Proton transport through self-generated waves in impulsive flares

Energetic proton transport through self-generated Alfven waves in impulsive (gamma -ray) flares is studied using the method of Monte Carlo simulations . Protons are traced inside a flux tube after they are released from a poin t source located inside the loop until they hit the boundary of the 1-D sim ulation box and escape. As they stream from the source towards the boundari es, the particles generate Alfven waves through the streaming instability. We consider both open and closed field lines. In the closed field line case , the escaping particles precipitate and produce observable secondary emiss ions; for the open field line, particles precipitate only from one end of t he field line, and escape freely to the interplanetary medium from the othe r end. For a sufficiently large number of accelerated protons per unit area , >> n(0)V(A)/Omega (p) where n(0) is the plasma density, V-A the Alfven sp eed, and Omega (p) the proton gyro-frequency, the particle flux from the so urce produces a turbulent trap that expands at Alfven speed in both directi ons from the source. The resulting gamma -ray emission from the loop legs c onsists of a precursor, related to the quick propagation of particles when the trap has not formed yet, and of a delayed brightening in the loop leg c loser to the source, related to the opening of the turbulent trap as the se lf-generated waves reach the solar surface. For impulsive injections lastin g << L=(2V(A)), where L is the loop length, the second emission may be supp ressed by adiabatic deceleration in the expanding turbulent trap. For open field lines, our model is capable of producing the small ratio of the numbe rs of interplanetary-to-interacting protons typically observed in impulsive flares, if the proton source is located close to the Sun.