Simulations of second-order Fermi acceleration of electrons: Solving the injection problem

Abstract

The boosting of electrons from a Maxwellian distribution into a suprathermal power‐law tail has long been recognized as an important bottleneck governing the subsequent acceleration of some of these electrons to relativistic energies. This is the seed or injection problem. I study this boosting process using a test‐particle simulation code, following the full equations of motion of tens of thousands of electrons chosen from a thermal population as they move through general time‐dependent magnetic fields. Inhomogeneities in the magnetic field are provided by finite swarms of moving current loops with Maxwellian velocity distributions and power‐law distributions of loop size and dipole moment strength.Whether bulk heating or boosting occurs is found to depend on the size of the swarm thermal speed compared to the electron thermal speed. When the swarm thermal speed is comparable to the electron thermal speed the entire electron population is heated by encounters with the rapidly moving current loops, approx...