RUDI GAELZER

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 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 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.

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.

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 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 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 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.

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.

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.