A tunable bragg cavity for an efficient millimeter FEL driven by electrostatic accelerators

A comparison between three possible cavity configurations, the confocal cavity, the ring cavity and the Bragg cavity is presented for a millimeter FEL set within the high voltage head of an electrostatic accelerator. A simple mechnical design to make the Bragg cavity tunable is proposed. The usual theory of the sinusoidal Bragg corrugation, in cylindrical geometry, is extended to the rectangular corrugation and, further, the theory of the Bragg mirror is extended to rectangular geometry. The features of a Bragg mirror in cylindrical and rectangular geometry are compared.