Formation of power-law electron spectra in collapsing magnetic traps

The energy distribution of the fast electrons captured into a collapsing magnetic trap in the solar corona is calculated as a function of the trap length and diameter. It is shown that if the electrons injected into the trap have a power-law spectrum, then their spectrum remains a power-law one with the same slope throughout the acceleration process for both the Fermi and betatron acceleration mechanisms. For electrons with a thermal injection spectrum, the model predicts two types of hard X-ray sources, thermal and nonthermal. Thermal sources are formed in traps dominated by the betatron mechanism. Nonthermal sources with a power-law spectrum are formed when electrons are accelerated by the Fermi mechanism.