Various highly dynamic processes in the magnetized coronal and interplanetary plasmas can produce major acceleration of charged particles to considerable non-thermal energies. In particular, high energy particles can be produced by shock waves in the heliospheric environment, such as solar energetic particles, the energetic storm particle (ESP) events, related to transient interplanetary shock waves, and those associated with the shocks bounding corotating interaction regions (CIRs), produced by the interaction between fast and slow solar wind streams. The kinetic energy spectra of several energetic particles enhancements at interplanetary shocks have been investigated through the Shannon’s differential entropy, as proposed by [1]. Data from LET and HET instruments onboard the STEREO spacecraft were used to cover a wide energy range from ~ 4 MeV to 100 MeV, as well as EPAM data, on board the ACE spacecraft, respectively, in the lower energy range 0.047 – 4.75 MeV. The spectral features were found to be consistent with the Weibull like shape. Moreover, we show that the Weibull spectrum can be theoretically derived as the asymptotic steady state solution of the diffusion loss equation by assuming anomalous diffusion for particle velocity. The evaluation of Weibull’s parameters obtained from particle observations and the power spectral density of the turbulent fluctuations in the shock region, support this scenario and suggest that stochastic acceleration can contribute significantly to the acceleration of high energetic particles at collisionless shock waves.

[1] Laurenza M., Consolini G., Storini M. and Damiani A., Astrophysics and Space Sciences Transactions, 8, 19–24, 2012.