Proton acceleration in long duration flares

Abstract

The acceleration and trapping of protons necessary to explain long duration, high energy, gamma-ray solar flares is modeled as a single process within a coronal loop, where an injected proton spectrum is transported and accelerated by MHD turbulence. The loop is modeled as a leaky box where second-order Fermi-acceleration is a result of the turbulence. Protons accelerated in the coronal loop escape from the ends of the loop (precipitation) into the chromosphere or lower corona where they produce gamma-ray emission. The model provides a method for computing the proton spectrum as it evolves from an initial power law under coupled spatial and momentum diffusion. With reasonable coronal parameters the model yields time-extended relativistic proton precipitation, which peaks up to several hundred seconds after injection. Momentum diffusion is inversely proportional to spatial diffusion for an assumed Alfvén wave field within the coronal loop. Assuming a magnetic field on the order of 100 G, δB/B need only be a few percent if the loop is 10⁵ km in length in order to describe the temporal behavior of the high-energy gamma-ray flare of 3 June 1982.