VELOCITY POWER SPECTRA FROM CROSS-FIELD TURBULENCE IN THE PROTON KINETIC REGIME

Numerical hybrid simulations with particle protons and fluid electrons are conducted for turbulent fluctuations with spatial variations in a plane perpendicular to the background magnetic field. In the turbulent phase, the proton bulk velocity spectrum has a dissipation range starting at a smaller wavenumber than the magnetic spectrum dissipation range. The steepened portion of the proton bulk velocity spectrum is constrained to a smaller wavenumber with an increasing ratio of background proton plasma to magnetic pressure beta(p). The form of the magnetic spectrum does not depend on beta(p). The collisionless proton and fluctuation interaction which heats protons mainly across the magnetic field is deemed to be the result of a viscous-like interaction based, in part, on the dependence of the velocity spectrum on beta(p)