We present a simple model of anisotropic pickup ion distributions on a
flux tube containing both a radial segment and segments oriented perp
endicular to the radial direction. The flux tube is carried away from
the Sun by a constant speed solar wind. We model the pitch-angle scatt
ering of these ions by a hemispherical approximation, which assumes th
at the scattering is instantaneous except through the pitch angle of 9
0 degrees, where the scattering is finite. The model includes a radial
ly dependent ionization of pickup ions, with the newly created ions co
ncentrated in the sunward hemisphere within the radial segment but dis
tributed equally between the hemispheres in the perpendicular segments
. The pickup ions stream along the magnetic field and decelerate in th
e expanding solar wind, but we assume that the radial segment is short
enough that the effects of adiabatic focusing may be neglected. For w
eak scattering through 90 degrees, the distributions exhibit nonlocal
properties due to ion streaming along the field from regions where con
ditions are different than observed locally. We find that this model c
an yield a depletion of antisunward ions in the radial segment of the
flux tube, such as has been observed, but the streaming of ions into t
he radial region limits the size of this effect unless the radial segm
ent is very long.