A theoretical perspective on particle acceleration by interplanetary shocks and the Solar Energetic Particle problem

Abstract Understanding the physics of Solar Energetic Particle (SEP) events is of importance to the general question of particle energization throughout the cosmos as well as playing a role in the technologically critical impact of space weather on society. The largest, and often most damaging, events are the so-called gradual SEP events, generally associated with shock waves driven by coronal mass ejections (CMEs). We review the current state of knowledge about particle acceleration at evolving interplanetary shocks with application to SEP events that occur in the inner heliosphere. Starting with a brief outline of recent theoretical progress in the field, we focus on current observational evidence that challenges conventional models of SEP events, including complex particle energy spectra, the blurring of the distinction between gradual and impulsive events, and the difference inherent in particle acceleration at quasi-parallel and quasi-perpendicular shocks. We also review the important problem of the seed particle population and its injection into particle acceleration at a shock. We begin by discussing the properties and characteristics of non-relativistic interplanetary shocks, from their formation close to the Sun to subsequent evolution through the inner heliosphere. The association of gradual SEP events with shocks is discussed. Several approaches to the energization of particles have been proposed, including shock drift acceleration, diffusive shock acceleration (DSA), acceleration by large-scale compression regions, acceleration by random velocity fluctuations (sometimes known as the “pump mechanism”), and others. We review these various mechanisms briefly and focus on the DSA mechanism. Much of our emphasis will be on our current understanding of the parallel and perpendicular diffusion coefficients for energetic particles and models of plasma turbulence in the vicinity of the shock. Because of its importance both to the DSA mechanism itself and to the particle composition of SEP events, we address in some detail the injection problem. Although steady-state models can improve our understanding of the diffusive shock acceleration mechanism, SEP events are inherently time-dependent. We therefore review the time-dependent theory of DSA in some detail, including estimating possible maximum particle energies and particle escape from the shock complex. We also discuss generalizations of the diffusive transport approach to modeling particle acceleration by considering a more general description based on the focused transport equation. The escape of accelerated particles from the shock requires that their subsequent transport in the interplanetary medium be modeled and the consequence of interplanetary transport can lead to the complex spectra and compositional profiles that are observed frequently. The different approaches to particle transport in the inner heliosphere are reviewed. The various numerical models that have been developed to solve the gradual SEP problem are reviewed. Explicit comparisons of modeling results with observations of large SEP events are discussed. A summary of current progress and the outlook on the SEP problem and remaining open questions conclude the review.