Perpendicular ion heating by anisotropic whistler turbulence at electron scales

Magnetic energy spectrum in the solar wind turbulence is observed in very broad scale range, extending from Magnetohydrodynamic (MHD) scales to electron scales. The frequency spectrum observed at a position of spacecraft has a power-law feature, but its index is different depending on the frequency range. In low frequencies (< 0.1Hz) corresponding to the MHD scales in the solar wind at 1AU, where the Taylor hypothesis (scale size = solar wind speed / observed frequency) is assumed, the power-law index -5/3 is typically observed. This scale range is referred to as the inertial range. At higher frequencies, which correspond to the shorter scales, the power-law spectrum tends to be steeper than the inertial range. The steeper spectrum is considered to be due to the dissipation and/or dispersion effect of kinetic-wave turbulence. Many authors have discussed nonlinear properties and dissipation processes of the kinetic-wave turbulence at the ion and electron scales in theory, simulation, and observation. By using particle-in-cell simulation that includes kinetic effects of both ions and electrons, we study the ion heating by anisotropic whistler turbulence at electron scales that is of the order of electron inertial length. Whistler turbulence cascades their fluctuation energy in wavenumber space more preferentially to the perpendicular direction to the background magnetic field than parallel. The highly obliquely propagating whistler waves have electric fluctuations at wavenumbers perpendicular to the background magnetic field. By interacting with the perpendicular electric fluctuations, the ions are stochastically scattered into the perpendicular direction. Our simulation results show that whistler turbulence can transfer their fluctuation energy into not only electrons but also the perpendicular energy of ions. It suggests that whistler turbulence even at the electron scales contributes the perpendicular heating of protons in the solar wind. Whistler turbulence could be important role to scatter 90 pitch angle protons in the solar wind.