A linear theory and design study for a gyrotron backward-wave oscillator†

A linear theory for a gyrotron backward-wave oscillator (gyro-BWO) is developed. The theory solves a reduced one-dimensional Maxwell-Vlasov equation in the form of a linear integro-differential equation using the Laplace transformation. The relative amplitudes among the waveguide modes and beam modes are completely determined and enable one to calculate gyro-BWO start-oscillation conditions. Using this analysis and including velocity spread effects, a design of a millimetre-wave gyro-BWO has been carried out based on the operating parameters of an existing electron gun. Tunability over a range of 86 GHz to 103 GHz is predicted with output power estimated to be ～ 1 kW.     

Geometrical Effects on the Performance of Coaxial-Waveguide Gyrotron Traveling-Wave Amplifiers

This theoretical investigation examines the feasibility of improving the stability of the coaxial-waveguide gyrotron traveling-wave tube (gyro-TWT) by selecting the geometrical parameter C, i.e., the ratio of the outer radius to the inner radius. The effects of the geometrical parameter C on the start-oscillation currents of oscillation modes are analyzed to determine the optimum operating conditions. Simulation results indicate that the coaxial gyro-TWT with distributed wall losses can be stably operated at a higher beam current by optimizing C. Additionally, the saturated behaviors of the operating TE₀₁ mode are evaluated for several C values to investigate the geometrical effects on the amplification of the coaxial gyro-TWT. Moreover, performance of the fundamental harmonic coaxial gyro-TWT achieved with the optimized C value is predicted under stable operating conditions.     

A Lossy Dielectric-Ring Loaded Waveguide With Suppressed Periodicity for Gyro-TWTs Applications

A dielectric-loaded (DL) waveguide is an attractive possibility for interaction circuits with high-power sources in the millimeter-wave regime down to tenths of millimeters, particularly for gyrotron-traveling-wave-tube amplifiers (gyro-TWTs). We present results on a systematic investigation of the influence of the periodically loaded lossy dielectric on the propagation characteristics of the operating modes, which reveals that a complex mode in the periodic system can be mapped to a corresponding mode in an empty waveguide or a uniform DL waveguide. Dielectric losses not only induce modal transitions between different modes with similar field structures and close phase velocities in the uniform system but also unify the discrete mode spectrum into a continuous spectrum in the periodic system. Since the lossy dielectric functions as a power sink, the higher order Bloch harmonic components arising from the structural periodicity are suppressed, and the mode spectrum of the lossy periodic system degenerates into that of an empty waveguide. This alleviates the potential danger of spurious oscillations induced by the higher order harmonic components, making the periodic lossy DL waveguide promising in a high-power millimeter-wave gyro-TWT.     

W-Band Second-Harmonic Gyrotron Traveling Wave Amplifier with Distributed-Loss and Severed Structures

The second harmonic TE₀₂ gyrotron traveling wave amplifier (gyro-TWT) is a high-power, broadband, millimeter-wave amplifier with a low applied magnetic field. Mode-selective interaction circuits were applied to suppressing spurious oscillations. However, the mode-selective interaction circuit may perturb the operating mode in the gyro-TWT. A multi-stage gyro-TWT design with distributed-loss and severed structures is proposed to stabilize the amplification. This study presents a nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation (gyro-BWO) and reflective oscillation. The lossy and severed sections of the multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of the absolute instability, gyro-BWO, and reflection oscillation. The multi-stage gyro-TWT is predicted to yield a peak output power of 215 kW at 89.9 GHz with an efficiency of 14.3 %, a saturated gain of 60 dB and a bandwidth of 1.7 GHz for a 100 kV, 15 A electron beam with an axial velocity spread Δν _z/ν _z = 5%.     

A Stable 0.2-THz Coaxial-Waveguide Gyrotron Traveling-Wave-Tube Amplifier with Distributed Losses

For high-power operation, a THz gyrotron traveling-wave-tube (gyro-TWT) amplifier must operate in a high-order waveguide mode to enlarge the transverse dimension of an interaction waveguide. However, a gyro-TWT amplifier operating in a high-order waveguide mode is susceptible to spurious oscillations. To improve the device stability, in this study, we investigate the possibility of using a coaxial waveguide with distributed losses as the interaction structure. For the same required attenuation, all threatening oscillating modes can be suppressed using different combinations of losses of inner and outer cylinders. This provides flexibility in designing distributed losses when considering the ohmic loading of the interaction structure. We predict that the 0.2-THz gyro-TWT can stably produce a peak power of 14 kW with an efficiency of 23 %, a 3-dB bandwidth of 3.5 GHz, and a saturated gain of 50 dB for a 20-kV 3-A electron beam with a 5 % velocity spread and 1.0 velocity ratio.     

Study on the Suppression of Gyro-BWO by Distributed Wall Losses

In this paper, the effect of distributed wall losses on the starting length and starting frequency of a TE₂₁ mode gyro-BWO is investigated for different operating magnetic fields by using a linear theory. Numerical results show that, for the efficient suppression of a gyro-BWO in a distributed wall losses gyro-TWA consisting of a lossy section followed by a copper section, the wall losses applied in the lossy section should be able to provide a cold attenuation approximately equal to the linear growth rate of the gyro-BWO in the case of wall losses neglected and the copper section length should be shorter than the starting length of the corresponding gyro-BWO without wall losses loaded.     

First-order symmetric modes for a slightly lossy coaxialtransmission line

A complete set of solutions for Maxwell's equations to first order in the normalized surface impedance z_s of the coaxial conductors is found. The derivation of the fields outlined assumes a vacuum dielectric and an infinitely thick outer conductor. It starts from J.P. Stratton's work (1941) with a derivation of the determinantal equation for finding the eigenvalues for both the principal and waveguide modes in a lossy line. The first-order determinantal equation is found, preceded by an equation for calculating the proportionality constant for the fields intermediate between the center and outer conductor. The equations for lossy waveguide modes are new, and the principal mode fields include a term missing from the expressions that are found elsewhere in the literature. The resulting characteristic admittance and distributed line parameters are calculated; the distributed line resistance is significantly different from other calculations found in the literature     

A multipole analysis of a dielectric loaded coaxial rectangularwaveguide

A multipole analysis of a coaxial rectangular waveguide whose inner conductor is circular is made in order to determine the TE and TM modes of the system. The analysis is based on using multipole (dipole, quadrupole etc.) electric and magnetic current sources to generate field solutions in the waveguide. These solutions are used to match the electromagnetic boundary condition in a homogeneous coaxial rectangular waveguide and to determine the TE and TM eigenvalues of the waveguide system. Eigenvalue results are compared with results of the generalized spectral domain method and to eigenvalue results for a ridged waveguide. Propagation in a coaxial rectangular waveguide is also studied when the coaxial rectangular waveguide is loaded with lossy inhomogeneous dielectric material. A variational formula is used to relate the TEM, TE, and TM modes of an empty coaxial rectangular waveguide to the propagation in the loaded inhomogeneous dielectric waveguide     

Stability analysis of TE01 gyrotron travelling wave amplifiers

The fundamental harmonic TE₀₁ gyrotron travelling wave amplifier (gyro-TWT) is a high-power, broadband, millimetre-wave amplifier with a low ohmic dissipation and a large guiding centre radius. However, spurious oscillations may reduce the amplification of the gyro-TWT. The stability of severed and distributed-loss gyro-TWTs is analysed, using a self-consistent simulation code. A nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation (gyro-BWO) and reflective oscillation, is presented. Simulation results indicate that attenuating severs in the severed gyro-TWT do not suppress spurious oscillations, and that increasing the wall losses to suppress gyro-BWO in the distributed-loss gyro-TWT degrades the efficiency of the gyro-TWT amplifier. A multi-stage distributed-loss gyro-TWT design is developed to stabilize the amplification. The lossy and severed sections of the multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of absolute instability and gyro-BWO, respectively. The multi-stage gyro-TWT is predicted to yield a peak output power of 155?kW at 32.9?GHz with an efficiency of 15%, a saturated gain of 45?dB and a bandwidth of 2.2?GHz for a 100?kV, 10?A electron beam with an axial velocity spread Δv_z /v_z = 5%.     

TE21模回旋返波振荡的起振分析

该文基于回旋行波放大器的线性理论,对TE₂₁模回旋返波振荡起振长度和起振频率随导引中心半径、电压、速度比、注电流及工作磁场等参数的变化进行了详细的数值模拟,并给出了相应的物理解释,分析了TE₂₁模基波和二次谐波回旋返波振荡特点,研究了分布损耗对回旋返波振荡的抑制效果。所得结果对回旋行波放大器和回旋返波振荡器的设计有参考意义。     

Ohmic selection in open coaxial resonators: An experimental study

A study of ohmic selective properties of open coaxial cylindrical resonators has been conducted experimentally and compared with theory. The resonator consists of an inner cylinder made of silicon carbide symmetrically located inside an outer cylindrical, tube shaped waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated quality factors. Mode discrimination is achieved both by exploring selective ohmic effects and examining the electrodynamical properties of the coaxial cylindrical waveguide. The effectiveness of a silicon carbide coaxial insert in providing ohmic mode selection is demonstrated in that the totalQ factors of TE _mp modes with radial indexp≥2 become well below the quality factors for surface TE _m1 modes. It has been verified that both structure and number of resonant modes are strongly dependent on the diameter and the resistivity of the coaxial insert.     

Cold tests of open coaxial resonators in the range 9–17 GHz

A study of selective properties of coaxial open cylindrical resonators have been conducted experimentally and compared with theory. The resonator consists of an inner circular cylinder symmetrically located inside an outer weakly irregular open waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated loaded quality factors. It has been verified that the structure and the number of resonant modes are both strongly dependent on the diameter of the coaxial insert. Such an electrodynamical system proves to be useful in guided wave applications requiring, for example, filters, frequency-tunable resonators and devices for analyzing the modal composition of a signal.     

Modeling of discontinuities in general coaxial waveguide structuresby the FDTD-method

The finite-difference time-domain (FDTD) method is used to model generalized coaxial waveguide structures with discontinuities. The cross section of the waveguide consists of a closed outer conductor and one or two inner conductors of arbitrary shape. The cross section can have any number of dielectric materials with losses. The singular field-behavior near sharp edges is explicitly included in the finite-difference scheme. Any kind of discontinuity can be handled: changes in cross-section as well as changes of material parameters. From the time-domain data, frequency-domain data (S-parameters) are obtained using Fourier-transform techniques     

Experimental Study of a Slot Antenna Excited by a TE011 Mode Coaxial Cavity

A slot antenna is developed to excite the high harmonic waveguide mode for generating large-area plasmas. This antenna consists of a TE₀₁₁ mode coaxial cavity with the axial slots positioned on equal interval on the inner wall. The waves radiated from those slots can excite the high harmonic mode in the central area. With the azimuthal symmetric wave field of the TE₀₁₁ mode, the number of the slots can be chosen to match the field pattern of the high harmonic mode. In this report, the dispersion relation of the coaxial waveguide, the coupling scheme and the mode competition of the cavity are studied. A method has been successfully developed to suppress the TE₁₂₁ mode which is the most competing mode to the TE₀₁₁ mode.     

Eigenmodes of coaxial quad-ridged waveguides. Numerical results

The results of numerical investigation of coaxial quad-ridged waveguides’ eigenmodes of two configurations (with ridges on inner or on outer perfectly conducting circular cylinder) for different cross-section dimensions are presented. In particular, dependences of cutoff wave numbers on geometrical dimensions ratios for the first three TE modes and for the first TM mode have been investigated and transversal electric field components distributions for these eigenmodes and for theTEM mode have been obtained. Besides, the optimization of coaxial quad-ridged waveguides has been carried out at antiphase excitation in order to provide maximal single-mode operation frequency band for the first TE mode. As a result two optimal configurations of coaxial quad-ridged waveguides with single-mode operation bandwidth ratios 4.6:1 have been designed. It has been defined that the waveguide with the ridges at the inner conducting circular cylinder has smaller cross-section dimensions at the fixed single-mode operation frequency band. Calculations are conducted utilizing the mathematical models obtained in [1] by the integral equations technique taking correctly into account of singular behavior of the field at ridges’ edges. Reliability of the results obtained is confirmed by the calculations based on finite difference time domain technique, which is implemented in the software package CST Microwave Studio at mesh size λ/100.     

A Comparison of the Attenuation of High-Order Mode in Coaxial Waveguide due to Inner and Outer Conductor Losses

In this paper, comparison studies of mode attenuation in coaxial waveguides due to inner and outer conductor losses are carried out analytically. Numerical results for some typical high-order modes are presented. This study is helpful for guiding the loading of distributed losses in coaxial gyrotron traveling wave amplifiers.     

Eigenmodes of sectoral coaxial ridged waveguides

The results of numerical investigation of sectoral coaxial ridged waveguides eigenmodes of two configurations (with a ridge on inner or outer wall) for different cross-section dimensions are presented. In particular, dependences of cutoff wave numbers on geometrical dimensions ratios for first four modes are investigated, electric field components distributions for these modes have been obtained and the optimization of sectoral coaxial ridged waveguides has been carried out to provide maximal single-mode operation frequency band. Two optimal configurations of waveguides with single-mode operation bandwidth ratio 5.6:1 are obtained. It is shown that smaller cross-section dimensions at the fixed single-mode operation frequency band has the waveguide with the ridge at the inner round wall. The size of the gap between the ridge and the round wall of optimal waveguide is identical for both configurations and is determined by the required ratio of cutoff frequencies of two lower TE modes. Calculations are conducted utilizing the mathematical model obtained in [1] by the integral equation technique with the correct account of singular behavior of the field at the ridge.     

Gyrotron coaxial cylindrical resonators with corrugated innerconductor: Theory and experiment

Gyrotron coaxial resonators with a longitudinally slotted inner cylinder are examined analytically using a surface impedance model, from which expressions for the electromagnetic field, ohmic quality (Q) factor, and characteristic equation of the transverse eigenvalues χ _m,p are obtained. The major attributes of such resonators are expressed by the dependence of χ_m,p on the parameter C-defined as the ratio of the outer to inner radii of the coaxial structure. In that connection, the effect of the corrugation parameters on χ_m,p is particularly investigated on the basis of an expression derived for the slope function dχ_m,p,p/dC. It is shown that the χ_m,p(C) curve may either exhibit oscillatory behavior or present a flat portion over a wide range of C depending on the corrugation parameters chosen. The theory is checked against experiment in which resonant frequencies and total Q factors were measured for TE modes operating in the range of 8-16 GHz in a coaxial cavity with 40 slots. Good agreement is found in that the magnitude of the relative error in frequency is less than 0.5%. Corrugated coaxial resonators prove to be relevant to megawatt gyrotrons where highly selective cavities are required to ensure high conversion efficiency     

Complex TM models in a generalized Goubau line with arbitrary conductivities

The modal equation for the wavenumbers of the complex transverse magnetic (TM) modes of an open circular-cylinder coaxial waveguide with central conductor is studied for the case when the inner and outer materials have arbitrary conductivity. Analytic approximations for the wavenumhers of all of the modes are obtained for large contrast between the inner and outer materials, and simple numerical algorithms for calculating the wavenumbers are obtained for arbitrary contrast. It is shown that when the conductivities are zero, the wavenumbers group together in a set of four complex values, symmetric in the complex plane, but that the symmetry and the grouping can both be destroyed by adding conductivity to the materials. For fixed conductivities, there are principal modes (with no low-frequency cutoffs) and secondary modes (with low-frequency cutoffs) but one type mode can be converted into the other type by changing the conductivities. A numerical study of the modal equation shows how the modes of a Goubau line can be related to those of a coaxial transmission line. It shows also that the values of individual solutions of the modal equation can depend on the history of the conductivity values of the waveguide.     

分布损耗回旋行波管线性分析与稳定性研究

研究了分布损耗材料导电特性的下降能够增强回旋行波管注-波互作用段对电磁波的衰减,提高了绝对不稳定性振荡的起振电流和竞争模式回旋返波振荡的起振长度;但同时减小了回旋行波管的线性增长率及其轴向功率和高频场增益.给出了石墨乳涂敷圆波导结构回旋行波管工作参数,采用电子束电流,I_0=10A、注-波互作用段长度L=10cm时的设计结果,在兼顾功率和增益的条件下,能够有效抑制不稳定性,保证其稳定工作.