Magnetic Energy Transfer and Distribution between Protons and Electrons for Alfvenic Waves at Kinetic Scales in Wavenumber Space

Turbulent dissipation is considered a main source of heating and acceleration in cosmic plasmas. The alternating current Joule-like term, <delta j center dot delta E >, is used to measure the energy transfer between electromagnetic fields and particles. Because the electric field depends on the reference frame, in which frame to calculate <delta j center dot delta E > is an important issue. We compute the scale-dependent energy transfer rate spectrum in wavevector space, and investigate the electric-field fluctuations in two reference frames: delta E in the mean bulk flow frame and delta E' in the local bulk flow frame (non-inertial reference frame). Considering Alfvenic waves, we find that <delta j center dot delta E'>, which neglects the contribution of work done by the ion inertial force, is not consistent with the magnetic field energy damping rate (2 gamma delta B-2) according to linear Maxwell-Vlasov theory, while <delta j center dot delta E > is exactly the same as 2 gamma delta B-2 in wavenumber space (k(parallel to), k(perpendicular to)), where gamma is the linear damping rate. Under typical conditions of solar wind at 1 au, we find in our theoretical calculation that the field energy is mainly converted into proton kinetic energy leaving the residual minor portion for electrons. Although the electrons gain energy in the direction perpendicular to the mean magnetic field, they return a significant fraction of their kinetic energy in the parallel direction. Magnetic-field fluctuations can transfer particle energy between the parallel and perpendicular degrees of freedom. Therefore, <delta j(parallel to) center dot delta E-parallel to > and <delta j(parallel to) center dot delta E-perpendicular to > do not solely describe the energy transfer in the parallel direction and perpendicular direction, respectively.