We investigate the conditions under which parallel-propagating Alfvén/ion-cyclotron (A/IC) waves and fast-magnetosonic/whistler (FM/W) waves are driven unstable by the differential flow and temperature anisotropy of alpha particles in the solar wind. We focus on the limit in which w α 0.25v A , where w α is the parallel alpha-particle thermal speed and v A is the Alfvén speed. We derive analytic expressions for the instability thresholds of these waves, which show, e.g., how the minimum

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... the minimum unstable alpha-particle beam speed depends upon w α /v A , the degree of alpha-particle temperature anisotropy, and the alpha-to-proton temperature ratio. We validate our analytical results using numerical solutions to the full hot-plasma dispersion relation. Consistent with previous work, we find that temperature anisotropy allows A/IC waves and FM/W waves to become unstable at significantly lower values of the alpha-particle beam speed U α than in the isotropic-temperature case. Likewise, differential flow lowers the minimum temperature anisotropy needed to excite A/IC or FM/W waves relative to the case in which U α = 0. We discuss the relevance of our results to alpha particles in the solar wind near 1 AU.