Perpendicular Ion Heating by Reduced Magnetohydrodynamic Turbulence

TL;DR

This study tests a theoretical model of stochastic ion heating by simulating test particles in RMHD turbulence, confirming the model's accuracy and exploring how turbulence properties influence heating efficiency.

Contribution

The paper provides numerical validation of the stochastic ion heating formula in RMHD turbulence and investigates how turbulence parameters affect heating rates and constants.

Findings

Heating rates match the theoretical formula well.

Stronger stochastic heating occurs in strong RMHD turbulence.

Constants c_1 and c_2 vary with turbulence properties and ion speeds.

Abstract

Recent theoretical studies argue that the rate of stochastic ion heating in low-frequency Alfv\'en-wave turbulence is given by $Q_\perp = c_1 [(\delta u)^3 /\rho] \exp(-c_2/\epsilon)$, where $\delta u$ is the rms turbulent velocity at the scale of the ion gyroradius $\rho$, $\epsilon = \delta u/v_{\perp \rm i}$, $v_{\perp \rm i}$ 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 $\sim 1$. The best-fit values of $c_2$ decrease (i.e., stochastic heating becomes more effective) as the grid size and Reynolds number of the RMHD simulations increase. As an example, in a $1024^2 \times 256$ RMHD simulation with a dissipation wavenumber of order 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 Alfv\'en 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 $\sim 3$ while $c_2$ changes very little as the ion thermal speed increases from values $\ll v_{\rm A}$ to values $\sim v_{\rm A}$, where $v_{\rm A}$ is the Alfv\'en speed. We discuss the importance of these results for perpendicular ion heating in the solar wind.