The Fermi mechanism for the acceleration of ions to energies of hundreds of keV at the Earth's bow shock is generally accepted, but the origin of the necessary suprathermal seed particle population is not known. The two current hypotheses are leakage from the magnetosheath, and acceleration directly out of the solar wind at the shock surface. Observations of 3D ion distributions close to the shock are presented from the 3D Plasma and Energetic Particle experiment on the WIND spacecraft. A model is developed to trace the trajectories of these particles back to the shock using plasma and magnetic field observations to reconstruct the shock geometry and magnetic turbulence encountered by the particle.; We use this model to interpret the observations. We follow the trajectories of ions in the observed distribution just downstream of the shock, and show that the phase space density that leaks through the shock is too low to explain the observed upstream ions.; We then use the model to predict the evolution of observed solar wind ion distributions as they encounter the shock. The model predicts a fraction of the solar wind will reflect off the shock. We find that turbulence increases the fraction that reflects, and the predicted reflecting phase space density agrees with the observed upstream distribution. The simulations correctly predict the velocity and pitch angle of the observed upstream ions, and also the evolution of gyrophase with time. A comparison between the simulations and observations shows that the reflected ions have a broader distribution in gyrophase than predicted. We show that this is not due to interactions with the upstream medium, and present an argument that it is caused by local variations in the shock normal direction caused by magnetic turbulence convecting into the shock.; The model also predicts that, under certain conditions, ions can undergo multiple encounters with the shock, gaining energy as they grad-B drift in the convective electric field. We present observations in agreement with these predictions, showing that ions can be accelerated up to at least {dollar}sim{dollar}7 keV at the shock surface, directly out of the solar wind.
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