This paper deals with the acceleration of low-energy ions at collisionless shocks in which the average upstream magnetic field is perpendicular to the direction of shock propagation. Here we address the issue of whether these shocks can efficiently accelerate low-energy particles by performing test-particle orbit integrations using synthesized turbulent magnetic fields. We focus on two distinctly different magnetic-field-fluctuations spectra: one in which field-line random walk dominates and one in which it is negligible. We suggest that simple scattering off of convecting magnetic field fluctuations cannot readily account for the acceleration of non-accelerated interstellar pickup ions, that are presumably the source of anomalous cosmic rays, by the solar-wind termination shock.

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