Incorporating kinetic physics into a two-fluid solar-wind model with temperature anisotropy and low-frequency alfvn-wave turbulence

We develop a one-dimensional solar-wind model that includes separate energy equations for the electrons and protons, proton temperature anisotropy, collisional and collisionless heat flux, and an analytical treatment of low-frequency, reflection-driven, Alfvén-wave (AW) turbulence. To partition the turbulent heating between electron heating, parallel proton heating, and perpendicular proton heating, we employ results from the theories of linear wave damping and nonlinear stochastic heating. We account for mirror and oblique firehose instabilities by increasing the proton pitch-angle scattering rate when the proton temperature anisotropy exceeds the threshold for either instability. We numerically integrate the equations of the model forward in time until a steady state is reached, focusing on two fast-solar-wind-like solutions. These solutions are consistent with a number of observations, supporting the idea that AW turbulence plays an important role in the origin of the solar wind.