Shock acceleration in the solar corona

In this thesis acceleration of energetic particles at collisionless shock waves in space plasmas is studied using numerical simulations, with an emphasis on physical conditions applicable to the solar corona. The thesis consists of four research articles and an introductory part that summarises the main findings reached in the articles and discusses them with respect to theory of diffusive shock acceleration and observations. This thesis gives a brief review of observational properties of solar energetic particles and discusses a few open questions that are currently under active research. For example, in a few large gradual solar energetic particle events the heavy ion abundance ratios and average charge states show characteristics at high energies that are typically associated with flare-accelerated particles, i.e. impulsive events. The role of flare-accelerated particles in these and other gradual events has been discussed a lot in the scientific community, and it has been questioned if and how the observed features can be explained in terms of diffusive shock acceleration at shock waves driven by coronal mass ejections. The most extreme solar energetic particle events are the so-called ground level enhancements where particle receive so high energies that they can penetrate all the way through Earth's atmosphere and increase radiation levels at the surface. It is not known what conditions are required for acceleration into GeV/nuc energies, and the presence of both very fast coronal mass ejections and X-class solar flares makes it difficult to determine what is the role of these two accelerators in ground level enhancements. The theory of diffusive shock acceleration is reviewed and its predictions discussed with respect to the observed particle characteristics. We discuss how shock waves can be modeled and describe in detail the numerical model developed by the author. The main part of this thesis consists of the four scientific articles that are based on results of the numerical shock acceleration model developed by the author. The novel feature of this model is that it can handle complex magnetic geometries which are found, for example, near active regions in the solar corona. We show that, according to our simulations, diffusive shock acceleration can explain the observed variations in abundance ratios and average charge states, provided that suitable seed particles and magnetic geometry are available for the acceleration process in the solar corona. We also derive an injection threshold for diffusive shock acceleration that agrees with our simulation results very well, and which is valid under weakly turbulent conditions. Finally, we show that diffusive shock acceleration can produce GeV/nuc energies under suitable coronal conditions, which include the presence of energetic seed particles, a favourable magnetic geometry, and an enhanced level of ambient turbulence.