A STUDY ON THE RELATIONSHIP BETWEEN THE SPONTANEOUS RADIATION AND THE STIMULATED RADIATION IN TRANSITION RADIATION FREE ELECTRON LASERS
渡越辐射自由电子激光中自发辐射与受激辐射的关系

As a fundamental theorem in free electron lasers, Madey Theorem reveals the relationship between the spontaneous radiation and the stimulated radiation. In this paper, this problem is studied for transition radiation free electron lasers. The results show that there is a formula corresponding to the first part of Madey Theorem, but the former is more complicated; while the second part remains the same. Then the results obtained are used to simplify the small signal gain calculation.