Abstract Based on Dulk and Marsh’s approximate theory about nonthermal gyrosynchrotron radiation, one simple impulsive microwave burst with a loop-like structure is selected for radio diagnostics of the coronal magnetic field and column density of non-thermal electrons, which are calculated from the brightness temperature, polarization degree, and spectral index, as well as the turnover frequency, observed by using the Nobeyama Radioheliograph and the Nobeyama Radio Polarimeters, respectively. Very strong variations (up to one or two orders of magnitude) of the calculated transverse and longitudinal magnetic fields with respect to the line-of-sight, as well as the calculated electron column density, appear in the looptop and footpoint sources during the burst. The absolute magnitude and varied range of the transverse magnetic field are evidently larger than those of the longitudinal magnetic field. The time evolution of the transverse magnetic field is always anti-correlated with that of the longitudinal magnetic field, but positively correlated with that of the electron column density. These results strongly support the idea that quantifying the energy released in a flare depends on a reconstruction of the coronal magnetic field, especially for the transverse magnetic field, and they are basically consistent with the recent theoretical and observational studies on the photospheric magnetic field in solar flares.

Keywords Sun: flares — Sun: magnetic fields — Sun: radio radiation

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