This thesis makes two contributions to the solar literature. The first is the development and application of a formal statistical framework for describing short-term (daily) variation in the level of magnetic activity on the Sun. Modelling changes on this time-scale is important because rapid developments of magnetic structures on the sun have important consequences for the space weather experienced on Earth (Committee On The Societal & Economic Impacts Of Severe Space Weather Events, 2008). The second concerns how energetic particles released from the Sun travel through the solar wind. The contribution from this thesis is to resolve a mathematical discrepancy in theoretical models for the transport of charged particles.