arXiv subjects

Marian Lazar

Publications and source records attributed to Marian Lazar.

At least 19 recordsLinked to original sources

arXiv2026

Wave instabilities in anisotropic regularized Kappa plasmas: New plasma dispersion functions and numerical validation

Plasmas in space and astrophysical environments are frequently found in (quasi-)stationary states not in thermal equilibrium, indicated by velocity distribution functions (VDFs) featuring nonthermal characteristics, such as Lorentzian high-energy tails and kinetic (temperature and strahl/beam) anisotropies. For decades, in-situ observations of electrons and ions in the solar corona, solar wind or planetary magnetospheres have been modelled using so-called Kappa VDFs, whose standard form, however - depending on the considered VDF moment - imposes stringent constraints on the minimum value of the Kappa power-law parameter. Such limitations have posed difficulties on the derivation of a fully-consistent hydrodynamic formulation of suprathermal plasmas. To improve this situation, the recently proposed regularized Kappa VDF avoids strict constraints on the Kappa parameter by introducing an exponential, regularizing cut-off. In this work we assume that the plasma particles are described by regularized-Kappa VDFs that feature anisotropies not only in their thermal velocity spread parameters but also in their exponential cut-offs. The dielectric tensor components for waves propagating along a magnetic field are derived, in terms of new plasma dispersion functions. The resulting dispersion equations are solved with two complementary techniques, namely by using the analytical expressions derived here and by employing the ALPS code. This is done for physical parameters that give rise to electromagnetic and electrostatic instabilities. Both approaches show excellent agreement and the results demonstrate how an anisotropy in the regularizing cut-off of VDFs can serve, depending on an instability's nature, either as a stabilization factor or as an additional free energy source.

physics.plasm-ph↗

arXiv2026

Modeling complex plasma instabilities in space plasmas - Three-component electron formalism of heat-flux instabilities

Despite the fact that electrons observed in situ in space plasmas have three major components-the quasi-thermal core, suprathermal halo, and strahl-the analysis of instabilities triggered by kinetic, velocity-space anisotropies (such as relative drifts and temperature anisotropy) generally considers only two. We demonstrate that realistic modeling with all three components is achievable in the present analysis focusing on heat-flux instabilities. In the absence of particle collisions, these instabilities regulate the heat flux carried mainly by suprathermal electrons. The velocity distributions were modeled according to in situ observations, with a Maxwellian core and Kappa-distributed halo and strahl. We exploited advanced numerical codes capable of solving the linear dispersion and stability properties of plasma systems with Maxwellian and Kappa distributions. The unstable solutions differ significantly from those obtained with simplified two-component models (such as core-strahl or core-beam). The growth rates predict the excitation and interplay of two unstable modes, whistler and/or firehose heat-flux instabilities. The numerical solver 'ALPS' was successfully applied to systems with regularized Kappa distributions, for which analytical derivation of dispersion relations is not straightforward. The two instabilities are triggered by the relative drifts, core-strahl and halo-strahl, and may have new consequences for heat-flux regulation. Particularly important are cases when the core-strahl instability is in competition with the instability driven by the halo-strahl drift, as well as when the two instabilities have the same nature and accumulate. Future studies are motivated to confirm these predictions in quasilinear theories and numerical simulations.

physics.plasm-ph↗

arXiv2026

Kinetic-based macro-modeling of the solar wind at large heliocentric distances: Kappa electrons at the exobase

Recent evidence from Parker Solar Probe on the suprathermal electrons with Kappa-type velocity distributions in the outer corona has revived interest in the kinetic-based macro-modelling of the solar (SW), aiming to explain its properties. Invoked in kinetic modelling of nonequilibrium plasmas, standard Kappa distributions (SKDs) have been adjusted to the regularized Kappa distributions (RKDs) to fix the inconsistencies of SKD and develop consistent fluid modelling of space plasmas. We propose a new analysis of these properties at large heliocentric distances based on the existence of RKD electrons at the exobase. This new semi-analytic formalism is inspired by the methodology proposed initially by Meyer-Vernet and Issautier (1998), https://doi.org/10.1029/98ja02853. Compared to SKDs, the results for RKDs have extended applicability, since all moments can be defined and calculated consistently for all values of the $κ$ parameter, even lower than the critical ones (e.g., $κ_c=3/2$ imposed to the second-order moment) of SKDs. However, the excess energy of the more energetic suprathermal electrons associated with low values of $κ\lesssim 3/2$, is regulated by the RKD-specific cutoff parameter $α< 1$. The estimates for, e.g., the temperature and bulk velocity of the SW, remain at realistic values even for small $3/2 < κ\lesssim 2$, which would otherwise exceed specific observations. One can thus model a higher abundance of suprathermal electrons at the exobase (e.g., $κ\leqslant 3/2$), which is plausible for the sources of energetic events (flares and coronal mass ejections), and also in the astrospheres of stars with coronas hotter than the Sun's.

astro-ph.SR↗

arXiv2026

Quasi-linear approach of bi-Kappa distributed electrons with dynamic $κ$ parameter. EMEC instability

In recent years, significant progress has been made in the velocity-moment-based quasi-linear (QL) theory of waves and instabilities in plasmas with nonequilibrium velocity distributions (VDs) of the Kappa (or $κ$) type. However, the temporal variation of the parameter $κ$, which quantifies the presence of suprathermal particles, is not fully captured by such a QL analysis, and typically $κ$ remains constant during plasma dynamics. We propose a new QL modeling that goes beyond the limits of a previous approach, realistically assuming that the quasithermal core cannot evolve independently of energetic suprathermals. The case study is done on the electron-cyclotron (EMEC) instability generated by anisotropic bi-Kappa electrons with $A=T_\perp/T_\parallel > 1$ ($\parallel, \perp$ denoting directions with respect to the background magnetic field). The parameter $κ$ self-consistently varies through the QL equation of kurtosis (fourth-order moment) coupled with temporal variations of the temperature components, relaxing the constraint on the independence of the low-energy (core) electrons and suprathermal high-energy tails of VDs. The results refine and extend previous approaches. A clear distinction is made between regimes that lead to a decrease or an increase in the $κ$ parameter with saturation of the instability. What predominates is a decrease in $κ$, i.e., an excess of suprathermalization, which energizes suprathermal electrons due to self-generated wave fluctuations. Additionally, we found that VDs can evolve toward a quasi-Maxwellian shape (as $κ$ increases) primarily in regimes with low beta and initial kappa values greater than five. Instability-driven relaxation only partially resolves temperature anisotropy in bi-Kappa electron VDs, as wave fluctuations generally act to further energize suprathermal electrons.

physics.plasm-ph↗

arXiv2025

Electrostatic waves in astrophysical Druyvesteyn plasmas: I. Langmuir waves

Plasmas in various astrophysical systems are in non-equilibrium states as evidenced by direct in-situ measurements in the solar wind, solar corona and planetary environments as well as by indirect observations of nonthermal sources of waves and emissions. Specific to observed non-equilibrium plasmas are non-Maxwellian velocity distributions with suprathermal tails, most often described by Kappa (power-law) distributions. In this paper, we introduce an alternative modeling for linear waves in plasmas described by the generalized Druyvesteyn distribution model. This model can reproduce not only high-energy tails, but also low-energy flat-tops of velocity distributions, like those of electrons in interplanetary shocks and the solar transition region. The wave dispersion relation of longitudinal waves is derived in terms of the newly introduced Druyvesteyn dispersion function. The dispersion curves as well as damping rates of high-frequency Langmuir waves are numerically computed for the isotropic case, and their analytical approximations are provided in the limit of weak damping. We thus offer a new tool for modeling longitudinal waves, and in particular Langmuir waves under the specific conditions of Druyvesteyn distributions.

physics.plasm-ph↗

arXiv2025

Heat-flux Instabilities of Regularized Kappa Distributed Strahl Electrons Resolved with ALPS

The fluid behavior of the solar wind is affected by the heat flux carried by the suprathermal electron populations, especially the electron strahl (or beam) that propagates along the magnetic field. In turn, the electron strahl cannot be stable, and in the absence of collisions, its properties are regulated mainly by self-generated instabilities. This paper approaches the description of these heat-flux instabilities in a novel manner using regularized Kappa distributions (RKDs) to characterize the electron strahl. RKDs conform to the velocity distributions with suprathermal tails observed in situ, and at the same time allow for consistent macromodeling, based on their singularity-free moments. In contrast, the complexity of RKD models makes the analytical kinetic formalism complicated and still inaccessible, and therefore, here heat-flux instabilities are resolved using the advanced solver ALPS. Two primary types of instabilities emerge depending on plasma conditions: the whistler and firehose heat-flux instabilities. The solver is successfully tested for the first time for such instabilities by comparison with previous results for standard distributions, such as Maxwellian and Kappa. Moreover, the new RKD results show that idealized Maxwellian models can overrate or underestimate the effects of these instabilities, and also show differences from those obtained for the standard Kappa, which, for instance, underestimate the firehose heat-flux growth rates.

physics.plasm-ph↗

arXiv2025

Temperature anisotropy instabilities of solar wind electrons with regularized Kappa-halos resolved with ALPS

Space plasmas in various astrophysical setups can often be both very hot and dilute, making them highly susceptible to waves and fluctuations, which are generally self-generated and maintained by kinetic instabilities. In this sense, we have in-situ observational evidence from the solar wind and planetary environments, which reveal not only wave fluctuations at kinetic scales of electrons and protons, but also non-equilibrium distributions of particle velocities. This paper reports on the progress made in achieving a consistent modeling of the instabilities generated by temperature anisotropy, taking concrete example of those induced by anisotropic electrons, such as, electromagnetic electron-cyclotron (whistler) and firehose instabilities. The effects of the two main electron populations, the quasi-thermal core and the suprathermal halo indicated by the observations, are thus captured. The low-energy core is bi-Maxwellian, and the halo is described for the first time by a regularized (bi-)$κ$-distribution (RKD), which was recently introduced to fix inconsistencies of standard $κ$-distributions (SKD). In the absence of a analytical RKD dispersion kinetic formalism (involving tedious and laborious derivations), both the dispersion and (in)stability properties are directly solved numerically using the numerical Arbitrary Linear Plasma Solver (ALPS). The results have an increased degree of confidence, considering the successful testing of the ALPS on previous results with established distributions.

physics.plasm-ph↗

arXiv2024

Expanding CGL: The CGL double-adiabatic approximation in the Expanding Solar Wind

Different in situ satellite observations within 0.3 to 1 AU from the Sun reveal deviations in the thermodynamics of solar wind expansion. Specifically, these deviations challenge the applicability of the double adiabatic or CGL theory, indicating potential influences such as perpendicular heating and/or parallel cooling of ions. The study aims to investigate the plasma expansion phenomena using the Expanding Box Model (EBM) coupled with an ideal MHD description of the plasma. The primary objective is to understand the observed deviations from the CGL predictions, and how the expansion can affect the conservation of the adiabatic invariants, particularly focusing on the impact of transverse expansion on the CGL equations. To address the plasma expansion, we employed the Expanding Box Model (EBM) coupled with the ideal-MHD formalism used for CGL theory. This model provides a unique system of reference co-moving with the solar wind, allowing for the incorporation of transverse expansion into the double adiabatic equations. Solving the equations for different magnetic field profiles, we compute the evolution of anisotropy and plasma beta, which deviates from CGL predictions and empirical observations. This deviation is attributed to the plasma cooling effect induced by the Expanding Box Model (EBM). Results suggest that heating mechanisms play a crucial role in counteracting plasma cooling during expansion.

physics.plasm-ph↗

arXiv2023

First Principle Description of Plasma Expansion Using the Expanding Box Model

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time we develop a first-principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios.

physics.plasm-ph↗

arXiv2023

Interplay Between Anisotropy- and Skewness-driven Whistler Instabilities in the Solar Wind under the Core-Strahlo model

Temperature anisotropy and field-aligned skewness are commonly observed non-thermal features in electron velocity distributions in the solar wind. These characteristics can act as a source of free energy to destabilize different electromagnetic wave modes, which may alter the plasma state through wave-particle interactions. Previous theoretical studies have mainly focused on analyzing these non-thermal features and self-generated instabilities individually. However, to obtain a more accurate and realistic understanding of kinetic processes in the solar wind, it is necessary to examine the interplay between these two energy sources. By means of linear kinetic theory, in this paper we investigate the excitation of the parallel-propagating whistler mode, when it is destabilized by electron populations exhibiting both temperature anisotropy and field-aligned strahl or skewness. To describe the solar wind electrons, we adopt the Core-Strahlo model as an alternative approach. This model offers the advantage of representing the suprathermal features of halo and strahl electrons, using a single skew-Kappa distribution already known as the strahlo population. Our findings show that when the electron strahlo exhibits an intrinsic temperature anisotropy, this suprathermal population becomes a stronger and more efficient source of free energy for destabilizing the whistler mode. This suggests a greater involvement of the anisotropic strahlo in processes conditioned by wave-particle interactions. Present results also suggest that the contribution of core anisotropy can be safely disregarded when assessing the importance of instabilities driven by the suprathermal population. This allows for a focused study, particularly regarding the regulation of electron heat flux in the solar wind.

astro-ph.SR↗

arXiv2022

Comparing the counter-beaming and temperature anisotropy driven aperiodic electron firehose instabilities in collisionless plasma environments

The electron firehose instabilities are among the most studied kinetic instabilities, especially in the context of space plasmas, whose dynamics is mainly controlled by collisionless wave-particle interactions. This paper undertakes a comparative analysis of the aperiodic electron firehose instabilities excited either by the anisotropic temperature or by the electron counter-beaming populations. Two symmetric counter-beams provide an effective kinetic anisotropy similar to the temperature anisotropy of a single (non-drifting) population, with temperature along the magnetic field direction larger than that in perpendicular direction. Therefore, the counter-beaming plasma is susceptible to firehose-like instabilities (FIs), parallel and oblique branches. Here we focus on the oblique beaming FI, which is also aperiodic when the free energy is provided by symmetric counter-beams. Our results show that, for relative small drifts or beaming speeds ($U$), not exceeding the thermal speed ($α$), the aperiodic FIs exist in the same interval of wave-numbers and the same range of oblique angles (with respect to the magnetic field direction), but the growth rates of counter-beaming FI (CBFI) are always higher than those of temperature anisotropy FI (TAFI). For $U/α> 1$, however, another electrostatic two-stream instability (ETSI) is also predicted, which may have growth rates higher than those of CBFI, and may dominate in that case the dynamics.

physics.plasm-ph↗

arXiv2022

Revisiting the Ulysses electron data with a triple fit of velocity distributions

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 populations with different properties. We apply a 2D nonlinear least square fitting procedure, using the Levenberg-Marquardt algorithm, to simultaneously fit the velocity electron data (up to a few keV) with a triple model combining three distinct populations: the more central quasi-thermal core and suprathermal halo, and a second suprathermal population consisting mainly of the electron strahl (or beaming population with a major field-aligned drift). The recently introduced $κ$-cookbook is used to describe each component with the following anisotropic distribution functions (recipes): Maxwellian, regularized kappa-, and generalized kappa-distributions. The temperature anisotropy quantified by the best fits is considered as a case study of the main parameters characterizing electron populations. By comparison to the core, both suprathermal populations exhibit higher temperature anisotropies, which slightly increase with the energy of electrons.

astro-ph.SR↗

arXiv2022

Towards a realistic evaluation of transport coefficients in non-equilibrium space plasmas

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 parameterisation without mathematical divergences or physical inconsistencies. All transport coefficients derived here, i.e., the diffusion and mobility coefficients, electric conductivity, thermoelectric coefficient and thermal conductivity, are finite and well defined for all values of $κ> 0$. Moreover, for low values of $κ$ (i.e., below the SKD poles), the transport coefficients can be orders of magnitudes higher than the corresponding Maxwellian limits, meaning that significant underestimations can be made if suprathermal electrons are ignored.

physics.plasm-ph↗

arXiv2021

Transport coefficients enhanced by suprathermal particles in nonequilibrium heliospheric plasmas

In heliospheric plasmas the transport of energy and particles is governed by various fluxes (e.g., heat flux) triggered by different forces, electromagnetic fields, and gradients in density or temperature. In the outer corona and at relatively low heliocentric distances in the solar wind (i.e., < 1 AU), particle-particle collisions play an important role in the transport of energy, momentum, and matter, described within classical transport theory by the transport coefficients, which relate the fluxes to their sources. The present paper aims to improve the evaluation of the main transport coefficients in such nonequilibrium plasmas, on the basis of an implicit realistic characterization of their particle velocity distributions, in accord with the in situ observations. Of particular interest is the presence of suprathermal populations and their influence on these transport coefficients. Using the Boltzmann transport equation and macroscopic laws for the energy and particle fluxes, we derived electric conductivity, thermoelectric coefficient, thermal conductivity, diffusion, and mobility coefficient. These are conditioned by the electrons, which are empirically well described by the Kappa distribution, with a nearly Maxwellian core and power-law tails enhanced by the suprathermal population. Here we have adopted the original Kappa approach that has the ability to outline and quantify the contribution of suprathermal populations. Without exception, the transport coefficients are found to be systematically and markedly enhanced in the presence of suprathermal electrons, due to the additional kinetic energy with which these populations contribute to the dynamics of space plasma systems. The present results also show how important an adequate Kappa modeling of suprathermal populations is, which is in contrast to other modified interpretations that underestimate the effects of these populations.

astro-ph.SR↗

arXiv2020

Towards a general quasi-linear approach for the instabilities of bi-Kappa plasmas. Whistler instability

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.

physics.plasm-ph↗

arXiv2020

Generalized anisotropic $κ$-cookbook: 2D fitting of Ulysses electron data

Observations in space plasmas reveal particle velocity distributions out of thermal equilibrium, with anisotropies (e.g., parallel drifts or/and different temperatures, $T_\parallel$ - parallel and $T_\perp$ - perpendicular, with respect to the background magnetic field), and multiple quasithermal and suprathermal populations with different properties. The recently introduced (isotropic) $κ$-cookbook is generalized in the present paper to cover all these cases of anisotropic and multi-component distributions reported by the observations. We derive general analytical expressions for the velocity moments and show that the common (bi-)Maxwellian and (bi-)$κ-$distributions are obtained as limiting cases of the generalized anisotropic $κ$-cookbook (or recipes). Based on this generalization, a new 2D fitting procedure is introduced, with an improved level of confidence compared to the 1D fitting methods widely used to quantify the main properties of the observed distributions. The nonlinear least-squares fit is \led{applied to electron data sets} measured by the Ulysses spacecraft confirming the existence of three different populations, a quasithermal core and two suprathermal (halo and strahl) components. In general, the best overall fit is given by the sum of a Maxwellian and two generalized $κ$-distributions.

astro-ph.SR↗

arXiv2020

The $κ$-cookbook: a novel generalizing approach to unify $κ$-like distributions for plasma particle modeling

In the literature different so-called $κ$-distribution functions are discussed to fit and model the velocity (or energy) distributions of solar wind species, pickup ions or magnetospheric particles. Here we introduce a generalized (isotropic) $κ$-distribution as a "cookbook", which admits as special cases, or "recipes", all the other known versions of $κ$-models. A detailed analysis of the generalized distribution function is performed, providing general analytical expressions for the velocity moments, Debye length, and entropy, and pointing out a series of general requirements that plasma distribution functions should satisfy. From a contrasting analysis of the recipes found in the literature, we show that all of them lead to almost the same macroscopic parameters with a small standard deviation between them. However, one of these recipes called the regularized $κ$-distribution provides a functional alternative for macroscopic parameterization without any constraint for the power-law exponent $κ$.

astro-ph.SR↗

arXiv2020

Linear Dispersion Theory of Parallel Electromagnetic Modes for Regularized Kappa-Distributions

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 compute the wavenumber dispersion of the frequency and damping or growth rates for the electromagnetic modes in plasmas characterized by the RKD. This task is accomplished by using the grid-based kinetic dispersion solver LEOPARD developed for arbitrary gyrotropic distributions [P. Astfalk and F. Jenko, J. Geophys. Res. 122, 89 (2017)]. By reproducing previous results obtained for the SKD and Maxwellian, we validate the functionality of the code. Furthermore, we apply the isotropic as well as the anisotropic RKDs to investigate stable electromagnetic electron-cyclotron (EMEC) and ion-cyclotron (EMIC) modes as well as temperature-anisotropy-driven instabilities, both for the case $T_\perp / T_\parallel > 1$ (EMEC and EMIC instabilities) and for the case $T_\perp / T_\parallel < 1$ (proton and electron firehose instabilities), where $\parallel$ and $\perp$ denote directions parallel and perpendicular to the local time-averaged magnetic field. Provided that the cutoff parameter $α$ is small enough, the results show that the RKDs reproduce the dispersion curves of the SKD plasmas at both qualitative and quantitative levels. For higher values, however, physically significant deviation occurs.

physics.plasm-ph↗