Effects of alpha-proton drift velocity on alpha particle firehose instability

In situ measurements have shown that the less-abundant alpha particles are characterized by temperature anisotropy which could drive the anisotropy-driven kinetic instabilities in the solar wind. In the collisionless plasma, the differential alpha-proton flow velocity V d = V α - V p usually has a non-zero value of the order of the local Alfvén velocity. The presence of such differential flow may affect the properties of dispersion relations for anisotropy-driven instabilities. Based upon linear Vlasov dispersion theory in a homogeneous plasma, the present study investigates the effects of the alpha-proton drift velocity on the parallel and oblique firehose instabilities driven by an excessive parallel temperature anisotropy of alpha particles, where the parallel and oblique represent directions of fluctuation propagation relative to the background magnetic field. It is found that for oblique firehose mode as well as parallel mode, the dispersion properties are affected by the presence of the alpha-proton drift velocity, which in turn results in the increase of the maximum growth rates as V_d increases and consequently leads to the modification of the marginal stability conditions in the parameter space (β ∥ α, T ⊥ α / T ∥ α). We discuss the relevance of our results to the measured temperature anisotropy of alpha particles in the solar wind context.