Solar microwave bursts and injection pitch-angle distribution of flare electrons

We calculate the time variation of the energy and pitch angle of high-energy electrons injected into a magnetic loop and subsequently trapped there because of magnetic mirroring. We use the evolving distribution in the calculation of gyrosynchrotron emission, as an aid to interpretation of a particular microwave burst observed using the Owens Valley Solar Array (OVSA) during a GOES class C2.8 flare on 1993 June 3. The electrons are assumed to have a Gaussian pitch-angle distribution, whose width and mean pitch angle are calculated as they evolve in time, taking into account the electron energy loss and a specific magnetic loop structure set as a model for the target active region. Various temporal behaviors of the microwave spectrum are found as a function of injection and trap conditions, which can be used to infer some of the injection properties directly from the observed microwave spectra. As a main result we found that initial pitch-angle distribution plays an important role in the microwave spectral evolution. This is largely due to the fact that pitch-angle diffusion of electrons under Coulomb collisions markedly differs at those electron energies to which the microwave spectrum is sensitive. This effect cannot be reproduced by adjusting the trap properties and therefore could be used to determine whether the initial pitch-angle distribution is isotropic or narrowly beamed. The microwave burst spectra observed during the 1993 June 3 flare are found to be most consistent with the hypothesis of an initially narrow beamed injection (≤30°) into a low-density (∼4 × 10⁹ cm^-3) magnetic trap. This result explains the observed asymmetric microwave time curve consisting of a relatively short rise (∼32 s) and a long decay (≥5 minutes) in terms of a transport effect rather than acceleration characteristics. The physical connection of the proposed microwave model to hard X-ray models in thin/thick targets is briefly discussed.