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A novel method of generation and amplification of microwave energy is described, based on space-charge interaction of electron streams of different velocities. The electron streams are generated within a common space which, in the presence of electrons, behaves as a unidirectional transmission medium having negative attenuation. The basic theory of the new method is developed, and formulas and curves are given for propagation constant, electronic, gain, and bandwidth which can be achieved with the device based on the new method. This device is called the "electron-wave tube." The design and performance of the "two-beam"-type and the "single-beam"-type experimental electron-wave tubes are described. Electronic gains of the order of 80 db at a frequency of 3000 Mc and electronic bandwidths of over 30 per cent have been observed in experimental electron-wave tubes. It is pointed out that, since no passive circuit is required in the amplifying region of the electron-wave tube, the new method is important in the development of tubes for millimeter waves.