We investigate the conditions under which parallel-propagating Alfvén/ion-cyclotron waves are driven unstable by an isotropic ( T ⊥α = T ∥α ) population of alpha particles drifting parallel to the magnetic field at an average speed U α with respect to the protons. We derive an approximate analytic condition for the minimum value of U α needed to excite this instability and refine this result using numerical solutions to the hot-plasma dispersion relation. When the alpha-particle number density is ≃ 5% of the proton number density and the two species have similar thermal speeds, the instability requires that β p ≳ 1, where β p is the ratio of the proton pressure to the magnetic pressure. For 1 ≲ β p ≲ 12, the minimum U α needed to excite this instability ranges from 0.7 v A to 0.9 v A , where v A is the Alfvén speed. This threshold is smaller than the threshold of ≃ 1.2 v A for the parallel magnetosonic instability, which was previously thought to have the lowest threshold of the alpha-particle beam instabilities at β p ≳ 0.5. We discuss the role of the parallel Alfvénic drift instability for the evolution of the alpha-particle drift speed in the solar wind. We also analyze measurements from the Wind spacecraft's Faraday cups and show that the U α values measured in solar-wind streams with T ⊥α ≈ T ∥α are approximately bounded from above by the threshold of the parallel Alfvénic instability.
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