RUDI GAELZER

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.

We investigate propagation and amplification of the auroral kilometric radiation over the geomagnetic poles using a particular model for the physical parameters in the auroral zone, which takes into account density gradients perpendicular to the geomagnetic field. The propagation of the waves is investigated with the canonical set of equations of the geometrical optics, taking into account thermal effects and considering both the energetic and the background electron populations, with the components of the dielectric tensor calculated in the locally homogeneous plasma approximation. It is shown that the spatial scale of inhomogeneity perpendicular to the magnetic field is an important factor in the amplification, although less favorable than indicated by previous studies using the method of Poeverlein to obtain the trajectory of the radiation.

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.

Velocity distribution functions (VDFs) that exhibit a power-law dependence on the high-energy tail have been the subject of intense research by the plasma physics community. Such functions, known as kappa or superthermal distributions, have been found to provide a better fitting to the VDFs measured by spacecraft in the solar wind. One of the problems that is being addressed on this new light is the temperature anisotropy of solar wind protons and electrons. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well-established. However, for kappa distributions, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation, relative to the ambient magnetic field. Contributions to the general case of obliquely-propagating electromagnetic waves have been scarcely reported so far. The absence of a general treatment prevents a complete analysis of the wave-particle interaction in kappa plasmas, since some instabilities can operate simultaneously both in the parallel and oblique directions. In a recent work, Gaelzer and Ziebell [J. Geophys. Res. 119, 9334 (2014)] obtained expressions for the dielectric tensor and dispersion relations for the low-frequency, quasi-perpendicular dispersive Alfvén waves resulting from a kappa VDF. In the present work, the formalism introduced by Ref. 1 is generalized for the general case of electrostatic and/or electromagnetic waves propagating in a kappa plasma in any frequency range and for arbitrary angles. An isotropic distribution is considered, but the methods used here can be easily applied to more general anisotropic distributions, such as the bi-kappa or product-bi-kappa.

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.

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.

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.

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectively emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.

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 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 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.

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.

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.