Charge Exchange Losses and Stochastic Acceleration in the Solar Wind
  Stochastic acceleration of particles under a pressure balance condition can accommodate the universal $p^{-5}$ spectra observed under many different conditions in the inner heliosphere. In this model, in order to avoid an infinite build up of particle pressure, a relationship between the momentum diffusion of particles and the adiabatic deceleration in the solar wind must exist. This constrains both the spatial and momentum diffusion coefficients and results in the $p^{-5}$ spectrum in the presence of adiabatic losses in the solar wind. However, this theory cannot explain the presence of such spectra beyond the termination shock, where adiabatic deceleration is negligible. To explain this apparent discrepancy, we include the effect of charge exchange losses, resulting in new forms of both the spatial and momentum diffusion coefficients that have not previously been considered. Assuming that the turbulence is of a large-scale compressible nature, we find that a balance between momentum diffusion and losses can still readily lead to the creation of $p^{-5}$ suprathermal tails, including those found in the outer heliosphere. 
Ciaran Kenny, Peter Duffy
astro-ph.HE