Abstract
The theory of shock acceleration is first reviewed briefly including a discussion of the basic diffusive transport equation and a list of its successes in accounting for many energetic particle populations throughout the heliosphere, in particular many energetic storm particle (ESP) events. The difficulties in applying the theory to the acceleration of solar energetic particles (SEPs) in gradual events at a CME-driven shock wave are then enumerated: complex temporal and spatial dependence, sensitivity of the predictions to the values of the transport coefficients, unknown injection rates, the importance of nearly scatter-free propagation in interplanetary space, and competing adiabatic deceleration in the solar wind. Nevertheless, a CME-driven shock is the most promising origin for the gradual ion events. It is shown that finite shock lifetime, while providing an energy cutoff of ∼ 1 MeV/nucleon at the orbit of Earth (consistent with ESP events), may actually allow the acceleration of ions to ∼ 100 MeV/nucleon when the shock is at ∼ 20 solar radii. The shock origin also accounts for the observed elemental and charge-state composition of gradual events, and the global scale of their origin near the Sun.
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