RUDI GAELZER

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.

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.

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.

The derivation of explicit exprEssions for the effective dielectric tensor to be utilized in the dispersion relation for weakly inhomogeneous Plasmas is discussed. The general exprEssions obtained are useful for situations with simultaneous existence of weak inhomogeneities in density and magnetic field. The particular case of a Maxwellian distribution in velocity space for the electron population is discussed, and relatively compact exprEssions for the dielectric tensor are obtained which depend on the inhomogeneous Plasma dispersion function introduced by [Gaelzer et al., Phys. Rev. E55, 5859 (1997)] and ultimately on the well-known Fried-Conte function and its derivatives.

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.

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 effects of velocity distribution functions (VDF) that exhibit a power-law dependence on the high-energy tail have been the subject of intense research by the space plasma community. Such functions, known as superthermal or kappa distributions, have been found to provide a better fitting to the VDF measured by several spacecraft in the plasma environment of the solar wind. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well-established. However, for kappa distributions, either isotropic or anisotropic, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation. Contributions for the general case of obliquely-propagating waves have been scarcely reported so far. In this work we introduce a mathematical formalism that provides expressions for the dielectric tensor components and subsequent dispersion relations for oblique propagating dispersive Alfvén waves (DAW) resulting from a kappa VDF. We employ an isotropic distribution, but the methods used here can be easily applied to more general anisotropic distributions, such as the bi-kappa or product-bi-kappa. The effect of the kappa index and thermal corrections on the dispersion relations of DAW is discussed.

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.

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.

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 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 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 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.

The statistical mechanical reformulation of weak turbulence theory for unmagnetized plasmas including fully electromagnetic effects was carried out by Yoon [Phys. Plasmas 13, 022302 (2006)]. However, the wave kinetic equation for the transverse wave ignores the nonlinear three-wave interaction that involves two transverse waves and a Langmuir wave, the incoherent analogue of the so-called Raman scattering process, which may account for the third and higher-harmonic plasma emissions. The present paper extends the previous formalism by including such a term.

In this paper, we derive the dielectric tensor for a plasma containing particles described by an
anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are
written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer
and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation,
and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed
here and in the previous paper provides a mathematical framework for the study of electromagnetic
waves propagating at arbitrary angles and polarizations in a superthermal plasma.

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.

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.

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.