Mathematical Modeling of the Formation of Type IIId Solar Decameter Radio Bursts with Echo Components

Using numerical simulation, we investigate the possibility that echo components of type IIId solar decameter bursts can be produced through refraction of radio emission in a coronal plasma with large-scale regular electron density inhomogeneities. It is shown that the observed time profiles of radio burst intensity with three or four maxima can be related to the presence in the middle corona of streamers and a localized regular nonuniformity whose electron density exceeds background electron density by a factor of more than 3 – 4. The nonuniformity scale in this case is comparable with the optical diameter of the solar disk. The observed radio burst echo components with delays longer than 3 s are explained by the production of additional radio emission propagation modes within a “transverse" refraction waveguide arising between the localized electron density nonuniformity and deeper layers in the corona. As these additional modes are reflected from the streamers, they can reach the Earth. Calculations of the time profile of radio burst intensity take into consideration the influence of scattering by turbulent coronal inhomogeneities and of collisional absorption. Comparison of the modeling results with the observational data shows that the calculated values of some profile parameters differ from the observed values. One of the possible reasons is that the method used does not take into account the diffraction leakage of radio emission through the large-scale nonuniformity.