IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 64, NO. 11, NOVEMBER 2017
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Investigation of a Ka-Band High-Power Sheet Beam Relativistic Extended Interaction Oscillator Zhenbang Liu, Hua Huang, Lurong Lei, Xiao Jin, Shifeng Li, and Lele Li
Abstract — The sheet beam relativistic extended interaction oscillator (REIO) is a very important highpower millimeter-wave source for many actual and potential applications. A Ka-band sheet beam REIO is designed by means of particle-in-cell (PIC) simulation. In the design, we adopt a sheet electron beam with dimensions of 45 mm × 1.5 mm to reduce the space charge effect and the extended interaction cavities to increase the power capacity. The results of the PIC simulation demonstrate the device can generate an output power of 404 MW at 30 GHz with an efficiency of 20%. In addition, we develop the experiment on a short-pulse accelerator. In the experiment, the oscillator generates a millimeterwave power of 125 MW with a beam current of 4 kA, a beam voltage of 500 kV, and guiding magnetic field of 1 T. The frequency of the output millimeter wave is 30.6 GHz and the pulsewidth is 16 ns. The experiment proves that millimeter wave of over 100 MW can be generated with the sheet beam REIO. Index Terms — High-power millimeter wave, Ka-band, relativistic extended interaction oscillator (REIO), sheet beam.
I. I NTRODUCTION
H
IGH-POWER millimeter wave is attractive for many applications, such as high-resolution radar, communication, and plasma heating research [1]–[4]. The vacuum electron device is still one of the most efficient sources to generate a high-power millimeter-wave signal due to its low energy loss and high energy conversion efficiency [5], [6]. During recent decades, the sheet beam devices have attracted great attention due to lots of advantages. The output power can be increased through enlarging the sheet beam cross section, in which the current density for beam-wave interaction will be decreased. In addition, it is relatively easier to be fabricated by 2-D planar techniques, which benefits for extending the operating frequency to high-frequency range [7], [8]. Manuscript received June 14, 2017; revised July 21, 2017 and August 21, 2017; accepted August 22, 2017. Date of publication August 31, 2017; date of current version October 20, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 11605191 and Grant 11475158, and in part by the Science Foundation of the China Academy of Engineering Physics under Grant 2015B0402096. The review of this paper was arranged by Editor M. Thumm. (Corresponding author: Zhenbang Liu.) The authors are with the Science and Technology on High Power Microwave Laboratory, Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2017.2744804
Fig. 1. Sketch structure of the sheet beam REIO.
In this paper, we put forward a Ka-band sheet beam relativistic oscillator with extended-interaction slow-wave structures (SWSs). Similar to the structure of multiwave Cerenkov generators, segmented SWSs are used in this device to modulate the relativistic electron beam and increase the power conversion efficiency [9], [10]. In order to keep the electric field below the breakdown level, a structure of two output antennas is adopted in this device. The structure of the relativistic extended-interaction oscillator (REIO) is displayed in Fig. 1. This paper is organized as follows. In Section II, the design and simulation of the Ka-band REIO are briefly introduced. The transmission process of the intense relativistic sheet beam is investigated by means of the particle-in-cell (PIC) simulation and experiment in Section III. In Section IV, the experiment of the Ka-band REIO is carried out, and the experimental results are presented. Finally, some conclusions are given in Section V. II. D ESIGN AND S IMULATION OF THE D EVICE For a high output power, the electric field in the device is critical. However, the dimensions of the devices are comparable to their operating wavelength. The transverse dimensions of the devices dramatic decrease when the operating frequency increases to Ka band, and the power capacity of the devices is limited by the dimensions [11]–[14]. In order to increase the power capacity, the sheet beam cross section should be enlarging. However, the mode competition may affect the stable operation of the device when the sheet beam cross section is too large, so the dimensions of the sheet beam should be optimized. Considering that, a sheet electron beam with cross-sectional dimensions of 45 mm × 1.5 mm is adopted in the REIO.
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Fig. 2. Plots of FN (θ¼ ) of the multiple-gap resonator versus θ¼ .
In the simulation, PIC simulation code CHIPIC is used to investigate the beam-wave interaction process and the emission of the sheet beam, which is developed by the University of Electronic Science and Technology of China[15]. As shown in Fig. 1, two extended interaction SWSs are adopted in the device, and the two SWSs are isolated by a rectangular drift. A cathode with cross-sectional dimensions of 45 mm × 1.2 mm is adopted for the REIO, while the rectangular beam tunnel is 48 mm × 3.5 mm. The whole system, from the cathode to the output section, is immersed in a uniform magnetic field of about 1 T, which is the same as the experimental condition. The SWS1# is the modulation section with four periods, which working mode is π mode. The SWS2# is the output section with three periods, which working mode is 2π mode. The SWS1# is the modulation section. The π mode is propitiously excited by the electron beam, when the electron load conductance of the cavity is negative. The power exchange function FN (θ0 ) of N-gap multiple-gap resonator is given in (1), as shown at the bottom of this page, for the π mode [16]. The FN (θ0 ) is the power exchange function, N is the number of the gaps, and the θ0 is direct current transit angle. By this relation, we could get the optimum gap transmit angle. The plots of FN (θ0 ) of the multiple-gap resonator versus θ0 are illustrated in Fig. 2. As shown in Fig. 2, the optimum gap transit angle for three-gap cavity is 2.06 with FN (θ0 ) of −3.9. The optimum gap transit angle for four-gap cavity is 2.35 with FN (θ0 ) of −9.79. The optimum gap transit angle for five-gap cavity is 2.53 with FN (θ0 ) of −19.66. The modulation sections with different gap numbers have been investigated. The modulated currents with different gap numbers are displayed in Fig. 3. The beam voltage and beam current are 500 kV and 4 kA, respectively. As shown in Fig. 3, the stable time for modulated current is 38, 9, and 8 ns, respectively. The stable time for modulated ⎡
N−1
Fig. 3. Waveforms of modulated current with (a) three gap, (b) four gap, and (c) five gap.
current is too long when the modulation section is three gap. And the amplitude of the modulated current is decreased, when the modulation section is five gap, maybe for the reason of mode competition. Considering these, the four-gap extended interaction cavity is adopted. The SWS2# is the output section. The power exchange function FN (θ0 ) of N-gap extended interaction cavity for 2π mode is shown as follows [17]: FN (θ0 ) = [2 − 2 cos(Nθ0 ) − Nθ0 sin(Nθ0 )] θ02 . (2) The design of the three-gap output section is similar to the paper [17]. We write this paper, in which the three-gap extended cavity with operating mode of 2π mode is studied explicitly. The geometric model of the REIO and the distributing of the operating mode electric field are displayed in Fig. 4. The xz cross-sectional dimension of the REIO with inclusion of the output coupler (except the diode) is about 80 mm × 65 mm. Both the SWSs period and the rectangular drift length between the two SWSs are designed gradually increasing to strengthen the beam-wave coupling and avoid ⎤
(−1) (N − n) cos(nθ0 ) + (−1) 2 cos(Nθ0 ) ⎥ ⎢ (4N − 2) + 8 ⎢ ⎥ n=1 ⎥ FN (θ0 ) + ⎢ θ02 ⎢ ⎥ N−1 ⎣ ⎦ (−1)n n(N − n) sin(nθ0 ) + (−1) N Nθ0 sin(Nθ0 ) + 4θ0 n=1
n
N
(1)
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Fig. 6. Spectrum of the output millimeter wave.
Fig. 4. Geometric model of REIO and the distributing of the electric field in (a) xz section and (b) xy cross section of the output coupler.
operating frequency is pure by Fig. 6. The total output power will decrease to 240 MW when the beam voltage is 500 kV and current is 2 kA. However, the efficiency increases to about 24% and the maximum electric field decreases to 1.4 MV/cm. The electron beam is injected into the beam tunnel with voltage and current of artificially value, when the PIC simulation code is used to investigate the beam-wave interaction process. The whole diode structure is not included in this process. The mesh for simulating the beam-wave interaction process is very small, for the reason of describing all the cavities precise. Then, the total numbers of the meshs are very large. The whole diode is a big structure, with dimensions of about 140 mm × 140 mm × 50 mm. The mesh numbers will exceed the limit of the simulation code when the whole diode is included in the beam-wave interaction process. So the diode structure should be designed separately. III. T RANSMISSION OF THE I NTENSE R ELATIVISTIC S HEET B EAM
Fig. 5. Waveforms of the output millimeter wave from (a) output hole 1# and (b) output hole 2#.
conceivable mode competition. The quality factor Q L of the output cavity is about 130. As shown in Fig. 4, the maximum electric field is about 1.8 MV/cm, which is below the breakdown electric field [18]. The output millimeter-wave power of the two output holes is shown in Fig. 5. The beam voltage and current are 500 kV and 4 kA, respectively. And the guiding magnetic field is 1 T. The spectrum of the output millimeter wave is displayed in Fig. 6. As shown in Fig. 5, the output average power at every output hole is 202 MW, and then the total average power of the millimeter wave is 404 MW, corresponding to efficiency of 20%, and frequency of 30 GHz. And the
For a relativistic sheet beam device, the transmission of the relativistic sheet beam is critical. The space charge limited current of the sheet drift is about 16.2 kA by means of the theoretical calculation with the given dimensions, which is larger than the working current. The emission and transmission processes of the sheet electron beam were simulated by means of the explosive emission model. The trajectories of the electrons are displayed in Fig. 7. Fig. 7(a) is the yz section of the whole diode, Fig. 7(b) is the xy cross section at the entrance of beam tunnel, and Fig. 7(c) is the xy cross section at the end of beam tunnel. The length of the beam tunnel is about 65 mm. The explosive emission electron beam current is 4 kA, when the diode voltage is 500 kV and the guiding magnetic field is 1 T. As shown in Fig. 7, the electrons are uniformity in the middle part. But the edge parts are crimped for effect of the guiding magnetic field and the space charge field. It can be seen from Fig. 7, which most of the electrons emit from the edge sides of the cathode. The electron beam expands, when it transfers in the beam tunnel. The dimensions of sheet electron beam are about 45 mm × 1.5 mm at the entrance of beam tunnel, and the dimensions increase to 46 mm × 2.7 mm at the end of beam tunnel. The sheet electron beam current at the end of the drift tube is 3.6 kA, which indicates the circulating rate of the electron beam is 90% due to lose of a few electrons in the beam tunnel. The expanding of the electron beam can be suppressed when the
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Fig. 9. Spot of the sheet electron beam.
Fig. 7. Trajectories of the electrons at (a) yz section, (b) xy section 1(b), and (c) xy section 2(c).
Fig. 8. Waveforms of the sheet electron beam'i1-voltage, 2-current, and 3-Faraday cup current'j.
guiding magnetic field is increased. The loss of electrons can be avoided when we increase the guiding magnetic field to about 2 T in simulation. The experiments of the emission and transmission of sheet electron beam are performed on a short-pulse accelerator. The voltage and current of the sheet electron beam are shown in Fig. 8. The whole system, from the diode to the output section, was immersed in a maximum magnetic field of about 1 T generated by a compressed solenoid magnet. In order to improve uniformity of the electrons, the edges of the cathode have been radiusing corners in the experiment. The beam voltage was measured with a resistive voltage divider, while the beam current was measured with a Rogowski coil at the entrance of the device. The electron beam was produced
by means of a graphite cathode explosive emission. The diode voltage is 500 kV, the sheet electron beam current is 4 kA with pulsewidth of 50 ns, and a Faraday cup is used to measure the current at the end of the beam tunnel, but the Faraday cup current is only 2.4 kA, so the circulating rate of the electron beam is 60%. Comparing with the simulation result, much more electrons lost in the experiment. The REIO works at high-frequency range, the dimensions for both the structure and the electron beam are very small. Moreover, the accelerator and the solenoid magnet are large and heavy, which bring much difficulty in the assemblage. There may be a few displacements in the axes between the cathode and the REIO as well as the solenoid magnet, which would cause the electrons loss greater in the experiment. The spot of the sheet electron beam also indicated this. The circulating rate of the electron beam would decrease to about 60% in simulation, if the axes of cathode and REIO shifted with the displacements of 0.5 and 0.45 mm in x-direction and y-direction, respectively. The spot of the sheet electron beam from a single pulse of one shot is shown in Fig. 9. The target was placed at the end of the beam tunnel, which was about 80 mm downstream from the cathode. The distance between the cathode and the anode is 15 mm. As shown in Fig. 9, the spot of the sheet electron beam is similar to the simulation one, the electrons are uniformity in the middle part, but the edge parts are crimped distinctly. And the edge parts are asymmetry, which indicates that the axes of the cathode and the device as well as the guiding magnetic field are not concentric. This result in the electrons interception by the tube wall. The cross dimensions of the spot are 47 mm × 2.9 mm, while the cross dimensions of the cathode are 45 mm × 1.2 mm, indicating the sheet electron beam expands dramatically, which is consistent with the simulation result. IV. R ESULTS OF THE E XPERIMENT Based on the foundation of simulation results, the experiment of the Ka-band high-power REIO with sheet electron beam has been carried out. The sketch structure of the experimental system is shown in Fig. 1. The sketch of the measurement system is shown in Fig. 10. The detector 1# was made up of BJ-260 straight waveguides, waveguide attenuators, and waveguide-to-coaxial
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Fig. 10. Sketch of the measurement system.
Fig. 12. Output millimeter wave and spectrum waveforms (1-beam voltage, 2-waveform of demodulation, 3-rf waveform of mixing, and 4-spectrum of mixing).
Fig. 11. (a) Simulation model of the antenna. (b) Distributing of the electric field in vacuum window.
converters. The detector 2# and detector 3# were made up of BJ-260 straight waveguides, waveguide attenuators, and RF-diode crystal detectors. The detectors were placed 6.5m away from the antenna, which satisfied the far-field condition. The millimeter-wave generator and measuring equipment are surrounded by the absorbing grass and absorbing wall to ensure no reflected millimeter wave transmitting to the detectors. The millimeter-wave frequency was measured by means of mixing the output wave with a standard signal by a calibrated mixer. The output power was measured with the calibrated RF-diode crystal detectors. When the far-field radiation pattern in the horizontal plane was measured, the detector 2# was fixed as a reference along the largest gain direction of the antenna, at the central line of the millimeter-wave generator, and the detector 3# was moved from about −25° to 25°. The far-field radiation pattern in the horizontal plane was measured and normalized. The distributing of the electric field in vacuum window is shown in Fig. 11, in which the input millimeter-wave power is 200 MW with frequency of 30 GHz. The maximum electric field is about 28.7 kV/cm, which is below the breakdown electric field. It is believed that the maximum power that can be supported by one antenna is over 200 MW. The typical output millimeter-wave waveform and its spectrum for one shot are shown in Fig. 12. As shown in Fig. 12, the pulsewidth of the output millimeter wave is about 16 ns with the pulsewidth of the electron beam voltage of 50 ns, which indicates pulse shortening occurs. The mixing frequency was also measured, when the frequency of the standard signal was 28 GHz, the mixing frequency was 2.6 GHz, then the frequency of the standard signal was increased to 28.5 GHz, the mixing frequency was 2.1 GHz, so the frequency of the output millimeter wave was 30.6 GHz. The radiation pattern of the output millimeter wave is displayed in Fig. 13.
Fig. 13. Radiation pattern of output millimeter wave.
As shown in Fig. 13, the radiation pattern is TE11 mode, and the experimental measurement accords with the simulation calculation. The output power of the generator is then calculated by integrating over the radiation pattern. The output power radiated from antenna1# is 60 MW, and the output power radiated from antenna2# is 65 MW. We can obtain that the total output power is 125 MW. The sheet beam REIO works at high-frequency range. The dimensions for both the structure and the electron beam are very small, and the requests of the dimensions precision are very strict in millimeter-waveband, which bring much difficulty in the device manufacture and assemblage. So the experimental conditions are different from the simulation one. The resonance frequency of output cavity would change about 520 MHz, if one key dimension changes 0.1 mm. In order to approach the experimental conditions, the frequency departure between SWS1# and SWS2# was set to 520 MHz in simulation. An asymmetry electron beam was launched into the beam tunnel with more electrons in the edge sides. The electron beam is similar to the one in Fig. 7. The axes of cathode and REIO shifted with the displacements of 0.5 and 0.45 mm in x-direction and y-direction, respectively. The output millimeter waves at these conditions are displayed in Fig. 14. The beam voltage and current are 500 kV and 4 kA, respectively. And the guiding magnetic field is 1 T. As shown in Fig. 14, the output power from hole 1# is 71 MW, and the output power from hole 2# is 66 MW, so the total output power decreases to 137 MW. The frequency is 30 GHz. Also the maximum electric field is 1.8 MV/cm
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Fig. 14. Output millimeter wave from (a) output hole 1# and (b) output hole 2#.
in simulation, which is close to the breakdown threshold, so the pulse shortening may be caused by intense RF breakdown. The maximum electric field could be decreased by radiusing cavity corners. We plan to put both the accelerator and the solenoid magnet on a steel rail, which would help to construct the concentric system, and the experimental circulating rate of the sheet electron beam may be increased. The maximum magnetic field generated by the solenoid magnet is only 1 T in this experiment, the guiding magnetic field should be increased. A superconduct magnet may be used in next experiment. The superconduct magnet can generate maximum magnetic field of 3 T, which would help to improve the transmission of relativistic sheet beam and increase the experimental radiation power. V. C ONCLUSION This paper presents a Ka-band high-power sheet beam REIO. A sheet electron beam with dimensions of 45 mm × 1.5 mm was adopted to reduce the space charge effect. The extended interaction cavity and the structure of two output antennas have been adopted in this device to increase the power capacity. The experiment was performed on a shortpulse accelerator. When the diode voltage is 500 kV and the sheet beam current is 4 kA with a guiding magnetic field of 1 T, an output power of 125 MW is generated, the frequency of the output millimeter wave is 30.6 GHz and the pulsewidth is 16 ns. The experiment proves that millimeter wave of over 100-MW output power can be generated by the sheet beam REIO. R EFERENCES [1] B. E. Carlsten, W. T. Roybal, and P. J. Tallerico, “Modifications to harmonic current bunching of electron beams from RF cavities due to radial boundary conditions,” IEEE Trans. Electron Devices, vol. 52, no. 12, pp. 2791–2799, Dec. 2005.
[2] V. V. Rostov, A. A. El’chaninov, I. V. Romanchenko, and M. I. Yalandin, “A coherent two-channel source of Cherenkov superradiance pulses,” Appl. Phys. Lett., vol. 100, no. 22, p. 224102, Dec. 2012. [3] T. C. Luce, “Applications of high-power millimeter waves in fusion energy research,” IEEE Trans. Plasma Sci., vol. 30, no. 3, pp. 734–754, Jun. 2002. [4] J. H. Booske, “Plasma physics and related challenges of millimeterwave-to-terahertz and high power microwave generation,” Phys. Plasmas, vol. 15, no. 5, pp. 055502-1–055502-16, May 2008. [5] J. H. Booske et al., “Vacuum electronic high power terahertz sources,” IEEE Trans. THz Sci. Technol., vol. 1, no. 1, pp. 54–75, Sep. 2011. [6] Y.-M. Shin, J. Zhao, L. R. Barnett, and N. C. Luhmann, Jr., “Investigation of terahertz sheet beam traveling wave tube amplifier with nanocomposite cathode,” Phys. Plasmas, vol. 17, no. 12, p. 123105, 2010. [7] N. Kumar, U. N. Pal, D. K. Pal, R. Prajesh, and R. Prakash, “Experimental investigation of a 1 kA/cm2 sheet beam plasma cathode electron gun,” Rev. Sci. Instrum., vol. 86, no. 1, p. 013503, Jan. 2015. [8] K. T. Nguyen, J. A. Pasour, T. M. Antonsen, P. B. Larsen, J. J. Petillo, and B. Levush, “Intense sheet electron beam transport in a uniform solenoidal magnetic field,” IEEE Trans. Electron Devices, vol. 56, no. 5, pp. 744–752, May 2009. [9] J. Zhu, T. Shu, J. Zhang, G. Li, and Z. Zhang, “Experimental investigation of a Ka band high power millimeter wave generator operated at low guiding magnetic field,” Phys. Plasmas, vol. 18, no. 5, p. 053101, May 2011. [10] J. Zhang, H.-H. Zhong, Z. Jin, T. Shu, S. Cao, and S. Zhou, “Studies on efficient operation of an X-band oversized slow-wave HPM generator in low magnetic field,” IEEE Trans. Plasma Sci., vol. 37, no. 8, pp. 1552–1557, Aug. 2009. [11] N.-C. Chen, T.-H. Chang, C.-P. Yuan, T. Idehara, and I. Ogawa, “Theoretical investigation of a high efficiency and broadband subterahertz gyrotron,” Appl. Phys. Lett., vol. 96, no. 16, p. 161501, Aug. 2011. [12] A. V. Savilov, “Compression of complicated RF pulses produced from the super-radiant backward-wave oscillator,” Appl. Phys. Lett., vol. 97, no. 9, p. 093501, Aug. 2010. [13] I. V. Bandurkin, Y. K. Kalynov, and A. V. Savilov, “High-harmonic gyrotron with sectioned cavity,” Phys. Plasmas, vol. 17, no. 7, p. 073101, Jul. 2010. [14] M. Friedman, J. Pasour, and D. Smithe, “Modulating electron beams for an X band relativistic klystron amplifier,” Appl. Phys. Lett., vol. 71, no. 25, pp. 3724–3726, Dec. 1997. [15] J. Zhou, D. G. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and simulation,” IEEE Trans. Plasma Sci., vol. 37, no. 10, pp. 2002–2011, Oct. 2009. [16] Z. K. Fan, Q. X. Liu, S. X. Liu, C. M. Zhou, and H. Y. Hu, “The linear theory of the transit-time effect in a multiple-cavity resonator,” High Power Laser Particle Beams, vol. 11, no. 5, pp. 633–638, May 1999. [17] Y. Zhao et al., “Analysis and simulation of a multigap sheet beam extended interaction relativistic klystron amplifier,” IEEE Trans. Plasma Sci., vol. 43, no. 6, pp. 1862–1870, Jun. 2015. [18] R. Xiao, C. Chen, J. Sun, X. Zhang, and L. Zhang, “A high-power high-efficiency klystronlike relativistic backward wave oscillator with a dual-cavity extractor,” Appl. Phys. Lett., vol. 98, no. 10, p. 101502, Mar. 2011.
Zhenbang Liu was born in Guangxi, China, in 1986. He received the B.S. and Ph.D. degrees from the Department of Engineering Physics, Tsinghua University, Beijing, China, in 2008 and 2013, respectively. His current research interests include pulsed power technology and high-power microwave sources.
LIU et al.: INVESTIGATION OF KA-BAND HIGH-POWER SHEET BEAM REIO
Hua Huang was born in Chongqing, China, in 1970. He received the B.S. degree in radio physics from Sichuan University, Chengdu, China, in 1993, and the M.S. and Ph.D. degrees in physical electronics from the Graduate School of China Academy of Engineering Physics, Beijing, Chaina, in 2001 and 2006, respectively. His current research interests include highpower microwave sources, microwave measurement, and antenna technology.
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Xiao Jin was born in Gansu, China, in 1969. He received the Ph.D. degree in physics of wireless electronics from the Graduate School of China Academy of Engineering Physics, Beijing, China, in 2000. His current research interests include highpower microwave sources and pulsed power technology.
Shifeng Li was born in Anhui, China, in 1990. He is currently pursuing the Ph.D. degree with the University of Electronic Science and Technology of China, Chengdu, China. He has been with the Institute of Physical Electronics, CAEP. His current research interests include Ka band extended interaction relativistic klystron.
Lurong Lei was born in Sichuan, China, in 1975. She received the M.S. degree in physics of wireless electronics from the Graduate School of China Academy of Engineering Physics, Beijing, China, in 2007. Her current research interests include highpower microwave sources and pulsed power technology.
Lele Li was born in Hena, China, in 1990. He is currently pursuing the M.S. degree in physics of radio physics with the Graduated Student School of China Academy of Engineering Physics, Beijing, China. His current research interests include intense relativistic electron beams technology.
