Ion acceleration in connection with a modulated solar wind termination shock: phase space propagation and complete energy spectra

Using the general kinetic transport equation for cosmic ray particles the e nergization of heliospheric pick-up ions (PUI's) to Anomalous Cosmic Ray pa rticles (ACR's) by means of non-linear wave-particle interactions is descri bed. After creation of PUI's with initial energies of 1 keV/nuc they underg o phase space diffusion by Fermi-l and Fermi-2 scattering processes in the heliosphere and at the termination shook and eventually appear as ACR's in the 10 MeV/nuc energy regime for which spatial diffusion becomes important. We present ion energy spectra derived from a fully consistent theoretical context and covering the range from 1 keV/nuc to 100 MeV/nuc. Our solutions of the kinetic transport equation reflect the effect of simultaneous opera tions of convective and diffusive transport processes in heliospheric phase space. As demonstrated in our calculations the kick-up from pick-up's to A CR's in our approach completely works on known physical grounds with no nee d to prescribe a specific injection of seed ACR's at the shock. The spectra resulting near the termination shock are far from being pure power-laws as is expected in classical shock acceleration theories. Thus the idea to sta rt from measured VOYAGER ACR spectra and to apply a necessary demodulation up to a pure power-law cannot be used to find the shock location.