Thermodynamic Constraints on Solar Wind Radial Profiles

In this paper, we use thermodynamics to develop the radial density profile of the solar wind, which is described by kappa distributions. First, we show the connection of kappa distributions with polytropic processes, emphasizing the two “paths”—i.e., a kappa distribution of particle energies designates a polytropic relationship among the plasma moments, and, conversely, a polytropic relationship among plasma moments designates a kappa distribution of particle energies. We consider a radially dependent bulk speed and the various Hamiltonian terms for the solar wind. This generalizes earlier approaches that allowed for only a simple radially dependent potential energy and a constant bulk speed. Then, we study the profiles of density and other thermodynamic parameters and show how these can be used to determine unmeasured or missing solar wind parameters. As a proof of concept, an example analysis is performed to determine the magnetic field magnitude from observations of the plasma moments and validated with Voyager observations.