Compression acceleration in astrophysical plasmas and the production of f(v) ∞ v ^-5 spectra in the heliosphere

We present a new derivation of the acceleration of fast charged particles by random compressions and expansions based on a quasilinear approximation applied to the Parker transport equation, and explore its consequences. This process has been suggested in a recent series of papers by Fisk & Gloeckler (F&G) as the origin of the quiet-time suprathermal ion population observed throughout the inner heliosphere with an omnidirectional distribution function close to the form f(v)∞ v ^-5. Our derivation does not agree with a recent equation derived by F&G. We show that, while our equation conserves particles, the F&G equation does not. Solutions of the correct quasilinear equation are presented, which show that the compressive acceleration process does not produce power-law velocity spectra with indices less than (i.e., softer than) -3. We show that the transport equations for two other types of stochastic acceleration, by a spectrum of Alfvén waves and by transit-time damping of oblique magnetosonic waves, yield comparable acceleration rates but also do not produce power-law spectra with indices less than -3. Conversely, the process of diffusive shock acceleration, responsible for energetic storm particle events, corotating ion events and probably most large solar energetic particle (SEP) events, readily produces power-law velocity spectra with indices in a range including -5. It is suggested that the quiet-time suprathermal ion population is composed predominantly of remnant ions from these events as well as a contribution from impulsive SEP events.