Resonant interactions between protons and oblique Alfven/ion-cyclotron waves in the solar corona and solar flares

We consider interactions between protons and Alfven/ion-cyclotron (A/IC) waves in collisionless low-beta plasmas in which the proton distribution function f is strongly modified by wave pitch-angle scattering. If the angle theta 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 eta, where eta similar or equal to nu(2)(perpendicular to) + 1.5 nu(2/3)(A) vertical bar nu(parallel to)vertical bar(4/3). Here, nu(perpendicular to) and nu(parallel to) are the velocity components perpendicular and parallel to the background magnetic field, and nu(A) is the Alfven speed. If f = f(eta), then A/IC waves with theta = 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. 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 theta = 0. The resulting amplification of theta = 0 waves leads to an angular distribution of A/IC waves that is sharply peaked around. = 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., 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(eta). 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 theta = 0