Nonlinear evolution of the electromagnetic electron-cyclotron instability in bi-Kappa distributed plasma

Electron temperature anisotropies and electron beams are nonthermal features of the observed nonequilibrium electron velocity distributions in the solar wind. In collision-poor plasmas these nonequilibrium distributions are expected to be regulated by kinetic instabilities through wave–particle interactions. This study considers electron instabilities driven by the interplay of core electron temperature anisotropies and the electron beam, and first gives a comprehensive analysis of instabilities in arbitrary directions to the background magnetic field. It clarifies the dominant parameter regime (e.g., parallel core electron plasma beta , core electron temperature anisotropy , and electron beam velocity V eb) for each kind of electron instability (e.g., the electron beam-driven electron acoustic/magnetoacoustic instability, the electron beam-driven whistler instability, the electromagnetic electron cyclotron instability, the electron mirror instability, the electron firehose instability, and the ordinary-mode instability). It finds that the electron beam can destabilize electron acoustic/magnetoacoustic waves in the low- regime, and whistler waves in the medium- and large- regime. It also finds that a new oblique fast-magnetosonic/whistler instability is driven by the electron beam with in a regime where and A ec < 1. Moreover, this study presents electromagnetic responses of each kind of electron instability. These results provide a comprehensive overview for electron instability constraints on core electron temperature anisotropies and electron beams in the solar wind.

Recently, a realistic parameterization was proposed for the kinetic anisotropy and the resulting instabilities in the solar wind plasma. This parameterization is based on observations of the particle velocity distribution, which always comprises a Maxwellian population at low energies, viz. the core, and a suprathermal halo in the tail of the distribution which is best described by the Kappa (power law) models. The cyclotron instability, driven by an anisotropic electron halo, was found to be inhibited by the finite thermal spread in the core, and this effect is highly dependent on the halo‐core relative density. In this paper, the interplay between the Kappa and Maxwellian populations is further investigated for more complex (less idealized) situations when both the core and halo temperatures are anisotropic. Growth of this instability is markedly stimulated by the core anisotropy. The wave numbers that are stable for an isotropic core become unstable even for small anisotropies of this population. Just a modest increase of the core anisotropy from A c = T ⊥ / T ∥ =1.2 to 2 causes the growth rates to enhance by 1 order of magnitude, and the range of unstable wave numbers to extend considerably. When the anisotropies in the core and halo are comparable, the growth rate exhibits two distinct peaks, the first driven by the halo at lower wave numbers and the second driven by the core. However, the first peak is inhibited by the suprathermal populations, while the second peak is sustained, suggesting a more intricate connection between the core and Kappa populations.

The whistler anisotropy (or electromagnetic electron cyclotron) instability may be operative in many geomagnetic and heliospherical environments, including the radiation belt, solar wind, and the solar corona. The present investigation carries out a comparative analysis between the two‐dimensional particle‐in‐cell simulation of weakly growing whistler anisotropy instability and the velocity moment‐based two‐dimensional quasi‐linear theory under the assumption of bi‐Maxwellian electron distribution function. It is shown that the simplified quasi‐linear theory provides a qualitative agreement with the more rigorous particle‐in‐cell simulation, but some discrepancies are also found. Possible causes for the differences in either method are discussed, and future improvements on the theory are suggested. Potential applicability of the present finding in the context of the space and astrophysics is discussed.

Measurements conducted in interplanetary space and in the vicinity of planets of the solar system have shown plasma structures produced by the solar wind that resemble fluid dy- namic features; namely, vortex rotations within the earths magnetosphere and also along the Venus wake. In both planets the solar wind encounters different obstacles since the earth is protected by its intrinsic magnetic field that is compressed by the dynamic pressure of the solar wind to form a large size cavity (the magnetosphere) that bounds its direct approach to the earths vicinity. At Venus the conditions are different since the planet does not have an internal magnetization that would produce an earth-type magnetic obstacle to the solar wind. Instead, the latter reaches directly upon the upper layers of the planets atmosphere and interacts with its ionized components (the ionosphere). The outcome of this interaction is a plasma wake of large extent whose geometry is similar to that of the earths magneto- spheric tail but that arises from conditions that are different in both planets. While there is evidence for the observation of fluid-like vortices as the solar wind streams along the wake of the earth and Venus there is a major issue as to the manner in which they are produced. In fact, since the solar wind is a collisionless plasma; namely its charged particles barely exe- cute collisions among them (their mean free path is comparable to one astronomical unit) it should not be expected that it behaves as a continuum when it interacts with planetary ob- stacles. The opposite has been verified by a variety of observations with indications that the physical properties of both the solar wind fluxes and the planetary particles that are being eroded through their interaction can be described in terms of fluid dynamic processes (a re- view of this issue was presented by Perez-de-Tejada, 2012). The motion of the solar wind particles as they interact with the earths magnetic field is de- scribed in terms of gyromagnetic trajectories as they move across the magnetic field lines.

The polytropic behavior of space plasmas defines a power law between the plasma moments during the transition of the plasma from one state to another under constant specific heat. Knowledge of the polytropic index—the power-law exponent—is essential for understanding the dynamics of plasma particles, while a full kinetic description can be established by the study of the velocity distribution of plasma particles. The particle velocities of collisionless space plasmas, such as the solar wind, follow the kappa distribution function. The kappa index, the parameter that labels and governs these distributions, is an independent variable that describes the state of plasmas and is required for a complete description of the plasma properties. Previous studies showed and demonstrated how the kappa and polytropic indices are related to each other in the presence of potential energy, and their relationship also depends on the potential degrees of freedom. This paper extends these analyses and derives the kappa and polytropic indices of the solar wind proton plasmas using Wind observations during the last two solar cycles. We examine and show the systematic long-term correlation between these indices, the magnetic field strength, and the solar activity.

<p>Proton and electron spectra in the plasma sheet usually consist of spectral core and high energy tail. These two populations are formed by different processes, driven by the various combinations of the solar wind parameters.These processes include different time delays and may act differently on protons or electrons. In this work we evaluate empirically the magnitude and the time delay of the impact of different solar wind parameter combinations on the protons and electrons with energies (30-300 keV) and reveal the mechanisms behind these impacts. To do this we build a model of the fluxes at different energy channels in the transition region (nightside central plasma sheet between 6 and 15 Re) for the THEMIS spacecraft observations in 2007-2018. We use normalized values of solar wind parameter combinations (incl. speed, density, pressure, electric field, etc) as inputs of the model, with regression coefficients indicating their impact magnitudes. We investigate different time delays up to 16 hours. The model obtained shows that protons and electrons are controlled differently by solar wind parameters: dynamic pressure is important for protons, whereas solar wind speed and VBs are important for electrons. Larger time delays are required to describe higher energy electron fluxes.</p>

In impulsive SEP events, electrons and ions are accelerated at the Sun in a small region, during a short period and then “injected” into the solar wind, propagating to 1 AU and are observed by various spacecraft. Their propagation in the solar wind is a competing process between magnetic focusing due to large scale magnetic field geometry and pitch angle scattering due to small scale turbulence in the magnetic field. In a collisionless plasma like the solar wind, the effect of the pitch angle scattering is to alter particle pitch angles in a random but continuous manner during their propagation. Here we briefly discuss a direct Monte‐Carlo method that solves the transport equation by following individual particle trajectories. Mathematically, the approach can be understood under the framework of stochastic differential equation method. By casting the underlying Fokker‐Planck equation to a set of equations consisting of deterministic pieces and stochastic pieces, one can treat the Lorentz force of the larg...

Aims.We aim at analytically modelling the solar wind proton trajectories during their interaction with a partially ionised cometary atmosphere, not in terms of bulk properties of the flow but in terms of single particle dynamics.Methods.We first derive a generalised gyromotion, in which the electric field is reduced to its motional component. Steady-state is assumed, and simplified models of the cometary density and of the electron fluid are used to express the force experienced by individual solar wind protons during the interaction.Results.A three-dimensional (3D) analytical expression of the gyration of two interacting plasma beams is obtained. Applying it to a comet case, the force on protons is always perpendicular to their velocity and has an amplitude proportional to 1/r2. The solar wind deflection is obtained at any point in space. The resulting picture presents a caustic of intersecting trajectories, and a circular region is found that is completely free of particles. The particles do not lose any kinetic energy and this absence of deceleration, together with the solar wind deflection pattern and the presence of a solar wind ion cavity, is in good agreement with the general results of the Rosetta mission.Conclusions.The qualitative match between the model and the in situ data highlights how dominant the motional electric field is throughout most of the interaction region for the solar wind proton dynamics. The model provides a simple general kinetic description of how momentum is transferred between these two collisionless plasmas. It also shows the potential of this semi-analytical model for a systematic quantitative comparison to the data.

In a collisionless, magnetized plasma, particles may stream freely along magnetic field lines, leading to "phase mixing" of their distribution function and consequently, to smoothing out of any "compressive" fluctuations (of density, pressure, etc.). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma-one of the most fundamental physical phenomena that makes plasma different from a conventional fluid. Nevertheless, broad power law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial-scale range and is, therefore, cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power law spectra. This "fluidization" of collisionless plasmas occurs, because phase mixing is strongly suppressed on average by "stochastic echoes," arising due to nonlinear advection of the particle distribution by turbulent motions. Other than resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless, except at very small scales. The universality of "fluid" turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

Aims. We study how a fast solar wind stream embedded in a slow solar wind influences the spread of solar energetic protons in interplanetary space. In particular, we aim at understanding how the particle intensity and anisotropy vary along interplanetary magnetic field (IMF) lines that encounter changing solar wind conditions such as the shock waves bounding a corotating interaction region (CIR). Moreover, we study how the intensities and anisotropies vary as a function of the longitudinal and latitudinal coordinate, and how the width of the particle intensities evolves with the heliographic radial distance. Furthermore, we study how cross-field diffusion may alter these spatial profiles. Methods. To model the energetic protons, we used a recently developed particle transport code that computes particle distributions in the heliosphere by solving the focused transport equation (FTE) in a stochastic manner. The particles are propagated in a solar wind containing a CIR, which was generated by the heliospheric model, EUHFORIA. We study four cases in which we assume a delta injection of 4 MeV protons spread uniformly over different regions at the inner boundary of the model. These source regions have the same size and shape, yet are shifted in longitude from each other, and are therefore magnetically connected to different solar wind conditions. Results. The intensity and anisotropy profiles along selected IMF lines vary strongly according to the different solar wind conditions encountered along the field line. The IMF lines crossing the shocks bounding the CIR show the formation of accelerated particle populations, with the reverse shock wave being a more efficient accelerator than the forward shock wave. The longitudinal intensity profiles near the CIR are highly asymmetric in contrast to the profiles obtained in a nominal solar wind. For the injection regions that do not cross the transition zone between the fast and slow solar wind, we observe a steep intensity drop of several orders of magnitude near the stream interface (SI) inside the CIR. Moreover, we demonstrate that the longitudinal width of the particle intensity distribution can increase, decrease, or remain constant with heliographic radial distance, reflecting the underlying IMF structure. Finally, we show how the deflection of the IMF at the shock waves and the compression of the IMF in the CIR deforms the three-dimensional shape of the particle distribution in such a way that the original shape of the injection profile is lost.

Various plasma waves and instabilities are abundantly present in the solar wind plasma, as evidenced by spacecraft observations. Among these, propagating modes and instabilities driven by temperature anisotropies are known to play a significant role in the solar wind dynamics. In situ measurements reveal that the threshold conditions for these instabilities adequately explain the solar wind conditions at large heliocentric distances. This paper pays attention to the combined effects of electron firehose instability driven by excessive parallel electron temperature anisotropy (T⊥e < T∥e) at high beta conditions, and electromagnetic ion cyclotron instability driven by excessive perpendicular proton temperature anisotropy (T⊥i > T∥i). By employing quasilinear kinetic theory based upon the assumption of bi-Maxwellian velocity distribution functions for protons and electrons, the dynamical evolution of the combined instabilities and their mutual interactions mediated by the particles is explored in depth. It is found that while in some cases, the two unstable modes are excited and saturated at distinct spatial and temporal scales, in other cases, the two unstable modes are intermingled such that a straightforward interpretation is not so easy. This shows that when the dynamics of protons and electrons are mutually coupled and when multiple unstable modes are excited in the system, the dynamical consequences can be quite complex.

Development of a theory of hydromagnetic waves and discontinuities which is appropriate for the solar wind. The experimental evidence for the various waves, discontinuities, and some of the instabilities which are predicted by this theory is reviewed. Nearly all of the discontinuities given by the theory are shown to exist in the solar wind. These include tangential discontinuities, forward and reverse fast and slow shocks, perpendicular shocks, and Alfven shocks. Parallel shocks and contact discontinuities have not been found. A number of special cases are considered which show the basic physical properties of hydromagnetic waves in an anisotropic, multifluid, collisionless plasma. A treatment of discontinuities is presented which most resembles those of Chao (1970) and Hudson (1970). On the basis of the experimental results reviewed it is concluded that hydromagnetic theory is applicable to the solar wind.

Using a hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvénic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfvénic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale “critical balance” between their characteristic linear and nonlinear frequencies. Eventually the plasma becomes unstable to kinetic firehose instabilities, which excite rapidly growing magnetic fluctuations at ion-Larmor scales. The consequent pitch-angle scattering of particles maintains the temperature anisotropy near marginal stability, even as the turbulent plasma continues to expand. The resulting evolution of parallel and perpendicular temperatures does not satisfy double-adiabatic conservation laws, but is described accurately by a simple model that includes anomalous scattering. Our results have implications for understanding the complex interplay between macro- and microscale physics in various hot, dilute, astrophysical plasmas, and offer predictions concerning power spectra, residual energy, ion-Larmor-scale spectral breaks, and non-Maxwellian features in ion distribution functions that may be tested by measurements taken in high-beta regions of the solar wind.

Finite heat flux often exists in space and astrophysical plasmas, which can be a free energy source for heat flux instability. The solar wind is a well-known example of such plasmas and a number of previous studies have investigated the characteristics of heat flux instability in the context of solar wind. In the literature there exists some uncertainties regarding the properties of heat flux instability. While some linear theories predict the association of the heat flux instability with right-hand polarized whistler waves, other studies argue for left-hand polarized unstable modes. The present study investigates the nonlinear development of initially unstable left-hand heat flux mode by means of particle-in-cell simulation. It is found that while the early phase is characterized by the left-hand polarization, in agreement with linear theory, as the wave amplitude becomes high and the instability enters the nonlinear phase, the dominant wave mode gradually switches over to the right-hand polarized waves. Such a behavior is related to the pitch angle scattering of the heat flux carrying electrons by nonlinear interaction with large-amplitude waves. The present study shows that the heat flux instability generally requires nonlinear treatment such that characterizing its behavior with linear theories may not always be adequate.

Spacecraft measurements in the solar wind offer the opportunity to study magnetohydrodynamic (MHD) turbulence in a collisionless plasma in great detail. We review some of the key results of the study of this medium: the presence of large amplitude Alfvén waves propagating predominantly away from the Sun; the existence of an active turbulent cascade; and the presence of intermittency similar to that in neutral fluids. We also discuss the presence of anisotropy in wavevector space relative to the local magnetic field direction. Some models suggest that MHD turbulence can evolve to a state with power predominantly in wavevectors either parallel to the magnetic field (‘slab’ fluctuations) or approximately perpendicular to it (‘2D’). We review the existing evidence for such anisotropy, which has important consequences for the transport of energetic particles. Finally, we present the first results of a new analysis which provides the most accurate measurements to date of the wave-vector anisotropy of wavevector power in solar wind MHD turbulence.