Acceleration of low-energy ions in the quiet-time solar wind and at the termination shock

At the location where Voyager I crossed the Termination Shock (TS) only low-energy (40 - similar to 2000 keV/nuc) particles were accelerated but not the higher energy Anomalous Cosmic Rays (ACRs). Immediately upstream of the TS and, most remarkably, in the entire inner heliosheath traversed by Voyager I during more than a year, the spectral index of the particle velocity distribution functions was observed to be a power law with spectral index -5. Such unvarying spectral indices over such a long time period are not easily explained using diffusive shock acceleration, a theory that is also not valid given the pervasive, highly anisotropic beams that dominate the region upstream of the shock. Power law spectra with index -5 are not only observed in the inner heliosheath but also throughout the heliosphere in all regions explored so far. These ubiquitous suprathermal, f proportional to nu(-5) power law tails extend to more than a few MeV during quiet times. The tail strength increases and the roll-over energy decreases with increasing level of turbulence. We argue that power law spectra with the unique spectral index of -5 are expected if the tails are formed by stochastic acceleration due to random compressions and expansions generated in part by variations in the pressure of the suprathermal (several keV/nucleon) particles, and a cascade in energy, analogous to turbulent Kolmogorov cascades. Furthermore, we argue that the -5 spectral shapes of the low-energy pickup ions observed at the Termination Shock, both upstream and downstream, require that the pressure of the these tail particles is behaving like that of a simple ideal gas, without heat flux, and that the intensity increase across the Termination Shock can be determined by assuming that the pressure of the accelerated particles behaves according to the Rankine-Hugoniot relationship.