Relation between the Spatial Distribution and Spectral Index of Superthermal Electron Distribution in Solar cm-Radio Sources

A series of solar cm-radio bursts are analyzed by a new inverse method estimating spatial changes of the superthermal electron distribution in solar cm-radio burst sources. It is found that the measure of the spatial change of superthermal electrons in the radio source ν n is always greater than that for the magnetic field ν B and it is linearly dependent on the spectral index of the electrons δ as ν n ≈0.5 δ . This relation is explained in the simplified flare-loop model integrating the analytical solutions of the Fokker – Planck equation. The mean value of ν B is found to be 0.36±0.04, which is very close to the value of ν B =0.38±0.02 derived from the dependence of the magnetic field strength on the height in the active region measured by RATAN-600.