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The new in situ measurements of the Solar Orbiter mission contribute to the knowledge of the suprathermal populations in the solar wind, especially of ions and protons whose characterization, although still in the early phase, seems to suggest a major involvement in the interaction with plasma wave fluctuations. Recent studies point to the stimulating effect of suprathermal populations on temperature anisotropy instabilities in the case of electrons already being demonstrated in theory and numerical simulations. Here, we investigate anisotropic protons, addressing the electromagnetic ion-cyclotron (EMIC) and the proton firehose (PFH) instabilities. Suprathermal populations enhance the high-energy tails of the Kappa velocity (or energy) distributions measured in situ, enabling characterization by contrasting to the quasi-thermal population in the low-energy (bi-)Maxwellian core. We use hybrid simulations to investigate the two instabilities (with ions or protons as particles and electrons as fluid) for various configurations relevant to the solar wind and terrestrial magnetosphere. The new simulation results confirm the linear theory and its predictions. In the presence of suprathermal protons, the wave fluctuations reach increased energy density levels for both instabilities and cause faster and/or deeper relaxation of temperature anisotropy. The magnitude of suprathermal effects also depends on each instability's specific (initial) parametric regimes. These results further strengthen the belief that wave-particle interactions govern space plasmas. These provide valuable clues for understanding their dynamics, particularly the involvement of suprathermal particles behind the quasi-stationary non-equilibrium states reported by in situ observations.

Recent studies have revealed new unstable regimes of the counter-beaming electrons specific to hot and dilute plasmas from astrophysical scenarios. The (counter-)beaming electron firehose instability (BEFI) is induced for highly oblique angles of propagation relative to the magnetic field, resembling the fast growing and aperiodic mode triggered by the temperature anisotropy. It is investigated here for space plasma conditions that includes the influence of an embedding background plasma of electrons and protons. Kinetic theory is applied to prescribe the unstable regimes, and differentiate from the regimes of interplay with other instabilities. Linear theory predicts a systematic inhibition of the BEFI, by reducing the growth rates and the range of unstable wave-number with increasing the relative density of the background electrons. To obtain finite growth rates, the beam speed does not need to be high (just comparable to thermal speed), but beams must be dense enough, with a relative density at least 15-20\% of the total density. The plasma conditions favorable to this instability are reduced under the influence of background electrons. PIC simulations confirm not only that BEFI can be excited in the presence of background electrons, but also the inhibiting effect of this population. In the regimes of transition to electrostatic (ES) instabilities, BEFI is still robust enough to develop as a secondary instability, after the relaxation of beams under a quick interaction with ES fluctuations. BEFI resembles the properties of firehose heat-flux instability triggered by the electron strahl. However, BEFI is driven by a double (counter-beaming) strahl, and develops at oblique angles, which makes it effective in the regularization of the electron counter-beams observed in closed magnetic field topologies and interplanetary shocks., Comment: Paper accepted for publication in Astronomy and Astrophysics (12.12.2022)

Firehose-like instabilities (FIs) are cited in multiple astrophysical applications. Of particular interest are the kinetic manifestations in weakly-collisional or even collisionless plasmas, where these instabilities are expected to contribute to the evolution of macroscopic parameters. Relatively recent studies have initiated a realistic description of FIs, as induced by the interplay of both species, electrons and protons, dominant in the solar wind plasma. This work complements the current knowledge with new insights from linear theory and the first disclosures from 2D PIC simulations, identifying the fastest growing modes near the instability thresholds and their long-run consequences on the anisotropic distributions. Thus, unlike previous setups, these conditions are favorable to those aperiodic branches that propagate obliquely to the uniform magnetic field, with (maximum) growth rates higher than periodic, quasi-parallel modes. Theoretical predictions are, in general, confirmed by the simulations. The aperiodic electron FI (a-EFI) remains unaffected by the proton anisotropy, and saturates rapidly at low-level fluctuations. Regarding the firehose instability at proton scales, we see a stronger competition between the periodic and aperiodic branches. For the parameters chosen in our analysis, the a-PFI is excited before than the p-PFI, with the latter reaching a significantly higher fluctuation power. However, both branches are significantly enhanced by the presence of anisotropic electrons. The interplay between EFIs and PFIs also produces a more pronounced proton isotropization., Comment: Accepted in ApJ

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., $\beta_{p \parallel}\gtrsim 1$. 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 contribute with an additional free energy. In this work we use both linear and extended quasi-linear (QL) frameworks to characterize the unstable periodic proton firehose modes (propagating parallel to the magnetic field) under the influence of suprathermal protons. Linear theory predicts a systematic stimulation of the instability, suprathermals amplifying the growth rates and decreasing the instability thresholds to lower anisotropies and lower plasma betas ($\beta_{p \parallel}<1$). In perfect agreement with these results, the QL approach reveals a significant enhancement of the resulting electromagnetic fluctuations up to the saturation with a stronger back reaction on protons, leading also to a faster and more efficient relaxation of the temperature anisotropy., Comment: Accepted for publication at ApJ

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 collision-poor plasmas, where particle-particle collisions are rare but wave-particle interactions appears to play a dominant role in the dynamic. In the present paper we derive the full set of components of the dispersion tensor for magnetized plasma populations modeled by drifting bi-Kappa distributions. A new solver called DIS-K (DIspersion Solver for Kappa plasmas) is proposed to solve numerically the dispersion relations of high complexity. The solver is validated by comparing to the damped and unstable wave solutions obtained with other codes, operating in the limits of drifting Maxwellian and non-drifting Kappa models. These new theoretical tools enable more realistic characterizations, both analytical and numerical, of wave fluctuations and instabilities in complex kinetic configurations measured in-situ in space plasmas., Comment: Accepted for publication in Journal of Plasma Physics

Important efforts are currently made for understanding the so-called kinetic instabilities, driven by the anisotropy of different species of plasma particles present in the solar wind and terrestrial magnetosphere. These instabilities are fast enough to efficiently convert the free energy of plasma particles into enhanced (small-scale) fluctuations with multiple implications, regulating the anisotropy of plasma particles. In this paper we use both linear and quasilinear (QL) frameworks to describe complex unstable regimes, which realistically combine different temperature anisotropies of electrons and ions (protons). Thus parameterized are various instabilities, e.g., proton and electron firehose, electromagnetic ion cyclotron, and whistler instability, showing that their main linear properties are markedly altered by the interplay of anisotropic electrons and protons. Linear theory may predict a strong competition of two instabilities of different nature when their growth rates are comparable. In the QL phase wave fluctuations grow and saturate at different levels and temporal scales, by comparison to the individual excitation of the proton or electron instabilities. In addition, cumulative effects of the combined proton and electron induced fluctuations can markedly stimulate the relaxations of their temperature anisotropies. Only whistler fluctuations inhibit the efficiency of proton firehose fluctuations in the relaxation of anisotropic protons. These results offer valuable premises for further investigations in numerical simulations, to decode the full spectrum of kinetic instabilities resulting from the interplay of anisotropic electrons and protons in space plasmas., Comment: Accepted for publication at MNRAS

In collision-poor space plasmas protons with an excess of kinetic energy or temperature in direction perpendicular to background magnetic field can excite the electromagnetic ion cyclotron (EMIC) instability. This instability is expected to be highly sensitive to suprathermal protons, which enhance the high-energy tails of the observed velocity distributions and are well reproduced by the (bi-)Kappa distribution functions. In this paper we present the results of a refined quasilinear (QL) approach, able to describe the effects of suprathermal protons on the extended temporal evolution of EMIC instability. It is thus shown that suprathermals have a systematic stimulating effect on the EMIC instability, enhancing not only the growth rates and the range of unstable wave-numbers, but also the magnetic fluctuating energy density reached at the saturation. In effect, the relaxation of anisotropic temperature becomes also more efficient, i.e., faster in time and closer to isotropy., Comment: 10 pages, 7 figures, Submitted to Physics of Plasmas

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 to overcome these limitations, in the present paper we present the results of an extended investigation of ion-ion instabilities, which show that their dispersion and stability properties (e.g. growth rates, wave frequencies, and the unstable wave numbers) are highly sensitive to the influence of suprathermal populations and anisotropic electrons. These results offer valuable explanations for the origin of the enhanced low-frequency fluctuations, frequently observed in space plasmas and associated with proton beams., Comment: Accepted for publication at ApJ

Relative drifts between different species or particle populations are characteristic to solar plasma outflows, e.g., in the fast streams of the solar winds, coronal mass ejections and interplanetary shocks. This paper characterizes the dispersion and stability of the low-beta alpha/proton drifts in the absence of any intrinsic thermal anisotropies, which are usually invoked in order to stimulate various instabilities. The dispersion relations derived here describe the full spectrum of instabilities and their variations with the angle of propagation and plasma parameters. The results unveil a potential competition between instabilities of the electromagnetic proton cyclotron and alpha cyclotron modes. For conditions specific to a low-beta solar wind, e.g., at low heliocentric distances in the outer corona, the instability operates on the alpha cyclotron branch. The growth rates of the alpha cyclotron mode are systematically stimulated by the (parallel) plasma beta and/or the alpha-proton temperature ratio. One can therefore expect that this instability develops even in the absence of temperature anisotropies, with potential to contribute to a self-consistent regulation of the observed drift of alpha particles., Comment: Accepted for publication at Astrophysics and Space Science

The heat transport in the solar wind is dominated by the suprathermal electron populations, i.e., a tenuous halo and a field-aligned beam/strahl, with high energies and antisunward drifts along the magnetic field. Their evolution may offer plausible explanations for the rapid decrease of the heat flux with the solar wind expansion, typically invoked being the self-generated instabilities, or the so-called heat flux instabilities (HFIs). The present paper provides a unified description of the full spectrum of HFIs, as prescribed by the linear kinetic theory for high beta conditions ($\beta_e \gg 0.1$) and different relative drifts ($U$) of the suprathermals. HFIs of different nature are distinguished, i.e., electromagnetic, electrostatic or hybrid, propagating parallel or obliquely to the magnetic field, etc., as well as their regimes of interplay (co-existence) or dominance. These alternative regimes of HFIs complement each other and may be characteristic to different relative drifts of suprathermal electrons and various conditions in the solar wind, e.g., in the slow or fast winds, streaming interaction regions and interplanetary shocks. Moreover, these results strongly suggest that heat flux regulation may not involve only one but several HFIs, concomitantly or successively in time. Conditions for a single, well defined instability with major effects on the suprathermal electrons and, implicitly, the heat flux, seem to be very limited. Whistler HFIs are more likely to occur but only for minor drifts (as also reported by recent observations), which may explain a modest implication in their regulation, shown already in quasilinear studies and numerical simulations., Comment: Submitted to ApJ

Depending on the physical conditions involved the beam plasma systems may reveal new unstable regimes triggered by the wave instabilities of different nature. We show through linear theory and numerical simulations the existence of an aperiodic electromagnetic instability which solely develops and control the stability of two symmetric plasma populations counter-moving along the regular magnetic field with a relative drift, $v_d$, small enough to not exceed the particle thermal speed, $\alpha_e$. Emerging at highly oblique angles this mode resembles properties of the aperiodic firehose instability driven by temperature anisotropy. The high growth rates achieved with increasing the relative drift or/and decreasing the plasma beta parameter lead to significant saturation levels of the fluctuating magnetic field power, which explain the relative fast relaxation of electrons. For $v_d>\alpha_e$ this instability can coexist with the electrostatic two-stream instability, dominating the long-term dynamics of the plasma as soon as $v_d$ has relaxed to values smaller than the thermal speed., Comment: Submitted to: Plasma Phys. Control. Fusion on Jan. 31 2020

Recent statistical studies of observational data unveil relevant correlations between whistler fluctuations and the anisotropic electron populations present in space plasmas, e.g., solar wind and planetary magnetospheres. Locally, whistlers can be excited by two sources of free energy associated with anisotropic electrons, i.e., temperature anisotropies and beaming populations carrying the heat flux. However, these two sources of free energy and the resulting instabilities are usually studied independently preventing a realistic interpretation of their interplay. This paper presents the results of a parametric quasilinear study of the whistler instability cumulatively driven by two counter-drifting electron populations and their anisotropic temperatures. By comparison to individual regimes dominated either by beaming population or by temperature anisotropy, in a transitory regime the instability becomes highly conditioned by the effects of both these two sources of free energy. Cumulative effects stimulate the instability and enhance the resulting fluctuations, which interact with electrons and stimulate their diffusion in velocity space, leading to a faster and deeper relaxation of the beaming velocity associated with a core heating in perpendicular direction and a thermalization of the beaming electrons. In particular, the relaxation of temperature anisotropy to quasi-stable states below the thresholds conditions predicted by linear theory may explain the observations showing the accumulation of these states near the isotropy and equipartition of energy., Comment: accepted for publication at MNRAS

In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy $A = T_{\perp}/T_\parallel>$ (with $\perp, \parallel$ respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the kinetic instabilities and the resulting fluctuations, which, in turn, scatter the electrons and reduce their anisotropy. In order to capture these mutual effects we use a quasilinear kinetic approach and PIC simulations, which provide a comprehensive characterization of the whistler instability under the influence of suprathermal electrons. Analysis is performed for a large variety of plasma conditions, ranging from low-beta plasmas encountered in outer corona or planetary magnetospheres to a high-beta solar wind characteristic to large heliospheric distances. Enhanced by the suprathermal electrons, whistler fluctuations stimulate the relaxation of temperature anisotropy, and this influence of suprathermals increases with plasma beta parameter., Comment: accepted for publications at Astrophysics and Space Science

In collision-poor plasmas from space, e.g., solar wind or stellar outflows, the heat-flux carried by the strahl or beaming electrons is expected to be regulated by the self-generated instabilities. Recently, simultaneous field and particle observations have indeed revealed enhanced whistler-like fluctuations in the presence of counter-beaming populations of electrons, connecting these fluctuations to the whistler heat-flux instability (WHFI). This instability is predicted only for limited conditions of electron beam-plasmas, and was not captured in numerical simulations yet. In this letter we report the first simulations of WHFI in particle-in-cell (PIC) setups, realistic for the solar wind conditions, and without temperature gradients or anisotropies to trigger the instability in the initiation phase. The velocity distributions have a complex reaction to the enhanced whistler fluctuations conditioning the instability saturation by a decrease of the relative drifts combined with induced (effective) temperature anisotropies (heating the core electrons and pitch-angle and energy scattering the strahl). These results are in good agreement with a recent quasilinear approach, and support therefore a largely accepted belief that WHFI saturates at moderate amplitudes. In anti-sunward direction the strahl becomes skewed with a pitch-angle distribution decreasing in width as electron energy increases, that seems to be characteristic to self-generated whistlers and not to small-scale turbulence., Comment: Accepted for publication in ApJL

In situ observations of the solar wind show a limited level of particle temperature anisotropy with respect to the interplanetary magnetic field direction. Kinetic electromagnetic instabilities are efficient to prevent the excessive growth of the anisotropy of particle velocity distribution functions. Among them, the firehose instabilities are often considered to prevent the increase of the parallel temperature and hence to shape the velocity distribution functions of electrons and protons in the solar wind. We present a non-linear modeling of the parallel firehose instability, retaining a kinetic description for both the electrons and protons. One-dimensional (1D) fully kinetic Particle-In-Cell simulations using the Energy Conserving semi-implicit method (ECsim) are performed to clarify the role of the electron temperature anisotropy in the development of the parallel proton firehose instability. We found that in the presence of an electron temperature anisotropy, such that the temperature parallel to the background magnetic field is higher than the temperature in the perpendicular direction, the onset of the parallel proton firehose instability occurs earlier and its growth rate is faster. The enhanced wave fluctuations contribute to the particle scattering reducing the temperature anisotropy to a stable, nearly isotropic state. The simulation results compare well with linear theory. A test case of 1D simulations at oblique angles with respect to the magnetic field is also considered, as a first step to study the cumulative effect of protons and electrons on the full spectrum of instabilities.

Context. Solar outflows are a considerable source of free energy which accumulates in multiple forms like beaming (or drifting) components and/or temperature anisotropies. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, the self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the electron temperature ($T$) in fast solar winds are not explained yet. Aims. This paper provides an advanced quasilinear description of the whistler instability driven by the anisotropic electrons in conditions typical for the fast solar winds. The enhanced whistler-like fluctuations may constrain the upper limits of temperature anisotropy $A \equiv T_\perp /T_\parallel > 1$, where $\perp, \parallel$ are defined with respect to the magnetic field direction. Methods. Studied are the self-generated whistler instabilities, cumulatively driven by the temperature anisotropy and the relative (counter)drift of the electron populations, e.g., core and halo electrons. Recent studies have shown that quasi-stable states are not bounded by the linear instability thresholds but an extended quasilinear approach is necessary to describe them in this case. Results. Marginal conditions of stability are obtained from a quasilinear theory of the cumulative whistler instability, and approach the quasi-stable states of electron populations reported by the observations.The instability saturation is determined by the relaxation of both the temperature anisotropy and the relative drift of electron populations., Comment: Accepted for publication in A&A

The hot beaming (or strahl) electrons responsible for the main electron heat-flux in the solar wind are believed to be self-regulated by the electromagnetic beaming instabilities, also known as the heat-flux instabilities. Here we report the first quasi-linear theoretical approach of the whistler unstable branch able to characterize the long-term saturation of the instability as well as the relaxation of the electron velocity distributions. The instability saturation is not solely determined by the drift velocities, which undergo only a minor relaxation, but mainly from a concurrent interaction of electrons with whistlers that induces (opposite) temperature anisotropies of the core and beam populations and reduces the effective anisotropy. These results might be able to (i) explain the low intensity of the whistler heat-flux fluctuations in the solar wind (although other explanations remain possible and need further investigation), and (ii) confirm a reduced effectiveness of these fluctuations in the relaxation and isotropization of the electron strahl and in the regulation of the electron heat-flux., Comment: accepted for publication MNRAS

In the solar wind an equipartition of kinetic energy densities can be easily established between thermal and suprathermal electrons and the instability conditions are markedly altered by the interplay of these two populations. The new thresholds derived here for the periodic branch of firehose instability shape the limits of temperature anisotropy reported by the observations for both electron populations. This instability constraint is particularly important for the suprathermal electrons which, by comparison to thermal populations, are even less controlled by the particle-particle collisions. An extended quasilinear approach of this instability confirms predictions from linear theory and unveil the mutual effects of thermal and suprathermal electrons in the relaxation of their temperature anisotropies and the saturation of growing fluctuations., Comment: ApJ in press

In collision-poor plasmas from space, e.g., solar wind, terrestrial magnetospheres, kinetic instabilities are expected to play a major role in constraining the temperature anisotropy of plasma particles, but a definitive answer can be given only after ascertaining their properties in these environments. Present study describes the full spectrum of electron firehose instabilities in the presence of suprathermal electron populations which are ubiquitous in space plasmas. Suprathermal electrons stimulate both the periodic and aperiodic branches, remarkable being the effects shown by the aperiodic mode propagating obliquely to the ambient magnetic field which markedly exceeds the growth rates of the parallel (periodic) branch reported recently in Lazar et al., (2017a, MNRAS 464, 564). Derived exclusively in terms of the plasma parameters, the anisotropy thresholds of this instability are also lowered in the presence of suprathermal electrons, predicting an enhanced effectiveness in the solar wind conditions. These results may also be relevant in various other astrophysical contexts where the firehose instabilities involve, e.g., solar flares, sites of magnetic field reconnection, accretion flows or plasma jets leading to shocks and co-rotating interactions in heliosphere, interstellar medium and galaxy clusters., Comment: Submitted for publication to MNRAS

In space plasmas kinetic instabilities are driven by the beaming (drifting) components and/or the temperature anisotropy of charged particles. The heat-flux instabilities are known in the literature as electromagnetic modes destabilized by the electron beams (or strahls) aligned to the interplanetary magnetic field. A new kinetic approach is proposed here in order to provide a realistic characterization of heat-flux instabilities under the influence of electrons with temperature anisotropy. Numerical analysis is based on the kinetic Vlasov-Maxwell theory for two electron counter-streaming (core and beam) populations with temperature anisotropies, and stationary, isotropic protons. The main properties of electromagnetic heat-flux instabilities are found to be markedly changed by the temperature anisotropy of electron beam $A_b = T_\perp / T_\parallel \ne 1$, leading to stimulation of either the whistler branch if $A_b > 1$, or the firehose branch for $A_b<1$. For a high temperature anisotropy whistlers switch from heat-flux to a standard regime, when their instability is inhibited by the beam., Comment: accepted for publication in Physics of Plasmas

In the solar wind electron velocity distributions reveal two counter-moving populations which may induce electromagnetic (EM) beaming instabilities known as heat flux instabilities. Depending on plasma parameters two distinct branches of whistler and firehose instabilities can be excited. These instabilities are invoked in many scenarios, but their interplay is still poorly understood. An exact numerical analysis is performed to resolve the linear Vlasov-Maxwell dispersion and characterize these two instabilities, e.g., growth rates, wave frequencies and thresholds, enabling to identify their dominance for conditions typically experienced in space plasmas. Of particular interest are the effects of suprathermal Kappa-distributed electrons which are ubiquitous in these environments. The dominance of whistler or firehose instability is highly conditioned by the beam-core relative velocity, core plasma beta and the abundance of suprathermal electrons. Derived in terms of relative drift velocity the instability thresholds show an inverse correlation with the core plasma beta for the whistler modes, and a direct correlation with the core plasma beta for the firehose instability. Suprathermal electrons reduce the effective (beaming) anisotropy inhibiting the firehose modes while the whistler instability is stimulated., Comment: Accepted for publication in MNRAS

This letter presents the results of an advanced parametrization of the solar wind electron temperature anisotropy and the instabilities resulting from the interplay of the (bi-)Maxwellian core and (bi-)Kappa halo populations in the slow solar wind. A large set of observational data (from the Ulysses, Helios and Cluster missions) is used to parametrize these components and establish their correlations. The instabilities are significantly stimulated in the presence of suprathermals, and the instability thresholds shape the limits of the temperature anisotropy for both the core and halo populations re-stating the incontestable role that the selfgenerated instabilities can play in constraining the electron anisotropy. These results confirm a particular implication of the suprathermal electrons which are less dense but hotter than thermal electrons.

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 $\kappa$. 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 populations present in the solar wind, as well as from their destabilizing effects predicted by these two alternating approaches. Methods. Two fitting models are contrasted, namely, the global Kappa and the dual Maxwellian-Kappa models, which are currently invoked in theory and observations. The destabilizing effects of suprathermal electrons are characterized on the basis of a kinetic approach which accounts for the microscopic details of the velocity distribution. Results. In order to be relevant, the model is chosen to accurately reproduce the observed distributions and this is achieved by a dual Maxwellian-Kappa distribution function. A statistical survey indicates a $\kappa$-dependent temperature of the suprathermal (halo) electrons for any heliocentric distance. Only for this approach the instabilities driven by the temperature anisotropy are found to be systematically stimulated by the abundance of suprathermal populations, i.e., lowering the values of $\kappa$-index., Comment: Submitted to A&A