Perpendicular ion heating by low-frequency Alfvén-wave turbulence in the solar wind

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 = δυ_ρ/ ψ₁, where υ₁ (υ_∥) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B₀, and δυ_ρ (δB _ρ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when ε ε _crit, where ε_crit is a constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when ε > ε_crit, the proton heating rate exceeds half the cascade power that would be present in strong balanced KAW turbulence with the same value of δυ_ρ, and magnetic-moment conservation is violated even when ω Ω. For the random-phase waves in our test-particle simulations, ε_crit = 0.19. For protons in low-β plasmas, ε ≃ β ^-1/2δB_ρ/B₀, and ε can exceed ε_crit even when δB_ρ/B₀ ε_crit. The heating is anisotropic, increasing υ₁² much more than υ_∥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.