Proton Heating in Imbalanced Alfvénic Turbulence

Alfvénic turbulence in the low-β solar wind is often highly imbalanced, with the outward-propagating Alfvén fluctuations being much more energetic than the inward-propagating ones. Under these conditions, a "helicity barrier" allows only the balanced portion of the turbulent flux to proceed past proton gyroscales. We have performed two Pegasus++ hybrid-kinetic particle-in-cell (PIC) simulations of imbalanced turbulence at proton β=[0.3,1/16], which robustly demonstrate the emergence of the helicity barrier at the lowest to-date β in a hybrid-PIC simulation and further motivate the presence of the barrier in the low-β solar wind. Both simulations realize a saturated state in which the ratio of proton to electron heating is consistent with the ratio of imbalanced to balanced turbulent flux and fluctuations exhibit a critically balanced cascade down to proton inertial length scales parallel (k_‖d_p ~ 1) and proton gyroradius scales perpendicular (k_⊥ρ_p ~ 1) to the mean magnetic field. Using both a Fokker—Planck and quasi-linear analysis, we detail the kinetic processes responsible for the energization of protons in our simulations. We then synthesize these processes into a model for proton heating in low-β, imbalanced, Alfvénic turbulence that can be validated using solar-wind observations.