Parametric cross‐field current instability in solar coronal holes

We consider a parametric instability of fast and Alfvén waves with length scales of the order of the proton inertial length. The instability is driven by currents that are associated with these pump waves and that flow in the direction perpendicular to the background magnetic field. The initial pump waves generate secondary ion cyclotron waves with length scales below the proton gyroradius. The important property of the cross‐field current instability is that it can exist at relatively low amplitudes of the pump waves. As a result, it can be excited in the solar corona, where turbulent fluctuations are much smaller than in the distant solar wind. The instability of the pump wave provides an additional mechanism of wave damping compared to direct cyclotron damping. This mechanism starts to operate in the region of spatial scales where the direct cyclotron damping is weak. We show that the wave amplitudes, derived from an observed spectrum of density fluctuations, are sufficient to excite the cross‐field current instability and that the turbulent heating associated with the instability is fast enough to provide a heating mechanism for protons in the coronal holes.