Plasma radiation of power-law electrons in magnetic loops: application to solar decimeter-wave continua

It is shown that flare-produced fast electrons with a power-law energy distribution trapped in magnetic loops are capable to produce plasma waves at the upper hybrid frequency due to a loss-cone instability. Conditions for instability are obtained in dependence of the parameters of the power-law distribution and the magnetic-loop parameters. The growth rate of the plasma waves has been calculated and their energy density has been estimated in the frame of quasi-linear saturation. This instability has been considered as the cause of the solar decimetric continuum which exhibits a strong temporal and spatial correlation with regions of flare-energy release and sources of microwave bursts. The strong absorption of the first harmonic in the decimeter range and also the peculiarities of the conversion of the plasma waves into electromagnetic waves yield a preference of the generation of the decimetric continuum at the second harmonic of the plasma frequency. In this case the polarization of the radiation corresponds to the ordinary wave mode in a wide cone of propagation angles around the direction perpendicular to the magnetic field.