Thermal conduction alone can not explain the acceleration of the solar wind to fast wind speed for plasma temperatures of 1 – 2 MK commonly deduced from observations in open magnetic structures. The 2.5D MHD and multi-fluid models show that Alfvén wave spectrum in the MHD frequency range (millihertz) accelerates the fast solar wind to the observed speed of 800 km s–1 and provides the necessary energy to heat the solar wind. The advantage of the WKB approximation is that it allows incorporating the effects of Alfvén wave heating and acceleration in global 3D MHD models. However, the models that include fully resolved waves provide more accurate and realistic account of the interaction between the waves and the solar wind plasma than the WKB approximation and the MHD models that use ad-hoc heating function, momentum input, or variation of the polytropic index with distance from the Sun. The main limitations of the wave-driven solar wind MHD models are that the heating is described by Ohmic and viscous dissipation with empirical dissipation coefficients, and the exact kinetic process that underlay the fluid description can only be modeled in detail by kinetic approach.
Multi-fluid models extend beyond MHD by providing insights on the compositional variation of the solar wind plasma, on separate heating processes for electrons, protons, and heavy ions, and on the interactions between the various plasma constituents. The results of multi-fluid models are compared directly with observations of the coronal emission, consisting of ion emission lines, and white light polarized brightness that comes from electron Thompson scattering. These comparisons provide more stringent observational constrains on solar wind models than can be achieved with single fluid MHD, since all modeled particle species must conform to the observed properties (e.g., electron temperature, proton temperature, relative abundance of heavy ions in various magnetic structures, wave signatures in separate fluids, etc.), and the various fluids are coupled through Coulomb and electromagnetic interactions.
The 1D and 2D hybrid models provide the next level of physical modeling, and are reliable tools that have been tested and used for decades to study ion kinetic processes in space plasmas. The reviewed studies concentrate on the resonant dissipation of wave spectrum in the multi-ion solar wind plasma and include the effects of beams. The models show that the high frequency waves in the proton and ion gyrosresonant frequency range can heat the solar wind heavy ions preferentially and anisotropically and produce the anisotropic ion velocity distributions deduced from observations. High-amplitude waves can lead to beam formation, while solar wind expansion can lead to perpendicular cooling of the ions. The hybrid models show that heating can be enhanced further by the instability of super-Alfvénic beams of heavy ions. The reviewed studies show that protons are not heated significantly by these waves due to resonant absorption by heavier ions. Thus, the spectrum of waves that heats and accelerates the solar wind must contain both, low-frequency (non-resonant) and high-frequency Alfvén waves. The hybrid models do not include the kinetics of electrons, and their possible role in solar wind energy balance and the dissipation of low-frequency waves is not modeled beyond the fluid description.
The planned NASA Solar Probe Plus mission and the European Solar Orbiter missions will provide new measurements in the unexplored region of the inner heliosphere. In particular, in-situ measurement of non-Maxwellian features in proton, ion, and electron velocity distributions such as anisotropy and beams, and measurement of magnetic fluctuations spectrum in the acceleration region of the solar wind close to the Sun will provide the necessary information that will improve our understanding of solar wind acceleration and heating. These measurements will provide improved constraints for future theoretical studies and numerical models of solar wind plasma heating and acceleration for all levels of plasma approximations.