• A.E. Charman, J.S. Wurtele
  UCB, Berkeley, California
• G. Penn
  LBNL, Berkeley, California

Funding: Division of High energy Phyiscs, DOE; and DARPA, DOD

Within the framework of a Hilbert space formalism, we derive a maximum-power variational principle (MPVP) applicable to classical spontaneous radiation from prescribed current sources. The principe appears similar to, but actually is distinct from, other well-known variational principles associated with Hamilton's principle of stationary action or Rumsey's methods involving "reaction." The techniques have been developed for and applied to the case of undulator radiation from relativistic electron beams, specifically to X-ray generation using an harmonic cascade. Such processes are currently evaluated using extensive calculations or simulation codes which can be slow to evaluate and difficult to set up. The variational principle emerged as a natural step in a simple analytic algorithm to predict the output of a harmonic generation beamline in the low-gain regime based on trial functions for the output radiation. Full three-dimensional effects are included, and it may be generalized to include further effects such as asymmetric beams and misalignments. This method has been implemented and compared with simulation results using the FEL code GENESIS, both for single stages of harmonic generation and for the LUX project.