Acceleration and heating processes in a collapsing magnetic trap

We study the acceleration processes in a collapsing magnetic trap formed in the cusp structure of the flare model, using a test-particle numerical method. Coulomb collisions and scattering are included. It was found that if the trap collapse is sufficiently fast and the energies of the injected electrons are sufficiently high, thus overcoming the collisional losses, electrons can be accelerated in this secondary acceleration process to very high energies depending on the initial magnetic trap ratio R = B-max/B-init. The computations, made for R = 10 and R = 100 with isotropically injected 5-28.4 keV electrons and a background plasma density of about n(e) = 10(10) cm(-3), show that the high-energy electrons are accumulated in the central part of the collapsing magnetic trap where their velocities are nearly perpendicular to the magnetic field. This effect gives us a new possibility to explain the formation of loop-top sources observed in hard X-ray and radio emission. A further interesting aspect is that these electrons later on escape from this collapsing trap because its trap ratio decreases to R --> 1. The time evolution of the energy of the trapped electrons and their energy flux at the end points of the trap (footpoints) are computed for cases without and with collisions. The effect of collisions on the energy spectrum of the accelerated electrons is also shown. The X-ray spectra along the collapsing trap are evaluated. Finally, we suggest a test of this model considering radio waves in the decimetric frequency range.