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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 minimumdoi:10.1088/0964-1726/14/5/035 fatcat:cbkv333x7ncyfizw3mgcztriiu