Current density with magnetic flux contours at in (a) fluid and (b) hybrid simulations.
Magnetic field power spectra at for the hybrid and MHD simulations. The Hall scale and MHD Kolmorogorov dissipation scale are shown for reference. The Hall scale, where dispersive kinetic Alfvén waves arise, occurs when , where is the sound speed and is the magnetosonic speed (Ref. 28).
Hybrid and MHD comparison: (a) magnetic energy , fluid flow energy , their sum, the change in thermal energy , and total energy vs time. (b) Flow enstrophy and magnetic enstrophy vs time.
(a) : change in in the hybrid run; : exchange between and ; : electron kinetic energy; : sum of these, total dissipated. (b) and are cumulative dissipation through bulk flow and magnetic channels, their sum, change in thermal energy. (c) Parallel and perpendicular proton temperatures vs time.
Flow of energy through the turbulent hybrid simulations. Bold arrows denote significant energy conversion through a channel. Light dashed arrows denote little or no energy conversion through a channel. represents cyclotron damping, represents magnetic dissipation, and represents dissipation of proton bulk flow.
Effective (a) resistivity and (b) viscosity vs time.
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