The Gyratron, CARM and FEL devices: An analytical unified formulation for the small signal analysis

We review the classical single particle theory for the Gyratron and CARM (Cyclotron Autoresonance Maser) devices. We formulate the theory in order to map the relevant equations on those of Free Electron Laser magnetic Undulator devices. The article comments on the validity of such an approach and on the possibility of exploiting the wealth of scaling rules, currently adopted in the design of FEL devices, either in the single passage and oscillator regime. The relevance of that procedure in the design of the FRASCATI-CARM on going experiment will be discussed.