Synchrotron resonance maser

Attention is drawn to an obscure formula derived from relativistic quantum electrodynamics in the mid-'60s by Sokolov and Ternov for induced absorption and emission from highly relativistic electrons in a static uniform magnetic field. From their results, we develop handy formulae and graphs to help in preliminary designs for radiation sources to operate at high synchrotron harmonics. Approximate design parameters are given for 100 kW oscillators operating at wavelengths below 3mm, employing magnetic fields of less than 12 kG. It is shown that the Sokolov-Ternov formula can also be deduced from classical relativistic plasma wave theory, but for a numerical factor in one term. This term is shown to describe a gain mechanism which has apparently received scant notice in the gyrotron literature.