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.

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.

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.

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.

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.

We utilize a kinetic approach to the problem of wave propagation in dusty plasmas, taking into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions. The components of the dielectric tensor are written in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius. The formulation is quite general and valid for the whole range of frequencies above the plasma frequency of the dust particles, which are assumed motionless. The formulation is employed to the study of electrostatic waves propagating along the direction of the ambient magnetic field, in the case for which ions and electrons are described by bi-Maxwellian distributions. The results obtained in a numerical analysis corroborate previous analysis, about the important role played by the dust charge variation, particularly on the imaginary part of the dispersion relation, and about the very minor role played in the case of electrostatic waves by some additional terms appearing in the components of the dielectric tensor, which are entirely due to the occurrence of the dust charge variation.

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.

A kinetic formulation developed to analyze wave propagation in dusty plasmas, which takes into account the charge variation of the dust particles, is utilized to study the propagation and damping of Alfven waves propagating in oblique directions relative to the ambient magnetic field. A dusty plasma containing spherical and immobile dust grains in a homogeneous ambient magnetic field is considered. The charging process of the dust grains is assumed to be associated with the capture of electrons and ions by the dust particles during inelastic collisions between them and plasma particles. The dispersion relation and the damping rates of obliquely propagating Alfven waves are obtained assuming Maxwellian distributions for electrons and ions in equilibrium. For the numerical analysis of the dispersion relation we use the average values of the inelastic collision frequency as an approximation, instead of the momentum dependent expressions originally derived in the kinetic formulation, and study the modifications which the presence of the dust particles causes in both the propagation and the damping of the Alfven waves. In particular is discussed the competition between the different damping mechanisms, namely, the Landau damping and the damping associated with the dust charge variation, and it is shown that the inelastic collision frequency plays a pivotal role in the magnitude of the damping rates.

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.

A kinetic approach to the problem of wave propagation in dusty plasmas, which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, is utilized as a starting point for the development of a new formulation, which writes the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius. The formulation is quite general and valid for the whole range of frequencies above the plasma frequency of the dust particles, which were assumed motionless. The formulation is employed to the study of electrostatic waves propagating along the direction of the ambient magnetic field, in the case for which ions and electrons are described by Maxwellian distributions. The results obtained in a numerical analysis corroborate previous analysis, about the important role played by the inelastic collisions between electrons and ions and the dust particles, particularly on the imaginary part of the dispersion relation. The numerical analysis also show that additional terms in the components of the dielectric tensor, which are entirely due these inelastic collisions, play a very minor role in the case of electrostatic waves, under the conditions considered in the present analysis.

The present paper reports on the first two-dimensional (2D) self-consistent solution of weak turbulence equations describing the evolution of electron-beam-plasma interaction in which quasilinear as well as nonlinear three-wave decay processes are taken into account. It is found that the 2D Langmuir wave decay processes lead to the formation of a quasicircular ring spectrum in wave number space. It is also seen that the 2D ring-spectrum of Langmuir turbulence leads to a tendency to isotropic heating of the electrons. These findings contain some important ramifications. First, in the literature, isotropization of energetic electrons, detected in the solar wind for instance, is usually attributed to pitch-angle scattering. The present finding constitutes an alternative mechanism, whose efficiency for other parametric regimes has to be investigated. Second, when projected onto the one-dimensional (1D) space, the 2D ring spectrum may give a false impression of Langmuir waves inverse cascading to longer wavelength regime, when in reality, the wavelength of the turbulence does not change at all but only the wave propagation angle changes. Although the present analysis excludes the induced scattering, which is another process potentially responsible for the inverse cascade, the present finding at least calls for an investigation into the relative efficacy of the inverse-cascading process in 1D vs 2D.

Numerical solutions for equations of weak turbulence theory that describe the beam-plasma interaction are obtained in two dimensions (2D). The self-consistent theory governs quasilinear processes as well as nonlinear decay and scattering processes. It is found that the Langmuir turbulence scatters into a quasi-circular ring spectrum in 2D wave number space, accompanied by quasi-isotropic heating of the electrons. When projected onto the one-dimensional (1D) space, 2D Langmuir turbulence spectrum appears as an inverse cascade, when in reality, the wavelength of the turbulence does not change but only the wave propagation angle changes. These findings are similar to those obtained in a previous analysis in which scattering processes were not taken into account, but it is found that the scattering term leads to a quantifiably higher scattering rate.

Electron distributions with various degrees of asymmetry associated with the energetic tail population are commonly detected in the solar wind near 1 AU. By numerically solving one-dimensional electrostatic weak turbulence equations the present paper demonstrates that a wide variety of asymmetric energetic tail distributions may result. It is found that a wide variety of asymmetric tail formation becomes possible if one posits that the solar wind electrons are initially composed of thermal core plus field-aligned counterstreaming beams, instead of the customary thermal population plus a single beam. It is shown that the resulting nonlinear wave-wave and wave-particle interactions lead to asymmetric nonthermal tails. It is found that the delicate difference in the average beam speeds associated with the forward versus backward components is responsible for the generation of asymmetry in the energetic tail.

Effects due to the prEsence of charged dust particles on the growth rate of instabilities of low frequency electromagnetic waves propagating along the ambient magnetic field are investigated, using a kinetic theory which takes into account the collisional charging of the dust particles. For perpendicular ion temperature larger than the parallel ion temperature the dustless Plasma features the proton cyclotron anisotropy instability, which is gradually reduced by the prEsence of the dust population, until complete disappearance for sufficiently large dust density. For perpendicular ion temperature smaller than the parallel ion temperature the dustless Plasma features the proton fire-hose instability, which is also reduced by the prEsence of the dust population. The results obtained show that the fire-hose instability is more easily quenched by the prEsence of the dust than the proton cyclotron instability. For both instabilities, the prEsence of the dust affects the dispersion relation by the charge imbalance produced by the electron capture by the dust particles, and by the damping effect originated from the collisional charging of the dust particles.

We prEsent a detailed derivation of the effective dielectric constant to be used in the dispersion relation for electrostatic waves in the case of a Plasma immersed in a inhomogeneous magnetic ?eld, with inhomogeneity perpendicular to the direction of the magnetic ?eld.

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.

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.

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 Langmuir wave turbulence generated by a beam–plasma interaction has been studied since the early days of plasma physics research. In particular, mechanisms which lead to the quasi-power-law spectrum for Langmuir waves have been investigated, since such a spectrum defines the turbulence characteristics. Meanwhile, the generation of harmonic Langmuir modes during the beam–plasma interaction has been known for quite some time, and yet has not been satisfactorily accounted for thus far. In paper I of this series, nonlinear dispersion relations for these harmonics have been derived. In this paper (paper II), generalized weak turbulence theory which includes multiharmonic Langmuir modes is formulated and the self-consistent particle and wave kinetic equations are solved. The result shows that harmonic Langmuir mode spectra can indeed exhibit a quasi-power-law feature, implying multiscale structure in both frequency and wave number space spanning several orders of magnitude.

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.

In the present article, the classic problem of nonlinear frequency shifts of electrostatic plasma eigenmodes in an unmagnetized plasma (i.e., the Langmuir and ion-acoustic waves) is revisited. In the standard literature, only the frequency shift of Langmuir waves by the finite-amplitude Langmuir waves themselves is usually treated. In the present approach, the discussion is generalized to include the ion-sound waves. The significance of the present article is that the analytical approach employed in the present discussion can be utilized to resolve certain apparently singular terms in the induced scattering coefficients of the wave kinetic equations. The detailed discussion of such a problem will be reported in a forthcoming article.

The present paper is a followup to an earlier paper (accepted in Physics of Plasmas, 2002) in which the nonlinear frequency shifts of electrostatic plasma eigenmodes in an unmagnetized plasma were investigated, and in which a promise was made that the methodology employed in such a study will be employed to deal with certain induced scattering terms which contain apparent singularities. This paper implements the analytical technique developed in the first paper, and demonstrates how these singular terms can be regularized.

In this article, numerical solutions of the generalized weak turbulence equation [P. H. Yoon, Phys. Plasmas 7, 4858 (2000)] are carried out. In the generalized weak turbulence theory, the generation of the 2pe-harmonic Langmuir mode is treated as a fundamental process in turbulent beam-plasma interaction process, in addition to, and concomitant to, the well-known nonlinear processes such as Langmuir and ion-sound mode coupling and wave-particle interactions. The present numerical analysis shows that the harmonic mode, which is a solution to a nonlinear dispersion equation, hence a “nonlinear” eigenmode, grows primarily due to an induced emission process, which is a “linear” wave-particle interaction process. The harmonic Langmuir mode generation has been observed since the late 1960s in laboratory experiments, simulations, and in space. However, adequate and quantitative theoretical explanation has not been forthcoming. The present work represents a step toward an understanding of such a phenomenon.

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.