A Parallel-Propagating Alfv\'enic Ion-Beam Instability in the High-Beta Solar Wind

We investigate the conditions under which parallel-propagating Alfv\'en/ion-cyclotron waves are driven unstable by an isotropic ($T_{\perp \alpha} = T_{\parallel\alpha}$) population of alpha particles drifting parallel to the magnetic field at an average speed $U_{\alpha}$ with respect to the protons. We derive an approximate analytic condition for the minimum value of $U_{\alpha}$ 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 $\simeq 5$ of the proton number density and the two species have similar thermal speeds, the instability requires that $\beta_{\rm p} \gtrsim 1$, where $\beta_{\rm p}$ is the ratio of the proton pressure to the magnetic pressure. For $1\lesssim \beta_{\mathrm p}\lesssim 12$, the minimum $U_{\alpha}$ needed to excite this instability ranges from $0.7v_{\mathrm A}$ to $0.9v_{\mathrm A}$, where $v_{\mathrm A}$ is the Alfv\'en speed. This threshold is smaller than the threshold of $\simeq 1.2v_{\mathrm A}$ for the parallel magnetosonic instability, which was previously thought to have the lowest threshold of the alpha-particle beam instabilities at $\beta_{\mathrm p}\gtrsim 0.5$. We discuss the role of the parallel Alfv\'enic drift instability for the evolution of the alpha-particle drift speed in the solar wind. We also analyze measurements from the \emph{Wind} spacecraft's Faraday cups and show that the $U_{\alpha}$ values measured in solar-wind streams with $T_{\perp \alpha}\approx T_{\parallel\alpha}$ are approximately bounded from above by the threshold of the parallel Alfv\'enic instability.