Though pick-up ions ( PUIs ) are a well known phenomenon in the inner heliosphere , their phase-space distribution nevertheless is a theoretically unsettled problem .
Especially the question of how pick-up ions form their suprathermal tails , extending to far above their injection energies , still now is unsatistactorily answered .
Though Fermi-2 velocity diffusion theories have revealed that such tails are populated , they nevertheless show that resulting population densities are much less than seen in observations showing power-laws with a velocity index of “ -5 ” .
We first investigate here , whether or not observationally suggested power-laws can be the result of a quasi-equilibrium state between suprathermal ions and magnetohydrodynamic turbulences in energy exchange with eachother .
We demonstrate that such an equilibrium can not be established , since it would require too high pick-up ion pressures enforcing a shock-free deceleration of the solar wind .
We furthermore show that Fermi-2 type energy diffusion in the outer heliosphere is too inefficient to determine the shape of the distribution function there .
As we can show , however , power-laws beyond the injection threshold can be established , if the injection takes place at higher energies of the order of 100 keV .
As we demonstrate here , such an injection is connected with modulated anomalous cosmic ray ( ACR ) particles at the lower end of their spectrum when they again start being convected outwards with the solar wind .
Therefore , we refer to these particles as ACR-PUIs .
In our quantitative calculation of the pick-up ion spectrum resulting under such conditions we in fact find again power-laws , however with a velocity power index of “ -4 ” and fairly distance-independent spectral intensities .
As it seems these facts are observationally well supported by VOYAGER measurements in the lowest energy channels .