Perpendicular ion heating by reduced magnetohydrodynamic turbulence

Recent theoretical studies argue that the rate of stochastic ion heating in low-frequency Alfvén-wave turbulence is given by Q _τ = c ₁ ((δu)³/ρ)exp (- c ₂/ε), where δu is the rms turbulent velocity at the scale of the ion gyroradius ρ, ε = δu/v _τ, v _τi is the perpendicular ion thermal speed, and c ₁ and c ₂ are dimensionless constants. We test this theoretical result by numerically simulating test particles interacting with strong reduced magnetohydrodynamic (RMHD) turbulence. The heating rates in our simulations are well fit by this formula. The best-fit values of c ₁ are ∼1. The best-fit values of c ₂ decrease (i.e., stochastic heating becomes more effective) as the Reynolds number and the number of grid points in the RMHD simulations increase. As an example, in a 1024² × 256 RMHD simulation with a dissipation wavenumber of the order of the inverse ion gyroradius, we find c ₂ = 0.21. We show that stochastic heating is significantly stronger in strong RMHD turbulence than in a field of randomly phased Alfvén waves with the same power spectrum, because coherent structures in strong RMHD turbulence increase orbit stochasticity in the regions where ions are heated most strongly. We find that c ₁ increases by a factor of ∼3 while c ₂ changes very little as the ion thermal speed increases from values ≪v _A to values ∼v _A, where v _A is the Alfvén speed. We discuss the importance of these results for perpendicular ion heating in the solar wind.