The Diffusion Mean Free Path Upstream of Earth's Quasi-Parallel Bow Shock

We have analyzed a number of diffuse upstream particle events observed by Cluster when the spacecraft separation was between 1 and 1.5 Earth radii. The spatial gradient of the partial ion densities parallel to the magnetic field has been determined in several energy bands as a function of distance from the bow shock. For the events investigated the e-folding distance increases with decreasing solar wind speed. Assuming that upstream diffusion is balanced by downstream convection we can determine the spatial diffusion mean free path as a function of energy. Since the mean free path is proportional to the e-folding distance and proportional to the solar wind speed the mean free path is approximately independent of solar wind velocity.