We consider an ion transport equation describing the source, convection, adiabatic acceleration, and quasi-linear velocity diffusion of cometary pickup ions. The equation is solved numerically along solar wind plasma flow lines for the environment of comet Halley, to obtain distributions at positions on the Giotto spacecraft trajectory which may be compared with observations. We use realistic input models for the observed spectrum of upstream and downstream propagating wave turbulence and for the ion source and mass loading of the solar wind. The ion resonance condition is not approximated in the diffusion term and we obtain full two-dimensional (ptich angle and velocity) numerical distributions which show pitch angle scattering about the wave scattering centers at ¿VA where VA is the Alfv¿n wave speed in the solar wind frame. Peak ion phase-space densities approximately follow the bispherical shell geometry. The energy distributions F(v) agree well with Giotto observations at lower v but in the high-energy tail there is evidence possibly for the first-order Fermi acceleration mechanism taking place in the comet Halley foreshock region. ¿ American Geophysical Union 1992