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The Astrophysical Journal


We consider ion heating by turbulent Alfvén waves (AWs) and kinetic Alfvén waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies ω smaller than the ion cyclotron frequency Ω. We focus on plasmas in which β < 1, where β 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 ε = δv ρ/v , where v (v ) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B 0, and δv ρB ρ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when ε << εcrit, where εcrit is a constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when ε>εcrit, the proton heating rate exceeds half the cascade power that would be present in strong balanced KAW turbulence with the same value of δv ρ, and magnetic-moment conservation is violated even when ω << Ω. For the random-phase waves in our test-particle simulations, εcrit = 0.19. For protons in low-β plasmas, ε ~ β–1/2δB ρ/B 0, and ε can exceed εcrit even when δB ρ/B 0 << εcrit. The heating is anisotropic, increasing v 2 much more than v 2 when β << 1. (In contrast, at β > 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 ε 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.