A study of the transport of pick-up ions throughout the heliosphere is
presented. First, the basic features of the pick-up ion velocity dist
ributions and their evolution under the influence of either the second
-order Fermi process or transit-time damping as mechanisms for momentu
m diffusion are studied. Second, the distributions are computed for va
rious regions of the heliosphere and the two types of momentum diffusi
on are compared with respect to their efficiency to form tails of the
distributions towards higher energies. Third, it is assumed that both
processes are operating simultaneously. For all cases, implications fo
r the acceleration efficiency of anomalous cosmic rays across the sola
r wind termination shock surface are discussed. The distributions are
obtained as solutions of a transport equation including, in addition t
o momentum diffusion, terms to describe the convection and adiabatic c
ooling of pick-up ions in the expanding solar wind plasma as well as,
in difference to earlier work, a source function based on a realistic
model of the distribution of neutral particles within the heliosphere.