Particle acceleration at CME driven shock waves

A dynamical time-dependent model of particle acceleration at coronal mass ejection (CME) driven shock waves is presented. We consider first a one-dimensional model applicable to shock waves of arbitrary strength. The model includes the determination of the particle's injection energy, the maximum energy of particles accelerated at the shock, energetic particle spectra at all spatial and temporal locations, and the dynamical distribution of particles that are trapped in the post shock flow and those that escape upstream and downstream of the evolving shock complex. We then consider the extension of this model to two dimensions. The 2-dimensional model computes the variation of the shock strength both temporally and spatially and illustrates how this effects the evolution of the energetic particle spectra and intensities.