A simple model for the formation of 'reflected', 'intermediate', and 'diffuse' ion distributions upstream of earth's bow shock

Detailed energetic ion and low-frequency wave experiments on ISEE 1, 2, and 3, have established correlations between the types of ion populations and waves observed to exist in the earth's foreshock region. The present calculation has the objective to quantitatively test the picture obtained for the earth's foreshock region. An analysis is conducted of the coupled spatial and temporal evolution of upstream protons and hydromagnetic waves by means of a simple model in which the protons are represented by counterstreaming beams which resonate with hydromagnetic waves, exciting the outward propagating modes and damping the inward propagating modes at a single wave number.