rectified and converted to DC electric power. The incident laser beam goes out after interacting with the REB. Hence any fraction of the laser beam is not absorbed in the system and is not reduced to a heat to be rejected. 4. Discussion We consider an optimal parameters to design the system depicted in Fig. 5. When the electrons are turned at the region between regions I and II, they lose their energy by producing the radiation of the electromagnetic field. Considering an electron turning in a uniform magnetic field, the energy loss due to a synchrotron radiation is [4], Here B is the intensity of the uniform magnetic field. For larger value of y, the energy loss due to the synchrotron radiation becomes large while the conversion efficiencies r/b and i]s become large. When we consider the turning by a radius of 1 m, the rate for the REB to lose its kinetic energy is The frequency of the synchrotron radiation is where is a frequency in a microwave region. It means that y must be as small as possible in order to attain a smaller 2. Since the smaller 2 is necessary for a compactness of the system, it suggests that y must be chosen to be as small as possible. As for a frequency of the scattered wave, it becomes smaller and reaches the microwave region for a larger value of y. However the request for a larger value of y is contrary to other factors; the reduction of the synchrotron radiatin loss and the interaction length L (i.e., the compactness of the system). Hence we must give up the idea of using the scattered wave and pay attention to using only the kinetic energy of the REB, since the fraction of energy converted from the laser beam to the scattered wave is much smaller in comparison to the REB kinetic energy. Within this perspective, we must consider (1) the reduction of synchrotron radiation loss, (2) the compactness of the system and (3) an appropriate efficiency. Requirements (1) and (2) suggest that the y value must be selected to be as small as possible, within the constraint of attaining an appropriate conversion efficiency. For example, if the parameters <yAf=27tX 1010 (sec-1) and y=2 are chosen, we obtain 2 = 24 cm, cor=2^x 1.67 x 108 (sec-1) and Ir/mc1y=\5 x 10-6 (sec-1). A high power density operation becomes possible for a greater density of the REB. When the density of the REB becomes large, the stability of the REB ring may become a critical problem. In general, the cooperation phenomenon is expected to occur in
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