On the influence of the shape of kappa distributions of ions and electrons on the ioncyclotron instability

The dispersion relation for ion-cyclotron waves propagating along the direction of the ambient magnetic field is investigated numerically by considering different forms of kappa functions as velocity distributions of ions and electrons. General forms of kappa distributions, isotropic and anisotropic, are defined and used to obtain the dispersion relations for ion-cyclotron waves. With suitable choice of parameters, the general forms reduce to anisotropic versions of the kappa distributions most frequently employed in the literature. The analysis is focused in cases with a small value of the kappa index, for which the non thermal character of the kappa distributions is enhanced. The results show the effects of the superthermal tails of the velocity distributions of both particle species (ions and electrons) on the growth rate of the ion-cyclotron instability. It is seen that different forms of anisotropic kappa distributions, which are used in the current literature, can have a significantly different effect on the growth rates of the instability

Effects of dust particles charged by inelastic collisions and by photoionization on Alfven waves in a stellar wind

Using a kinetic description of a homogeneous magnetized dusty plasma with Maxwellian distribution of electrons and protons and dust particles charged by inelastic collisions and by photoionization, we analyse the dispersion relation considering the case where waves and radiation propagate exactly parallel to the ambient magnetic field. The investigation emphasizes the changes that the photoionization process brings to the propagation and damping of the waves in a stellar wind environment, since Alfvén waves are believed to play a significant role in the heating and acceleration processes that take place in the wind. The results show that, in the presence of dust with negative equilibrium electrical charge, the Alfvén mode decouples into the whistler and ion cyclotron modes for all values of wavenumber, but when dust particles acquire neutral or positive values of electrical charge, these modes may couple for certain values of wavenumber. It is also seen that the whistler and ion cyclotron modes present null group velocity in an interval of small wavenumber, and that the maximum value of wavenumber for which the waves are non-propagating is reduced in the presence of the photoionization process. For very small values of wavenumber, the damping rates of the modes could change significantly from very small to very high values if the sign of the dust electrical charge is changed

Generation of harmonic Langmuir mode by beam-plasma instability

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 2vpe-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

Nonlinear development of weak beam-plasma instability

Nonlinear interactions of tenuous electron beam, background, unmagnetized plasma, and self-consistently generated Langmuir and ion-sound waves are analyzed in the framework of plasma weak turbulence kinetic theory. Full numerical solutions of the complete weak turbulence equations are obtained for the first time, which show the familiar plateau formation in the electron beam distribution and concomitant quasi-saturation of primary Langmuir waves, followed by fully nonlinear processes which include three-wave decay and induced-scattering processes. A detailed analysis reveals that the scattering off ions is an important nonlinear process which leads to prominent backscattered and long-wavelength Langmuir wave components. However, it is found that the decay process is also important, and that the nonlinear development of weak Langmuir turbulence critically depends on the initial conditions. Special attention is paid to the electron-to-ion temperature ratio, Te /Ti , and the initial perturbation level. It is found that higher values of Te /Ti promote the generation of backscattered Langmuir wave component, and that a higher initial wave intensity suppresses the backscattered component while significantly enhancing the long-wavelength Langmuir wave component

The oblique firehose instability in a bi-kappa magnetized plasma

In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfvén) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in the solar wind, some solutions of the dispersion equation, corresponding to the unstable mode, are presented. In order to implement the dispersion solver, several new mathematical properties of the special functions occurring in a kappa plasma are derived and included. The results presented here suggest that the superthermal characteristic of the distribution functions leads to reductions to both the maximum growth rate of the instability and of the spectral range of its occurrence

The general dielectric tensor for bi-kappa magnetized plasmas

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

Group velocity of obliquely propagating Alfvén waves in a magnetized dusty plasma

In this work, we investigate the characteristics of the group velocity of obliquely propagating Alfvén in a dusty plasma typical of a stellar wind. The dispersion relation is derived with the aid of the kinetic theory for a magnetized dusty plasma consisting of electrons and ions, with distribution of momenta described by a Maxwellian function. The dust particles are considered to be immobile and have all the same size; they are electrically charged by absorption of plasma particles via inelastic collisions and by photoionization. We numerically solve the dispersion relation and calculate the components of group velocity (along and transverse to the magnetic field) for the normal modes, namely the compressional and shear Alfvén (CAW and SAW). The results show that the direction of the group velocity of CAWs is greatly modified with the wave-vector direction. On the other hand, SAWs will present group velocity propagating practically along the magnetic field. The changes in dust parameters, such as number density and equilibrium electrical charge, may significantly change the waves’ characteristics. It is seen that for sufficiently high dust to ion number density ratio, the SAWs may present perpendicular group velocity propagating in opposite direction to the perpendicular phase velocity, in a small interval of wavenumber values; we also notice that this interval may change, or even vanish, when the flux of radiation incident on the dust is altered, changing the equilibrium electrical charge of the grains

Oblique Alfvén waves in a stellar wind environment with dust particles charged by inelastic collisions and by photoionization

The characteristics of Alfvén waves propagating in a direction oblique to the ambient magnetic field in a stellar wind environment are discussed. A kinetic formulation for a magnetized dusty plasma is adopted considering Maxwellian distributions of electrons and ions, and immobile dust particles electrically charged by absorption of plasma particles and by photoionization. The dispersion relation is numerically solved and the results are compared with situations previously studied where dust particles were not charged by photoionization, which is an important process in a stellar wind of a relatively hot star. We show that the presence of dust causes the shear Alfvén waves to present a region of wavenumber values with zero frequency and that the minimum wavelength for which the mode becomes dispersive again is roughly proportional to the radiation intensity to which the dust grains are exposed. The damping rates of both shear and compressional Alfvén waves are observed to decrease with increasing radiation flux, for the parameters considered. For the particular case where both modes present a region with null real frequency when the radiation flux is absent or weak, it is shown that when the radiation flux is sufficiently strong, the photoionization mechanism may cause this region to get smaller or even to vanish, for compressional Alfvén waves. In that case, the compressional Alfvén waves present non-zero frequency for all wavenumber values, while the shear Alfvén waves still present null frequency in a certain interval of wavenumber values, which gets smaller with the presence of radiation

Dielectric tensor for inhomogeneous plasmas in inhomogeneous magnetic field

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. E 55, 5859 (1997)] and ultimately on the well-known Fried–Conte function and its derivatives

Multiple harmonics of electron waves studied using weak turbulence theory in a two-dimensional formulation

Electrostatic waves with frequencies that are integer multiples of the electron plasma frequency have been observed since the early days of laboratory experiments on beam–plasma interactions, and also in experiments made in the space environment. These waves have also appeared in numerical experiments, and can be explained in the context of weak turbulence theory. This paper presents results obtained by numerical solution of the equations of weak turbulence theory, which show the coupled time evolution of the amplitudes of harmonic waves and of the amplitudes of Langmuir and ion acoustic waves, and the time evolution of the electron distribution function. The results are obtained considering a two-dimensional geometry, considering harmonics up to n ¼ 5, and are consistent with earlier results obtained by one-dimensional analyses