A Hilbert-Space Variational Principle for Spontaneous Wiggler and Synchrotron Radiation

Within the framework of Hilbert space theory, we have developed a maximum-power variational principle applicable to classical spontaneous radiation from prescribed classical harmonic current sources. A simple proof is summarized for the case of three-dimensional fields propagating in vacuum, and specialization to the case of paraxial optics is discussed. The techniques have been developed to model undulator radiation from relativistic electron beams (for which an example involving high harmonic generation is reviewed), but are more broadly applicable to synchrotron or other radiation problems, and may generalize to certain structured media.