Resonant Interactions Between Protons and Oblique Alfvén/Ion-Cyclotron Waves in the Solar Corona and Solar Flares

We consider interactions between protons and Alfvén/ion-cyclotron (A/IC) waves in collisionless low-β plasmas in which the proton distribution function f is strongly modified by wave pitch-angle scattering. If the angle θ between the wave vector and background magnetic field is zero for all the waves, then strong scattering causes f to become approximately constant on surfaces of constant η, where η ≃ v 2 ⊥ + 1.5 v 2/3 A | v ∥ | 4/3 . Here, v ⊥ and v ∥ are the velocity components perpendicular and parallel to the background magnetic field, and v A is the Alfvén speed. If f = f (η), then A/IC waves with θ = 0 are neither damped nor amplified by resonant interactions with protons. In this paper, we argue that if some mechanism generates high-frequency A/IC waves with a range of θ values, then wave–particle interactions initially cause the proton distribution function to become so anisotropic that the plasma becomes unstable to the growth of waves with θ = 0. The resulting amplification of θ = 0 waves leads to an angular distribution of A/IC waves that is sharply peaked around θ = 0 at the large wavenumbers at which A/IC waves resonate with protons. Scattering by this angular distribution of A/IC waves subsequently causes f to become approximately constant along surfaces of constant η, which in turn causes oblique A/IC waves to be damped by protons. We calculate the proton and electron contributions to the damping rate analytically, assuming Maxwellian electrons and f = f (η). Because the plasma does not relax to a state in which proton damping of oblique A/IC waves ceases, oblique A/IC waves can be significantly more effective at heating protons than A/IC waves with θ = 0.