Cascade of Whistler-mode Turbulence from Ion to Electron Kinetic Scales: Particle-In-Cell simulation

Turbulent cascade of magnetic fluctuations in MHD scale typically shows a spectrum of magnetic fluctuation energy with a power-law index about -5/3. At kinetic scales, where ion and electron kinetic properties are dominant, the magnetic fluctuations often show the magnetic spectrum steeper than that of MHD scale. It suggests that the kinetic properties have important roles to cascade and dissipate the kinetic-scale fluctuations. At smaller scales, such as the electron inertial length and electron Larmor radius, the solar wind observations have showed much steeper spectra. It is believed that fluctuations cascading from the MHD scale are finally dissipated at the electron scales. However, the cascade process itself is highly nonlinear, so it is expected that the turbulent cascade and the kinetic dissipation associated with quasi-linear/nonlinear physics are intermingled in plasma turbulence at the both ion and electron scales. Several wave modes, such as kinetic Alfven mode, whistler mode, and nonlinear fluctuations, are considered to be dominant in the kinetic scales. Here we focus on nonlinear dynamics of whistler-mode turbulence. We have done two-dimensional electromagnetic particle-in-cell simulations to demonstrate the forward cascade of whistler-mode turbulence from scales close to MHD regime to electron kinetic scales. Electromagnetic fluctuations at scales well larger than ion inertial length are applied as an initial condition for the particle-in-cell simulation. The applied fluctuations satisfy the dispersion relation of whistler mode. The simulation demonstrates the forward cascade of whistler-mode turbulence from the large scales to electron scales self-consistently. The spectrum of magnetic fluctuation energy shows power-law spectra whose index is different at scales. Discussion will focus on properties of the power-law index, wavenumber anisotropy, and dissipation of whistler-mode turbulence.