Four-Dimensional Frequency-Wavenumber Spectra from Hybrid Kinetic Simulations of Quasi-Perpendicular Turbulence

We carry out three-dimensional hybrid kinetic simulations of a strong decaying turbulence. The simulations use particle protons and massless fluid electrons. The turbulence is initiated with a seed spectrum that includes Alfven wave-modes at low wavenumbers. From the temporal and spatial distribution of the simulation output in the quasi-steady phase, we have calculated a four-dimensional frequency-wavenumber spectrum of the turbulence. Our analysis shows that kinetic Alfven waves can be identified in the vicinity of the seed spectrum and produce a peak in power consistent with their linear dispersion relation. Farther away from the seed spectrum, the signature of the Alfven modes disappears among other fluctuations that are not described by any dispersion relations. This has significant implications in that this portion of the spectrum corresponds to fluctuations where interactions with protons should dissipate the energy cascade. Furthermore, at intermediate wavenumbers where the signature is still identifiable but beyond the seed spectrum, its frequency broadening becomes comparable to the frequency itself. Therefore, the application of conventional linear waves may not be justified to describe turbulence even if their signature is still present and even less so when it disappears at higher wavenumbers. With larger rms amplitudes of the turbulence, the departures from wave-mode properties become more pronounced. This suggests that stronger nonlinearity makes the turbulent fluctuations behave less like wave modes until the conventional wave-mode approach is no longer valid.