RUDI GAELZER

The dispersive characteristics and absorption coefficient of Alfvén waves propagating parallel to the ambient magnetic field are discussed, taking into account the effects of both the charged dust particles present in the interplanetary medium and the superthermal character of the electron distribution function, using physical parameters relevant for solar and stellar winds. The solar wind electrons are described by an isotropic $ąppa$ distribution and the protons are described by a Maxwellian. The results are valid for a frequency regime well above the dust-plasma and dust-cyclotron frequencies. However, the theoretical formulation is fully kinetic and the dust charge variation is taken into account. The charging process of the dust is assumed to be associated with the capture of electrons and ions by the dust particles during inelastic collisions with the plasma particles. The dispersion relation for parallel-propagating Alfvén waves is numerically solved and the solutions are compared with particular situations where either the dust particles are absent or the electrons are described by a Maxwellian. It is shown that the presence of both the charged dust particles and the superthermal character of the electron distribution function sensibly modify the dispersion relation of low-frequency and long-wavelength Alfvén waves and significantly increase the absorption coefficient, strongly suggesting that both effects are equally important for a realistic description of the physical processes that occur in solar and stellar winds and that are influenced by the Alfvén waves, such as the energization of particles and the turbulent cascade of magnetic fluctuations.

We investigate amplification of the auroral kilometric radiation over the geomagnetic poles. The physical parameters needed for the calculation are obtained from a particular model that approximately reproduces the conditions in the auroral zone, taking into account density gradients perpendicular to the geomagnetic field and also the parallel magnetic field gradient. The components of the dielectric tensor are calculated in the locally homogeneous plasma approximation, and the dispersion relation is exactly solved with all harmonics and powers of the Larmor radius needed for the convergency of the solution. We also make a ray tracing study in the geometrical optics approximation, using the method of Poeverlein. The ray tracing study shows that the spatial scale of inhomogeneity, perpendicular to the magnetic field, is a very important factor in the amplification and that the distance to obtain a given amplification can be substantially reduced when the density gradient is increased.

We utilize a kinetic description to study the dispersion relation of Alfvén waves propagating parallelly to the ambient magnetic field in a dusty plasma, taking into account the fluctuation of the charge of the dust particles, which is due to inelastic collisions with electrons and ions. We consider a plasma in which the velocity distribution functions of the plasma particles are modelled as anisotropic kappa distributions, study the dispersion relation for several combinations of the parameters κ∥ and κ⊥, and emphasize the effect of the anisotropy of the distributions on the mode coupling which occurs in a dusty plasma, between waves in the branch of circularly polarized waves and waves in the whistler branch.

We present general expressions for the components of the dielectric tensor of magnetized dusty plasmas, valid for arbitrary direction of propagation and for situations in which populations of dust particles of different sizes are present in the plasma. These expressions are derived using a kinetic approach which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, and features the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius, and is valid for the whole range of frequencies above the plasma frequency of the dust particles, which are assumed to be motionless. The integrals in velocity space which appear in the dielectric tensor are solved assuming that the electron and ion populations are described by anisotropic non-thermal distributions characterized by parameters κ ∥ and κ ⊥ , featuring the Maxwellian as a limiting case. These integrals can be written in terms of generalized dispersion functions, which can be expressed in terms of hypergeometric functions. The formulation therefore becomes specially suitable for numerical analysis.

Ion-acoustic enhancements are investigated within the context of turbulent beam-plasma interaction processes. The analysis assumes a pair of counterstreaming electron beams interacting with the background plasma. Two-dimensional velocity space and two-dimensional wave number space are assumed for the analysis, with physical parameters that characterize typical ionospheric conditions. The solutions of the electrostatic weak turbulence theory show that the ion-acoustic wave levels are significantly enhanced when the computation is initialized with a pair of counterstreaming beams in contrast to a single beam. We suggest that this finding is highly relevant for the observed ion-acoustic enhancements in the Earth's ionosphere that are known to be correlated with auroral activity.

This Letter reports on the results of numerical simulations which may provide a possible explanation for the strahl broadening during quiet solar conditions. The relevant processes involved in the broadening are due to kinetic quasi-linear wave-particle interaction. Making use of static analytical electron distribution in an inhomogeneous field, it is found that self-generated electrostatic waves at the plasma frequency, i.e., Langmuir waves, are capable of scattering the strahl component, resulting in energy and pitch-angle diffusion that broadens its velocity distribution significantly. The present theoretical results provide an alternative or complementary explanation to the usual whistler diffusion scenario, suggesting that self-induced electrostatic waves at the plasma frequency might play a key role in broadening the solar wind strahl during quiet solar conditions.

The decay of beam-generated Langmuir wave into another Langmuir wave and an ion-acoustic wave is a well-known problem with wide-ranging applications. However, most discussions in the literature are based upon simple one-dimensional approximation. Recently, the present authors carried out a fully self-consistent two-dimensional analysis of the beam-driven Langmuir wave decay problem. The main focus of the present authors' work to date had been on the nonlinear evolution of Langmuir turbulence and its influence on the electrons. Relatively little attention had been paid to the ion-acoustic wave generation. In the present discussion, the focus is placed on the dynamics of ion-acoustic turbulence that results from the decay of beam-generated Langmuir wave. The present analysis considers three electron components, the dense core, a primary beam and a counter-streaming beam. We find that the ion-sound turbulence level sensitively depends on the properties of the counter-streaming beam.

Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.

The nonlinear interaction of a single or a bidirectional electron beam and a background plasma is analyzed on the basis of electrostatic weak turbulence theory. It is found that for a sufficiently high electron beam density, the nonlinear interaction produces quasi-isotropic electron population. This is in contrast to our previous finding in which a relatively low electron beam density was adopted, and for which complete isotropization was not achieved. The present finding may thus provide a possible explanation for the observed isotropic solar wind electron distribution within the context of electrostatic nonlinear theory involving Langmuir and ion-sound turbulence, without the resorting to additional mechanisms such as the pitch angle scattering by electromagnetic whistler turbulence.

The electron distributions detected in the solar wind feature varying degrees of anisotropic high-energy tail. In a recent work the present authors numerically solved the one-dimensional electrostatic weak turbulence equations by assuming that the solar wind electrons are initially composed of thermal core plus field-aligned counterstreaming beams, and demonstrated that a wide variety of asymmetric energetic tail distribution may result. In the present paper, the essential findings in this work are tested by means of full particle-in-cell simulation technique. It is found that the previous results are largely confirmed, thus providing evidence that the paradigm of local electron acceleration to high-energy tail by self-consistently excited Langmuir turbulence may be relevant to the solar wind environment under certain circumstances. However, some discrepancies are found such that the nearly one-sided energetic tail reported in the numerical solution of the weak turbulence kinetic equation is not shown.

We study the dispersion relation for low frequency waves in the whistler mode propagating along
the ambient magnetic field, considering ions and electrons with product-bi-kappa (PBK) velocity
distributions and taking into account the presence of a population of dust particles. The results
obtained by numerical analysis of the dispersion relation show that the decrease in the j indexes in
the ion PBK distribution contributes to the increase in magnitude of the growth rates of the ion
firehose instability and the size of the region in wave number space where the instability occurs. It
is also shown that the decrease in the j indexes in the electron PBK distribution contribute to
decrease in the growth rates of instability, despite the fact that the instability occurs due to the
anisotropy in the ion distribution function. For most of the interval of j values which has been
investigated, the ability of the non-thermal ions to increase the instability overcomes the tendency
of decrease due to the non-thermal electron distribution, but for very small values of the kappa
indexes the deleterious effect of the non-thermal electrons tends to overcome the effect due to the
non-thermal ion distribution.

The dispersion relation for parallel propagating waves in the ion-cyclotron branch is investigated
numerically by considering that the velocity distribution of the ion population is a function of type
product-bi-kappa. We investigate the effects of the non-thermal features and of the anisotropy associated with this type of distribution on the ion-cyclotron instability, as well as the influence of different forms of the electron distribution, by considering Maxwellian distributions, bi-kappa distributions, and product-bi-kappa distributions. The cases of ions described by either Maxwellian or bi-kappa distributions are also considered, for comparison. The results of the numerical analysis show that the increase in the non-thermal character associated with the anisotropic kappa distributions for ions contributes to enhance the instability as compared to that obtained in the Maxwellian case, in magnitude and in wave number range, with more significant enhancement for the case of ion product-bi-kappa distributions than for the case of ion bi-kappa distributions. It is also shown
that the ion-cyclotron instability is decreased if the electrons are described by product-bi-kappa distributions, while electrons described by bi-kappa distributions lead to growth rates which are very
similar to those obtained considering a Maxwellian distribution for the electron population.

We investigate the dispersion relation for low frequency electromagnetic waves propagating parallel to the ambient magnetic field, considering that the velocity distributions of ions and electrons can be either bi-Maxwellian of product bi-kappa distributions. The effect of the anisotropy and non-thermal features associated to the product-bi-kappa distributions on the firehose instability are numerically investigated. The general conclusion to be drawn from the results obtained is that the increase in non-thermal features which is consequence of the decrease of the κ indexes in the ion distribution contributes to increase the instability in magnitude and wave number range, in comparison with bi-Maxwellian distributions with similar temperature anisotropy, and that the increase of non-thermal features in the electron distribution contributes to the quenching of the instability, which is nevertheless driven by the anisotropy in the ion distribution. Significant differences between results obtained either considering product-bi-kappa distributions or bi-kappa distributions are also reported.

The prEservation of Onsager symmetry for the effective dielectric tensor is discussed for a homogeneous Plasma immersed in a inhomogeneous magnetic ?eld, using the unperturbed orbits correct up to order $k\_B$, which is the scalelength of the field inhomogeneity. General features of the calculation of the components of the tensor are discussed and detailed calculations are developed for the $zz$ component, which is shown to satisfy the conditions for Onsager symmetry, in agreement with prEvious results obtained using less prEcise exprEssions for the unperturbed orbits.

We compare and discuss several approximations to the dispersion relation for electrostatic waves in inhomogeneous Plasmas, either obtained directly from Poisson?s equation, or from the dielectric constant obtained using a dielectric tensor derived using the plAne wave approximation, or from the dielectric constant derived using the effective dielectric tensor.

A local dispersion relation that describes inhomogeneity-driven instabilities in the lower-hybrid range is derived following a procedure that correctly describes energy exchange between waves and particles in inhomogeneous media, correcting some inherent ambiguities associated with the standard formalism found in the literature. Numerical solutions of this improved dispersion relation show that it constitutes a unified formulation for the instabilities in the lower-hybrid range, describing the so-called modified two-stream instability, excited by the ion cross-field drift, including the ion Weibel instability, and also describing the lower-hybrid drift instability, which is due to inhomogeneity effects on the electron population.

In this paper an electromagnetic particle code is used to investigate the spontaneous thermal emission. Specifically we perform particle-in-cell simulations employing a non-relativistic isotropic Maxwellian particle distribution to show that thermal fluctuations are related to the origin of spontaneous magnetic field fluctuation. These thermal fluctuations can become seed for further amplification mechanisms and thus be considered at the origin of the cosmological magnetic field, at microgauss levels. Our numerical results are in accordance with theoretical results presented in the literature.

It is by now well known that electron beams play an important role in generating radio emissions such as type II and type III radio bursts, commonly observed by spacecraft in the interplanetary medium. Electron beams streaming back from Earth's bow shock into the solar wind have been proposed as a possible source for the electron plasma waves observed by spacecraft in the electron foreshock. Recent observations suggest that during the natural evolution of the foreshock plasma, multiple electron beams could be injected over a period of time, losing their individual identity to coalesce into a single beam. In this work, we use an electromagnetic particle-in-cell (PIC) code &\#8220;KEMPO 1D, adapted&\#8221; to simulate two electron beams that are injected into a plasma at different times. The first beam disturbs the background plasma and generates Langmuir waves by electron beam-plasma interaction. Subsequently, another beam is inserted into the system and interacts with the first one and with the driven Langmuir waves to produce electromagnetic radiation. The results of our simulation show that the first beam can produce electrostatic harmonics of the plasma frequency, while the second beam intensifies the emission at the harmonics that is produced by the first one. The behavior of the second beam is strongly determined by the preexisting Langmuir wave electric fields. The simulations also show, as a result of the interaction between both beams, a clear nonlinear frequency shift of the harmonic modes as well as an increase of electromagnetic and kinetic energies of the wave-particle system.

Generation of harmonic Langmuir modes during beam–plasma interaction is studied by means of nonlinear theoretical calculations and computer simulations. The present Vlasov simulation of multiple harmonic Langmuir modes (up to 12th harmonics), generalizes the previously available simulations which were restricted to the second harmonic only. The frequency-wave-number spectrum obtained by taking the Fourier transformation of simulated electric field both in time and space shows an excellent agreement with the theoretical nonlinear dispersion relations for harmonic Langmuir waves. The saturated wave amplitude features a quasi-power-law spectrum which reveals that the harmonic generation process may be an integral part of the Langmuir turbulence.

The solar wind electrons observed at 1 AU are characterized by velocity distribution functions (VDF) that deviate from the Maxwellian form in a high energy regime. Such a feature is often modeled by a kappa distribution. In the present paper a self-consistent theory of quiet-time solar wind electrons that contain a power-law tail component, f ∝ v-α is discussed. These electrons are assumed to be in dynamic equilibrium with enhanced electrostatic fluctuations with peak frequency near the plasma frequency (i.e., the Langmuir turbulence). In order to verify the theoretical prediction, the solar wind electrons in the high-energy range known as the super-halo distribution detected by WIND and STEREO spacecraft are compared against the theoretical model where it was found that the theoretical power-law index is intermittent with regard to the observed range of indices, thus indicating that the turbulent equilibrium model of suprathermal solar wind electrons may be valid.

Generation of electrostatic multiple harmonic Langmuir modes during beam–plasma interaction process has been observed in laboratory and spaceborne active experiments, as well as in computer simulation experiments. Despite earlier efforts, such a phenomenon has not been completely characterized both theoretically and in terms of numerical simulations. This paper is a first in a series of three papers in which analytic expressions for harmonic Langmuir mode dispersion relations are derived and compared against the numerical simulation result.

Charged particle acceleration takes place ubiquitously in the Universe including the near-Earth heliospheric environment. Typical in situ spacecraft measurements made in the solar wind show that the charged particle velocity distribution contains energetic components with quasi scale-free power-law velocity dependence, f ∼ v − α , for high velocity range. In this Review a theory of quiet-time solar-wind electrons that contain a suprathermal component is discussed, in which these electrons are taken to be in dynamical equilibrium with Langmuir turbulence. This Review includes an overview of the Langmuir turbulence theory, as well as a discussion on asymptotic equilibrium solution of Langmuir turbulence/suprathermal electron system. Theoretical predictions of high-energy electron velocity power-law distribution index is then compared against the recent observations of the superhalo electron velocity distribution made by instruments onboard WIND and STEREO spacecraft. It is shown that the theoretical prediction of velocity power-law index is intermediate to the observed range.