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An analysis is presented of a traveling-wave tube in which unmodulated dc current is continuously introduced along the length of the tube and is removed after traveling a fixed distance in the presence of the circuit field. This change in the dc current distribution as compared with that of a conventional traveling-wave tube results in three forward growing waves instead of one, one growing exponentially as in the conventional tube, one growing linearly, and one growing as the square of distance. Expressions for the over-all gain of a forward-wave amplifier of this type are derived as a function of the usual parameters plus an additional parameter related to the distance traveled by electrons in the interaction space. The power output of this device is found to depend on saturation of individual current elements rather than of the beam as a whole, with the result that, after saturation is once reached, the power output is independent of input power. An estimate of the value of the saturation power level is obtained from the linear analysis.