Solar wind bulk velocity fluctuations acting as velocity space diffusion on comoving ions

From most in-situ plasma observations made in the outer heliosphere it became evident that above the injection border of pick-up ions (≃1 keV), an extended suprathermal ion tail is found which in most cases can be fitted by a power law with velocity power indices of (−6) ≤ γv ≤ (−4). As has been shown by theory such energetic ion tails cannot be explained by Fermi-2 type velocity diffusion, since in the outer heliosphere both Alfvenic and magnetoacoustic turbulences become too weak. Here we come to a new solution of this unsolved problem by studying the action of solar wind bulk velocity fluctuations on ions co-moving with the wind. As we show the passage of such fluctuations results in energization of each individual ion and systematic evolution of the ion distribution function towards suprathermal tails. From the basic knowledge that we can obtain on this process we can calculate the velocity divergence of the ion phasespace flow and thus can derive a velocity diffusion operator. As we can show here this operator leads to a velocity diffusion coefficient proportional to the square of the ion velocity and, when employed in the phasespace transport equation, together with terms for convective changes, cooling processes and pick-up ion injection, interestingly enough, permits to find solutions for suprathermal power law tails with power indices of γv ≃ −5 as very often observed