Angular Distribution of Synchrotron Radiation in Low Frequency

The angular distribution of energy for synchrotron radiation in low frequency band (ω«ω_c) is obtained by rigorously solving the Nicolo Tartaglia equation. The result shows that the critical angle increases with decreasing frequency, but it cannot exceed 90°. The relation between critical angle θ_c and frequency is common covering all wavelengths. For the small angle case, it is consistent with the result obtained by Jackson. With the increase of emanative angle, the radiant intensity increases first, then decays.