On Stochastic Heating and Its Phase-space Signatures in Low-beta Kinetic Turbulence

We revisit the theory of stochastic heating of ions and investigate its phase-space signatures in kinetic turbulence of relevance to low-β portions of the solar wind. In particular, we retain a full scale-dependent approach in our treatment, and we explicitly consider the case in which electric-field fluctuations can be described by a generalized Ohm's law that includes Hall and thermoelectric effects. These two electric-field terms provide the dominant contributions to stochastic ion heating when the ion-Larmor scale is much smaller than the ion skin depth, ρ_i ≪ d_i, which is the case at β ≪ 1. Employing well-known spectral scaling laws for Alfvén-wave and kinetic-Alfvén-wave turbulent fluctuations, we obtain scaling relations characterizing the field-perpendicular particle-energization rate and energy diffusion coefficient associated with stochastic heating in these two regimes. Phase-space signatures of ion heating are then investigated using three-dimensional hybrid-kinetic simulations of continuously driven Alfvénic turbulence at low β (namely, β_i = β_e = 0.3 and β_i = β_e = 1/9). In these simulations, energization of ions parallel to the magnetic field is subdominant compared to its perpendicular counterpart (Q_∥,i ≪ Q_⊥,i), and the fraction of turbulent energy that goes into ion heating is ≈75% at β_i = 0.3 and ≈40% at β_i ≃ 0.1. The phase-space signatures of ion energization are consistent with Landau-resonant collisionless damping and a (β-dependent) combination of ion-cyclotron and stochastic heating. We demonstrate good agreement between our scale-dependent theory and various signatures associated with the stochastic portion of the heating. We discuss briefly the effect of intermittency on stochastic heating and the implications of our work for the interpretation of stochastic heating in solar-wind spacecraft data.