Proton heating by parallel Alfvén wave cascade

In a recent series of papers, the present authors developed a kinetic theory for low-frequency turbulence propagating parallel to the ambient magnetic field. Making use of this theory, it was shown that low-frequency Alfvénic turbulence may cascade to ion-cyclotron frequency range and beyond by nonlinear three-wave decay processes. The significance of such a finding is that it may lead to the proton heating by cyclotron resonance. However, the actual proton heating process was not demonstrated. The present paper complements the previous works by including the proton heating in the discussion. It is found that the left-hand circularly polarized Alfvén-cyclotron turbulence leads to a moderate heating of the protons in the perpendicular direction and cooling in the parallel direction. It is also found that ion-acoustic turbulence is generated by the decay instability process. Finally, the heating rate is shown to increase in inverse proportion to the time scale of the wave source.