PERPENDICULAR ION HEATING BY LOW-FREQUENCY ALFVEN-WAVE TURBULENCE IN THE SOLAR WIND

We consider ion heating by turbulent Alfven waves (AWs) and kinetic Alfven waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies omega smaller than the ion cyclotron frequency Omega. We focus on plasmas in which beta less than or similar to 1, where beta is the ratio of plasma pressure to magnetic pressure. As in previous studies, we find that when the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity epsilon = delta nu(rho)/nu(perpendicular to) where nu(perpendicular to) (nu(parallel to)) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B-0, and delta nu(rho), (delta B-rho) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when epsilon << epsilon(crit), where suit is a constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when epsilon > epsilon(crit), the proton heating rate exceeds half the cascade power that would be present in strong balanced KAW turbulence with the same value of delta nu(rho), and magnetic-moment conservation is violated even when omega << Omega. For the random-phase waves in our test-particle simulations, epsilon(crit) = 0.19. For protons in low-beta plasmas, epsilon similar or equal to beta(-1/2)delta B-rho/B-0, and epsilon can exceed epsilon(crit) even when delta B rho/B-0 << epsilon(crit). The heating is anisotropic, increasing nu(2)(perpendicular to) much more than nu(2)(parallel to) when beta << 1. (In contrast, at beta greater than or similar to 1 Landau damping and transit-time damping of KAWs lead to strong parallel heating of protons.) At comparable temperatures, alpha particles and minor ions have larger values of epsilon than protons and are heated more efficiently as a result. We discuss the implications of our results for ion heating in coronal holes and the solar wind.