A Basic Research on the Application of Relativistic Electron Beam to New Electromagnetic Wave Sources

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We have investigated theoretically the operation characteristics of two dimensional radiating system using a relativistic electron beam coupled to an open periodic structure, with a particular emphasis on the Smith-Purcell radiation and the Smith-Purcell free electron laser. The study is based on a self-consistent analysis that takes into account the effects of the radiated fields back on the electron beam. The optimum parameters to achieve an efficient and realistic radiating system have been brought out. The important conclusions are summarized as follows:1. The Smith-Purcell radiation by a relativistic electron beam propagating parallel to a reflection grating was analyzed using a singular perturbation technique. This radiation can be interpreted as a radiative leakage of slow space-charge waves perturbed by the presence of periodic structure. The analytical expression for the leakage coefficient was presented in closed form. It was shown that there exist the optimum velocity, thickness, and location of the electron beam to yield a maximum leakage coefficient for a given wave frequency. Under this optimum operation, we can achieve an electron-beam active tntenna which radiates in the backward direction with a gain of several times of 10 dB and a half beamwidth less than 1゜.2. The smith-Purcell free electron laser stems from the coupling of the electron beam to the electromagnetic eigen surface waves bound to the grating, and hence the perturbation approach can not be applied to its analysis. We have applied the mode-matching method and first succeeded the numerical analysis. The maximum growth rate and the center frequency of the laser were numerically evaluated, which depend on the grating dimensions and the electron beam configuration. The optimum parameters for the laser operation were presented. Our analysis is a full-wave analysis that is valid in spontaneous emission regime as well as in stimulated emission resime.