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Home , Cavity magnetron, Cherenkov radiation, Electronic oscillator, John Ambrose Fleming, TM (triode), Twystron

Review of the high-power tube sources based on Cherenkov

Weiye Xu 1*, Handong Xu 1**

1Institute of Plasma , Chinese Academy of Sciences, 230031 Hefei, Anhui, China *[email protected] *[email protected]

Abstract: Since the first (X-ray tube) was invented by Wilhelm Röntgen in , after more than one hundred years of development, the average power density of the vacuum tube microwave source has reached the order of 108 [MW][GHz]2. In the high-power microwave field, the vacuum devices are still the mainstream microwave sources for applications such as scientific instruments, , , magnetic confinement fusion heating, microwave weapons, etc. The principles of microwave generation by vacuum tube microwave sources include Cherenkov or Smith-Purcell radiation, , and . In this paper, the vacuum tube microwave sources based on Cherenkov radiation were reviewed. Among them, the multi- Cherenkov generators can produce 15 GW output power in X-band. Cherenkov radiation vacuum tubes that can achieve continuous-wave operation include Traveling Wave Tubes and Magnetrons, with output power up to 1MW. Cherenkov radiation vacuum tubes that can generate of the order of 100 GHz and above include Traveling Wave Tubes, Backward Wave Oscillators, Magnetrons, Surface Wave Oscillators, Orotrons, etc.

compressor to generate a strong flow. Among 1. Introduction various vacuum tube microwave sources, the virtual High-power microwave (HPM) source generally oscillator (VCO) is the most popular choice for making refers to a microwave source with a peak output power impulse sources such as microwave bombs. It has a simple exceeding 100MW or an average output power exceeding and compact structure and can generate a strong 100kW and a range between 0.3-300GHz. The wide-spectrum single-pulse microwave. There are also many performance index for evaluating high-power microwave reports of using backward wave oscillators (BWO) as the 2 pulse microwave sources [6]. In addition, there are sources is the quality factor [1] Pavf (Pav is the average power, and f is the frequency). The higher the quality factor, ultra-wideband pulse microwave sources that feed the better. Driven by applications such as magnetically high-power pulses directly to the without using a confinement , microwave-assisted drilling, vacuum tube [7, 8]. The non-impulse microwave source uses microwave weapons, communications, , high-energy a continuously operating high- power source or a RF accelerators, wireless power transmission, and material pulsed high-voltage power source with a relatively high duty processing, the quality factor of microwave devices is cycle to drive the to generate an electron beam. increasing at an order of magnitude every ten years. The In 1896, Wilhelm Röntgen invented the first vacuum average power density of the vacuum tube microwave source tube in Germany, the X-ray tube. In 1904, the British has reached the order of 108 [MW][GHz]2. The maximum physicist invented the first vacuum power density record was created by the Free Electron . In 1906, invented the first vacuum . Looking at the actual demand, HPM is in the United States. Gradually, vacuum tubes have developing towards the goals of high power, high efficiency, been used in more and more applications, including control and wide frequency band. In terms of power, there are two devices, scientific instruments, electronic gramophones, FM development directions, one is high peak power and the , , radars, , etc. With the invention other is high average power. and development of solid-state devices, the application of High-power microwave sources can be divided into vacuum devices in the fields of communications and two categories, impulse microwave sources and non-impulse consumer has gradually withdrawn from the microwave sources. Generally speaking, the impulse historical stage. But in the high-power microwave field, microwave source refers to a microwave source whose rising vacuum devices are still the mainstream. edge is on the order of sub-nanoseconds or picoseconds. It The magnetron was granted its first patent in 1935, includes a primary drive (pulse generation system or and in 1940 the British first deployed the magnetron on a explosive), a pulse compression system, a microwave source, radar. After decades of development, many types of and an antenna. Impulse sources usually convert energy into high-power vacuum tube microwave sources have been short-pulse electromagnetic radiation through low- produced. Since 1960, the development of high-energy storage and rapid release of energy. The main physics theory and technology has promoted the introduction for pulse generation include Marx generators [2, 3], of pulsed power technology. The generation of high-current Blumlein Line [4, 5] technology, etc. In electromagnetic (I> MA) relativistic electron beams with energy close to the bombs, explosives are used as the primary drive, and the static energy of (510 keV) and high-voltage pulses generated by the explosion drives a pulse with of several megavolts or higher has become a

1 reality, which has expanded the range of high-power equal to the phase vp of the RF wave. The M-type . Many high-voltage operating devices that rely microwave tube has a compact structure, a low working on strong currents, such as relativistic , have voltage, and a high efficiency, which can reach more than emerged. At the same time, some devices based on the 80%. Such microwave tubes include magnetrons and relativity effect, such as and free electron crossed-field (CFAs), which can be used in radar (FEL), have also appeared. Table 1 lists the current main , microwave heating, and some other fields. high-power microwave sources, which can be divided into High-power microwave devices with three types: O-type, M-type, and space-charge type. effects, such as virtual cathode oscillators [9], generally do O-type device refers to the device whose electron not require an external guidance for operation. beam drifts in the same direction as the applied magnetic Compared with other types of high-power microwave field. Among them, O-type slow-wave devices use the axial sources, they have the advantages of simple structure, low slow-wave structure to achieve electron beam clustering and requirements on the quality of the electron beam, high power beam interaction. capacity, relatively easy tuning, low impedance, etc. M-type device refers to the device whose drift However, they also have shortcomings such as relatively low direction of the relativistic electron beam is perpendicular to beam-wave power conversion efficiency, a messy frequency the magnetic field. The average drift velocity (푣푑 = 퐸/퐵) of spectrum, and impure modes. the electron under the action of the is

Table 1 High-power vacuum tube microwave sources. The red ( gray shading) in the table indicates the strong current relativity devices, the purple (dark gray shading) indicates the weak current relativity devices, and the black (no shading) indicates the non-relativistic devices. Slow wave (vp< c) Fast wave (vp > c) Traveling Wave Tube (TWT) Free Electron Laser (FEL) Relativistic TWT Gyrotron Backward Wave Oscillator (BWO) Gyro BWO Relativistic BWO Gyro TWT Multi-Save Cherenkov Generator Gyro Klystron (MWCG) Relativistic Diffraction Generator Gyro O-type (RDG) Surface Save Oscillator (SWO) Auto- (CARM) Orotron Magnicon Flimatron Klystron Relativistic Klystron Transit Time Oscillator (TTO) Magnetron Relativistic Magnetron M-type Crossed-Field (CFA) Magnetically Insulated Oscillator (MILO) Space-charge type Virtual Cathode Oscillator (VCO)

Vacuum tube microwave sources can be divided into Cherenkov or Smith-Purcell radiation, transition radiation, high-current relativity devices, weak-current relativity and Bremsstrahlung [1, 10]. devices, and non-relativity devices according to the Cherenkov radiation refers to the radiation generated properties of the electron beam. High-current relativistic when electrons move in a medium when the speed of the beam microwave sources are used to generate short-pulse, electrons is greater than the speed of the electromagnetic high-peak-power microwaves and are used in fields such as moving in the medium. It also includes radiation accelerators. At present, the peak power of several typical when the electrons move in a periodic slow wave structure. high-current relativistic microwave devices has reached the Typical devices based on Cherenkov radiation include level of GW to dozens of GW, the pulse width can reach 100 traveling wave tubes (TWTs), backward wave oscillators ns, and the frequency ranges from P band (230MHz ~ (BWOs), surface wave oscillators (SWOs), multi-wave 1000MHz) to millimeter wave band, and the energy of a Cherenkov generators (MWCGs), relativistic diffraction single pulse is tens to thousands of joules, with a repetition generators (RDGs), Magnetrons, Crossed-Field Amplifier frequency of tens of Hz. Weak-current relativistic and (CFA), magnetically insulated transmission line oscillators non-relativistic microwave sources can generate microwaves (MILOs), etc. with high average power and long pulses. Transition radiation refers to the radiation when The main principles of microwave generation by electrons pass through interfaces with different refractive vacuum tube microwave sources are as follows: slow-wave indices, and also includes radiation when passing through

2 disturbances in the same medium such as conductive grids, 2. Cherenkov or Smith-Purcell metal sheets or gaps on the surface of conductors. The main Cherenkov radiation is a kind of short- difference from Cherenkov radiation is that the field electromagnetic radiation emitted by charged particles when interacting with the electron beam is a standing wave field. it was moving in a medium and its velocity was faster than Devices based on the transit radiation include transit time the in the medium, which was discovered by oscillators (TTOs), , and the like. former Soviet physicist Cherenkov in 1934 [18]. Bremsstrahlung refers to the radiation when electrons Smith-Purcell radiation is the phenomenon of radiated light move in an external electromagnetic field at a varying speed. when free electrons sweep across the grating surface Generally speaking, electrons move in an oscillating form. discovered by S. J. Smith and E. M. Purcell in 1953 [19]. At this time, the frequency of the electromagnetic wave These two radiation principles are similar [20] and can be radiated by the electron is consistent with the frequency of attributed to the role of slow-wave structures. its , or the frequency of a certain harmonic that it In a periodic system, electrons interact with oscillates. Microwave sources based on this include free electromagnetic waves [21], when the direction of electron lasers (FELs), , and Cyclotron electromagnetic wave propagation is the same as the Auto-Resonance (CARMs). direction of electron movement, Theories for analyzing the beam-wave interaction of ̅ vacuum tube microwave sources include small-signal linear 휔 − 푘푧푣푧 ≃ n푘푣푧, (1) theory and large-signal nonlinear theory. The beam-wave where ， ω is the angular frequency, k is the interactions in HPM devices are complex, making accurate z longitudinal wave number, 푘̅ = 2휋/퐿, L is the period length analytical analysis difficult, and the cost of experimenting of the slow wave structure. When the electron beam interacts and developing high-power microwave sources is high. In with the fundamental wave, n=0; When the electron beam order to accurately analyze the beam interaction state, a large number of numerical simulation methods have been studied, interacts with higher harmonics, n≠0. and the PIC (Particle In Cell) method has been widely used. When the direction of electromagnetic wave John M. Dawson summarized the PIC method in 1983 [11]. propagation is opposite to the direction of electron movement (counterpropagating wave), The PIC method is based on the concept of "macro particles" ̅ [12]. PIC-based software includes MAGIC [13] developed 휔 + 푘푧푣푧 ≃ −n푘푣푧. (2) by MRC (Mission Research Corporation), Germany's CST MAFIA (now integrated into the CST Particle Studio), The most common Cherenkov devices are TWT and XOOPIC, MICHELLE developed by the University of BWO. The Brillouin diagram is shown in Fig. 1. The California, Berkeley, and so on. China's Northwest Institute difference between the maximum frequency at the π point of Nuclear Technology and Xi'an Jiaotong University have and the minimum frequency at the 0 point depends on the jointly developed a 2.5-dimensional PIC simulation software depth of the slow wave structure ripple [22]. UNIPIC [14], which can simulate high-power microwave Orthogonal field devices such as magnetrons and devices such as magnetron, VCO, BWO, and MILO. MILOs are different from linear devices such as TWTs. Electron-optical systems involve the generation, When electrons drift in a resonant structure, they convert the shaping, maintenance and collection of electron beams. At potential energy of the electrons into microwaves. However, present, many electron-optical system design simulation since the drift speed of the electron is close to the phase programs have been developed, including EGUN, CAMEO, velocity of the slow wave, they can still be regarded as the etc. EGUN is developed by Bill Herrmannsfeldt at Stanford Cherenkov devices [10]. Linear Accelerator Center (SLAC). It is powerful for electronic trajectory calculation [15][16]; CAMEO ( Electron Optics) is an electron gun design software designed by Cambridge University. Compared to vacuum devices, the development of solid-state devices is more widely known. Since Intel released the world's first microprocessor 4004 in 1971, the density of electronic components integrated on the chip has increased by seven orders of magnitude, and its growth rate follows Moore's law and doubles every two years. In fact, the development of vacuum devices also follows Moore's Law, but it is not the density of electronic components that increases, but the average power density [17]. This paper only reviews the development of vacuum Fig. 1. The Brillouin diagram of the TWT and the BWO. tube high-power microwave sources based on Cherenkov radiation due to space limitations. In fact, so far, there are so 3. Cherenkov radiation devices many papers related to the vacuum tubes. It is impossible for 3.1. Traveling Wave Tube (TWT) us to describe all related studies in detail, and only discuss Most literature believes that the traveling wave tube the most important basic principles and progress. was invented in the in 1943 by Australian-born engineer Rudolf Kompfner. In fact, Andrei Haeff of the United States also made important contributions.

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It can be said that he invented the prototype of the first such as traveling wave tubes in the centimeter wave band traveling wave tube and applied for a patent in 1933. Related and lower frequency and low power fields. Therefore, at information can be found in the IEEE Spectrum article present, researches on traveling wave tubes are mainly ‘Andrei Haeff and the Amazing Microwave Amplifier’ [23]. focused on (millimeter wave, THz), high After decades of development, some microwave power (tens, hundreds of kilowatts and above), and high electric vacuum device R&D companies in Europe and the bandwidth. United States already have many mature products, which are widely used in missile guidance, electronic countermeasures, radar, [24], and other fields. The traveling wave tube is mainly composed of an electron gun, a slow wave structure, a (a package or a periodic permanent magnet structure), and a collector. The electron gun emits an electron beam, and the microwave is amplified by the interaction of the slow wave structure, and the collector is used to absorb the remaining electron beam. The slow-wave structures are in the form of Fig. 2. The basic structure of the traveling wave tube. spirals, coupling cavities, folded , etc. [25]. Designing and analyzing the electron-optical system Millimeter wave and THz wave traveling wave tubes is of primary importance in designing a traveling wave tube. have been extensively studied. Among them, the folded Using finite element, finite difference and other slow-wave structure is more widely used because computational electromagnetic technology and PIC it is easier to fabricate than the spiral and coupled cavity, the all-metal structure is resistant to high power consumption, technology, some electron-optical CAD software has been developed, and the interaction between electromagnetic and the bandwidth is relatively wide [27]. However, the waves and electrons can be simulated and analyzed using a traveling wave tube of this structure has low coupling . In addition, the lumped circuit model can also be resistance and large attenuation, and its efficiency is used to analyze the traveling wave tube. The more widely generally low. John H. Booske et al. established a parametric used is the Pierce equivalent circuit model. In order to solve model [28] that can be used to simulate folded waveguide millimeter wave traveling wave tubes. At present, the the problem that the Pierce impedance tends to infinity at the cutoff frequency, Damien F G Minenna et al. established a research focus of millimeter wave traveling wave tubes discrete model that can be used for small signal analysis of includes slow wave structures [29], electron-optical systems, traveling wave tubes [26]. etc., in order to improve power and bandwidth. In order to The working frequency of the traveling wave tube increase the flexibility of traveling wave tubes, traveling can be from L band to THz band. Some typical research wave tubes with adjustable power and frequency have also been studied. progress is shown in Table 2 and 3. The development of solid-state devices has a huge impact on vacuum devices

Table 2 Research progress of L ~ V band traveling wave tube. Band Power Freq. Gain Efficiency Pulse Duty cycle Institute Model [W] [GHz] [dB] [%] length [s] [%] L 170k 1.2-1.4 28 100μ 5 TMD PT6049 L 12k 1.75-1.85 CW CPI VTL-6640 S 170k 3.1-3.5 22 1000μ 16 CPI VTS-5753 S~C 150[24] 3.4–4.2 50 73 CW TED TL4150 C 40k 5.85-6.425 11 CW CPI VTC-6660E X 100k 8. 5-9. 6 15 100μ 3.3 TED TH3897 X 15k 10.1-10.7 CW CPI VTX-6383 X~Ku 150 10.7– > 50 68 CW TED TH4795 12.75 Ku 60k 15.7-17.7 11 300μ 30 CPI VTU-5692C Ku~K 160 17.3–20.2 > 50 63 CW TED TH4816 K 50 ~26 > 50 55 CW TED TH4626 Ka 500 28.3-30 37-48 29 CW CPI VTA-6430A2 Ka 560 30 42.5 16 CW TED LD7319 Ka 35 32 > 50 54 CW TED TH4606C Ka 50k 34.5-35.5 10 CPI VTA-5710 Ka~V 40 37.5–42.5 48 50 CW TED THL40040CC V 100 43.5-45.5 30 CW TED TH4034C V 230 43.5-45.5 41 CW L3 8925HP V 21[30] 55-60 38 8.5 TTEG Note: TMD [31] is the abbreviation of TMD Technologies LLC in the United States. CPI is the abbreviation of Communications & Power Industries LLC in the United States. TED is the abbreviation of Thales Electronic Device in .

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L3 is the abbreviation of Communications Electron Technologies Incorporation (L3-ETI) in the United States. TTEG is the abbreviation of Thomson Tubes Electroniques GmbH, Germany.

Table 3 Research progress of millimeter wave and THz band traveling wave tubes. Band Average Peak Center 3dB Gain Effic Pulse Duty Institute Model power power [W] Freq. [Hz] bandwid [dB] iency lengt Cycle [W] th [Hz] [%] h [s] [%] W 50 93~95G CW CPI VTW649 5 W 3k[32] 95~96G 10 CPI VTW-57 95 W 3k 93.9~94.1G 10 CPI VTW-57 95A2 W 200 10 TTEG W 150 93~95G 15 10 TED TH4402- 1 W 100 93~95G 15 20 TED TH4402- 2 W 100 300 90.6G 30 L3 W 100 200 91.4G 30 L3 W >60[33] 94~110G >30 >1.7 1 CETC 12th institute W >250[27] 89.6~97.6G >30 >5.8 1 CETC 12th institute mm 35.5 79[34] 233G 2.4G~3G 23 2 50 NGC THz 259m[35] 640G 15G 22 10 NGC THz 71m 670G 15G 17 0.5 NGC THz 39m 850G 15G 22 11 NGC THz 29m 1030G 5G 20 0.3 NGC Note: NGC is short for Northrop Grumman Corporation in the United States. CETC 12th institute is the abbreviation of China Electronics Technology Group Corporation 12th Research Institute, i.e. Beijing Vacuum Electronics Research Institute.

In the 1980s, relativistic TWTs using relativistic mode [36]. China's Northwest Institute of Nuclear electron beams began to develop. In 1990, Donald Shiffler Technology (NINT) and other research institutes have also and others of Cornell University reported an X-band conducted research on relativistic TWTs. Table 4 lists some corrugated waveguide relativistic TWTs. It uses a field research progress of relativistic TWTs. The study found that emission cathode as a pulse energy source, and an electron plasma filling in microwave devices can improve beam is generated by a field emission cathode immersed in a performance and increase output power. The University of magnetic field. The electron beam has a voltage of up to 850 Maryland, the University of Electronic Science and kV and a current of 1 kA. It has gained a gain of 13 ~ 35 dB Technology of China, etc. have conducted theoretical and at 8.76 GHz, and its output power range is 3 ~ 100 MW. The experimental research on plasma-filled traveling wave tubes amplifier is designed to operate in the narrow band of TM01 and made some progress [37, 38].

Table 4 Research progress of relativistic TWTs. Band Peak power Freq. Gain Efficiency Pulse Beam Beam Institute [W] [GHz] [dB] [%] length [s] voltage [V] current [A] X 3M-100M 8.76 13-35 11 100n 850k 1k Cornell University X 70M[39] 9 20 100n 700k 500 Cornell University X 2.1G[40] 9.3 41 10n 680k 7.5k NINT X 1.2G 10.3 35 10n 580k 5.9k NINT mm 70k (simulation 220 28.5 CETC 12th institute result)[41]

3.2. Backward Wave Oscillator (BWO) MW, 10 ns high-power microwave output in the former A backward wave oscillator is also a Cherenkov [42]. device. Unlike a traveling wave tube, in a backward wave The BWO structure is similar to that of the TWT, as oscillator, the wave is opposite to the shown in Fig. 3 and is mainly composed of an electron gun, direction of electron movement, so it is called a backward a magnet, a slow-wave structure, a Bragg reflector, a wave oscillator (or a backward wave tube). The BWO is the collector, and an output window. The Bragg reflector is used first experimentally verified high-current relativistic to reflect microwaves to the output , and can also be high-power microwave source. In 1973, it produced 400 replaced by cut-off waveguides, resonant reflectors, etc. 5

There is also a type of BWO with microwave output near the and THz wave) BWOs, and the other is the research of end of the electron gun. A BWO with this structure high-power relativistic BWOs. sometimes installs a terminal absorber near the terminal of the slow-wave structure of the collector to absorb the forward wave and prevent the wave reflection from adversely affecting the tube. J. A. Swegle et al. established the linear theory of the BWO [43-46], and gave a basic analysis of the beam-wave interaction of the BWO. B. Levush established a set of nonlinear equations describing the beam-wave interaction of the BWO, and considered the effects of reflections at both ends [47]. In the slow-wave structure of the BWO, the electron beam generates velocity and density Fig. 3. The basic structure of the BWO. modulation under the action of microwaves, and the The research institutes for millimeter wave and clustered electrons transfer energy to the microwave in the terahertz BWOs include 's ISTOK company, the US deceleration region of the high-frequency field. In contrast to CCR company, the US MICROTECH company, and the the group velocity, the of the wave and the CETC 12th institute. Among them, the ISTOK has developed direction of the electron beam are the same in the BWO, and the BWO with a frequency covering 36 GHz to 1400 GHz their velocity is close to equal. Due to the of the [50]. Table 5 lists the research progress of non-relativistic return wave in the slow-wave structure, when the electron millimeter wave and terahertz BWOs by research institutions beam voltage is changed (that is, the electron beam velocity represented by ISTOK. is changed), the oscillation frequency that satisfies the phase Like the millimeter wave TWT, in the millimeter condition changes accordingly. In general, due to the wave BWO, a folded waveguide is mostly used as a slow dispersion characteristics of its slow-wave structure with wave structure. The main research directions of millimeter dvp/dω>0 (where vp is the phase velocity), the oscillation wave and THz BWOs include increasing frequency, using frequency increases with the increase of the electron beam multi-stage depressed collectors and other technologies to voltage. When a stable frequency is required, an external improve efficiency, improve output coupling efficiency, reference can be used to achieve phase lock [48, 49]. reduce the required magnetic field or reduce the volume of At present, there are two main research directions of magnet system . Progress has also been made in the research BWOs. One is the study of high-frequency (millimeter wave of the multi-frequency BWOs [51] and the plasma-filled BWOs [38].

Table 5 Research progress of non-relativistic millimeter wave and terahertz BWOs. Band Power [mW] Freq. Efficiency Pulse Beam Beam Institute Model [GHz] [%] length [s] voltage [V] current [mA] Ka~V 15-40 36-55 ~0.1 400-1200 20-25 ISTOK OB-69 V~W 12-30 52-79 ~0.1 400-1200 20-25 ISTOK OB-70 W~mm 6-30 78-119 ~0.05 500-1500 20-25 ISTOK OB-71 mm 6-20 118-178 ~0.05 500-1500 20-25 ISTOK OB-86 mm 6-15 177-260 ~0.05 700-1900 15-22 ISTOK OB-24 mm~THz 1-10 258-375 ~0.005 1000-4000 25-40 ISTOK OB-30 THz 1-5 370-535 ~0.005 1000-4500 25-40 ISTOK OB-32 THz 1-5 530-714 ~0.002 1500-6000 30-45 ISTOK OB-80 THz 1-5 690-850 ~0.002 1500-6000 30-45 ISTOK OB-81 THz 0.5-5 790-970 ~0.001 1500-6000 30-45 ISTOK OB-82 THz 0.5-3 900-1100 ~0.001 1500-6000 30-45 ISTOK OB-83 THz 0.5-2 1070-1200 ~0.001 1500-6000 30-45 ISTOK OB-84 THz 0.5-2 1170-1400 ~0.001 1500-6000 30-45 ISTOK OB-85 THz >8k (simulation 340-368.2 ~3 CW 11k-17k 20 IECAS result) [52] Note: IECAS is short for Institute of Electronics, Chinese Academy of Sciences.

The relativistic BWO has the characteristics of high Institute of Nuclear Technology, the China’s National power, high efficiency, and simple structure. The relativistic University of Defense Technology (NUDT), and the China BWOs are widely used in high-power microwave weapons Academy of Physics (CAEP). and other fields. The institutions that study relativistic In order to improve power, a large over-mode BWOs include the Russian Institute of Applied Physics slow-wave structure is generally used. So far, the maximum (IAP), the Russian Institute of High Current Electronics peak power has exceeded 5 GW in S-band, X-band and other (IHCE), the University of Maryland, Cornell University, the frequencies. For a small over-mode BWO (D/λ is about 1.8, University of New Mexico, the China’s Northwestern D is the diameter of the interaction zone, λ is the free-space

6 wavelength), at 550kV, the maximum power obtained is 0.8 the research directions now is the relativistic BWOs with the GW and the frequency is 10 GHz [53]. The research low guiding magnetic field. In addition, higher power, higher progress of the relativistic BWOs is shown in Table 6. It is pulse width, and higher efficiency BWOs are also important worth noting that the efficiency of some ultra-short pulse research directions. To increase the pulse width, the pulse relativistic BWOs exceeds 100%. This is the use of the shortening effect needs to be overcome [55]. For example, spatial accumulation effect of energy in ultra-short Xingjun Ge of the National University of Defense microwave pulses, which produces pulses with peak power Technology used two cavities to reduce the RF field, and significantly higher than the power of the electron beam. introduced a large-radius collector to reduce the number of Related progress can refer to literature [54]. secondary electrons generated by electron bombardment. The main disadvantage of the relativistic back wave The microwave output power was 2 GW with 110 ns pulse oscillator is that it generally requires a large magnetic field (> length in the S-band [56]. 2T), and the magnet system is too large. Therefore, one of

Table 6 The research progress of the relativistic BWOs. Band Peak Freq. Efficiency Pulse length Beam Beam Institute power [W] [Hz] [%] [s] voltage [V] current [A] L 1.05G[57] 1.61G 14.4 38n 703k 10.6k NUDT S 1G[58] 3.6G 20 100ns (can run 700k 7k NUDT at 10Hz repeat frequency) S 5.3G[59] 3.6G 30 25ns 1.2M 15k IHCE S 2G[56] 3.755G 30 110n 820k 8.1k NUDT X 5.06G[60] 8.25G 25 13.8n 1M 20k CAEP, Tsinghua University X 0.8G[53] 10G 24 550k 6k IHCE X 0.55G[61] 9.45G 17 8n 620k 5.2k University of New Mexico X 0.9G[62] 9.4G 29 32ns 500k 6.2k SWUST, CAEP X 1.4G[63] 9.4G 26 30ns 790k 6.7k CAEP X 3G[64] 7.5 30n 2M 20k IHCE Ka 1.1G[65] 38G ~150 0.2n 290k 2.3k IERAS, IHCE Ka 400M[66] 38G 66 0.2n 290k 2.1k IERAS, IHCE mm 100k[67] 140G 0.1 1-2n 100k 1k CAEP THz 600k[68] 340G 0.6 1.66n 100k 900 CAEP Note: SWUST is short for China’s Southwest University of Science and Technology. IERAS is short for Institute of Electrophysics, Russian Academy of Sciences.

3.3. Surface Wave Oscillator Surface wave oscillator (Cerenkov Oscillator With the Bragg Reflection ) is a very powerful high-power microwave and terahertz wave source. In order to improve the power capacity, a large-size over-mode waveguide is used [69]. The maximum value of the electromagnetic wave appears near the surface of the slow wave structure, so it is called the surface wave oscillator. For a smooth-walled cylindrical waveguide, for TMmn mode, the relationship between the allowable maximum power Pmax and the maximum electric field Fig. 4. Brillouin plot of a surface wave oscillator, where kz is strength Emax,w near the waveguide wall is [70], the longitudinal wave number.

kV 2 퐸 [ ]휆[cm] 푃 [GW] = 8.707(1 + 훿 ) ( 푚푎푥,푤 cm ) × 푚푎푥 0,푚 511

2 휋 ′4 휐푚,푛 2 1 퐷 √1 − ( ′) 2 . (3) 4 2휋퐷 휐푚,푛 Where, 퐷′ = 휋퐷/휆 ， D is the inner diameter of the waveguide, λ is the free space wavelength, νm,n is the root of the m-order Bessel Function Jm(x)=0. When m=0, δ0,m=1, otherwise δ0,m=0. Using an over-mode waveguide can increase D’, thereby increasing power capacity.

Fig. 5. The basic structure of the surface wave oscillator and the schematic diagram of electron clustering. 7

In the millimeter wave band, many simulations and The surface wave oscillator generally operates in the experiments have been done by China's Northwest Institute fundamental mode TM01. The intersection of the Doppler of Nuclear Technology, Russian Institute of Applied Physics, line of the electron beam ω=kzvz and the dispersion curve of etc. Most of the simulation results are good, but the the TM01 mode is located to the left near the point π, as experimental results are very inefficient. Moreover, in the shown by the intersection of the Vp2 Doppler line and TM01 millimeter wave band, the output mode of the surface wave mode dispersion curve shown in Fig. 4. The group velocity oscillator is not pure, and there are many high-order modes of the generated wave is positive, and the phase velocity is mixed [21, 72]. also positive, which is in a traveling wave state [71].

Table 7 Advances in simulation and experimental research of surface wave oscillators. Band Peak power Freq. 1 dB Efficiency Pulse Institute Years Research [MW] [GHz] bandwidth [%] length [ns] form X 500[70] 8.3 15 20 University of 2000 Experiment Maryland Ka 50[21] 33.3 6 15~30 IAP 1984 Experiment E 12 62.5 4 10~15 IAP 1984 Experiment D 8 125 3 5~10 IAP 1984 Experiment

D 680[73] 140 90.67 0.11 Xi’an Jiaotong 2009 Simulation University D 2.6[72] 154 1.4 1.5 NINT 2013 Experiment D 5[69] 148 0.7 3 NINT 2013 Experiment mm 0.5[21] 333 0.2 3~5 IAP 1984 Experiment

3.4. Multi-Wave Cherenkov Generator (MWCG) slow-wave region, the electron beam interacts with Multi-wave Cherenkov generator (MWCG for short) electromagnetic waves efficiently, so the high-power is one of the most powerful microwave devices. Similar to microwaves are generated and output through the output surface wave oscillator, in order to obtain high output power, window. Usually, the two-stage slow-wave structures are an over-mode structure is used. MWCG uses a two-stage symmetrical, and there are also studies of MWCG using slow wave structure with the same space period and requires asymmetric slow-wave structure [76]. a strong axial magnetic field. Both sections of the slow-wave The horizontal and vertical dimensions of the structure work near the π point of the dispersion curve. Its slow-wave structures of each segment of MWCG are close basic structure is shown in Fig. 6 [74]. to each other, and surface waves cannot be generated like the SWOs. The electron beams interact with surface waves and body waves simultaneously inside the MWCGs. Due to the open electromagnetic structure and complex electron beam physical process of MWCGs, there is no complete self-consistent non-linear theory to analyze the interaction process. The approximate linear theory can be used to analyze the electromagnetic field, the starting current, etc. [77]. Fig. 6. The basic structure of MWCG. 1 is the magnetic field A large number of theoretical and experimental coil, 2 is the , 3 is the cathode, 4 is the relativistic studies on MWCG have been conducted by research electron beam, 5 is the beam collimator, 6 is the first-stage institutions represented by the Russian Institute of High slow-wave region, 7 is the fast-wave drift tube section, 8 is Current Electronics since the 1980s [78]. Some research the second-stage slow wave region, 9 is a horn structure that progress is shown in Table 8. At present, the MWCG can absorbs residual electron beams, and 10 is a generate a maximum of 15GW in the 3cm band. In recent output window [75]. years, combined with the advantages of other microwave The electron beam undergoes speed modulation in the tubes such as klystrons, research on new devices such as first-stage slow wave region; then it is converted into density Cherenkov generators in the form of klystrons has appeared modulation in the drift tube section (fast wave region) to [79]. form an electron pre-grouping; In the second-stage

Table 8 The progress in experimental research of MWCGs. Band Peak power [GW] Freq. [GHz] Efficiency [%] Pulse length [s] Institute Years X 0.2 8.8-9.77 10 0.5μ-0.6μ IHCE 1990 X 15 10 50 60n~70n IHCE 1990 X 0.85 [76] 9.23 30 30n IHCE 2013 Ka 3 30.86 20 60n~80n IHCE 1990

8

Ka 1.5 [77] 34.80 15 60n~80n IHCE 1990 Ka 0.5~0.6 [80] 33.94 6~7 20n IHCE 2000

3.5. Relativistic Diffraction Generator (RDG) The relativistic diffraction generator (RDG) also uses an over-mode structure. In an RDG, the microwave field is distributed in structural space, as opposed to devices based on interactions with surface waves (SWO, MWCG). The working range of the RDGs falls within the frequency region of 2π-type of the lower axially symmetric mode of the periodic waveguide [81]. At present, the highest peak power is recorded at 9 GW, and the wavelength is 9-11.3 mm [82]. Fig. 7. The basic structure of RDG.

Table 9 The progress in experimental research of RDGs. Band Peak power Freq. Efficiency Pulse Beam Beam Institute Years [GW] [GHz] [%] length [s] voltage [V] current [A] K-Ka 9 [82] 26.55-33.33 33 100n-350n 1.6M 17k IHCE 1990 V 2 41.7 IHCE 1990 V 7 44.1-46.2 29 200n-260n 1.5M 16k IHCE 1990 V 5.6 46.2 17 700n 1.7M 19k IHCE 1990

3.6. Orotron The typical schematic of the orotron is shown in Fig. Orotron is also called ‘diffraction radiation oscillator’ 9. The ortron consists of a cathode, a collector, a flat mirror or ‘laddertron’ [83]. The horizontal field of the Orotron is with periodic structure, a concave mirror, an output much larger than the vertical field (푘⊥ ≫ 푘푧), and it works in waveguide, etc. The open cavity is used to provide the the first harmonic state. effective selection of transverse modes [86]. The orotrons ̅ have the ability to produce millimeter waves and even THz ω ≃ 푘푣푧. (4) (terahertz) waves. The orotrons can output power from Relative to the π mode of an SWO, the Orotron several mW to tens of kW in weakly relativistic devices, and oscillation is called 2π mode. A linear theory was proposed can output power up to hundreds of MW in strong by Richard P. Leavitt et al [84] to calculate the starting relativistic devices. The output frequency of the orotrons current and the electronic tuning characteristics. A nonlinear ranges from 10 GHz to 361 GHz was observed in the orotron theory showing how to optimize the choice of the interaction experiments [86]. length and the ratio between ohmic and diffractive losses was proposed by Gregory S. Nusinovich [85].

Fig. 9. The basic structure of the Orotron. Fig. 8. The Brillouin diagram of the Orotron.

Table 10 The progress in experimental research of Orotrons. Band Peak Freq. Efficiency Pulse Institute Years Remark power [W] [GHz] [%] length [s] K 200[87] 25 1μ IPP, USSR 1969 V 100m[88] 53-73 60μ AER, HDL 1981 mm 50m[86] 140 10m IAP 2002 THz 30m 370 10m IAP 2002 Ka 120M[21] 37.5 4~10 6n~8n IAP 1984 Strong relativistic V 50M 60 5 6n~8n IAP 1984 Strong relativistic Note: AER, HDL is short for U.S. Army Electronics Research and Development Command, Harry Diamond Laboratories. IPP, 9

USSR is short for Inst. for Phys. Problems, Moscow, Soviet Union.

3.7. Flimatron (Smith-Purcell Free Electron Maser) collected by the anode. These electrons transfer energy to the If the electrons in the Cherenkov oscillator are microwave field, which is conducive to the establishment of synchronized with the first spatial harmonics of the wave, microwave oscillations in the magnetron, which can be the phase velocity of the wave is close to the speed of light, called favorable electrons. Those electrons in the microwave acceleration field get energy from the microwave field and ω ≃ 푘 c, (5) 푧 move toward the cathode, and finally hit the cathode. then the Smith-Purcell Free Electron Maser realized [89, 90]. Electrons in the microwave acceleration field are called The flicker image of the particles is different from the unfavorable electrons. The unfavorable electrons emit a large oscillation of the particles in a maser, so this device was number of secondary electrons when they bombard the called the flimatron. The radiation of a wave is similar to a cathode, which can increase the number of electrons in the free electron laser, and the angular frequency of the wave is, interaction zone. The maximum deceleration field is the 2 clustering center of electrons, and the electrons on both sides ω ≃ 훾 Ω, (6) of it move toward the clustering center. The maximum where， acceleration field area is the center of the electron's divergence, and nearby electrons move to the left and right ̅ Ω ≃ 푘푣푧. (7) sides, and finally turn into favorable electrons. In this way, The research progress is shown in Table 11. during the establishment of the oscillation, the number of unfavorable electrons is decreasing, the number of favorable Table 11 The progress in experimental research of electrons is increasing, and they are concentrated toward the Flimatrons. cluster center, and a spoke-shaped electron cloud is gradually formed in the interaction space, as shown in Fig. Ba Peak Freq. Efficien Pulse Institut Year 10. As the microwave field in the interaction zone decays nd power [GHz cy [%] lengt e s exponentially away from the anode surface, the microwave [MW] ] h field on the cathode surface is very weak, and the clustering K 60[21] 25 5 ~ns IAP 1984 of electrons is extremely small. There will be no obvious V 20 61.22 5 ~ns IAP 1984 electronic spokes near the cathode, but a uniform distributed W 3 90.91 5 ~ns IAP 1984 electronic wheel. The overall effect of the interaction between electrons and microwaves in a magnetron is that the 3.8. Magnetron electrons give energy to the microwave field, establishing a Magnetron is a kind of orthogonal field oscillator, stable microwave oscillation in the magnetron. which can also be classified as a Cherenkov radiation device. Since the advent of magnetrons, a large number of It has the advantages of high efficiency and low cost and is magnetron theories have been proposed [94-96], which greatly widely used in radar, industrial microwave heating, helped the development of magnetrons. With the household microwave ovens, and other fields. At the development of computer technology, the PIC program beginning of the 20th century, American Albert W. Hull first represented by MAGIC is widely used in the design and invented the magnetron [91][92]. In the 1930s, Н. Ф. simulation of magnetrons [97]. Aleksereff of the Soviet Union and J. T. Randall of the United Kingdom and others developed the multi- with practical value. The relevant history can be found in [93]. In World War II, the multi-cavity magnetrons were widely used in military radars, which greatly promoted the development of magnetrons. Subsequently, many new types of magnetrons such as coaxial magnetrons, voltage-tuned magnetrons, and long anode magnetrons were invented. Reports of relativistic magnetrons began to appear in the 1970s. The magnetron includes an electrical power input circuit, a magnet, a cathode, a slow-wave structure (anode), and an output structure. The magnetron usually works in π Fig. 10. The schematic diagram of the electronic spokes of a mode or 2π mode (in the case of π mode, the phase of the magnetron. microwave electric field at the mouth of two adjacent is 180 ° different). The electrons emitted from the The efficiency of the magnetron can reach 80%. At cathode make a cycloidal motion under the action of an the frequency of 915 MHz, the output orthogonal electromagnetic field. Adjust the DC voltage and power can reach 100 kW; at the frequency of 2.45 GHz, the magnetic field so that the average drift velocity of the continuous wave output power can reach 30 kW [98]. In electrons in the circumferential direction is equal to the terms of bandwidth, although orthogonal field devices like a phase velocity of the microwave field, and the electrons can magnetron are not as good as the traveling wave tubes, they interact with the microwave. The electrons in the microwave are better than the klystrons. In the field of magnetrons for deceleration field gradually transfer the energy to the microwave ovens, the main application frequency is 2.45 microwave field, move toward the anode, and are finally GHz with an efficiency of 70% [99]; the frequency of 5.8 10

GHz can also be used in microwave ovens, with efficiency with a 50 ns pulse width and a 0.01% duty cycle [103]. They currently around 50% and power close to 1 kW [100, 101]. have developed a series of millimeter wave space harmonic In the field of military radar, after several generations magnetrons, with frequencies from 95 GHz to 225 GHz, and of development, at the X-band, with a peak output power of the peak power up to 20 kW at 95 GHz [104]. 25kW, the life of the magnetron can reach 6000+ hours; Part of the research progress of magnetrons is shown when the output peak power is 4kW, the life can reach 15k + in Table 12. Among them, CPI has produced a series of hours. The latest generation of military magnetrons has magnetrons for air traffic control (frequency further improved its performance by improving mode 2.7GHz-34.5GHz, peak power up to 1MW), stability, developing new tuned output systems, and adopting (frequency 2.7GHz-8.5GHz, peak power up to 1MW), new rare-earth [102]. frequency agile radar (frequency 5.45GHz-32.1GHz, peak The use of non-π mode spatial harmonic magnetrons power up to 800kW), industrial applications is also an attractive option for developing high-power (896MHz-928MHz, continuous wave power 30-125kW), etc. millimeter wave, terahertz sources. For example, N. I. At present, the main research directions include high power, Avtomonov of the Institute of Astronomy of the high frequency, high efficiency, high pulse width or high National Academy of Sciences of Ukraine (IRANASU) repetition frequency, miniaturization, phase locking [105], reported that a space harmonic magnetron can output a peak and tunability. power of 1.3 kW and an average power of 0.13 W at a frequency of 210 GHz. It can continuously run for 500 h

Table 12 The progress in experimental research of non-relativistic magnetrons. Ba Peak Average Freq. [Hz] Effici Pulse Duty Beam Beam Institute Model nd power power ency length cycle voltage curren [W] [W] [%] [s] [%] [V] t [A] S 19k[105] 19k 2.45G 71 CW 11.7k 2.3k Sichuan University, China C 2.5M 2.5k 5.7G±10M 45 4μ 0.1 45-50k 110 CPI VMC3109 C 700[106] 5.8G 50 4.7k 0.3 UESTC C 1k[101] 5.8G 58 10ms 4.34k 0.416 CAEP (5Hz) X 1.5M 2.7k 9.3G±30M 45 3.5μ 0.18 34-37k 90A CPI VMX3100HP W 20k 95G 0.1μ IRANASU mm 1.7k 225G 0.05μ IRANASU Note: UESTC is short for University of Electronic Science and Technology of China.

In the 1970s, G. Bekefi, T. J. Orzechowski and other Applied Physics, Russia), UESTC (University of Electronic scientists began to apply pulse power technology and Science and Technology of China), and so on. The frequency explosion-cathode technology to magnetrons, and developed of the microwave generated by the relativistic magnetron has relativistic magnetrons [107, 108]. The main R&D covered the range of 1 ~ 10 GHz, and the microwave output institutions of relativistic magnetrons include PI (Physics power of a single device reaches several GW. Some research International Company, United States), TINP (Tomsk progress is shown in Table 13. Institute of , Russia), IAP (Institute of

Table 13 The progress in experimental research of relativistic magnetrons. Band Peak power Freq. Efficiency Pulse Beam Beam Institute Remark [W] [GHz] [%] length voltage current [s] [V] [A] L 13M[109] 1 0.8 100n 315k 5k University of Magnetic priming Michigan S 540M[110] 2.68 6.5 ~40n 489k 16.9k UESTC Permanent magnet packaging S 1G~1.6G[111] 2.83-2.95 6-10 <35n 750k 21k PI (one-vane extraction) S 2.4G-3.6G 2.85-2.90 15-23 <35n 750k 21k PI (six-vane extraction) S 1.7G[108] 3 35 30n 360k 12k MIT S 1G[112, 113] 3 9n University of Transparent New Mexico cathode; rapid start-of-oscillations; 11

high efficiency C 6.9G[114] 4.5 9 20n-40n 1.2M 10k PI (six-vane extraction) L 400M[115] 1.21 10 70n PI Frequency tunable 23.9% S 500M 2.82 10 70n PI Frequency tunable 33.4% S ~1G[110] 2.78 ~10 ~620k ~16.4 UESTC Frequency tunable 18% (500MHz) Note: MIT is short for Massachusetts Institute of Technology.

3.9. Crossed-Field Amplifier (CFA) CFA are shown in Fig. 11. The progress in experimental Crossed-field amplifier (CFA) is another type of research of CFAs is shown in Table 14. orthogonal field device developed on the basis of magnetrons. It began to develop in the middle of the 20th century. CFAs are widely used in radar transmitters and are generally used as the last stage of the amplification link. The CFA has the advantages of high efficiency, low operating voltage, high phase stability, compact size, etc., and its peak power can reach several MW [116]. CFAs can use cold without preheating and can be instantaneously started. The main disadvantages of CFAs are low gain and large . The gain is generally only 10~20 dB. Improving gain is the main research direction of CFAs. The cross-field amplifier is generally composed of a magnet, an electron gun, a slow-wave structure (anode), a bottom , a collector, and a microwave output structure. According to whether the direction of the phase velocity and the group velocity of the waves are in the same direction, the CFA can be divided into two types: forward wave CFA and backward wave CFA [117]. According to the electron beam injection method, it can be divided into injection type and distributed emission type. The distributed emission device has only one cathode (i.e., the electron gun). The injection type device has a bottom electrode in addition to an electron gun. According to the structure, the CFAs can be divided into reentrant CFA and non-reentrant CFA. Reentrant devices do not have separate collectors. The anode collects the remaining electrons. At present, the most widely used CFA device is the reentrant, distributed-emission, Fig. 11. The simple structure of the CFAs. (a) Reentrant, forward wave CFA. CFAs usually have slow wave structures distributed-emission, forward wave CFA; (b) Non-reentrant, similar to TWTs. The forward wave CFA usually uses helix injection-type, forward wave CFA. while backward wave CFA usually uses the bar line. The structure of a typical reentrant, distributed-emission, forward wave CFA and a non-reentrant, injection-type, forward wave

Table 14 The progress in experimental research of CFAs. Ba Peak Average Freq. [Hz] Effic Gai Pulse Duty Voltag Peak Institute Model nd powe power iency n lengt cycle e [V] curren r [W] [W] [%] [dB] h [s] [%] t [A] L 90k 2.88k 1.3G±50M 33 40μ 3.2 11k 25 CPI VXL1169 C 900k 4.5k 5.65G±250M 50μ 0.5 30k CPI VXC1659 S 250k[ 20k 2.9G±150M >52 13 300μ 8 18k 23.8 CETC 12th 116] institute S 220k 4.4k 3.3G±200M 38 50μ 2 16k 36 CPI VXS1925 X 300k[ 5.1k 9G±500M >57 >14 100μ 1.7 24k 21.8 CETC 12th 118] institute X 900k 900 9.2G±300M 39 0.83μ 0.1 38k 60 CPI SFD233G

12

3.10. Magnetically Insulated Transmission Line The MILOs do not require an external magnetic field. Oscillator (MILO) The DC magnetic field is provided by the internal current Magnetically insulated transmission line oscillator through the tube. This DC magnetic field together with the (MILO) and its linear theory were proposed by Raymond W. orthogonal DC electric field determines the electron drift Lemke and M. Collins Clark in the United States in 1987 speed. The DC magnetic field generated by MILO itself can [119]. Its structure is shown in Fig. 12. In 1995, Steve E. suppress the emission of electrons from the cathode to the Calico et al. proposed a load-limiting MILO with an anode anode. This self-insulation mechanism and low impedance electron collection structure [120], and obtained a peak can prevent the electron strike between the cathode and output power of up to 1GW. Its structure is shown in Fig. 13. anode, so MILO can withstand very high power. The It consists of a cathode, a slow wave structure, an RF (radio operation of MILO can be divided into three stages, which frequency) structure, and a collector (beam dump). are magnetic insulation formation, RF growing, and For the history of MILO, please refer to the paper [121]. microwave saturation [122], as shown in Fig. 14. Xiaoping Zhang of China’s National University of Defense Partial research progress of MILO is shown in Table Technology proposed a new MILO (V-MILO) with a virtual 15. The main disadvantage of MILO is that the efficiency is cathode oscillator (Vircator) as the load. Under the condition not high. The research directions of MILO mainly include of 540 kV beam voltage and 42 kA beam current, it can get a improving power, pulse width, and efficiency, solving the peak output power of 500 MW at 5 GHz, with an efficiency problem of RF breakdown, and studying the pulse of 2.3% [121]. At present, MILO has become one of the shortening mechanism. For example, Michael D. Haworth of highest single pulse ratio microwave energy output devices the United States proposed a field-forming cathode structure among all HPM devices. Various forms of MILO have been with a pulse width of 400 ns at a working voltage of 300 kV developed, including load-limiting MILO (the load types [123]. S.E. Calico of the United States designed a velvet include Vircator, MILO, Axial Dode, TTO, etc.). cathode and conducted repeated frequency operation experiments. Under the voltage of 400kV, 10 pulses were run at 5Hz frequency, and the consistency did not change much [124].

Fig. 12. The structure of the first MILO (line-limiting type).

Fig. 14. Three stages of MILO operation.

Fig. 13. The structure of the first load-limiting MILO.

Table 15 The progress in experimental research of MILOs. Band Power [W] Freq. Efficiency Pulse Beam Beam Institute Type [GHz] [%] length voltage current [s] [V] [A] L 2G[125] 1.2 7 175n 475k 60k U.S. Air Load-limiting type Force Lab L 3.57G[126] 1.23 7.9 46n 740k 61k CAEP Double step cathode & Load-limiting type L 2.2-2.5G[127] 1.76-1.78 7.3-7.9 515-538kV 58-61k NUDT Load-limiting type S 0.9G[128] 2.4 6 23n 500k 30k CNRS S 1G[122] 2.59 4.6 ~40n 665k 32.3k NUDT Cone-shape MILO S 500M[129] ~2.64 5.7 ~90n 350k 25k NUDT Cone-shape MILO Ku 89M[130] 12.9 0.3 15n 539k 57k CAEP Note: CNRS is short for French National Centre for Scientific Research. 13

2. Pinguet, S., Dupéroux, J., Delmote, P., Bieth, F., and 4. Summary Bischoff, R., 'Short-Pulse Marx Generator for High-Power The nature of all vacuum tube microwave sources Microwave Applications', Ieee Transactions on Plasma utilizes the interaction of electrons and waves. There are Science, 2013, 41, (10), pp. 2754-2757. some new beam-wave interaction structures that have been 3. Sakamoto, T. and Akiyama, H., 'Solid-State Dual Marx designed and studied [131]. There are also studies that use Generator with a Short Pulsewidth', Ieee Transactions on multiple sources to combine into one high-power source [6, Plasma Science, 2013, 41, (10), pp. 2649-2653. 131]. 4. Rossi, J.O., Barroso, J.J., and Ueda, M., 'Modeling of We have calculated the experimental results of the Wound Coaxial Blumlein Pulsers', Ieee Transactions on Cherenkov radiation vacuum microwave tubes. Considering Plasma Science, 2006, 34, (5), pp. 1846-1852. three indicators of frequency, power and pulse width, which 5. Novac, B.M., Wang, M., Smith, I.R., and Senior, P., 'A 10 are shown in Fig. 15. As can be seen from the figures, power, Gw Tesla-Driven Blumlein Pulsed Power Generator', Ieee frequency, and pulse width are contradictory parameters. The Transactions on Plasma Science, 2014, 42, (10), pp. larger the output power, the lower the frequency and the 2876-2885. smaller the pulse width. TWTs, BWOs, SWOs, MWCGs, RDGs, etc. can 6. Rostov, V.V., Elchaninov, A.A., Romanchenko, I.V., and produce GW-level output power in the 10 GHz band, but the Yalandin, M.I., 'A Coherent Two-Channel Source of pulses are less than 1 μs. Cherenkov Pulses', Applied Physics Letters, Cherenkov radiation vacuum tubes that can achieve 2012, 100, (22), p. 224102. continuous wave operation include TWTs and Magnetrons, 7. Andreev, Y.A., Gubanov, V.P., Efremov, A.M., Koshelev, with output power up to 1MW. V.I., Korovin, S.D., Kovalchuk, B.M., Kremnev, V.V., Plisko, V.V., Cherenkov radiation vacuum tubes that can generate Stepchenko, A.S., and Sukhushin, K.N., 'High-Power frequencies of the order of 100 GHz and above include Ultrawideband Source', in, Digest of TWTs, BWOs, Magnetrons, SWOs, Orotrons, etc. The Technical Papers. PPC-2003. 14th IEEE International Pulsed output power of SWOs can reach 10 MW level, but the pulse Power Conference (IEEE Cat. No.03CH37472), (2003) width is only ns level. The TWTs (folding TWTs) can output 8. Andreev, Y.A., Buyanov, Y.I., Efremov, A.M., Koshelev, an average power of 100 W at 91.4 GHz and 39.5 W at 233 V.I., Kovalchuk, B.M., Plisko, V.V., Sukhushin, K.N., Vizir, V.A., GHz. The Magnetrons (space harmonic magnetrons) can and Zorin, V.B., 'Gigawatt-Power-Level Ultrawideband output a peak power of up to 20 kW at 95 GHz and a peak Radiation Generator', in, Digest of Technical Papers. 12th power of 1.7 kW at 225 GHz. The Orotrons can output a IEEE International Pulsed Power Conference. (Cat. power of 50 mW at 140 GHz and 30 mW at 370 GHz. No.99CH36358), (1999) 9. Davis, H.A., Bartsch, R.R., Thode, L.E., Sherwood, E.G., and Stringfield, R.M., 'High-Power Microwave Generation from a Virtual Cathode Device', Letters, 1985, 55, (21), pp. 2293-2296. 10. Schamiloglu, E., 'High Power Microwave Sources and Applications', in, 2004 IEEE MTT-S International Microwave Symposium Digest (IEEE Cat. No.04CH37535), (2004) 11. Dawson, J.M., 'Particle Simulation of Plasmas', Review of Modern Physics, 1983, 55, (2), pp. 403-447. 12. Hongyu Wang, Wei Wei. Development of Particle-In-Cell Simulation: Physical Considerations and Computing Techniques.

Fig. 15. The ‘frequency – power - pulse duration’ http://wenku.baidu.com/link?url=DYWXvKDQzZ2AqlKfxWW experimental results of various vacuum microwave tubes. Xs-P-x62OXqwjgiLSq90hgcdYw_Vg7J9yiN4eIfVWDc_4NRAdo WOaQV2C9pV247VZwiPgeCOz6tB63uBvMTLfPZq 5. Acknowledgments 13. http://www.mrcwdc.com/ This work was supported in part by the National 14. Wang, J., Zhang, D., Liu, C., Li, Y., Wang, Y., Wang, H., Key R&D Program of China under Grant No. Qiao, H., and Li, X., 'Unipic Code for Simulations of High 2017YFE0300401 and 2016YFA0400600, and the Power Microwave Devices', Physics of Plasmas, 2009, 16, (3), National Magnetic Confinement Fusion Science Program p. 033108. of China under Grant No. 2015GB102003 and 15. http://egun-igun.com/ 2018YFE0305100. 16. https://www.aetjapan.com/english/software.php?Elec tronGuns_IonSources_design=EGUN 6. References 17. Granatstein, V.L., Parker, R.K., and Armstrong, C.M., 1. Ding, W., Principles of High Power Microwave 'Vacuum Electronics at the Dawn of the Twenty-First Generators (in Chinese), (Defence Industry Press, 2008) Century', Proceedings of the Ieee, 1999, 87, (5), pp. 702-716. 14

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