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 equation for the parallel component of the electron heat flux (parallel to the ambient magnetic field line) and differs from the equation derived for the proton heat flux due to the different nature of the distributions. Within the large $κ$ index, the equations for the two-fluid model tend to the equations obtained by the Maxwellian distribution. Using an iterated Crank-Nicolson method, the coupled equations are numerically solved for the fast solar wind conditions. We show that at (0.3 - 1) AU from the Sun, the electron density, components of temperature, and components of heat flux follow the power-law behavior. We also showed that near the Earth, the flow speed (electron or proton) increases with decreasing $κ$. We concluded that applying the small $κ$ index (the non-Maxwellian distribution), the extraordinary nature of the solar atmosphere, with its temperature of several million kelvin temperature for electrons, has been captured.
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…
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…
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…
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…
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）
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 c…
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…
We present two case studies of FAST electrostatic analyzer measurements of both highly nonthermal ($κ\lesssim$~2.5) and weakly nonthermal/thermal monoenergetic electron precipitation at $\sim$4000~km, from which we infer the properties of the magnetospheric source distributions via comparison of experimentally determined number density--, current density--, and energy flux--voltage relationships with corresponding theoretical relationships. We also discuss the properties of the two new theoretical number density--voltage relationships that we employ. Moment uncertainties, which are calculated …
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…
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
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 collisionless dissipation of anisotropic Alfvénic turbulence is a promising candidate to solve the solar wind heating problem. Extensive studies examined the kinetic properties of Alfvén waves in simple Maxwellian or bi-Maxwellian plasmas. However, the observed electron velocity distribution functions in the solar wind are more complex. In this study, we analyze the properties of kinetic Alfvén waves in a plasma with two drifting electron populations. We numerically solve the linearized Maxwell-Vlasov equations and find that the damping rate and the proton-electron energy partition for kin…
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…
The acceleration of charged particles by interplanetary shocks can drain a non-negligible fraction of the upstream ram pressure. For a sample of shocks observed in-situ at 1 AU by the ACE and Wind spacecraft, time-series of the non-Maxwellian components (supra-thermal and higher-energy) of the ion and electron energy spectra were acquired for each event. These were averaged for one hour before and after the time of the shock passage to determine their partial pressure. Using the MHD Rankine-Hugoniot jump conditions, we find that the fraction of the total upstream energy flux transferred to non…
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 …
Particle velocity distributions measured in the weakly collisional solar wind are frequently found to be non-Maxwellian, but how these non-Maxwellian distributions impact the physics of plasma turbulence in the solar wind remains unanswered. Using numerical solutions of the linear dispersion relation for a collisionless plasma with a bi-Maxwellian proton velocity distribution, we present a unified framework for the four proton temperature anisotropy instabilities, identifying the associated stable eigenmodes, highlighting the unstable region of wavevector space, and presenting the properties o…
In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account specially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very CPU-expensive codes, avoiding the analytic complexity of velocity phase space integ…
Estimating the temperature of the solar wind particles and their anisotropies is particularly important for understanding the origin of these deviations from thermal equilibrium as well as their effects. In the absence of energetic events the velocity distribution of electrons reveal a dual structure with a thermal (Maxwellian) core and a suprathermal (Kappa) halo. This paper presents a detailed observational analysis of these two components, providing estimations of their temperatures and temperature anisotropies and decoding any potential interdependence that their properties may indicate. T…
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-situ observations of the solar wind (SW) plasma from 0.29 to 1AU show that the protons and alpha particles are often non-Maxwellian, with evidence of kinetic instabilities, temperature anisotropies, differential ion streaming, and associated magnetic fluctuations spectra. The kinetic instabilities in the SW multi-ion plasma can lead to preferential heating of alpha particles and the dissipation of magnetic fluctuation energy, affecting the kinetic and global properties of the SW. Using for the first time a three-dimensional hybrid model, where ions are modeled as particle using the Particle…
Analysis of 15314 electron velocity distribution functions (VDFs) within $\pm$2 hours of 52 interplanetary (IP) shocks observed by the \emph{Wind} spacecraft near 1 AU are introduced. The electron VDFs are fit to the sum of three model functions for the cold dense core, hot tenuous halo, and field-aligned beam/strahl component. The best results were found by modeling the core as either a bi-kappa or a symmetric (or asymmetric) bi-self-similar velocity distribution function, while both the halo and beam/strahl components were best fit to bi-kappa velocity distribution function. This is the firs…
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）
We derive a set of self-consistent marginally stable states for a system of ion-cyclotron waves propagating parallel to the large-scale magnetic field through a homogeneous proton-electron plasma. The proton distributions and the wave dispersions are related through the condition that no further ion-cyclotron resonant particle scattering or wave growth/damping may take place. The thermal anisotropy of the protons in these states therefore defines the threshold value for triggering the proton-cyclotron anisotropy instability. A number of recent papers have noted that the anisotropy of solar win…
We present a kinetic stability analysis of the solar wind electron distribution function consisting of the Maxwellian core and the magnetic-field aligned strahl, a superthermal electron beam propagating away from the sun. We use an electron strahl distribution function obtained as a solution of a weakly collisional drift-kinetic equation, representative of a strahl affected by Coulomb collisions but unadulterated by possible broadening from turbulence. This distribution function is essentially non-Maxwellian and varies with the heliospheric distance. The stability analysis is performed with th…
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…
Plasmas in Earth's outer magnetosphere, magnetosheath, and solar wind are essentially collisionless. This means particle distributions are not typically in thermodynamic equilibrium and deviate significantly from Maxwellian distributions. The deviations of these distributions can be further enhanced by plasma processes, such as shocks, turbulence, and magnetic reconnection. Such distributions can be unstable to a wide variety of kinetic plasma instabilities, which in turn modify the electron distributions. In this paper the deviations of the observed electron distributions from a bi-Maxwellian…
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…
We study the behaviour of shocked wind-electrons leaving wind-driving stars after undergoing the outer wind termination shock. As an example, we describe the evolution of the keV-energetic electron distribution function downstream of the heliospheric termination shock. We start from a kinetic transport equation in the bulk frame of the heliosheath plasma flow taking into account shock-induced electron injection, convective changes, cooling processes, and whistler wave-induced energy diffusion. From this equation we proceed to an associated pressure moment of the electron distribution function …
The Damping and Instability of Ion-acoustic Waves in the Solar Wind: Solar Orbiter Observations
Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德太空科学实验室）；Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学月球与行星实验室）
Wave Emission and Absorption in a Near-Sun Proton-Cyclotron Wave Storm
University of Arizona（亚利桑那大学）；University College London（伦敦大学学院）；University of California, Berkeley（加州大学伯克利分校）；Smithsonian Astrophysical Observatory（史密森尼天体物理台）
Unconditional and conditional statistics is used for studying the histograms of magnetic field multi-scale fluctuations in the solar wind near the solar cycle minimum in 2008. The unconditional statistics involves the magnetic data during the whole year 2008. The conditional statistics involves the magnetic field time series splitted into concatenated subsets of data according to a threshold in dynamic pressure. The threshold separates fast stream leading edge compressional and trailing edge uncompressional fluctuations. The histograms obtained from these data sets are associated with both lar…
Given their uniqueness, the Ulysses data can still provide us with valuable new clues about the properties of plasma populations in the solar wind, and, especially, about their variations with heliographic coordinates. We revisit the electron data reported by by the SWOOPS instrument on-board of the Ulysses spacecraft between 1990 to early 2008. These observations reveal velocity distributions out of thermal equilibrium, with anisotropies (e.g., parallel drifts or/and different temperatures, parallel and perpendicular to the background magnetic field), and quasi-thermal and suprathermal popula…
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…
Solar wind charge-changing reactions are of paramount importance to the physico-chemistry of the atmosphere of a comet, mass-loading the solar wind through an effective conversion of fast light solar wind ions into slow heavy cometary ions. To understand these processes and place them in the context of a solar wind plasma interacting with a neutral atmosphere, numerical or analytical models are necessary. Inputs of these models, such as collision cross sections and chemistry, are crucial. Book-keeping and fitting of experimentally measured charge-changing and ionization cross sections of hydro…
In the near future, Parker Solar Probe and Solar Orbiter will provide the first comprehensive in-situ measurements of the solar wind in the inner heliosphere since the Helios mission in the 1970s. We describe a reprocessing of the original Helios ion distribution functions to provide reliable and reproducible data to characterise the proton core population of the solar wind in the inner heliosphere. A systematic fitting of bi-Maxwellian distribution functions was performed to the raw Helios ion distribution function data to extract the proton core number density, velocity, and temperatures par…
Suprathermal tails are a common feature of solar wind electron velocity distributions, and are expected in the solar corona. From the corona, suprathermal electrons can propagate through the steep temperature gradient of the transition region towards the chromosphere, and lead to non-Maxwellian electron velocity distribution functions (VDFs) with pronounced suprathermal tails. We calculate the evolution of a coronal electron distribution through the transition region in order to quantify the suprathermal electron population there. A kinetic model for electrons is used which is based on solving…
In the present paper, the proton velocity distribution function (VDF)in the solar wind is determined by solving numerically the kinetic evolution equation. We compare the results obtained when considering the effects of ex- ternal forces and Coulomb collisions with those obtained by adding effects of Alfven wave turbulence. We use Fokker-Planck diffusion terms due to Alfvenic turbulence, which take into account observed turbulence spectra and kinetic effects of finite proton gyroradius. Assuming a displaced Maxwellian for the proton VDF at the simulation boundary at 14 solar radii, we show tha…
Kinetic plasma processes have been investigated in the framework of solar wind turbulence, employing Hybrid Vlasov-Maxwell (HVM) simulations. The dependency of proton temperature anisotropy T_{\perp}/T_{\parallel} on the parallel plasma beta β_{\parallel}, commonly observed in spacecraft data, has been recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T_{\perp}/T_{\parallel} and β_{\parallel}, similar to solar wind sub-datasets. Moreover, both simulati…
Observations of the solar corona and the solar wind discover that the solar wind is unsteady and originates from the impulsive events near the surface of the Sun's atmosphere. How solar coronal activities affect the properties of the solar wind is a fundamental issue in heliophysics. We report a simulation and theoretical investigation of how nanoflare accelerated electron beams affect the kinetic-scale properties of the solar wind and generate coherent radio emission. We show that nanoflare-accelerated electron beams can trigger a nonlinear electron two stream instability, which generates kin…
We perform a statistical assessment of solar wind stability at 1 AU against ion sources of free energy using Nyquist's instability criterion. In contrast to typically employed threshold models which consider a single free-energy source, this method includes the effects of proton and He$^{2+}$ temperature anisotropy with respect to the background magnetic field as well as relative drifts between the proton core, proton beam, and He$^{2+}$ components on stability. Of 309 randomly selected spectra from the Wind spacecraft, $53.7\%$ are unstable when the ion components are modeled as drifting bi-M…
Energetic neutral atom (ENA) models typically require post-processing routines to convert the distributions of plasma and H atoms into ENA maps. Here we investigate how two different kinetic-MHD models of the heliosphere (the BU and Moscow models) manifest in modeled ENA maps using the same prescription and how they compare with Interstellar Boundary Explorer (IBEX) observations. Both MHD models treat the solar wind as a single-ion plasma for protons, which include thermal solar wind ions, pick-up ions (PUIs), and electrons. Our ENA prescription partitions the plasma into three distinct ion po…
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…
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）
There is wide observational evidence that electron velocity distribution functions (eVDF) observed in the solar wind generally present enhanced tails and field-aligned skewness. These properties may induce the excitation of electromagnetic perturbations through the whistler heat-flux instability (WHFI), that may contribute to a non-collisional regulation of the electron heat-flux values observed in the solar wind via wave-particle interactions. Recently, a new way to model the solar wind eVDF has been proposed: the core-strahlo model. This representation consist in a bi-Maxwellian core plus a …
