The proton–alpha drift instability is a possible mechanism of the alpha-particle deceleration and the resulting proton heating in the solar wind. We present hybrid numerical simulations of this instability with particle-in-cell ions and a quasi-neutralizing electron fluid for typical conditions at 1 au. For the parameters used in this paper, we find that fast magnetosonic unstable modes propagate only in the direction opposite to the alpha-particle drift and do not produce the perpendicular proton heating necessary to accelerate the solar wind. Alfvén modes propagate in both directions and heat the protons perpendicularly to the mean magnetic field. Despite being driven by the alpha temperature anisotropy, the Alfvén instability also extracts the energy from the bulk motion of the alpha particles. In the solar wind, the instabilities operate in a turbulent ambient medium. We show that the turbulence suppresses the Alfvén instability but the perpendicular proton heating persists. Unlike a static nonuniform background, the turbulence does not invert the sense of the proton heating associated with the fast magnetosonic instability and it remains preferentially parallel.
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