The energetic-electron spectra and hard X-ray radiation of solar flares

The formation of the fast-electron (> 10 keV) spectrum and the whistler tur bulence spectrum in a solar coronal trap is investigated using a quasi-line ar approach. Whistlers exert the dominant influence on the evolution of fas t electrons in coronal loops in which the magnetic field is < 200 G and the plasma density is less than or equal to 10(11) cm(-3), As a consequence of volume Landau damping of whistlers in flare loops, regimes not only of str ong, but also of weak and moderate pitch-angle diffusion of electrons are r ealized. The characteristic energy density of whistlers in coronal arches i s determined. The relation between the flux densities and hard X-ray spectr a at the bases and peaks of flares loops are derived. The time delay of the hard X-ray emission is determined not by the diffusion time, but by the ch aracteristic lifetime of trapped electrons; this can be used to estimate th e turbulence spectrum of whistlers (E-k(2) proportional to k(4)) and the sp ectrum of the source of fast electrons (S proportional to E-4).