IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 24, NO. 3, JUNE 1996
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Larald D. Moreland, E d Schamiloglu, Senior Member, ZEEE, Raymond W. Lemke, A. M. Roitman, S. D. Korovin, and V. V. Rostov
AbstractThis paper describes how finite length effects in highpower backward wave oscillators can be exploited in a controlled manner to achieve enhanc’edfrequency agility. Experiments were performed using a Sinus6 highpower relativistic repetetively pulsed electron beam accelerator. A uniform slow wave structure was used in these studies ;and its parameters were h e d . Sections of smoothwalled circulair waveguide of varying lengths were inserted both before and after the slow wave structure. Variations in the length of smooth,walledwaveguide on the order of a q~arterwavelengthof the generated electromagnetic radiation were found to significantly affect both microwave frequency and radiation efficiency in a periodiclike manner. The experimental results were reprolduced in TWOQUICK electromagnetic articleincell simulations. A bandwidth of about 500 MHz centered around 9.5 GH[z at hundreds of MW power levels has been achieved with clonstant beam and slow wave structure parameters.
I. INTRODUCTION
BACKWARD wave oscillator (BWO) is an electron beamdriven source of radiation in the centimeter and millimeter wavelengths. In the simple classical description of this device, an electron beam interacts with a backwardpropagating wave in an infinite uniform slow wave structure (SWS). In an actual finite length device there will be end reflections resulting in both forward and backward propagating harmonics. Since highpower BWO’s typically radiate the energy in the forward direction by reflecting the backward propagating harmonics from a cutoff neck at the entrance to the SWS, these forward propagating harmonics must be included in a complete description of this relativistic device. Researchers [ 11[3] have claimed that the forward traveling wave does not interact with the electron beam since the phase velocities of the wave’s spatial harmonics are not synchronous with the beam. Others recognized the possibility Manuscript received September 18, 1995; revised February 2, 1996. The work at the University of New Mexico was supported through a High Energy Microwave Devices Consortium funded by an AFOSRDOD MURI grant and administered through Texas Tech University, Lubbock. This work was supported in part by the Air Force Phillips Laboratory and the Department of Energy. The collaboration with the HCEI in Tomsk was supported in part by the National Research Council and a grant from the William and Mary Greve Foundation. L. D. Moreland and E. Schamiloglu are with the Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131 USA (email:
[email protected]). R. W. Lemke is with Division 9541, Sandia National Laboratories, Albuquerque, NM 87185 USA. A. M. Roitman, S. D. Korovin, and V. V. Rostov are with the High Current Electronics Institute, Siberian Branch, Russian Academy of Sciences, Tomsk 63405 1 Russia. Publisher Item Identifier S 00933813(96)046413.
of the interaction of beam electrons with fast asynchronous harmonics, but described this through a perturbation correction to the main interaction with the backward wave [4]. In addition, in [5] the interaction of electrons with the forward traveling wave is explained as a monotron effect for the case of short tubes, where the transit angle of electrons in the forward wave is about 27r. Recent studies [ 6 ] , [7] have suggested that the forward traveling wave does in fact have a significant interaction with the beam in finite length devices that is fundamentally different in nature from that proposed in [4] and [5]. The amplitude of the zeroth harmonic of the forward traveling wave at the beginning of the SWS is two to six times greater than the amplitude of the 1 harmonic of the backward wave [8]. For infinitely long devices this is not important since the zeroth harmonic of the forward wave is asynchronous with the beam. For finite length devices, the zeroth harmonic of the forward wave and the  1 harmonic of the backward wave comprise a standing wave which does have a significant interaction with the beam [9]. By changing the reflection conditions at both ends of the SWS, our experiments show how the phases of the forward and backward propagating harmonics, and their resultant total standing wave pattern influence the operation of the BWO. In particular, in this paper it is demonstrated that the bandwidth of operation of a BWO can be significantly increased by merely shifting the interaction region with respect to the position of the cutoff neck. A bandwidth of about 500 MHz has been achieved around a center frequency of 9.5 GHz at hundreds of MW power levels for constant beam and SWS parameters. The typical dispersion relation for the TMol mode in a uniform SWS has a period ho = 27r/d, where d is the ripple period (see [9] for a discussion of a typical dispersion relation relevant to this work). There is an infinite number of wavenumbers corresponding to a given frequency. Each value of wavenumber k represents a different spatial harmonic of the TMol mode The group velocity of each harmonic is given by the slope of the dispersion curve, and the magnitude of the group velocity is the same, with each successive harmonic alternating between a positive slope (forward wave) and a negative slope (backward wave). A backward traveling TMol wave in the SWS consists of all the harmonics with a negative slope. The relative amplitude of each harmonic depends on the boundary conditions. Similarly, a forward traveling TMol wave in the SWS consists of all the harmonics with a positive slope. In describing the various harmonics, we use the convention where the harmonic closest to the
00933813/96$05.00 0 1996 IEEE
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MORELAND er al.: HIGHPOWER RELATIVISTIC BACKWARD WAVE OSCILLATORS
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4 Fig. 1. Experimental setup for BWO experiments with forward and backward shifting. Shown in the diagram are (1) capacitive voltage divider, (2) Rogowski coil, (3) cutoff neck, (4) cathode, ( 5 ) AK gap, (6) magnetic field coils, (7) slow wave structure, (8) smooth circular waveguide and shifting lengths Li and 152, (9) electron beam, (10) output hom antenna, and (11) reflection ring.
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origin is the zeroth harmonic. Each successive harmonic is numbered sequentially. If the phase and group velocities of a given harmonic are in the same direction, the corresponding index is positive. If the phase and group velocities of a given harmonic are antiparallel, the corresponding index is negative. For a forward propagating wave, the value of k for the nth harmonic is given by 21rn k , = ko . d The corresponding values of k for a backward propagating wave are given by
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 24, NO. 3, JUNE 1996
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to the boundary conditions. The  1 harmonic of the backward propagating wave alternately accelerates and decelerates beam electrons, which results in the formation of periodic bunches of charge. Another interaction to consider is the asynchronous zeroth harmonic of the forward wave. Even though its phase velocity is greater than the electron beam velocity and slightly greater than the speed of light c, its amplitude can be greater than the amplitude of the  1 harmonic of the backward wave. In our experiment, the amplitude of the zeroth harmonic was calculated to be three times greater than the amplitude of the  1 harmonic [8]. This asynchronous harmonic can influence the output of the BWO by two means: 1) it can enhance the electron beam bunching through a mechanism analogous to a transit time oscillator, and 2) it can shift the phases of electron bunches. Due to the efficient bunching of electrons by the synchronous backward wave, there is opportunity for additional energy exchange of electrons with the forward traveling wave even though the total transit angle of electrons in the forward wave is greater than 27r. This energy exchange can either be positive or negative, depending on the total transit angle of the electrons in the forward wave. The initial formation of the electron bunches at the beginning of the SWS
influences their phase with respect to the electric field at the end of the SWS. The role of prebunched electrons in enhancing microwave generation efficiency was discussed in [9]. 11. EXPERIMENTAL AND SIMULATION RESULTS
An experiment was designed to study how the frequency and efficiency of microwave generation is affected by the phase difference between the forward and backward waves at the start of the SWS. These experiments were performed using a uniform slow wave structure and uniform guide magnetic field. The experiment is shown schematically in Fig. 1. The
Sinus6 electron beam accelerator [9] was used to generate electron beams with energies ranging from 450 to 700 keV and corresponding beam currents ranging from 3.5 to 6.0 kA in a 10ns pulse duration. An eightripple period SWS was used with each ripple having a period of 15 mm and corrugation amplitude of 2.25 mm. A long uniform magnetic field with magnitude 2.7 T was used for beam transport. The radiated power was measured using a crystal detector and the frequency was obtained on each shot by heterodyning this signal with a known frequency source. (Additional information on the experimental hardware, diagnostics, and typical responses for beam voltage and current, and radiated power density can be found in [9].) The RF efficiency was obtained by dividing the measured peak RF envelope power by the input beam power. The structure of the radiated mode was obtained by measuring the radiation pattern in the farfield of a 21cm diameter conical horn antenna and confirmed using a neon discharge bulb array. Both measurements were consistent with a molmode. The effects of changing the reflection conditions at the ends of the SWS were studied by introducing sections of smoothwalled waveguide between the cutoff neck and the entrance to the SWS, as shown in Fig. 1. We refer to this as “forward shifting.” These sections of smoothwalled waveguide also change the phase &, between the forward and backward traveling waves. According to [6], 40 can influence the operation of a BWO by changing the final phase of electron bunches with respect to decelerating electric fields at the end of the SWS. The results of experiments and TWOQUICK [ 101 simulations of the dependence of microwave generation efficiency and radiated frequency are shown in Figs. 2 and 3 . Note that we plot relative efficiency as a function of shifting in all cases in this article, where relative efficiency is
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