Authors: Silvina E. Guidoni, (American University / NASA GSFC), Judith T. Karpen (NASA GSFC), C. Richard DeVore (NASA GSFC)

Spectral single and double power laws are common in high-energy phenomena such as solar flares and solar energetic particles, including ground level enhancement events. It is not clear what physical processes determine the energy breaks and spectral indexes of these power laws. Here, we describe a first-principles model of pitch-angle and energy distribution-function evolution, which produces power laws and provides a physical interpretation for such spectral features (Guidoni et al. 2022, ApJ). In this model, a prescribed fraction of particles sequentially “hops” between shrinking flux ropes (accelerators) formed by flare reconnection. Each accelerator increases particle energies by a modest amount, but particles must visit only a few accelerators to increase their energies by orders of magnitude. The energy gain in each accelerator is derived using data from global magnetohydrodynamic simulations of an eruptive flare/coronal mass ejection as ambient conditions for the evolving particle distributions. We also describe our fully analytic method for forming and interpreting power laws, which requires only two constrained physical parameters of the acceleration region and is independent of the acceleration model, as well as preliminary results extending the analytical model to the formation of double power laws.