Evolution of kappa distributions under velocity space diffusion: A model for the observed relationship between their spectral parameters

Velocity space diffusion acting on superthermal ions whose distributions resemble kappa functions (Maxwellian core with a power law tail) will cause the distributions to evolve so that the high-energy spectral index kappa is linearly related to core temperature with a constant of proportionality that (1) scales inversely with the distribution's characteristic energy, (2) is independent of the diffusion coefficient, and (3) has a positive intercept. This type of behavior has been observed in five different studies covering the magnetospheres of Earth, Jupiter, and Saturn as well as the solar wind. These results indicate the following: (1) velocity space diffusion frequently plays the dominant role in shaping particle distribution functions in many diverse space plasma environments and (2) hotter distributions with steeper spectral indices are "older" distributions in that they have evolved considerably from the source distribution.