Abstract
Terahertz applications urgently require high performance and room temperature terahertz sources. The gyrotron based on the principle of electron cyclotron maser is able to generate watttomegawatt level terahertz radiation, and becomes an exceptional role in the frontiers of energy, security and biomedicine. However, in normal conditions, a terahertz gyrotron could generate terahertz radiation with high efficiency on a single frequency or with low efficiency in a relatively narrow tuning band. Here a frequency tuning scheme for the terahertz gyrotron utilizing sequentially switching among several whisperinggallery modes is proposed to reach high performance with broadband, coherence and high power simultaneously. Such modeswitching gyrotron has the potential of generating broadband radiation with 100GHzlevel bandwidth. Even wider bandwidth is limited by the frequencydependent effective electrical length of the cavity. Preliminary investigation applies a prebunched circuit to the singlemode wideband tuning. Then, more broadband sweeping is produced by mode switching in greatrange magnetic tuning. The effect of mode competition, as well as critical engineering techniques on frequency tuning is discussed to confirm the feasibility for the case close to reality. This multimodeswitching scheme could make gyrotron a promising device towards bridging the socalled terahertz gap.
Introduction
Terahertz (THz) sources mainly include two families, namely optical sources^{1} and electronic sources^{2}. Most of the electronic sources are developed from microwave band towards THz band. The gyrotron, as a member of vacuum electronic sources, demonstrates high efficiency and high power capability in THz band^{2,3,4,5,6,7,8,9}. A gyrotron employs a relativistic helical electron beam to interact with electromagnetic (EM) wave based on the instability of Electron Cyclotron Maser (ECM). Beamwave interaction with phasespace azimuthal bunching extracts kinetic energy from electron beam and transfers it to EM radiation^{3}. A gyrotron oscillator mostly operates in a single rotating waveguide mode. It produces coherent highpower output on a fixed frequency or in a limited tunable bandwidth. Gyrotrons with highpower capability are important to fusion plasma heating in International Thermonuclear Experimental Reactor (ITER) projects^{9,10,11}. As to other applications, such as high resolution radar^{12}, nondestructive inspection^{13} and dynamic nuclear polarization enhanced nuclear magnetic resonance (DNPNMR)^{14,15,16}, gyrotrons with coherent frequency tuning are more favored.
Frequencytunable gyrotrons have previously been investigated in detail^{14,15,16,17,18,19,20,21,22,23,24}. Generally speaking, there are three kinds of frequencytunable gyrotrons. The first is the discretefrequency steptunable gyrotron^{18,19,20,21}. University of Fukui produced Gyrotron FU Series which radiated on dozens of discrete frequencies between 38 GHz to 889 GHz^{19}. The frequency tuning range of the first kind of gyrotron appears to be wide but discrete. The second is the continuously frequencytunable opencavity gyrotron^{14,15,16}. The magnetic tuning via altering magnetic field strength B and electronic tuning via altering accelerating voltage V are normally applied, and frequency tuning bandwidth is about 1 GHz level. Due to the inherent highQ property of circuit, further extending of the frequency tuning range becomes challenging. In comparison with the gyrotrons above, the third kind of gyrotron, i.e. gyrotron backwardwave oscillator (gyroBWO) does demonstrate impressive continuous broadband frequency tuning^{3}. Other than extensive investigations on the upstreamoutput gyroBWO^{3}, T. H. Chang et al. carried out a downstreamoutput gyrotron experiment by employing backwardwave interaction in a conventional opencavity circuit^{22}. The experiment generates a 6GHz tuning range on the TE_{1,2} mode, which preliminarily demonstrates the competence of continuous broadband tuning. They further investigated an opencavity scheme tapered at the upstream end to improve the interaction efficiency^{23}. This special design provides a continuous tuning bandwidth of 6.9 GHz and efficient output over 25% for 0.2 THz TE_{0,2} mode gyrotron. On this basis, C. H. Du et al. proposed a prebunched circuit to realize a 10GHz continuous tuning range^{24}. Such prebunched interaction compresses the energymodulation length and extends the energyreleasing length of the beamwave interaction process, and finally demonstrates simultaneous advantages of broadband tuning and high efficiency.
In order to achieve continuous broadband THz radiation in a steptunable gyrotron, this paper proposes a scheme based on magneticfieldcontrolled multimode switching in backwardwave interaction. A 100GHz level tuning range is theoretically obtainable. As the cold beamwave dispersion relation shown in Fig. 1a, the highordermode system provides abundant mode spectrum resources that can be explored for multimode switching. A prebunched circuit shown in Fig. 1b is used to extend the tuning range of each mode. The advantages of steptunable gyrotrons and gyroBWOs are directly combined together for multimode switching and frequency sweeping. Finally, detailed discussions about mode competition and critical engineering techniques ensure the feasibility of broadband frequency sweeping and provide guidance for future proof of principle experiment.
Results
Tuning mechanism of broadband radiation
Here the basic principle is that the ECM system (Fig. 1c) is treated as an extractor of the electron cyclotron frequency. Theoretically speaking, when the beamwave synchronizing condition is satisfied with frequency ω following the equation (1), the kinetic energy of the electron beam with specific cyclotron frequency Ω _{ e } can be transferred into EM wave,
where k _{ z } is the wave number, v _{ z } is the longitudinal electron velocity, and s is the harmonic number. In a cylindrical open cavity, the inherent highQ standingwave modes possess discrete longitudinal indexes, which makes k _{ z } replaced by discrete wavenumbers as,
where L _{ eff } is the effective interaction length of the circuit. Accordingly, a gyrotron using a traditional open cavity tends to generate discrete frequencies on specific operating modes in the shape of standing wave. In our proposed scheme, the waveguide gyrotron circuit conveys a travelling wave with continuously varying wavenumber k _{ z }. Obviously, according to equation (1), such selfadjusting wavenumber k _{ z } together with magneticfieldcontrolled changing Ω _{ e } would help to generate continuous tuning wave frequency ω. Consequently, the travellingwave circuit features broader frequency tuning range than standingwave circuit. One factor limiting the continuous tuning bandwidth of conventional gyrotron is that the closed sidewall of the interaction circuit quantizes/discretizes the mode spectrum, and each mode only meets equation (1) in a limited band. Supposing a sequential set of modes meet equation (1) during the course of changing Ω _{ e } and each mode generates a reasonable band, an overall broadband tuning range can be approximately bridged.
Compared with traditional frequencytunable schemes, this scheme includes two significant advancements. Firstly, the feasibility of the backwardwave interaction by using a very highorder whisperinggallery mode is theoretically confirmed. The effective beamwave interaction and reasonable broadband tuning under singlemode operation are achieved. In consideration of suppressing mode competition and ohmic loss in THz band, whisperinggallery TE_{m,2} modes are selected as the operating modes. Secondly, the singlemode tuning develops into multimode switching. By increasing the magnetic field from lower to higher strengths, the gyrotron sequentially switches between a set of nearby whisperinggallery modes to achieve impressive broadband tuning capability. The multimode switching is confirmed by both frequencydomain and timedomain investigations.
In this paper, the magnetic tuning is employed for broadband radiation. Considering another conventional frequency tuning method i.e. electronic tuning, magnetic tuning is determined to be used for three reasons^{25}. Firstly, the B is proportional to Ω _{ e }. V is inversely proportional to Ω _{ e }, and indirectly changes Ω _{ e } by a small tuning to relativity factor γ. So, magnetic tuning is more sensitive and effective for broadband tuning^{25, 26}. Secondly, frequency tuning by changing voltage always takes steerable mode transformation or engineering control as the principal objective^{27, 28}, which goes against our original intention of broadband tuning. Thirdly, electronic tuning could easily cause arcing in the high voltage supply of electron gun and excessive variation of electron beam parameters, which deteriorates the stabilization of gyrotron system. When the tuning efficiency, practical purpose, and operational security are all synthesized, magnetic tuning is found to be more appropriate to the multimode frequency tuning scheme.
Broadband singlemode operation
The designed frequencytunable gyrotron employs a prebunched cavity loaded into the traditional opencavity interaction circuit. For a given mode, the upstream prebunched section introduces additional phase difference between the forwardwave and backwardwave components. Here EM wave performs more like a travelling wave rather than a highQ standing wave^{24}. Such prebunched circuit is potential to suppress gyromonotron oscillations (Fig. 1b). The upstream cutoff section can suppress EM wave leaking towards the electron gun. The forward wave brings reflected backwardwave energy to the downstream section. As a premise of multimode broadband tuning, each operating mode should improve efficiency and extend tuning range as much as possible. More detailed physics about ECM in prebunched circuit was addressed in early studies^{23, 24}.
To achieve sequential mode switching, highorder whisperinggallery modes are selected for operation. Whisperinggallery modes possess excellent mode selectivity and high power capacity. Furthermore, in order to decrease ohmic loss and improve mode homogeneity, high azimuthal index modes are selected. When azimuthal indexes are same, TE_{m,2} mode gets a greater distance between the peak electric field and waveguide wall than TE_{m,1} mode. Meanwhile, compared with TE_{m,3} mode, TE_{m,2} mode is easier to suppress competing modes. Therefore, TE_{m,2} mode becomes a reasonable choice for multimode switching operation (Fig. 1d). Investigation reveals that operating parameters of the THz frequencytunable gyrotron have no essential effect on broadband output. In this paper, we follow standard practices and experimental requirements, and propose the optimized parameter lists as shown in Table 1.
The design takes the TE_{12,2} mode as the center mode. With existing parameters, we get the cold dispersion relation of the TE_{12,2} mode and three representative helical electron beam modes as shown in Fig. 2a. The dashed lines represent the electron beam modes under three magnetic field strengths, corresponding to 1.02B _{ g }, 1.05B _{ g } and 1.08B _{ g }, respectively, where B _{ g } is the magnetic field strength where the electron beam line gets tangent to the TE_{12,2} mode line. The operating point of the EM wave is just around the cross point, which is closer to the cutoff point. As increasing the magnetic field strength, the beamwave cross point shifts from the righthalf forwardwave plane to the lefthalf backwardwave plane. Obviously, the leftside points correspond to a broader range of operating frequencies. From frequencydomain steadystate calculation^{3, 24}, Fig. 2b illustrates the axial mode profiles of the forward wave, the backward wave and the total wave. The results demonstrate that the backward wave is aroused in the middle of circuit and reinforced towards upstream until it grows into the highest strength around the prebunched cavity. Next, the backward wave encounters the upstream end with reflection, and rapidly transfers energy into the forward wave. This kind of inherent feedback mechanism of backward wave is the cause of oscillation. Finally, the backwardwave power is brought out of the cavity by the downstream forward wave.
A group of totalwave fluctuation corresponds to a specific axial mode. As increasing the magnetic field strength, the axial index is boosted accordingly. Figure 2c presents the evolutionary process of electron beam efficiencies for three axial modes. The electron beam absorbs a small amount of energy from EM waves in prebunched cavity for backwardwave modulation, and then releases incremental energy in adjacent uniform main cavity. Note that the strongest field of TE_{12,2} mode does not approach to the waveguide wall, the ohmic loss efficiency becomes steady about 3%. The difference between electron beam efficiency and ohmic loss efficiency is the output efficiency. When the magnetic field strength changing from 1.02B _{ g } to 1.08B _{ g }, the output efficiency in quasisteady segment decreases from around 28% to under 15% (Fig. 2d). Thus the beamwave energy exchange fades out in deep backwardwave interaction, and a higher frequency with a larger k _{ z } demonstrates severe fluctuations on the power profile due to forwardwave modulation^{23, 24}.
The frequencydomain singlemode simulation also indicates that the TE_{12,2} mode can generate radiation in a broad bandwidth of 17 GHz between 376 GHz and 393 GHz when the magnetic tuning sweeps over 0.8 T from 1.02B _{ g } to 1.08B _{ g } (Fig. 2d). Under multimode condition, this tuning range may be split because of competing modes nibbling frequency space. However, an obvious advantage is that there is a quasilinear correlation between the frequency response and magnetic field strength, disagreeing with intuitively predicted hyperbolic relation as reported in previous study^{14, 15}. This phenomenon can be explained from two aspects. Firstly, oscillation in backwardwave region is well above the cutoff frequency and normally with high wave number (k _{ z } ≫ 0). Secondly, the prebunched cavity provides additional space for interaction adjustment. For example, with low magnetic field strength, the EM energy is mostly confined in the main cavity. With high magnetic field strength, the effective backwardwave interaction region is extended, covering parts of upstream prebunched cavity and downstream taper. Such interaction adjustment leads to compensation to the frequency drift due to the Doppler shift k _{ z } v _{ z }.
Multiband radiation by sequentialmodeswitching operation
Based on nonlinear selfconsistent frequencydomain theory^{3, 24}, the calculated startoscillation currents basically reflect the intrinsic properties of operating modes in the designed circuit. Assuming constant electron beam parameters, the startoscillation currents I _{ st } of seven operating modes are shown in Fig. 3a. According to previous study about the backwardwave interaction circuit, a mode with lower I _{ st } takes high priority of dominating the oscillation and suppressing other modes^{22,23,24}. Here each current curve goes down first and then rebounds with increasing magnetic field strength. The lowest peak of the I _{ st } curve corresponds to the gyromonotron state in the main cavity. The backwardwave state takes places after the second depression, which is also the modetransitional zone. When the gyrotron working current is selected as 2 A, the startoscillation currents of all modes are mostly below the working current. Consequently, each mode can be excited and gets dominating access to beamwave interaction in a certain range of B with lowest I _{ st }.
Electrical length L/λ, as the ratio between the circuit length L and wavelength λ, is an important factor to limit the tuning bandwidth. Effective electrical length of the circuit can influence startoscillation modes. As illustrated in Fig. 3a, only TE_{m,2} modes (m = 9, 10, …, 15) are selected as the representative operating modes. For the mode with a smaller azimuthal index m, lower frequency results in a shorter electrical length, a smaller Q factor, and lower energy conversion efficiency. Finally, an overloworder mode never oscillates. Continuous magneticcontrolled frequency tuning range will be split by lowerorder mode due to short electrical length. On the other hand, once m and operating frequency become higher, the increased electrical length will reduce the I _{ st }. Increased electrical length compels the prebunched cavity to be relatively enlarged and regarded as a main cavity to excite powerful gyromonotron state. The depression and rebound in the front section of each highordermode curve in Fig. 3a get severer. The overlap of I _{ st } curves is gradually serious as magnetic field increasing which induces drastic competition between operating modes. As a result, appropriate electrical lengths of the interaction circuit determine available modes. This is an important reason why we cannot infinitely extend frequency tuning range by multimode switching.
The multimode switching is tested based on timedomain theory^{3, 24, 29}. Regarding TE_{9,2}, TE_{10,2}, …, TE_{15,2} as operating modes, the frequency spectrum without considering competing modes is presented in Fig. 3b. The summary of tuning parameters and output parameters is shown in Table 2. Weak lossy materials are loaded in prebunched cavity to prevent its cavityoscillation effect and improve the modulation competence for EM wave energy^{23, 24}. The magnetic tuning process from 10.71 T to 17.00 T corresponds to a linear variation in time domain. The gyrotron consecutively switches from a loworder mode to a highorder mode, and output frequency spectrum almost covers the band between 309 GHz and 462 GHz by seven modes during the effective magnetic tuning range of 11.18 T to 17.00 T. The intrinsic dispersion provides a limited region for gyromonotron state. In addition, during the process of increasing magnetic field, the established backwardwave oscillating mode is easier to extract electron beam energy than a latter gyromonotronstate mode. So, each mode mostly operates in backwardwave state. Obviously, startoscillation states of continuous frequency tuning in Fig. 3b are consistent with the prediction from startoscillation currents in Fig. 3a. The result also confirms the consistency and validity of the frequencydomain singlemode and the timedomain multimode analyses.
The frequency tuning spectrum for seven operating modes is quasicontinuous, however the output power (Fig. 3c) is continuous. It mainly ranges between 0.6 kW and 2 kW, corresponding to 7.5% to 25% efficiency, which is a little lower than that from frequencydomain singlemode simulation. There are two reasons leading to this phenomenon. One is that perfectly matched layer (PML) absorbing boundary condition used in timedomain simulation induces weak reflections. For frequencydomain simulation, ideal outgoingwave boundary condition induces no reflection. The other is that the magnetic field strength in timedomain simulation varies relatively fast with time due to limited calculation resource, which counts against establishing absolutely stable operation and sufficient energy conversion. In practical process, each mode will have more enough time to start oscillation. In addition, the output power demonstrates fluctuations for three reasons. The specific reasons are slightly different for loworder modes and highorder modes. Firstly, limited number of macroparticles is the common reason about the setting of simulation conditions. Increasing the macroparticle number by several times, the output power, especially in low frequency, filters out a lot of fluctuations. However, the time consuming of simulation linearly increases accordingly. Secondly, two intrinsic factors affect loworder modes and highorder modes, respectively. For loworder modes, periodic absorbing and releasing of forward wave energy is another important reason for power fluctuation (Fig. 2b), which cannot be avoided in downstreamoutput structure^{24}. For highorder modes, backwardwave axialmode competition is the primary cause to fluctuation, which is a natural phenomenon in a multimode system. This problem is related to parameter setting, mode selection and interaction structure design. Relevant theoretical exposition is shown in supplementary material.
Discussion and Conclusions
There are three aspects imposing potential limitations to available ECM tuning range. Firstly, the same interaction circuit demonstrates different effective electrical lengths for sequential whisperinggallery modes. Such difference results in limited number of available modes in a given circuit. Secondly, competing modes may induce additional disturbance to break off continuous tuning range. Thirdly, present engineering techniques such as controlling variation of electron beam parameters may not meet the broadband tuning requirements absolutely. In the following we will discuss the latter two points for the feasibility consideration of broadband THz frequency extracting of ECM.
Analysis of mode competition
To simulate realistic mode excitation, a scaled situation, involving mode switching among the TE_{11,2}, TE_{12,2} and TE_{13,2} mode, is displayed. Influence of all the threatening competing modes in this band will be investigated in this part. In the first place, the concept of the coupling impedance K is applied to briefly evaluating the beamwave coupling strength in a referential uniform cylindrical system. The larger K is, the easier beamwave interaction happens. Electron beam and EM wave characteristics, especially frequency and phase velocity, are simultaneously included in K. The analytical expressions are given as^{30}
where H _{ sm } is the coupling coefficient, k _{⊥} and k _{ z } are the transverse and longitudinal wave numbers, J _{ m } is the Bessel function of order m. Substituting the beamwave equations in ref. 1 into these two expressions, the relationship between the magnetic field strength and the coupling impedance is obtained as shown in Fig. 4a. Each peak corresponds to the singular cutoff point of a mode, where it assumes k _{ z } = 0. Comparing the absolute values of K for different modes, we can demonstrate the quantitative coupling strengths under different magnetic field strengths and operating frequencies. Anomalous intersections in impedance curves show that competing modes in the nearcutoff region are very dangerous for whisperinggallery modes.
The startoscillation current curves bring further comprehensive consideration of nonlinear interaction (Fig. 4b). The dashed lines represent the competing modes while the solid lines represent the operating modes. Each of the three operating modes can maintain the lowest startoscillation current region, apart from a small region of the TE_{6,4} mode as magnetic field around 13.3 T. Considering the general principle that modes with lowest startoscillation current are always predominant modes in a travellingwave circuit^{22,23,24}, mode competition is discovered to be possible but relatively feeble.
The timedomain analysis with mode competition gives a straightforward result as shown in Table 3 and Fig. 4c. In case of exciting the TE_{11,2} mode first, the TE_{12,2} and TE_{13,2} modes govern over the circuit successively. The spectrum of TE_{11,2}, TE_{12,2} and TE_{13,2} modes are 351–369 GHz, 373–392 GHz and 398–410 GHz, respectively. Compared with the ideal operation in Fig. 3b, TE_{11,2} and TE_{13,2} modes separately extend frequency responding range forwards and backwards because of no front and back extrusion from other modes. The mode selection, automatic switching and widemultiband radiation are all feasible under mode competition condition. The initial oscillation frequency for TE_{12,2} mode is 373 GHz, agreeing well with theoretical prediction in cold dispersion relation (Fig. 2a). Magnetic field strengths in two dynamic mode switching processes are located in the predicted ranges based on startoscillation current curves. Therefore, the consistency between coldfield stablestate calculation, frequencydomain calculation and timedomain analysis confirms the reliability of investigation again.
Figure 4d presents continuous output power with mode competition, which is rather higher than that in ideal condition (Fig. 3c). This is because that here the lower magnetic field sweeping rate provides more enough time for operating modes to realize sufficient energy conversion. To eliminate the difference of simulation setting, we conduct a comparative analysis (Fig. 4e). The results indicate that mode competition does not decrease the output power of operating modes, but only slightly alters the magnetic field strength of modeswitching point.
Critical engineering techniques
To cover the basics for future proof of principle experiment, we briefly discuss two limitations to the development of gyrotron system. One point is that, parameters of general electron gun are difficult to maintain constant values during magnetic tuning^{31, 32}. In supplementary material, we take magnetic injection gun (MIG) as an example to illustrate that relatively stable electron beam parameters are available by using auxiliary coils. A latest paper reveals that slight variation of electron beam parameters does not influence the essence of frequency tuning^{29}, which enhances the feasibility of multimode frequency tuning. The other point is that, if pulse magnet is employed, the start and stop of high pulse magnet will produce a powerful induction current. Normal copper circuit is easy to be intensively extruded and deformed by a force from the induction current^{5, 6}. To address this issue, electroplating or spraying techniques can be used to restructure a more robust composite circuit.
To conclude, this paper proposes a scheme of broadband THz radiation source based on multimode switching gyrotron. Tuning mechanism and simulation results confirm that the source is potential to generate broadband tuning range on the order of 100GHz level, boosting about two order of magnitudes higher than the stateofart techniques. Discussion about mode competition and engineering techniques provides a powerful evidence for the scheme feasibility. The proposed ECM THz extractor would become a general solution to generate highpower broadband coherent radiation from THz helical electron beam. That is to say, as long as helical electron beam exists, coherent THzwave would be excited.
Methods
Frequencydomain theory and timedomain theory
In frequencydomain theory and timedomain theory, the beamwave interaction equations derived from Maxwell’s equations, and the electron dynamics equations describing the movement of electron beam are employed together to simulate selfconsistent beamwave interaction. Frequencydomain calculation with outgoing wave boundary condition concentrates on one EM waveguide mode interacting with electron beam in stable state^{3, 24, 29}. Timedomain calculation with PML absorbing boundary condition demonstrates the timevarying beamwave energy exchange and could present timevarying multimode construction and the mode competition evolvement^{3, 24, 29}.
Macroparticle assumption and division of time segments
As a matter of fact, the electron trajectory in gyrodevices is similar to the moon movement in solar system. An electron (like ‘moon’) orbits the guiding center (like ‘Earth’) in Larmor circle along the magnetic flux line, while the guiding center orbits the cavity transverse center (like ‘Sun’). For simplifying the calculation model, a macroparticle with same electric quantity would substitute for several electrons in Larmor circle. Next, divided emission time segments of macroparticles is applied to approximate successive electron beam/stream. Under the premise of convergence precision, the sparse timedomain and spacedomain meshes in this way are beneficial to improve simulation efficiency.
References
 1.
Ferguson, B. & Zhang, X. Z. Materials for terahertz science and technology. Nature Mater. 1, 26–33 (2002).
 2.
Booske, J. H. et al. Vacuum electronic high power terahertz sources. IEEE Trans. Terahertz Sci. Technol. 1, 54–75 (2011).
 3.
Chu, K. R. The electron cyclotron maser. Rev. Modern Phys. 76, 489–540 (2004).
 4.
Glyavin, M. Y., Idehara, T. & Sabchevski, S. P. Development of THz gyrotrons at IAP RAS and FIR UF and their applications in physical research and highpower THz technologies. IEEE Trans. Terahertz Sci. Technol. 5, 788–797 (2015).
 5.
Glyavin, M. Y., Luchinin, A. G. & Golubiatnikov, G. Y. Generation of 1.5kW, 1THz coherent radiation from a gyrotron with a pulsed magnetic field. Phys. Rev. Lett. 100, 015101 (2008).
 6.
Bratman, V. L., Kalynov, Y. K. & Manuilov, V. N. Largeorbit gyrotron operation in the terahertz frequency range. Phys. Rev. Lett. 102, 245101 (2009).
 7.
Sirigiri, J. R. et al. Photonicbandgap resonator gyrotron. Phys. Rev. Lett. 86, 5628–5631 (2001).
 8.
Yuan, X. et al. A fullysealed carbonnanotube coldcathode terahertz gyrotron. Sci. Rep. 6, 32936 (2016).
 9.
Sakamoto, K. et al. Achievement of robust highefficiency 1 MW oscillation in the hardselfexcitation region by a 170 GHz continuouswave gyrotron. Nature Phys. 3, 411–414 (2007).
 10.
Alberti, S. Magnetic confinement fusion: plasma heating with millimetre waves. Nature Phys. 3, 376–377 (2007).
 11.
Darbos, C. et al. Status of the ITER electron cyclotron heating and current drive system. J. Infrared Millim. Terahertz Waves 37, 4–20 (2016).
 12.
Blank, M. et al. Development and demonstration of highaverage power Wband gyroamplifiers for radar applications. IEEE Trans. Plasma Sci. 30, 865–875 (2002).
 13.
Karpowicz, N. et al. Compact continuouswave subterahertz system for inspection. Appl. Phys. Lett. 86, 054105 (2005).
 14.
Torrezan, A. C. et al. Continuouswave operation of a frequencytunable 460GHz secondharmonic gyrotron for enhanced nuclear magnetic resonance. IEEE Trans. Plasma Sci. 38, 1150–1159 (2010).
 15.
Torrezan, A. C., Shapiro, M. A., Sirigiri, J. R., Temkin, R. J. & Griffin, R. G. Operation of a continuously frequencytunable secondharmonic CW 330GHz gyrotron for dynamic nuclear polarization. IEEE Trans. Electron Devices 58, 2777–2783 (2011).
 16.
Matsuki, Y. et al. Application of continuously frequencytunable 0.4 THz gyrotron to dynamic nuclear polarization for 600 MHz solidstate NMR. J. Infrared Millim. Terahertz Waves 33, 745–755 (2012).
 17.
Thumm, M. Novel applications of millimeter and submillimeter wave gyrodevices J. Infrared Millim. Terahertz Waves 22, 377–386 (2001).
 18.
Kreischer, K. E. & Temkin, R. J. Singlemode operation of a highpower, steptunable gyrotron. Phys. Rev. Lett. 59, 547–550 (1987).
 19.
Idehara, T. et al. Development of frequency tunable, medium power gyrotrons (Gyrotron FU series) as submillimeter wave radiation. IEEE Trans. Plasma Sci. 27, 340–354 (1999).
 20.
Gantenbein, G. et al. First operation of a stepfrequency tunable 1MW gyrotron with a diamond brewster angle output window. IEEE Trans. Electron Devices 61, 1806–1811 (2014).
 21.
Samartsev, A. et al. Efficient frequency steptunable megawattclass Dband gyrotron. IEEE Trans. Electron Devices 62, 2327–2332 (2015).
 22.
Chang, T. H., Idehara, T., Ogawa, I., Agusu, L. & Kobayashi, S. Frequency tunable gyrotron using backwardwave components. J. Appl. Phys. 105, 063304 (2009).
 23.
Chen, N. C., Chang, T. H., Yuan, C. P., Idehara, T. & Ogawa, I. Theoretical investigation of a high efficiency and broadband subterahertz gyrotron. Appl. Phys. Lett. 96, 161501 (2010).
 24.
Du, C. H. et al. Broadband tunable prebunched electron cyclotron maser for terahertz application. IEEE Trans. Terahertz Sci. Technol. 5, 236–243 (2015).
 25.
Dumbrajs, O. Tunable gyrotrons for plasma heating and diagnostics. RAU Scientific Reports, Comput. Model. New Technol. 2, 66–70 (1998).
 26.
Thumm, M. et al. Frequency steptunable (114–170 GHz) megawatt gyrotrons for plasma physics applications. Fusion Eng. Design 53, 407–421 (2001).
 27.
Idehara, T. et al. Rapid frequency stepswitching of a submillimeter wave gyrotron by modulation of the electron beam. Phys. Plasmas 1, 1774–1776 (1994).
 28.
Albertia, S. et al. European highpower CW gyrotron development for ECRH systems. Fusion Eng. Design 53, 387–397 (2001).
 29.
Qi, X. B. et al. Terahertz broadbandtunable minigyrotron with a pulse magnet. IEEE Trans. Electron Devices 64, 527–535 (2017).
 30.
Du, C. H. & Liu, P. K. Beamwave coupling strength analysis in a gyrotron travellingwave amplifier. J. Infrared Millim. Terahertz Waves 31, 714–723 (2010).
 31.
Donaldson, C. R. et al. A cusp electron gun for millimeter wave gyrodevices. Appl. Phys. Lett. 96, 141501 (2010).
 32.
Yuan, C. P., Chang, T. H., Chen, N. C. & Yeh, Y. S. Magnetron injection gun for a broadband gyrotron backwardwave oscillator. Phys. Plasmas 16, 073109 (2009).
Acknowledgements
This work is sponsored by the National Natural Science Foundation of China under Contracts 61531002, 61522101, and 61471007, and in part by the Beijing NOVA program (No. Z161100004916057) and the Opening Project of Wuhan National High Magnetic Field Center (HUST) under Contract 2015KF13.
Author information
Affiliations
Contributions
C.H.D. and P.K.L. presented the idea and guided the research work. S.P., C.H.D. and X.B.Q. analyzed the data, S.P., C.H.D. and P.K.L. cowrote the manuscript. All the authors discussed the results and commented on the manuscript.
Corresponding authors
Ethics declarations
Competing Interests
The authors declare that they have no competing interests.
Additional information
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Pan, S., Du, C., Qi, X. et al. Broadband terahertzpower extracting by using electron cyclotron maser. Sci Rep 7, 7265 (2017). https://doi.org/10.1038/s41598017075456
Received:
Accepted:
Published:
Further reading

Theoretical Investigations on ForwardWave and BackwardWave Operation of a FrequencyTunable Gyrotron
IEEE Transactions on Electron Devices (2020)

Broadband and highpower terahertz radiation source based on extended interaction klystron
Scientific Reports (2019)

Terahertz Broadband WhisperingGallery Mode Gyrotron BackwardWave Oscillator
IEEE Transactions on Electron Devices (2019)

Optimization of a HighPower Subterahertz Gyrotron Tunable in a Wide Frequency Range Allowing for the Limitations Imposed by the Magnetic System
Radiophysics and Quantum Electronics (2019)

Investigation of highorder mode excitation in a terahertz secondharmonic gyroBWO
Physics of Plasmas (2019)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.