Formation of shock‐spike events at quasi‐perpendicular shocks

<jats:p>This paper is an analysis of how shock‐spike particle events are formed by single‐encounter “shock‐drift” acceleration at quasi‐perpendicular fast‐mode interplanetary shocks. A set of time‐reversed equations, valid in the upstream or downstream solar wind frames, express a particle's initial or pre‐shock‐interaction kinetic energy and pitch angle as functions of its final or post‐shock‐interaction kinetic energy and pitch angle. These equations and particular forms of the initial or ambient energy spectrum and angular distribution yield model‐predicted intensity enhancements, energy spectra, and pitch angle distributions for comparison with spacecraft observations. It is shown that the final energy spectrum can be harder than, softer than, or equal to the ambient spectrum, depending upon, for example, the point along the final spectrum one chooses to examine, whether one looks at the upstream of downstream spectrum, and how rapidly the ambient spectrum decreases with increasing energy. It is shown that for a given form of the ambient energy spectrum, an upstream ambient angular distribution peaked toward (away from) the shock along the magnetic field yields a final energy spectrum that is harder (softer) in both the upstream and downstream regions than the spectrum produced for an isotropic ambient distribution. The single‐encounter scheme is shown to account for many features observed in the short‐lived, impulsive shock‐spike events. In particular, the existence of the high‐intensity spike in close temporal association (of the order of minutes) with the shock passage is consistent with a kinematical accumulation of particles accelerated and transmitted downstream of the shock. The single‐encounter acceleration process is also consistent with some features of energetic storm particle events observed at radial distances of 14–22 AU from the sun.</jats:p>