Comparison of the energy spectra between single shock and converging double-shock

Observations show that there are proton spectral ``breaks'' with energy $E_{\rm br}$ at 1-10MeV in some large solar energetic particle (SEP) events. Generally, single CME-driven shock applying diffusive acceleration mechanism would just predict a single power-law energy spectrum. This work discusses the difference of the energy spectra between a single shock and the converging double-shock. We apply a single shock and a converging double-shock models to the 2006 Dec 13 SEP event using particle simulation method, respectively. As results, we find that a single shock model just produce an energy spectrum with a single-power law, but a double converging-shock model can produce a ``broken'' energy spectrum splitting to double power-law, which is consistent with the observed energy spectrum by spacecraft.