Abstract
Interaction between an electron beam and an electromagnetic wave is analyzed on the basis of semiclassical quantum mechanics that includes the influence of electron scattering and thermal distribution. The result is applied to determine the gain coefficient of the unidirectional optical amplifier utilizing this interaction. A general formula of the gain is obtained, which is applicable not only to an electron beam in vacuum but also to a semiconductor. The gain in the optical region due to an electron beam in vacuum is calculated, and it is shown that the gain coefficient is strongly reduced by the energy broadening due to scattering. This reduction is more significant for lower frequencies. The thermal distribution of the electron energy also reduces the gain, although the influence is less than that of electron scattering. The gain obtained in the quantum mechanical analysis is compared with that of the classical analysis including electron scattering. The difference between the classical and quantum mechanical analyses approaches zero in the low-frequency limit, while it is large in the optical frequency range.
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