High-power terahertz-range planar gyrotrons with transverse energy extraction

To increase the output power of terahertz gyrotrons to several hundred kilowatts, we suggest using a planar geometry of interaction space with a sheet electron beam and transverse energy extraction. An advantage of this scheme in comparison with conventional cylindrical geometry is the possibility to ensure effective mode selection over the open transverse coordinate in combination with radiation outcoupling that leads to a substantial reduction of Ohmic losses. Similar to unstable resonators in optics for further growth of the radiation power it is beneficial to introduce waveguide tapering.     

Gyrotrons with echelette resonators

We consider gyrotrons with echelette resonators formed by diffraction gratings on the inner surface of a cone with the ribs perpendicular to the cone axis. The Q-factor of the operating cavity mode is controlled by the choice of grating parameters. Selective properties of the resonator are determined by the frequency dependence of the antireflection coefficient. Such resonators have a higher selectivity and more effective coupling with the output waveguide than cylindrical resonators, which allows gyrotron power to be increased. Echelette resonators can be used in gyrotrons at higher cyclotron harmonics owing to their higher selectivity without fear of exciting lower harmonics. Starting currents and efficiency of a gyrotron with an echelette resonator are found. Experimental studies of gyrotrons with echelette resonators confirmed the possibility to rarefy considerably the gyrotron oscillation spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, p. 691–698, June, 1996.This paper was supported in part by the International Science Foundation under Project No.R8Y300 (Theoretical and Experimental Study of Echelette-type Resonators for High-Power Gyrotrons) and the Russian Foundation for Fundamental Research under Grant No.93-02-15423.     

Low-frequency gyrotrons for fusion studies

A number of experimental plasma devices require high-power sources of electromagnetic radiation in a range of 5 to 30 GHz. In this paper, we consider gyrotrons as such sources. The difficulties of creating long-wavelength gyrotrons are discussed and the possibility to overcome them is shown for already existing and currently developed oscillators. We present the results of studies aimed at development of high-power, long-pulse, low-frequency gyrotrons in Russia, as well as the designs and performance parameters of industrial gyrotrons operated at frequencies 5 and 28 GHz with an output power of 0.5 MW. Several design versions of the gyrotrons with operating frequencies 17.5 and 28 GHz, an output power of up to 1 MW, and a pulse duration of up to 5 s are discussed and the design features which make it possible to overcome the difficulties of their manufacturing are considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 207–218, March 2006.     

Numerical Analysis of Weakly Relativistic Large Orbit Gyrotron with Permanent Magnet System

High-harmonic gyro-devices with axis-encircling electron beams known as large orbit gyrotrons (LOG) represent an appealing alternative to the conventional gyrotrons. In this paper we investigate the feasibility of such device operating with low current and low energy electron beams formed by a novel electron gun with a permanent magnet system. The results from the numerical experiments indicate the possibility to excite TE₄₁ mode at fourth harmonic of the cyclotron frequency. Simulations predict generation of microwave radiation with frequency 104 GHz and output power near 1 kW.     

Rigorous electrodynamic analysis of resonator systems of coaxial gyrotrons

An efficient and rigorous numerical method is developed for numerical analysis of resonators of coaxial gyrotrons used for plasma heating, drag current generation, and for other purposes in controlled thermonuclear fusion facilities with magnetic confinement. Results obtained may be used to simulate operation of coaxial gyrotrons, to optimize their resonators, and to develop efficient software intended for studying the physics of coaxial gyrotrons and for their design.     

Generation of Spatially Coherent Radiation in Free-Electron Lasers with Two-Dimensional Distributed Feedback

We study the possibility of using two-dimensional distributed feedback (DF) to generate spatially coherent radiation of ribbon and hollow relativistic electron beams whose transverse dimensions exceed the wavelength by several orders of magnitude. Such a feedback can be realized in planar and coaxial two-dimensional Bragg resonators with a two-period corrugation of their side walls. This corrugation gives rise to additional transverse (with respect to the reciprocal motion of the electrons) fluxes of electromagnetic energy which synchronize emission from different parts of the electron beam. Simulations of the onset of autooscillations in free-electron lasers (FELs) with a two-dimensional DF show the possibility of obtaining single-mode monochromatic coherent generation by beams with transverse dimensions up to 10²-10³ wavelengths. We also analyze the use of hybrid resonators composed of two-dimensional input and one-dimensional output Bragg mirrors. In such a scheme, the two-dimensional mirror ensures synchronization of the emission perpendicular to the electron beam, while reflection from the output one-dimensional mirror is sufficient for the self-excitation of the generator. In the case of a system closed in the transverse direction, such a scheme permits one to reduce significantly the ohmic losses resulting from the electromagnetic fluxes locked in the transverse direction. It is shown that the two-dimensional DF can also be used to synchronize radiation in a multibeam generator consisting of planar FEL modules fed by a ribbon electron beam and coupled via the transverse electromagnetic-energy fluxes which are formed by two-dimensional Bragg structures. The experimental studies aimed at realization of ultrahigh-power FELs with a two-dimensional DF are discussed.     

Selective excitation of high-order modes in circular waveguides

The excitation of very high-order modes in circular waveguides has been performed in a cavity with a connected up-taper with a geometry similar to those used in gyrotrons. A Gaussian beam was coupled to the cavity which was made translucent by an array of holes. With the help of a special optics, the amplitude as well as the phase distribution of the beam was matched to the mode to be excited in the resonant cavity. By simple rotation of one mirror to adjust the phase distribution together with the change of frequency to match the resonance condition, a large number of modes could be produced with one experimental set-up. Field measurements in the output waveguide show a high mode purity of the radiation and confirm the calculations. The method can be used for cold tests of electrodynamic systems operating with these modes, e.g. quasi-optical converters for gyrotrons.     

准光模式变换器研究与设计

研究了将回旋管及其他高功率微波器件的振荡输出模式转换成准高斯波束的准光模式变换器,实现了准高斯模TEM00的横向输出。利用几何光学分析了模式在波导中的传播,进一步分析了伏拉索夫（Vlasov）辐射器的工作机理,运用矢量绕射理论计算出辐射场; 通过编程设计了将94 GHz、模式为TE62的毫米波转化为准高斯波束的准光模式变换器。结果表明:通过设计Vlasov辐射器和两级反射镜,可以在窗口处得到准高斯波束, 整个系统的功率效率达到87.5%。     

Axisymmetric multistage cavity resonators

We study theoretically multistage cavity resonators as well as the gyrotrons manufactured on their basis. Coupled cavities with mode conversion and echelette cavities are particular cases of such devices. The possibilities of reducing the diffraction Q-factor of the operating mode of a cavity, with the preservation of its selective properties and significant increase in the gyrotron radiation power, and provision of high efficiency and acceptable heat ohmic load of the cavity at the first harmonic of the gyrofrequency are considered. Achievable parameters of the gyrotrons at the second and third harmonics with typical electron guns and cryomagnetic systems are analyzed.     

Numerical characterizations of unstable optical resonators and evaluation of the geometry effects

Unstable resonators have been widely used in high-power gas lasers as well as solid-state lasers. The phase and the spatial distribution of intensity of these lasers are very important in some applications such as material processing. In this paper, unstable resonators with three different geometries have been characterized numerically and the results have been compared and evaluated. Based on the Fresnel-Kirchhoff integral, the two-dimensional phase and intensity have been calculated for three different positive branch unstable resonators. The results show that the resonators with rectangular geometry have the best performance for near-field as well as far-field intensity, which is more suitable for material processing. The calculations also show that the maximum output power can be extracted from the rectangular resonator with spherical surface, while the circular resonator with spherical surface has minimum output power. The results also show that the laser has a higher divergence for the cylindrical resonator in compare with those for the circular and rectangular resonators.     

Scattering by structural inhomogeneities of CVD diamonds in the 100–1000 GHz range

We study the scattering of electromagnetic radiation by structural inhomogeneities of CVD diamond windows used to output the power produced by megawatt gyrotrons in the 100–1000 GHz range. It is shown that the scattering can make a significant contribution to the attenuation of the radiation starting from 200 GHz, and becomes a determinant factor near 1 THz. Even in the framework of the single-scattering approximation, about one-third of the scattered power is released beyond the window. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 12, pp. 1048–1057, December 2007.     

General theory and design of microwave open resonators

Based on the analysis of wave propagation in a waveguide with slowly varying cross-section, a general theory is developed for microwave open resonators with rotational-symmetric waveguides; this geometry has been extensively used in the gyrotrons. The theoretical analysis is carried through under the most general conditions, that is the cross-section radius r(z) of the resonator is a slowly varying arbitrary function of z and the resonator is open. The general expressions for the resonant frequencies and the Q have been derived. A design method for this kind of open resonator has been proposed. Calculation results for two practical resonators are presented.     

On the need to allow for variability of RF-field longitudinal structure in calculation of gyrotron efficiency

In high-power gyrotrons with open resonators that have nearly minimal diffraction Q, the longitudinal structure of the RF field can be affected by the electron beam. The need to allow for this effect in determination of the efficiencies of gyrotrons with resonators of conventional shape is investigated. It is shown that over wide ranges of gyrotron-parameter values of greatest practical interest, this effect is fairly small and, therefore, efficiency can be determined assuming a fixed RF-field longitudinal structure.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 9, pp. 1020–1026, September, 1991.     

双共焦波导结构二次谐波太赫兹回旋管谐振腔设计

准光共焦波导具有功率容量大、模式密度低的特点,能够有效地减少模式竞争对回旋管互作用的影响,有利于高次谐波太赫兹回旋管的设计.为提高太赫兹准光回旋管的互作用效率,在共焦柱面波导的基础上,研究了一种新型高频互作用结构——双共焦波导结构,设计了一种330 GHz二次谐波双共焦结构回旋管谐振腔并对其进行了理论分析和粒子模拟.研究结果表明,双共焦谐振腔中的高阶模式能够与高次电子回旋谐波发生稳定的相互作用,并且没有模式竞争现象,具备工作在太赫兹波段的潜力.相比普通共焦波导谐振腔,双共焦谐振腔能够增强准光回旋管的注波互作用强度,提高回旋管的输出功率和工作效率.此外,结果还表明双共焦波导中的电磁波模式是一种由两个独立的共焦波导模式叠加而成的混合模式.利用这种混合模式有望实现太赫兹回旋管的单注双频工作,为新型太赫兹辐射源的研究提供了新的途径.     

Gyrotron Radiation Affected by a Controlled Modulated Reflector: High Power Experiment

An experiment performed with the gyrotrons of the TJ-II ECRH system has been performed to influence the gyrotron output radiation with a relatively weak wave returned from an external mechanically modulated reflector. An original method is proposed for directly measuring the wavelength of electromagnetic radiation in the free space. The method has been demonstrated in measurements of the wavelength of a high-power gyrotron radiation in the millimeter wavelength range used for plasma ECR heating in the TJ-II stellarator.     

Nonlinear dynamics of free electron terahertz lasers with bragg mirrors based on coupling of traveling and quasi-critical waves

Combination of various modifications of Bragg structures makes it possible to control electromagnetic fluxes in the interaction space, thus ensuring spatial coherence of radiation for high superdimensionality in two transverse coordinates required, which is for the operation of free electron lasers with distributed feedback in the submillimeter range. We propose that coupling between traveling and quasi-critical waves in the input Bragg mirror be used for mode selection in the “narrow” transverse coordinate directed along the normal to the conductors forming a planar waveguide. A traditional Bragg structure coupling copropagating and counterpropagating wave flows can be used as the output mirror.     

Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.     

Some perspectives on the use of powerful gyrotrons for the electron-cyclotron plasma heating in large tokamaks

Conclusion The main problems for the further development of high efficiency powerful gyrotrons are obviously the elaboration of electron guns with a large current density and the ensuring of a stable single-mode operation in resonators with a large cross-section. For the increase in microwave pulse energy (with a pulse length of the order of the time of plasma confinement in large tokamaks) the investigation of the possibilities to diminish heating loads in the resonator and output window of a gyrotron is necessary.     

激光输出功率随耦合率及放大率的变化规律

建立了涵盖稳定腔和非稳腔的激光有源理论模型和激光开式谐振腔的边界条件。根据定态薛定谔方程与亥姆霍兹方程的等价性,采用量子力学方法求解谐振腔的亥姆霍兹波动方程,得到满足方程、边界条件、矩阵光学、稳定条件的本征解和本征方程。根据本征方程推导出横模数目随耦合率变化的规律,进而推导出激光输出功率随耦合率变化公式,以及激光输出功率随放大率的变化规律。该理论模型能够从稳定腔自然过渡到非稳腔,在小耦合率情况下退化到与传统公式基本一致的形式,又能在大耦合率情形下与实验结果符合得很好。     

Generation of spatially coherent radiation in free-electron masers with two-dimensional distributed feedback

The results of theoretical and experimental studies on the generation of spatially coherent electromagnetic radiation in a planar free-electron maser with two-dimensional distributed feedback are reported. A two-dimensional Bragg structure is used at the initial part of the interaction space to ensure the transverse synchronization of the radiation. The possibility of the narrowband generation in the 75-GHz frequency band is demonstrated experimentally for a sheet kiloampere electron beam whose width is 20 times larger than the wavelength.