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Electro-magnetic (EM) wave amplifiers by utilizing traveling electron beam in vacuum come to have attention as devices covering over extremely wide frequency range from the microwave to the X-ray regions. We point out that two different amplification mechanisms should exist according to the relation between the EM wavelength and the electron size. The first model is named as coherent electron wave (CEW) model. Another one is named as localized electron (LE) model. The boundary of these two models is locating in the THz region.