Coronal ion-cyclotron beam instabilities within the multi-fluid description

Context. Spectroscopic observations and theoretical models suggest resonant wave-particle interactions, involving high-frequency ion-cyclotron waves, as the principal mechanism for heating and accelerating ions in the open coronal holes. However, the mechanism responsible for the generation of the ion-cyclotron waves remains unclear. One possible scenario is that ion beams originating from small-scale reconnection events can drive micro-instabilities that constitute a possible source for the excitation of ion-cyclotron waves. Aims. In order to study ion beam-driven electromagnetic instabilities, the multi-fluid model in the low-β coronal plasma is used. While neglecting the electron inertia this model allows one to take into account ion-cyclotron wave effects that are absent from the one-fluid MHD model. Realistic models of density and temperature as well as a 2-D analytical magnetic field model are used to define the background plasma in the open-field funnel region of a polar coronal hole. Methods. Considering the WKB approximation, a Fourier plane-wave linear mode analysis is employed in order to derive the dispersion relation. Ray-tracing theory is used to compute the ray path of the unstable wave as well as the evolution of the growth rate of the wave while propagating in the coronal funnel. Results. We demonstrate that, in typical coronal holes conditions and assuming realistic values of the beam velocity, the free energy provided by the ion beam propagating parallel the ambient field can drive micro-instabilities through resonant ion-cyclotron excitation.