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 β p . The form of the magnetic spectrum does not depend on β 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 β p .
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