Transport Equation of Kappa Distributions in the Heliosphere

In this paper, we develop the transport equation of kappa, the fundamental thermodynamic parameter that labels kappa distributions of particle velocities. Using the recently developed concept of entropy defect, we are able to formulate the transport equation of kappa as a function of a general, positive or negative, rate of entropy change. Then, we derive the particular case of exchanging plasma ions with low-dimensionality, newly born pickup protons, which interact and decrease the entropy of the flow of otherwise kappa-distributed plasma protons. Finally, we apply the transport equation of kappa to the solar wind plasma protons, which leads to the radial profile of kappa values, as well as the evolution of the kappa distributions through the heliosphere. The results show that the solar wind kappa decreases with increasing heliocentric distance, corresponding to plasmas residing in stationary states far from classical thermal equilibrium. Moreover, in the outer heliosphere and the heliosheath, kappa reaches its lowest values and is spread across the far-equilibrium region of 1.5 < κ < 2.5, which coincides with independent observations provided by NASA's Interstellar Boundary Explorer mission.