Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation

A formulation for the characterization of superradiant and stimulated-superradiant radiative emission from bunched electron beams is presented. The radiation is characterized in terms of power and spectral power per radiation mode, which provide a measure of the useful spatially coherent radiation power and spectral power emitted by a radiation source. When the bunched electron beam emits superradiantly, these parameters scale like the square of the number of electrons, orders of magnitude more than spontaneous emission. The formulation applies to emission from single bunches, a finite number of bunches in a macropulse, or periodic bunching. It can be employed on any kind of e-beam radiation scheme. Specific analytic expressions are derived for coherent synchrotron radiation and prebunched free-electron laser, providing a basis for comparing and understanding their connection.