Spectral evolution of two-dimensional kinetic plasma turbulence in the wavenumber-frequency domain

We present a method for studying the evolution of plasma turbulence by tracking dispersion relations in the energy spectrum in the wavenumber-frequency domain. We apply hybrid plasma simulations in a simplified two-dimensional geometry to demonstrate our method and its applicability to plasma turbulence in the ion kinetic regime. We identify four dispersion relations: ion-Bernstein waves, oblique whistler waves, oblique Alfv\'en/ion-cyclotron waves, and a zero-frequency mode. The energy partition and frequency broadening are evaluated for these modes. The method allows us to determine the evolution of decaying plasma turbulence in our restricted geometry and shows that it cascades along the dispersion relations during the early phase with an increasing broadening around the dispersion relations.Comment: 11 pages, 4 figure

Four-dimensional energy spectrum for space–time structure of plasma turbulence

A parametric model of the inertial-range energy spectrum is constructed for plasma turbulence in the four-dimensional wave vector and frequency domain. The model is based on that of the Eulerian wavenumber-frequency spectrum developed for describing fluid turbulence, and includes wave vector anisotropies in the three-dimensional wave vector domain by approximating the spectrum to a set of ellipses. The shape of the four-dimensional spectrum is determined by the Doppler shift, the Doppler broadening, and anisotropy coefficients. The model is applied to the magnetic energy spectrum in the near-Earth solar wind measured by four Cluster spacecraft, and the set of the spectral parameters are determined observationally. In this way, space–time structure of plasma turbulence can be condensed into a small number of parameters, which is suitable for evaluating the energy spectra in observational and numerical studies on the quantitative basis

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Inertial-range spectrum of whistler turbulence

We develop a theoretical model of an inertial-range energy spectrum for homogeneous whistler turbulence. The theory is a generalization of the Iroshnikov-Kraichnan concept of the inertial-range magnetohydrodynamic turbulence. In the model the dispersion relation is used to derive scaling laws for whistler waves at highly oblique propagation with respect to the mean magnetic field. The model predicts an energy spectrum for such whistler waves with a spectral index −2.5 in the perpendicular component of the wave vector and thus provides an interpretation about recent discoveries of the second inertial-range of magnetic energy spectra at high frequencies in the solar wind

Propagation pattern of low frequency waves in the terrestrial magnetosheath

International audiencePropagation pattern (distribution of phase velocities) is determined in three dimensions in the terrestrial magnetosheath on a statistical basis using Cluster spacecraft observations. It is found that the anti-sunward propagation dominates and that the propagation direction is toward the magnetosheath flank at smaller zenith angles, while it is toward the magnetopause at larger angles. This pattern is axially symmetric regardless of the interplanetary magnetic field direction and agrees qualitatively with the density gradient directions in a hydromagnetic flow model of the magnetosheath, suggesting that the wave refraction mechanism is more significant than the wave drift effect

An explicit construction of non-tempered cusp forms on O(1,8n+1)O(1,8n+1)

We explicitly construct cusp forms on the orthogonal group of signature $(1,8n+1)$ for an arbitrary natural number $n$ as liftings from Maass cusp forms of level one. In our previous works, the fundamental tool to show the automorphy of the lifting was the converse theorem by Maass. In this paper, we use the Fourier expansion of the theta lifts by Borcherds instead. We also study cuspidal representations generated by such cusp forms and show that they are irreducible and that all of their non-archimedean local components are non-tempered while the archimedean component is tempered, if the Maass cusp forms are Hecke eigenforms. The standard $L$-functions of the cusp forms are proved to be products of symmetric square $L$-functions of the Hecke-eigen Maass cusp forms with shifted Riemann zeta functions