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Collisional analysis combines the effects of collisional relaxation and large-scale expansion to quantify how solar wind parameters evolve as the plasma expands through the heliosphere. Though previous studies have applied collisional analysis to the temperature ratio between protons (ionized hydrogen) andα-particles (fully ionized helium), this is the first study to exploreα-proton differential flow with collisional analysis. First, the mathematical model for the collisional analysis of differential flow was derived. Then, this model was applied to individualin-situobservations from Parker Solar Probe (PSP;r= 0.1–0.27 au) to generate predictions of theα-proton differential flow in the near-Earth solar wind. A comparison of these predicted values with contemporaneous measurements from the Wind spacecraft (r= 1.0 au) shows strong agreement, which may imply that the effects of expansion and Coulomb collisions have a large role in governing the evolution of differential flow through the inner heliosphere. 

Abstract Owing to its low density and high temperature, the solar wind frequently exhibits strong departures from local thermodynamic equilibrium, which include distinct temperatures for its constituent ions. Prior studies have found that the ratio of the temperatures of the two most abundant ions—protons (ionized hydrogen) andα-particles (ionized helium)—is strongly correlated with the Coulomb collisional age. These previous studies, though, have been largely limited to using observations from single missions. In contrast, this present study utilizes contemporaneous, in situ observations from two different spacecraft at two different distances from the Sun: the Parker Solar Probe (PSP;r= 0.1–0.3 au) and Wind (r= 1.0 au). Collisional analysis, which incorporates the equations of collisional relaxation and large-scale expansion, was applied to each PSP datum to predict the state of the plasma farther from the Sun atr= 1.0 au. The distribution of these predictedα–proton relative temperatures agrees well with that of values observed by Wind. These results strongly suggest that, outside of the corona, relative ion temperatures are principally affected by Coulomb collisions and that the preferential heating ofα-particles is largely limited to the corona.