrating electron beam is studied in support of recent laboratory experiments. It is assumed that the total plasma frequency $ω_{pe}$ is larger than the electron cyclotron frequency $Ω_e$. The fast-growing electrostatic beam-mode waves saturate in a few plasma oscillations by slowing down and relaxing the electron beam parallel to the background magnetic field. Upon their saturation, the finite amplitude ele…
Recent statistical studies of observational data unveil relevant correlations between whistler fluctuations and the anisotropic electron populations present in space plasmas, e.g., solar wind and planetary magnetospheres. Locally, whistlers can be excited by two sources of free energy associated with anisotropic electrons, i.e., temperature anisotropies and beaming populations carrying the heat flux. However, these two sources of free energy and the resulting instabilities are usually studied independently preventing a realistic interpretation of their interplay. This paper presents the result…
The hot beaming (or strahl) electrons responsible for the main electron heat-flux in the solar wind are believed to be self-regulated by the electromagnetic beaming instabilities, also known as the heat-flux instabilities. Here we report the first quasi-linear theoretical approach of the whistler unstable branch able to characterize the long-term saturation of the instability as well as the relaxation of the electron velocity distributions. The instability saturation is not solely determined by the drift velocities, which undergo only a minor relaxation, but mainly from a concurrent interactio…
The electrons are an essential particle species in the solar wind. They often exhibit non-equilibrium features in their velocity distribution function. These include temperature anisotropies, tails (kurtosis), and reflectional asymmetries (skewness), which contribute a significant heat flux to the solar wind. If these non-equilibrium features are sufficiently strong, they drive kinetic micro-instabilities. We develop a semi-graphical framework based on the equations of quasi-linear theory to describe electron-driven instabilities in the solar wind. We apply our framework to resonant instabilit…
Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth…
The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after Parker Solar Probe observations during its first perihelion at 0.166 au, consisting of a dense core and an anti-sunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilit…
The effects of kinetic whistler-wave instabilities on the runaway-electron (RE) avalanche is investigated. With parameters from DIII-D experiments, we show that RE scattering from excited whistler waves can explain several poorly understood experimental results seen in a variety of tokamaks. We find an increase of the avalanche growth rate and threshold electric field, bringing the present model much closer to observations than previous results. The excitation of kinetic instabilities and the scattering of resonant electrons are calculated self-consistently using a quasilinear model. We also e…
In this paper we show that the kinetic instabilities associated with runaway electron beams play an essential role for the production of high-level non-thermal electron-cyclotron-emission (ECE) radiation. Most of the non-thermal ECE comes from runaway electrons in the low-energy regime with large pitch angle, which are strongly scattered by the excited whistler waves. The power of ECE from runaway electrons is obtained using a synthetic diagnostic model based on the reciprocity method. The electron distribution function is calculated using a kinetic simulation model including the whistler wave…
In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy $A = T_{\perp}/T_\parallel>$ (with $\perp, \parallel$ respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the ki…
Self-mediation of runaway electrons via self-excited wave-wave and wave-particle interactions
University of Maryland, College Park（马里兰大学帕克分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）；School of Computational Science and Engineering, Georgia Institute of Technology（佐治亚理工学院计算科学与工程学院）
The scattering of electrons by heat-flux-driven whistler waves is explored with a particle-in-cell (PIC) simulation relevant to the transport of energetic electrons in flares. The simulation is initiated with a large heat flux that is produced using a kappa distribution of electrons with positive velocity and a cold return current beam. This system represents energetic electrons escaping from a reconnection-driven energy release site. This heat flux system drives large amplitude oblique whistler waves propagating both along and against the heat flux, as well as electron acoustic waves. While t…
For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a time scale much shorter than that of collisions, and the growth rat…
Context. Solar outflows are a considerable source of free energy which accumulates in multiple forms like beaming (or drifting) components and/or temperature anisotropies. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, the self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the …
In space plasmas kinetic instabilities are driven by the beaming (drifting) components and/or the temperature anisotropy of charged particles. The heat-flux instabilities are known in the literature as electromagnetic modes destabilized by the electron beams (or strahls) aligned to the interplanetary magnetic field. A new kinetic approach is proposed here in order to provide a realistic characterization of heat-flux instabilities under the influence of electrons with temperature anisotropy. Numerical analysis is based on the kinetic Vlasov-Maxwell theory for two electron counter-streaming (cor…
The velocity particle distributions measured in-situ in space plasmas deviate from Maxwellian (thermal) equilibrium, showing enhanced suprathermal tails which are well described by the standard Kappa-distribution (SKD). Despite its successful application, the SKD is frequently disputed due to a series of unphysical implications like diverging velocity moments, preventing a macroscopic description of the plasma. The regularized Kappa-distribution (RKD) has been introduced to overcome these limitations, but the dispersion properties of RKD-plasmas are not explored yet. In the present paper we co…
Employing linearized Vlasov-Maxwell system, the Weibel instability embedded in an ambient magnetic field is discussed for a semi-relativistic bi-Maxwellian distribution hoping such a scenario occurs in some relativistic environments e.g., gamma-ray burst sources and relativistic jet sources, supernovae, and galactic cosmic rays where the perpendicular temperature is much dominated over the parallel . The dispersion relations are analyzed analytically along with the graphical representation and the estimates of the growth rate are presented along with the instability threshold condition in the …
Differential flows among different ion species are often observed in the solar wind, and such ion differential flows can provide the free energy to drive Alfvén/ion-cyclotron and fast-magnetosonic/whistler instabilities. Previous works mainly focused on ion beam instability under the parameters representative of the solar wind nearby 1 au. In this paper we further study proton beam instability using the radial models of the magnetic field and plasma parameters in the inner heliosphere. We explore a comprehensive distribution of proton beam instability as functions of the heliocentric distance …
In collision-poor plasmas from space, e.g., solar wind or stellar outflows, the heat-flux carried by the strahl or beaming electrons is expected to be regulated by the self-generated instabilities. Recently, simultaneous field and particle observations have indeed revealed enhanced whistler-like fluctuations in the presence of counter-beaming populations of electrons, connecting these fluctuations to the whistler heat-flux instability (WHFI). This instability is predicted only for limited conditions of electron beam-plasmas, and was not captured in numerical simulations yet. In this letter we …
Transport equations for electron thermal energy in the high $β_e$ intracluster medium (ICM) are developed that include scattering from both classical collisions and self-generated whistler waves. The calculation employs an expansion of the kinetic electron equation along the ambient magnetic field in the limit of strong scattering and assumes whistler waves with low phase speeds $V_w\sim{v}_{te}/β_e\ll{v}_{te}$ dominate the turbulent spectrum, with $v_{te}$ the electron thermal speed and $β_e\gg1$ the ratio of electron thermal to magnetic pressure. We find: (1) temperature-gradient-driven whis…
In low-collisionality plasmas, velocity-space instabilities are a key mechanism providing an effective collisionality for the plasma. We use particle-in-cell (PIC) simulations to study the interplay between electron and ion-scale velocity-space instabilities and their effect on electron pressure anisotropy, viscous heating, and thermal conduction. The adiabatic invariance of the magnetic moment in low-collisionality plasmas leads to pressure anisotropy, $p_{\perp,j} > p_{||,j}$, if the magnetic field $\vec{B}$ is amplified ($p_{\perp,j}$ and $p_{||,j}$ denote the pressure of species $j$ [elect…
Important efforts are currently made for understanding the so-called kinetic instabilities, driven by the anisotropy of different species of plasma particles present in the solar wind and terrestrial magnetosphere. These instabilities are fast enough to efficiently convert the free energy of plasma particles into enhanced (small-scale) fluctuations with multiple implications, regulating the anisotropy of plasma particles. In this paper we use both linear and quasilinear (QL) frameworks to describe complex unstable regimes, which realistically combine different temperature anisotropies of elect…
The kinetic instabilities of the Weibel-type are presently invoked in a large variety of astrophysical scenarios because anisotropic plasma structures are ubiquitous in space. The Weibel instability is driven by a temperature anisotropy which is commonly modeled by a bi-axis distribution function, such as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been limited to a bi-Kappa distribution and found a suppression of this instability in the presence of suprathermal tails. In the present paper it is shown that the Weibel growth rate is rather more sensitive to the shape of the…
Modeling complex plasma instabilities in space plasmas - Three-component electron formalism of heat-flux instabilities
Ruhr-Universität Bochum（波鸿鲁尔大学）；KU Leuven（荷语鲁汶大学）；Comisión Chilena de Energía Nuclear（智利核能委员会）；Universidad Andres Bello（安德烈斯贝略大学）；University of Maria Curie-Skłodowska（玛丽亚·居里-斯克沃多夫斯卡大学）
Space plasmas are collisionpoor and kinetic effects prevail leading to wave fluctuations, which transfer the energy to small scales: wave-particle interactions replace collisions and enhance dispersive effects heating particles and producing suprathermal populations observed at any heliospheric distance in the solar wind. At large distances collisions are not efficient, and the selfgenerated instabilities constrain the solar wind anisotropy including the thermal core and the suprathermal components. The generalized power-laws of Kappa-type are the best fitting model for the observed distributi…
BO-PBK: A comprehensive solver for dispersion relations of obliquely propagating waves in magnetized multi-species plasma with anisotropic loss-cone drift product-bi-kappa distribution
Space plasmas are known to be out of (local) thermodynamic equilibrium, as observations show direct or indirect evidences of non-thermal velocity distributions of plasma particles. Prominent are the anisotropies relative to the magnetic field, anisotropic temperatures, field-aligned beams or drifting populations, but also, the suprathermal populations enhancing the high-energy tails of the observed distributions. Drifting bi-Kappa distribution functions can provide a good representation of these features and enable for a kinetic fundamental description of the dispersion and stability of these …
Context. Recent studies on Kappa distribution functions invoked in space plasma applications have emphasized two alternative approaches which may assume the temperature parameter either dependent or independent of the power-index $κ$. Each of them can obtain justification in different scenarios involving Kappa-distributed plasmas, but direct evidences supporting any of these two alternatives with measurements from laboratory or natural plasmas are not available yet. Aims. This paper aims to provide more facts on this intriguing issue from direct fitting measurements of suprathermal electron po…
Velocity distribution functions (VDFs) that exhibit a power-law dependence on the high-energy tail have been the subject of intense research by the plasma physics community. Such functions, known as kappa or superthermal distributions, have been found to provide a better fitting to the VDFs measured by spacecraft in the solar wind. One of the problems that is being addressed on this new light is the temperature anisotropy of solar wind protons and electrons. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well-established. However, for kappa distributio…
We use particle-in-cell (PIC) simulations of a collisionless, electron-ion plasma with a decreasing background magnetic field, $B$, to study the effect of velocity-space instabilities on the viscous heating and thermal conduction of the plasma. If $B$ decreases, the adiabatic invariance of the magnetic moment gives rise to pressure anisotropies with $p_{||,j} > p_{\perp,j}$ ($p_{||,j}$ and $p_{\perp,j}$ represent the pressure of species $j$ ($=i$ or $e$) parallel and perpendicular to the magnetic field). Linear theory indicates that, for sufficiently large anisotropies, different velocity-spac…
Plasma Instabilities in Arbitrary Distributions: Comparison between ALPS and BO
Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；Beijing VeloAlpha Technology Co., Ltd.（北京维奥拉科技有限公司）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学月球与行星实验室）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德太空科学实验室）；Changsha University of Science and Technology（长沙理工大学）
In the solar wind plasma an excess of kinetic temperature along the background magnetic field stimulates proton firehose modes to grow if the parallel plasma beta parameter is sufficiently high, i.e., $β_{p \parallel}\gtrsim 1$. This instability can prevent the expansion-driven anisotropy from increasing indefinitely, and explain the observations. Moreover, such kinetic instabilities are expected to be even more effective in the presence of suprathermal Kappa-distributed populations, which are ubiquitous in the solar wind, are less affected by collisions than the core population, but contribut…
In collision-poor plasmas from space, three distinct ion-ion instabilities can be driven by the proton beams streaming along the background magnetic field: left-hand resonant, non-resonant, and right-hand resonant instabilities. These instabilities are in general investigated considering only idealized proton beams with Maxwellian velocity distributions, and ignoring the implications of suprathermal populations, usually reproduced by the Kappa power-laws. Moreover, the existing theories minimize the kinetic effects of electrons, assuming them isotropic and Maxwellian distributed. In an attempt…
