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Protons and alpha particles in the fast solar wind are only weaklycollisional and exhibit a number of non-equilibrium features, includingrelative drifts between particle species. Two non-collisional mechanisms havebeen proposed for limiting differential flow between alpha particles andprotons: plasma instabilities and the rotational force. Both mechanismsdecelerate the alpha particles. In this paper, we derive an analytic expressionfor the rate $Q_{\mathrm{flow}}$ at which energy is released by alpha-particledeceleration, accounting for azimuthal flow and conservation of total momentum.We show that instabilities control the deceleration of alpha particles at $r<r_{\mathrm{crit}}$, and the rotational force controls the deceleration of alphaparticles at $r> r_{\mathrm{crit}}$, where $r_{\mathrm{crit}} \simeq 2.5\,\mathrm{AU}$ in the fast solar wind in the ecliptic plane. We find that$Q_{\mathrm{flow}}$ is positive at $r<r_{\mathrm{crit}}$ and $Q_{\mathrm{flow}}= 0$ at $r\geq r_{\mathrm{crit}}$, consistent with the previous finding thatthe rotational force does not lead to a release of energy. We compare the valueof~$Q_{\mathrm{flow}}$ at $r< r_{\mathrm{crit}}$ with empirical heating ratesfor protons and alpha particles, denoted $Q_{\mathrm{p}}$ and $Q_{\alpha}$,deduced from in-situ measurements of fast-wind streams from the \emph{Helios}and \emph{Ulysses} spacecraft. We find that $Q_{\mathrm{flow}}$ exceeds$Q_{\alpha}$ at $r < 1\,\mathrm{AU}$, and that $Q_{\mathrm{flow}}/Q_{\rm p}$decreases with increasing distance from the Sun from a value of about one at$r=0.29 - 0.42\,\mathrm{AU}$ to about 1/4 at 1 AU. We conclude that thecontinuous energy input from alpha-particle deceleration at $r<r_{\mathrm{crit}}$ makes an important contribution to the heating of the fastsolar wind.

astrophysical journal/the astrophysical journal

Deceleration of Alpha Particles in the Solar Wind by Instabilities and  the Rotational Force: Implications for Heating, Azimuthal Flow, and the  Parker Spiral Magnetic Field