Particle spectra at a CME‐driven shock often exhibit a power law to certain energies, then roll over exponentially beyond. However, there are cases where a spectrum evolves to another power law above a certain energy (e.g. the Oct. 29th, 2003 event). Here we introduce an effective “loss term” into the particle transport equation and study the consequent particle spectra behavior at a CME‐driven shock. The loss term represents the effect of particle leaking out from a finite shock and is related to the turbulence power at and near the shock. We show that the shape of particle spectra are tightly related to the form of upstream turbulence. Under certain circumstances, broken power‐law spectrum can be obtained. The physical meaning of the “loss term” and its relationship to the upstream turbulence is discussed.

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