The Heating of Test Particles in Numerical Simulations of Alfvénic Turbulence

We study the heating of charged test particles in three-dimensional numerical simulations of weakly compressible magnetohydrodynamic (MHD) turbulence (“Alfvénic turbulence”); these results are relevant to particle heating and acceleration in the solar wind, solar flares, accretion disks onto black holes, and other astrophysics and heliospheric environments. The physics of particle heating depends on whether the gyrofrequency of a particle Ω0 is comparable to the frequency of a turbulent fluctuation ω that is resolved on the computational domain. Particles with Ω0 ∼ ω undergo strong perpendicular heating (relative to the local magnetic field) and pitch angle scattering. By contrast, particles with Ω0 ω undergo strong parallel heating. Simulations with a finite resistivity produce additional parallel heating due to parallel electric fields in small-scale current sheets. Many of our results are consistent with linear theory predictions for the particle heating produced by the Alfvén and slow magnetosonic waves that make up Alfvénic turbulence. However, in contrast to linear theory predictions, energy exchange is not dominated by discrete resonances between particles and waves; instead, the resonances are substantially “broadened.” We discuss the implications of our results for solar and astrophysics problems, in particular the thermodynamics of the near-Earth solar wind. This requires an extrapolation of our results to higher numerical resolution, because the dynamic range that can be simulated is far less than the true dynamic range between the proton cyclotron frequency and the outer-scale frequency of MHD turbulence. We conclude that Alfvénic turbulence produces significant parallel heating via the interaction between particles and magnetic field compressions (“slow waves”). However, on scales above the proton Larmor radius Alfvénic turbulence does not produce significant perpendicular heating of protons or minor ions (this is consistent with linear theory, but inconsistent with previous claims from test particle simulations). Instead, the Alfvén wave energy cascades to perpendicular scales below the proton Larmor radius, initiating a kinetic Alfvén wave cascade. Subject headings: turbulence – MHD – plasma – particle acceleration – solar wind – accretion disks