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Up until the recent past, it was generally believed that the solarwind termination shock (TS) is the favourite site to accelerateions from the keV- to the MeV- energy levels by means of Fermi-1processes. When Voyager 1 was crossing the TS at the end of 2004,the registrations of this spacecraft showed, however, that beyondthe shock passage fluxes of anomalous cosmic rays kept increasingwith time. This obviously called for an acceleration site furtherdownstream of the shock in the heliosheath which had not beenidentified before. In this paper we thus investigate the processof energy diffusion due to wave-particle interactions (Fermi-2)operating on pick-up ions which are convected downstream of the TSwith the subsonic solar wind. We investigate the continuous effectof stochastic acceleration processes suffered by pick-up ions attheir interaction with heliosheath turbulences, while they areslowly convected with the subsonic solar wind towards theheliotail. As we can show, the inner heliosheath region, with anextent of about 100 AU around the solar wind stagnation point, isspecifically favourable for the energy processing of pick-up ionsby Fermi-2 processes up to MeV energies. In addition, we claim thatthis region is the origin of multiply-charged anomalous cosmic rayparticles that have been registered in recent times

Unexpected sites of efficient stochastic acceleration in the inner heliosheath