This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with the previous work [R. Guo, Phys. Plasmas \textbf{27}, 122104 (2020)]. We find that the polytropic equation of state can lead to the kappa distribution without any other assumptions in one dimension. In higher dimensions, an extra assumption that the global distribution must only depend on the energy is still needed. In addition, the self-consistence of the electrostatic potential is investigated in such plasmas. The study implies that in single-component plasmas, the potential is constrained by the Lane-Emden equation. However, in two-component plasmas, any arbitrary potential could exist with a suitable background ion density. Finally, we discuss the connections between the kappa distribution and the polytrope.
In this paper, we prove that the kappa distribution is the stationary solution of the Vlasov-Poisson system in an inhomogeneous plasma under the polytropic equation of state and an assumption restricting the local velocity distribution to a specific mathematical form. The profiles of density, temperature, and electric potential are obtained theoretically. The kappa index can be determined if the initial state is known. In order to verify the theory, particle-in-cell simulations are made and the results show excellent agreement with the theoretical predictions for density, temperature, and velo…
We derive annual skymaps of the proton temperature in the inner heliosheath (IHS), and track their temporal evolution over the years from 2009 to 2016 of Interstellar Boundary Explorer observations. Other associated thermodynamic parameters also determined are the density, kappa, that is, the parameter that characterizes kappa distributions, temperature rate, polytropic index, and entropy. We exploit the theory of kappa distributions and their connection with polytropes, to (i) express a new polytropic quantity Π that remains invariant along streamlines where temperature and density may vary, …
Transport processes in the fully ionized plasma with kappa-distribution and in strong magnetic field are studied. By analyzing the current density and the heat flux in the kappa-distributed plasma, we derive the corresponding transport coefficients, including the electric conductivity, the thermal conductivity and thermoelectric coefficient. Besides, we derive the coefficients of Hall, Nernst and Leduc-Righi effects in the kappa-distributed plasma. It is shown that these new transport coefficients depend strongly on the kappa-parameter and only in the limit kappa to infinity, they recover the …
By using the generalized Boltzmann equation of transport and the first-order approximation of Chapman-Enskog expansion on the kappa-distribution function, we study the thermal conductivity and Dufour effects in the weakly ionized and magnetized plasma. We show that in the kappa-distributed plasma, the thermal conductivity and Dufour coefficient are significantly different from those in the Maxell-distributed plasma, and the transverse thermal conductivity and Dufour coefficient in the kappa-distributed plasma are generally greater than those in the Maxwell-distributed plasma, and the Righi-Led…
We study the diffusion of charged particles in the weakly ionized plasma with the power-law kappa-distributions and without magnetic field. The electrons and ions have different kappa-parameters. We obtain the expressions of both diffusion and mobility coefficients of electrons and ions respectively in the plasma. We find that these new transport coefficient formulae depend strongly on the kappa-parameters in the power-law distributed plasma. When we take kappa to be infinite, these formulae reduce to the classical forms in the weakly ionized plasma with a Maxwellian distribution.
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…
The kappa-distributed fully ionized plasma with collisional interaction is investigated. The Fokker-Planck equation with Rosenbluth potential is employed to describe such a physical system. The results show that the kappa distribution is not a stationary distribution unless the parameter kappa tends to infinity. The general expressions of collisional relaxation rate of multiple-component plasma with kappa distribution are derived and discussed in specific cases in details. For the purpose of visual illustration, we also give those results numerically in figures. All the results show that the p…
We combine different measurements of the polytropic index of the proton plasma in the heliosphere: i) near-adiabatic index in the inner heliosphere ~1AU, ii) subadiabatic indices in the outer heliosphere ~20-40AU, and iii) near-zero indices in the inner heliosheath. These observations are unified by a single theoretical model of the polytropic index throughout its radial extent in the heliosphere; the corresponding fitting reveals the decreasing trend of the polytropic index with increasing heliocentric distance R. We anticipate that with increasing R, (i) the Debye length and mean-free-path d…
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…
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 linear electron acoustic waves propagating in plasmas with two kappa-distributed electrons and stationary ions are investigated. The temperatures of the two electrons are assumed to be the same, but the kappa indices are not. It shows that if one kappa index is small enough and the other one is large enough, a weak damping regime of the electron acoustic waves exists. The dispersions and damping rates are numerically studied. The parameter spaces for the weakly damped electron acoustic waves are analyzed. Moreover, the electron acoustic waves in the present model are compared with those in…
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 …
In this paper we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the prev…
The kinetic theory of $\mathrm{sech}^2 x$-type electron holes is studied. The potential of the electron holes is solved in the weak amplitude limit by the pseudo-potential method. We investigate the existence condition of the $\mathrm{sech}^2 x$ electron holes. It indicates that the derivatives of trapped and untrapped distributions at the separatrix play significant roles in determining the potential profile. The theory is then applied to the Kappa-distributed plasmas. The amplitude and width of the $\mathrm{sech}^2 x$ electron holes are analyzed. Finally, the theoretical results are verified…
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
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 …
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 res…
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…
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
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…
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…
We study the dispersion relation for parallel propagating ion-cyclotron (IC) waves in a dusty plasma, considering situations where the velocity dispersion along perpendicular direction is greater than along the parallel direction, and considering the use of product-bi-kappa (PBK) velocity distributions for the plasma particles. The results obtained by numerical solution of the dispersion relation, in a case with isotropic Maxwellian distributions for electrons and PBK distribution for ions, show the occurrence of the electromagnetic ion-cyclotron instability (EMIC), and show that the decrease …
The polytropic process characterizes the thermodynamics of space plasma particle populations. The polytropic index, $γ$, is particularly important as it describes the thermodynamic behavior of the system by quantifying the changes in temperature as the system is compressed or expanded. Using Wind spacecraft plasma and magnetic field data during $01/1995 - 12/2018$, we investigate the thermodynamic evolution in 336 Interplanetary Coronal Mass Ejection (ICME) events. For each event, we derive the index $γ$ in the sheath and magnetic ejecta structures, along with the pre- and post- event regions.…
The Sagdeev pseudopotential method is used to investigate the occurrence and the dynamics of fully nonlinear electrostatic solitary structures in a plasma containing suprathermal hot electrons, in the presence of massive charged dust particles in the background. The soliton existence domain is delineated, and its parametric dependence on different physical parameters is clarified.
The linear and nonlinear properties of large amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a non-Maxwellian state, characterized by an excess of superthermal particles, here modelled by a kappa-type long-tailed distribution function. Waves are assumed to propagate obliquely to the ambient magnetic field. Two types of electrostatic modes are shown to exist in the linear regime, and their properties are briefly analyzed. A nonlinear pseudopotential typ…
We investigate the existence conditions and propagation properties of electron-acoustic solitary waves in a plasma consisting of an electron beam fluid, a cold electron fluid, and a hot suprathermal electron component modeled by a $κ$-distribution function. The Sagdeev pseudopotential method was used to investigate the occurrence of stationary-profile solitary waves. We have determined how the soliton characteristics depend on the electron beam parameters. It is found that the existence domain for solitons becomes narrower with an increase in the suprathermality of hot electrons, increasing th…
A self-consistent model is presented for performing steady-state fully kinetic Particle-in-Cell simulations of magnetised plasma plumes. An energy-based electron reflection prevents the numerical pump instability associated with a typical open-outflow boundary, and is shown to be sufficiently general that both the plume kinetics and plasma potential demonstrate domain independence (within 4%). This is upheld by non-stationary Robin-type boundary conditions on the Poisson's equation, coupled to a capacitive circuit that allows physical evolution of the downstream potential drop in the transient…
This work extends the one-dimensional radiation-hydrodynamic imploding spherical argon plasma liner simulations of T. J. Awe et al. [Phys. Plasmas 18, 072705 (2011)] by using a detailed tabular equation-of-state (EOS) model, whereas Awe et al. used a polytropic EOS model. Results using the tabular EOS model give lower stagnation pressures by a factor of 3.9-8.6 and lower peak ion temperatures compared to the polytropic EOS results. Both local thermodynamic equilibrium (LTE) and non-LTE EOS models were used in this work, giving similar results on stagnation pressure. The lower stagnation pressu…
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…
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…
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 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…
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…
Heat capacities at fixed volume and pressure as a function of the degree of ionization are graphically depicted as functions of reciprocal temperature and ionization degree. The polytropic index is calculated as a function of the same variables; as it is not constant a partially ionized plasma can be only approximately polytropic fluid. In parallel, it is launched the idea that Alfvén waves can be used to heat the plasma in a propulsion jet with magnetic nozzle.
Recent studies have outlined the interest for the evaluation of transport coefficients in space plasmas, where the observed velocity distributions of plasma particles are conditioned not only by the binary collisions, e.g., at low energies, but also by the energisation of particles from their interaction with wave turbulence and fluctuations, generating the suprathermal Kappa-distributed populations. This paper provides a first estimate of the main transport coefficients based on regularised Kappa distributions (RKDs), which, unlike standard Kappa distributions (SKDs), enable macroscopic param…
Effects of non-thermal high-energy electrons on Langmuir wave-particle interaction are investigated by an initial value approach. A Vlasov-Poisson simulation is employed which is based on the splitting scheme by Cheng and Knorr [Cheng, C.Z. and G. Knorr, 1976: J. Comput. Phys. 22, 330-351.]. The kappa distribution function is taken as an example of non-thermal electrons. The modification is manifested as an increase in the Landau damping rate and a decrease in the real frequency for a long wavelength limit. A part of the analyses by the modified plasma dispersion function [Summers, D. and R.M.…
Observations show that plasma particles in the solar wind frequently display power-law velocity distributions, which can be isotropic or anisotropic. Particularly, the velocity distribution functions of solar wind electrons are frequently modeled as combination of a background Maxwellian distribution and a non-thermal distribution which is known as the "halo" distribution. For fast solar wind conditions, highly anisotropic field-aligned electrons, denominated as the "strahl" distribution, are also present. Motivated by these observations, the present paper considers a tenuous plasma with Maxwe…
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…
