How Alfvén waves energize the solar wind: heat versus work

A growing body of evidence suggests that the solar wind is powered to a large extent by an Alfvén-wave (AW) energy flux. AWs energize the solar wind via two mechanisms: heating and work. We use high-resolution direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole to investigate both mechanisms. In particular, we compute the fraction of the AW power at the coronal base ( $P_\textrm {AWb}$ ) that is transferred to solar-wind particles via heating between the coronal base and heliocentric distance $r$ , which we denote by $\chi _{H}(r)$ , and the fraction that is transferred via work, which we denote by $\chi _{W}(r)$ . We find that $\chi _{W}(r_{A})$ ranges from 0.15 to 0.3, where $r_{A}$ is the Alfvén critical point. This value is small compared with one because the Alfvén speed $v_{A}$ exceeds the outflow velocity $U$ at $r < r_{A}$ , so the AWs race through the plasma without doing much work. At $r>r_{A}$ , where $v_{A} < U$ , the AWs are in an approximate sense ‘stuck to the plasma’, which helps them do pressure work as the plasma expands. However, much of the AW power has dissipated by the time the AWs reach $r=r_{A}$ , so the total rate at which AWs do work on the plasma at $r>r_{A}$ is a modest fraction of $P_\textrm {AWb}$ . We find that heating is more effective than work at $r < r_{A}$ , with $\chi _{H}(r_{A})$ ranging from 0.5 to 0.7. The reason that $\chi _{H} \geq 0.5$ in our simulations is that an appreciable fraction of the local AW power dissipates within each Alfvén-speed scale height in RDAWT, and there are a few Alfvén-speed scale heights between the coronal base and $r_{A}$ . A given amount of heating produces more magnetic moment in regions of weaker magnetic field. Thus, paradoxically, the average proton magnetic moment increases robustly with increasing $r$ at $r>r_{A}$ , even though the total rate at which AW energy is transferred to particles at $r>r_{A}$ is a small fraction of $P_\textrm {AWb}$ .