In 1919 the Department of Electrical Engineering (EE) was established in Tohoku University (at that time, Tohoku Imperial University). In this Department a growing tendency towards research featured in science and technology for electrical communication. Great efforts made in these fields produced pioneering studies such as those of the Yagi-Uda antenna and slotted-anode type magnetrons in the late 1920s. The purpose of this article is to introduce the history of development of microwave electron-tube at Tohoku University, which was started with the Okabe's magnetron.

We present an analytical nonlinear adiabatic theory of the microwave electron device that we call the Autophase Microwave Tube (AMT). In contrast to the well-known Traveling Wave Tube (TWT), the AMT exploits a highly efficient non-synchronous beam-wave interaction for the amplification (or generation) of the HF electromagnetic waves, and, differently from klystron and such hybrid devices as twystron, it employs a continuous beam-wave interaction. Because of these distinctive features, the AMT presents a special class of microwave electron devices, which feature very high electronic efficiency (which tends to 100%) and large bandwidth. Here, we develop the theory that allows one to find the profiles of static longitudinal electric or magnetic field (or both) over the device length, which yield negligible de-bunching together with highly efficient amplification (generation) of the HF electromagnetic wave. The analysis of electron motion in the bunch is performed by means of Lyapunov stability theory. The numerical example illustrates the possibility of achieving the electronic efficiency of AMT as high as 92%. We compare different autophase regimes in the AMT and show that the profiling of the longitudinal static magnetic focusing field in the helix AMT with the non-azimuthally symmetric wave has many advantages with respect to other regimes.