1 Abstract— For relativistic Cherenkov devices we investigate the process of high-power microwave (HPM) pulse generation with its phase correlating to the sharp edge of an e-beam current pulse. Our theoretical consideration is referred to quasi- stationary and superradiative (SR) generation regimes when spontaneous emission of the e-beam edge serves as the seed for the development of further coherent oscillations. Phase correlation of the excited microwave pulses with the characteristics of the current pulse front and/or an initial external electromagnetic pulse provided additional confirmation of particle-in-cell (PIC) simulations. Pulse-to-pulse stability of the radiation phase within several percent of the oscillation period makes it possible to arrange multi-channel schemes producing mutually coherent microwave pulses. In the experiments that have been carried out, the cathodes of independent generators were powered by identical accelerating pulses from strictly synchronized voltage modulators, or by splitting the pulse from a single powerful modulator. For the 2-ns regime with the power of each Ka-band backward wave oscillator (BWO) about 100 MW, we demonstrate quadratic growth of the power density in the interference maximum of the directional diagram. In a short pulse SR regime, with the peak power of 600 MW in a single channel, for a four-channel 2-D array we attained a sixteen-fold radiation intensity gain. Index Terms— superradiance of electron bunches, current edge, microwaves, radiation phase, coherent summation. I. INTRODUCTION ROSPECTIVE scientific and technological applications stimulate interest in the generation of ultra-high power Manuscript received August 31, 2015. The work was supported by IEP UB RAS Project No. 0389-2014-0005 and, in part, by RFBR Grants Nos. 14-08- 01180 and 16-02-00029. N. S. Ginzburg, A. A. Golovanov and I. V. Zotova are with the Institute of Applied Physics RAS, N. Novgorod 603950, Russia (e-mail: ginzburg@appl.sci-nnov.ru). A. W. Cross and A. D. R. Phelps are with the Department of Physics, SUPA, University of Strathclyde, Glasgow G4 0NG, U.K. (e-mail: a.d.r.phelps@strath.ac.uk). I. V. Romanchenko and V. V. Rostov are with the Institute of High Current Electronics, SD RAS, Tomsk, 634055, Russia (e-mail: rostov@lfe.hcei.tsc.ru). K. A. Sharypov, V. G. Shpak, S. A. Shunailov, M. R. Ul’masculov, and M. I. Yalandin are with the Institute of Electrophysics, UD RAS, Ekaterinburg, 620016, Russia (e-mail: yalandin@iep.uran.ru). coherent radiation. Approaches that can be suggested to achieve this goal include the generation of radiation by a single source with an oversized electrodynamic system. In this case special methods (for example, 2D distributed feedback [1], [2]) are required to produce spatially coherent radiation. Other methods are based on time-amplitude HPM power compression schemes [3] and on the synchronization of a large number of moderate-power sources using a master oscillator [4]-[6]. At the same time for short-pulse sources, in particular, for HPM oscillators based on Cherenkov radiation from relativistic electron beams moving in a slow wave structure (SWS) [7], [8], there is an alternative opportunity associated with correlating the phase of a radiated pulse to the sharp edge of a current pulse. Actually, spontaneous emission of the bunch edge serves as the seed for stimulated processes that include electron self-bunching and subsequent radiation of a high-power electromagnetic (EM) pulse. If identical current pulses are sent simultaneously to several oscillators’ channels, identical in-phase microwave pulses are generated and the coherent summation of their amplitudes is possible. In fact, the methods of phase synchronization have been experimentally tested for two different types of operation regime. The first way is a conventional regime of a relativistic BWO with quasi-stationary generation [9]. In such a regime the parameters of generation (frequency and electron efficiency) are the same as in the steady-state regimes. Nevertheless, the phase of the generated signals is strongly correlated with the sharp edge of a current pulse. The second operating mode represents a regime of superradiance when the e-beam current pulse length is comparable with the cooperative length (see details in [7-8]), and such an electron bunch emits a single radiation pulse with the peak power exceeding the power in a steady-state regime. It is obvious that for both mentioned operating regimes the phase coupling to the sharp edge of a current pulse permits one to control the phase by a precise time shift in the beam current front. It should be noted that the physical model describing the transformation of spontaneous Cherenkov radiation (i.e. the radiation from unperturbed moving particles without the reverse effect of the field [10]) to stimulated radiation have been suggested in Ref. [11]. Development of such an Coherent Summation of Emission from Relativistic Cherenkov Sources as a Way of Production of Extremely High-Intensity Microwave Pulses Naum S. Ginzburg, Adrian W. Cross, Anton A. Golovanov, Alan D. R. Phelps, Member, IEEE, Ilya V. Romanchenko, Vladislav V. Rostov, Konstantin A. Sharypov, Valery G. Shpak, Sergey A. Shunailov, Marat R. Ul’masculov, Michael I. Yalandin, Member, IEEE, and Irina V. Zotova P