Particle acceleration and coronal mass ejection driven shocks: Shocks of arbitrary strength

There is substantial evidence suggesting that energetic particles observed in “gradual” solar energetic particle events are accelerated at shock waves driven out of the corona by coronal mass ejections (CMEs). We present a model of particle acceleration at interplanetary shock waves, assumed to be driven by CMEs, in which the upstream wave intensity, driven by the accelerated particles, is calculated self‐consistently using the steady‐state solution to the wave growth equation. This then allows for the self‐consistent calculation of the momentum dependent spatial diffusion coefficient which ultimately governs both the acceleration and subsequent evolution of the energetic particles. The model is consequently applicable to shock waves of arbitrary strength, a significant improvement on previous models which were generally only valid for very strong shock waves. The model is able to calculate minimum and maximum particles energies as the shock propagates out into the solar wind and can determine time‐dependent downstream spectra. The spectra of particles escaping into the relatively undisturbed upstream medium is also calculated and in future will be used as input to a detailed transport model to determine upstream spectra and intensity profiles. Although we do not compare the results with any individual observations, the model is able to reproduce some of the observed features of “gradual” SEP events. The self‐consistent calculation of the upstream wave intensity will in future allow this model to be extended to consider the acceleration of particles of various charge states and masses.