Energetic Particle Acceleration in the Heliosphere

There has been a remarkable discovery in the heliosphere. Ions accelerated in disparate plasma conditions - the quiet solar wind, disturbed conditions downstream from shocks, and throughout the heliosheath - all have the same spectrum, a power law with spectral index of -5 when expressed as a distribution function. An acceleration mechanism has been developed that can account for these observations, a pump mechanism, in which particles are pumped out of a core distribution through a series of compressions and expansions. The derivation of the governing equation of the pump mechanism and some important subtleties in the derivation are discussed.