The Form of Proton Energy Spectra from Self-Consistent Simulations of the Coronal Shock Acceleration

Abstract:

Acceleration of solar energetic particles (SEPs) is one of the key problems to be tackled by both Solar Probe Plus and Solar Orbiter missions as they will carry out in-situ measurements closer to the Sun than ever before. The data obtained will be used to validate numerical models of the acceleration processes. A suitable approach in this, especially in the case of shock-accelerated SEPs, is Monte Carlo simulations. Being based on consideration of individual particles interacting with the turbulence, Monte Carlo simulation models can provide detailed information on particle and turbulence distributions in the vicinity of the shock. However, the existing Monte Carlo models, relying on the quasi-linear approximation for interactions of particles with Alfvénic turbulence, often use a simplified way (neglect the pitch-angle dependence in the resonance conditions) to model the interactions. Earlier we showed that the effect of retaining the pitch-angle dependence on the Alfvén wave growth is important for self-consistent modeling of the acceleration process and developed a more accurate Monte Carlo treatment. In this presentation, we will mainly focus on the results of our Monte Carlo simulations on energy spectra of particles observed in large gradual SEP events. We have found that often-observed broken power-law spectra can result from stochastic re-acceleration of energetic (shock-accelerated) protons by enhanced Alfvénic turbulence in the shock's downstream region. Specifically, the resulting spectral form (power law or broken power law) is determined by the ratio of the energy density of shock-accelerated protons to the Alfvén wave energy density in the shock’s downstream region. Additionally, we will show results of our recent simulations of the foreshock evolution and compare them with the results obtained with other shock acceleration models. Finally, we will discuss implications of our results for the upcoming Solar Probe Plus and Solar Orbiter missions.