Bi-period undulator radiation and small signal free electron laser gain

Abstract

The theory of undulator radiation of a relativistic electron beam moving in a bi-period undulator is investigated. The electron trajectory and the bi-period undulator radiation tuning from bi-period to one period and vice versa is explained through a phase between the two period field components of the bi period undulator . The small signal gain of a free electron laser with the bi-period undulator has been derived and discussed. As the phase between the two field components of the bi-period undulator shifts away from π, the bi-period undulator trajectory offsets and bi-period undulator operates as one period free electron laser . At phase ∼π, the bi-period small signal free electron laser gain is three fold higher than the one period free electron laser.