Cascade and Damping of Alfvén-Cyclotron Fluctuations: Application to Solar Wind Turbulence

It is well-recognized that the presence of magnetic fields will lead to anisotropic energy cascade and dissipation of astrophysical turbulence. With the diffusion approximation and linear dissipation rates, we study the cascade and damping of Alfvén-cyclotron fluctuations in solar plasmas numerically for two diagonal diffusion tensors, one (isotropic) with identical components for the parallel and perpendicular directions (with respect to the magnetic field) and one with different components (non-isotropic). It is found that for the isotropic case the steady-state turbulence spectra are nearly isotropic in the inertial range and can be fitted by a single power-law function with a spectral index of −3/2, similar to the Iroshnikov-Kraichnan phenomenology, while for the non-isotropic case the spectra vary greatly with the direction of propagation. The energy fluxes in both cases are much higher in the perpendicular direction than in the parallel direction due to the angular dependence (or inhomogeneity) of the components. In addition, beyond the MHD regime the kinetic effects make the spectrum softer at higher wavenumbers. In the dissipation range the turbulence spectrum cuts off at the wavenumber, where the damping rate becomes comparable to the cascade rate, and the cutoff wavenumber changes with the wave propagation direction. The angle averaged turbulence spectrum of the isotropic model resembles a broken power-law, which cuts off at the maximum of the cutoff wavenumbers or the He cyclotron frequency. Taking into account the Doppler effects, the model naturally reproduces the broken power-law turbulence spectra observed in the solar wind and predicts that a higher break frequency always comes along with a softer dissipation range spectrum that may be caused by the increase of the Center for Space Science and Astrophysics, Department of Physics, Stanford University, Stanford, CA 94305; [email protected], [email protected] Kavli Institute of Particle Physics and Cosmology, Stanford University Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK; [email protected] Also Department of Applied Physics