Growing multispacecraft networks are broadening the opportunity of measuring energy spectra of energetic particles at interplanetary shocks over three decades or more in energy at the same distance (different from 1 AU) from the Sun. Energetic particles spectra at interplanetary shocks often exhibit a non-power law shape, even within two energy decades. We have introduced a 1D transport equation accounting for particle acceleration and escape, both allowed at all particle energies. The diffusion is contributed by self-generated turbulence close to the shock and by pre-existing turbulence far upstream. The upstream particle intensity profile steepens within one diffusion length from the shock as compared with diffusive shock acceleration rollover. The spectrum, controlled by macroscopic parameters such as shock compression, speed, far upstream diffusion coefficient and escape time at the shock, can be reduced to a log-parabola, that has been shown to describe the escape in a probabilistic approach. In the case of upstream uniform diffusion coefficient, the customarily used power law/exponential cut off solution is retrieved.
Particle acceleration, particle escape, interplanetary shocks