Particle velocity distribution functions (VDF) in space plasmas often show non Maxwellian suprathermal tails decreasing as a power law of the velocity. Such distributions are well fitted by the so-called Kappa distribution. The presence of such distributions in different space plasmas suggests a universal mechanism for the creation of such suprathermal tails. Different theories have been proposed and are recalled in this review paper. The suprathermal particles have important consequences concerning the acceleration and the temperature that are well evidenced by the kinetic approach where no closure requires the distributions to be nearly Maxwellians. Moreover, the presence of the suprathermal particles take an important role in the wave-particle interactions.
This paper presents the misestimation of temperature when observations from a kappa distributed plasma are analyzed as a Maxwellian. One common method to calculate the space plasma parameters is by fitting the observed distributions using known analytical forms. More often, the distribution function is included in a forward model of the instrument's response, which is used to reproduce the observed energy spectrograms for a given set of plasma parameters. In both cases, the modeled plasma distribution fits the measurements to estimate the plasma parameters. The distribution function is often c…
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 …
We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in kappa-distribution plasmas, with a particular focus on atomic processes important for solar physics. The relevant collision process rate coefficients are generated by summing appropriately weighted Maxwellian rate coefficients. This method reproduces the rate coefficients for a kappa distribution to an estimated accuracy of better than 5%. This is equal to or bett…
Transport coefficients in Lorentz plasma with the power-law kappa-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient and thermal conductivity for the power-law kappa-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the kappa-parameter, and in the limit of the parameter kappa to infinit they are reduced to the standard forms for a Maxwellian distribution.modified
We study the slowing down of particle beams passing through the dusty plasma with power-law kappa-distributions. Three plasma components, electrons, ions and dust particles, can have different kappa-parameter. We derive the deceleration factor (the velocity moment equation) and the slowing down time of a test particle, and numerically study the slowing down properties of an electron beam, a proton beam and a dust particle beam, respectively, in the kappa-distributed dusty plasma. We show that the slowing down properties of particle beams depend strongly on the kappa-parameters of the plasma co…
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…
In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfvén) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in…
The instability of the dust-acoustic waves driven by drifting electrons and ions in a dusty plasma is investigated by the kinetic theory. All the plasma components (electrons, ions and dust particles) are assumed to be the Lorentzian kappa-distributions. The spectral indexes kappa of the kappa-distributions for the three plasma components are different from each other. The obtained instability growth rate depends on the physical quantities of the plasma not only, but on the spectral indexes. The numerical results for the kappa-effect on the instability growth rate show that, if the normalized …
The recently developed concept of "entropic defect" is important for understanding the foundations of thermodynamics in space plasma physics, and more generally, for systems with physical correlations among their particles. Using this concept, this paper derives the basic formulation of the distribution function of velocities (or kinetic energies) in space plasma particle populations. Earlier analyses have shown how the formulation of kappa distributions is interwoven with the presence of correlations among the particles' velocities. This paper shows, for the first time, that the reverse is tr…
The X-ray emission of coronal flare sources can be explained considering the kappa electron distribution. Motivated by this fact, we study the problem of how hot plasma with the kappa distribution of electrons is confined in these sources. For comparison, we analyze the same problem but with the Maxwellian distribution. We use a 3-D particle-in-cell code, which is large in one direction and thus effectively only one-dimensional, but describing all electromagnetic effects. In the case with the Maxwellian distribution, and in agreement with the previous studies, we show a formation of the double…
Counterstreaming plasma structures are widely present in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. Filamentationally unstable mode is described by assuming that each of the counterstreaming plasmas has an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growt…
The Earth's magnetosphere represents a natural plasma laboratory that allows us to study the behavior of particle distribution functions in the absence of Coulomb collisions, typically described by the Kappa distributions. We have investigated the properties of these functions for ions and electrons in different magnetospheric regions, thereby making it possible to reveal the $κ$-parameters for a wide range of plasma beta ($β$) values (from $10^{-3}$ to $10^{2}$). This was done using simultaneous ion and electron measurements from the five Time History of Events and Macroscale Interactions dur…
A non-relativistic Fokker-Planck equation for the electron distribution function is formulated incorporating the effects of stochastic acceleration by whistler-mode waves and Coulomb collisions. The stationary solution $f$ to the equation, subject to a zero-flux boundary condition, is found to be a generalized Lorentzian (or kappa) distribution, which satisfies $f\propto v^{-2(κ+1)}$ for large velocity $v$, where $κ$ is the spectral index. The parameter $κ$ depends strongly on the relative wave intensity $R$. Taking into account the critical energy required for resonance of electrons with whis…
Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use of these distributions has been unjustly criticized because of a perceived lack of theoretical justification. We show that distributions very close to kappa-distributions are a consequence of the generalized entropy favored by nonextensive statistics, which provides the missing link for power-law models of non-thermal features from fundamental physics. With…
The quantum version of Olbert's kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partiti…
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…
In this paper we discuss the collisionless transport equations, continuity, momentum and energy conservation, derived from a kinetic exospheric model of the solar wind based on a kappa velocity distribution function of the electrons. The model is stationary and is based on a non-monotonic potential energy for the protons. The present study is carried out for an exobase located at 1.5 solar radii and for two different values of the kappa index. The maximum radial distance considered is equal to one astronomical unit. The moments of the velocity distribution function computed with the kinetic ex…
We develop the theoretical basis for the connection of the variety of anisotropic distributions with the statistical correlations among particles velocity components. By examining the most common anisotropic distribution, we derive the correlation coefficient among particle energies, show how this correlation is connected to the effective dimensionality of the velocity distribution, and derive the connection between anisotropy and adiabatic polytropic index. Having established the importance of correlation among particles in the formulation of anisotropic kappa distributions, we generalize 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）
The nonthermal particle acceleration during magnetic reconnection remains a fundamental topic in several astrophysical phenomena, such as solar flares, pulsar wind, magnetars, etc, for more than half a century, and one of the unresolved questions is its efficiency. Recently, nonthermal particle acceleration mechanisms during reconnection have been extensively studied by particle-in-cell simulations, yet it is an intriguing enigma as to how the magnetic field energy is divided into thermally heated plasmas and nonthermal particles. Here we study both non-relativistic and relativistic magnetic r…
Spatial intermittency in fully developed turbulence is an established feature of astrophysical plasma fluctuations and in particular apparent in the interplanetary medium by in situ observations. In this situation the classical Boltzmann-Gibbs extensive thermo-statistics, applicable when microscopic interactions and memory are short ranged, fails. Upon generalization of the entropy function to nonextensivity, accounting for long-range interactions and thus for correlations in the system, it is demonstrated that the corresponding probability distributions (PDFs) are members of a family of speci…
Solar flares produce hard X-ray emission of which the photon spectrum is often represented by a combination of thermal and power-law distributions. However, the estimates of the number and total energy of non-thermal electrons are sensitive to the determination of the power-law cutoff energy. Here we revisit an `above-the-loop' coronal source observed by RHESSI on 2007 December 31 and show that a kappa distribution model can also be used to fit its spectrum. Because the kappa distribution has a Maxwellian-like core in addition to the high-energy power-law tail, the emission measure and tempera…
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）
Modeling fast solar wind based on the kinetic theory is an important task for scientists. In this paper, we present a two-fluid model for fast solar wind with anisotropic Kappa-Maxwellian electrons and Bi-Maxwellian protons. In the simulation, the energy exchange between the plasma particles and low-frequency Alfvén waves is considered. A set of eleven coupled equations is derived by applying the zeroth- to fourth-order moments of the Vlasov equation and the modified electromagnetic Maxwell equations. A characteristic of the Kappa distribution (indicated by $κ$ index) is explicit in the equati…
We use observations from the Interstellar Boundary Explorer (IBEX) and Ulysses to explore the possibility that the interstellar neutral helium flowing through the inner solar system possesses an intrinsic non-Maxwellian velocity distribution. In fitting the IBEX and Ulysses data, we experiment with both a kappa distribution and a bi-Maxwellian, instead of the usual Maxwellian assumption. The kappa distribution does not improve the quality of fit to either the IBEX or Ulysses data, and we find lower limits to the kappa parameter of kappa>12.1 and kappa>6.0 from the IBEX and Ulysses analyses, re…
Energy distributions of precipitating electrons in Jupiter's auroral regions from combined Juno/JADE and Juno/JEDI measurements
Aix-Marseille Université, CNRS, CNES, Institut Origines, LAM（艾克斯-马赛大学，法国国家科学研究中心，法国国家空间研究中心，起源研究所，天体物理学与行星学实验室）；Laboratory of Planetary and Atmospheric Physics, STAR Institute, University of Liège（列日大学，STAR研究所，行星与大气物理实验室）；Université de Toulouse, CNRS, CNES, Institut de Recherche en Astrophysique et Planétologie（图卢兹大学，法国国家科学研究中心，法国国家空间研究中心，天体物理学与行星学研究所以）；Institut Supérieur de l’Aéronautique et de l’Espace (ISAE SUPAERO), Université de Toulouse（图卢兹大学，航空航天高级学院）；Weihai Institute for Interdisciplinary Research, Shandong University（山东大学，威海交叉科学研究院）；Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；Space Science and Engineering Division, Southwest Research Institute（西南研究院，空间科学与工程部）
Loading non-Maxwellian Velocity Distributions in Particle Simulations
Space Research Institute, Austrian Academy of Sciences（奥地利科学院空间研究所）；National Institute for Fusion Science（国立研究开发法人核聚变科学研究所）；Faculty of Engineering Sciences, Kyushu University（九州大学工学研究院）
We study the dust surface potential for the complex dusty plasma with negative ions and with a three-parameter non-Maxwell velocity distribution. The plasma contains electrons, positive ions, negative ions, and negatively charged dust particles. By using the current equilibrium condition, we derive the relationship between the normalized dust surface potential and the dusty plasma parameters such as the normalized dust number density, the temperature ratio of negative ions to electrons, the density ratio of negative ions to positive ions, and the charge number of negative ions. The numerical a…
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…
The paper develops a theoretical relationship between the polytropic index and the temperature anisotropy that may characterize space plasmas. The derivation is based on the correlation among the kinetic energies of particles with velocities described by anisotropic kappa distributions. The correlation coefficient depends on the effective dimensionality of the velocity distribution function, having its shape determined by the temperature anisotropies caused by the ambient magnetic field; on the other hand, the effective dimensionality is directly dependent on the polytropic index. This analysi…
The probability distributions (PDFs) of the differences of any physical variable in the intermittent, turbulent interplanetary medium are scale dependent. Strong non-Gaussianity of solar wind fluctuations applies for short time-lag spacecraft observations, corresponding to small-scale spatial separations, whereas for large scales the differences turn into a Gaussian normal distribution. These characteristics were hitherto described in the context of the log-normal, the Castaing distribution or the shell model. On the other hand, a possible explanation for nonlocality in turbulence is offered w…
