This dissertation describes a study of particle acceleration at shocks via the diffusive shock acceleration mechanism. Results for particle acceleration at both quasi-parallel and quasi-perpendicular shocks are presented to address the question of whether there are sufficient particles in the solar wind thermal core, modeled as either a Maxwellian or kappa- distribution, to account for the observed accelerated spectrum. Results of accelerating the theoretical upstream distribution are compared to energetic observations at 1 AU. It is shown that the particle distribution in the solar wind thermal core is sufficient to explain the accelerated particle spectrum downstream of the shock, although the shape of the downstream distribution in some cases does not follow completely the theory of diffusive shock acceleration, indicating possible additional processes at work in the shock for these cases. Results show good to excellent agreement between the theoretical and observed spectral index for one third to one half of both quasi-parallel and quasi-perpendicular shocks studied herein. Coronal mass ejections occurring during periods of high solar activity surrounding solar maximum can produce shocks in excess of 3-8 shocks per day. During solar minimum, diffusive shock acceleration at shocks can generally be understood on the basis of single independent shocks and no other shock necessarily influences the diffusive shock acceleration mechanism. In this sense, diffusive shock acceleration during solar minimum may be regarded as Markovian. By contrast, diffusive shock acceleration of particles at periods of high solar activity (e.g. solar maximum) see frequent, closely spaced shocks that include the effects of particle acceleration at preceding and following shocks. Therefore, diffusive shock acceleration of particles at solar maximum cannot be modeled on the basis of diffusive shock acceleration as a single, independent shock and the process is essentially non-Markovian. A multiple shock model is developed based in part on the box model of (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al. 1999) that accelerates particles at multiple shocks and decompresses the particles between shocks via two methods. The first method of decompression is based on the that used by Melrose and Pope (1993), which adiabatically decompresses particles between shocks. The second method solves the cosmic ray transport equation and adiabatically decompresses between shocks and includes the loss of particles through convection and diffusion. The transport method allows for the inclusion of a temporal variability and thus allows for a more representative frequency distribution of shocks. The transport method of decompression and loss is used to accelerate particles at seventy-three shocks in a thirty day time period. Comparisons with observations taken at 1 AU during the same time period are encouraging as the model is able to reproduce the observed amplitude of the accelerated particles and in part the variability. This work provides the basis for developing more sophisticated models that can be applied to a suite of observations.
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