Self-consistent nonlinear analysis of overmoded gyrotron oscillators

The self-consistent nonlinear analysis is presented for an overmoded gyrotron, in which the gyrotropic beam interacts with more than one cavity eigenmodes. The nonlinear equations are obtained in the slow time scale for the motion of each individual particle and for the evolution of the amplitude and frequency of each individual cavity eigenmode. A numerically efficient algebraic longtime-step algorithm is developed, which includes magnetostatic field tapering and time transients. Numerical examples are presented for the excitation and competition of the cavity eigenmodes.Work supported by the U.S. Naval Research Laboratory, Plasma Physics Division, under Contract No. N00173-79-C-0200.     

Linear theory of an electron cyclotron maser operating at the fundamental

The linear theory of an electron cyclotron maser (ECM) operating at the fundamental is developed. A set of analytic expressions, valid for all TE cavity modes, is derived for the starting current and frequency detuning using the Vlasov-Maxwell equations in the weakly relativistic limit. These results are applicable for an arbitrary electron velocity distribution as well as any longitudinal distribution of the RF field. It is shown that the starting current can be expressed in a simple form which contains the Fourier trans-form of the longitudinal field distribution. Analytic results are presented for specific longitudinal field variations, including uniform, sinusoidal, and Gaussian. It is found that the starting characteristics of an ECM are strongly influenced by the axial dependence of the RF field, but weakly affected by the velocity spread of the electron beam. The problem of multimode oscillation is treated in the linear theory by using a Slater expansion of the cavity field. The complete formulation for mode competition based on this expansion is presented and preliminary results are derived. This comprehensive analysis of ECM linear theory should be useful as a diagnostic of ECM performance and should facilitate comparison between theory and experiment.Work supported by U.S.D.O.E. Contract DE-AC-02-80ER52059Supported by U.S. Department of EnergySupported by National Science Foundation     

轴向提取矩形波导TE10模虚阴极振荡器

轴向提取矩形波导TE10模虚阴极振荡器可以不需要模式转换器或弯曲过渡波导而直接通过天线轴向辐射微波,从而使微波源及其辐射系统更加紧凑。粒子模拟结果表明,在400 keV,8.9 kA的束流条件下,轴向提取矩形波导TE10模虚阴极振荡器在2.12 GHz处可以获得功率为500 MW的高功率微波输出,功率效率为14%,频率、模式纯净。这些结果为相同波段同类装置的小型化提供了一条可能的技术途径。     

Generation of the Gaussian-like HE11 mode from gyrotron TEOn mode mixtures at 70 GHz

This work reports calculations and measurements on mode converters for the transformation of TEOn gyrotron mode mixtures (primarily TEO2) into the linearly polarized HE11 hybrid mode at 70 GHz. This mode is ideal for quasi-optical launching systems for ECRH of plasmas. Mode transducers with axisymmetric radius perturbations convert the gyrotron TEOn mode composition into the TEO1 mode. Proper matching of the phase differences between the various modes and of the perturbation amplitudes of the several converter sections is required. The TEO1 wave is used for long-distance transmission through smooth-walled overmoded waveguides. A mode converter with constant diameter and periodically perturbed curvature transfers the unpolarized TEO1 mode into the polarized TE11 wave. The experimentally determined TEOn-to-TEO1 conversion efficiency is (98.5±1)% (99% predicted) while the TEO1-to-TE11 transformer has a (94±2)% efficiency (93% theoretically); ohmic losses are included. The Gaussian-like HE11 mode with axisymmetric power distribution and almost no cross polarization is produced in a circumferentially corrugated TE11-to-HE11 mode transducer with a measured conversion efficiency of (98.3±1.5)% (98.5% predicted). The overall efficiency of the complete mode converter system in the desired mode was determined to be (91±2.5)%. High-power operation (200kW, 100ms) has been successfully demonstrated.     

同轴回旋自谐振脉塞放大器的线性分析

从同轴回旋自谐振脉塞(CARM)放大器的回旋动力学理论入手,详细分析了各参量对同轴CARM放大器的线性增益的影响。通过数值模拟,发现该器件的线性增益对及对同轴波导的外半径、电子导引中心半径以及加速电压的变化非常敏感,而随波导内半径的变化不敏感。经优化,当外半径为3.805 cm,导引中心半径为1.309 cm,内半径为1.039 cm,加速电压为54.9 kV时,器件的线性增益最高为294.96 dB/m。     

同轴回旋自谐振脉塞放大器的线性分析

 从同轴回旋自谐振脉塞(CARM)放大器的回旋动力学理论入手,详细分析了各参量对同轴CARM放大器的线性增益的影响。通过数值模拟,发现该器件的线性增益对及对同轴波导的外半径、电子导引中心半径以及加速电压的变化非常敏感,而随波导内半径的变化不敏感。经优化,当外半径为3.805 cm,导引中心半径为1.309 cm,内半径为1.039 cm,加速电压为54.9 kV时,器件的线性增益最高为294.96 dB/m。     

Linear analysis of a three-dimensional rectangular Cerenkov maser with a sheet electron beam

A linear theory of a rectangular Cerenkov maser (RCM) with a sheet electron beam is developed by using the field-match method. Based on the three-dimensional beam-wave interaction model proposed in this paper, a hybrid-mode dispersion equation and its analytical solution are derived for the RCM. Through numerical calculations, the effects of the beam-grating gap, beam thickness, current density, beam voltage and waveguide width on the linear growth rate are analysed. Moreover, the performance difference between the RCM with the closed transverse boundary and that with the upper open boundary is compared. The results show that the closed RCM model can avoid the effect of RF radiation on beam-wave interaction, which is more rational for practical applications.     

离子通道电子束回旋脉塞的等离子体波效应

研究了离子通道回旋电子束脉塞（ICECM）中的等离子体波非线性效应。利用流体理论与自洽非线性理论方法对ICECM中等离子体波效应的微观机理进行了分析。研究发现,等离子体波加强了电子束的纵向群聚,束-波互作用的能量交换效率及系统增益得到明显提高。数值模拟计算表明,对于中等等离子体密度、1.5kA电流和1MV加速电压的电子束,系统能够获得的脉冲功率和频率分别为200MW和280GHz的毫米波束。     

Linear analysis of cyclotron-cherenkov and cherenkov instabilities in dielectric-loaded coaxial waveguides

We present, based on the cold fluid theory, linear analysis of the Cherenkov and cyclotron-Cherenkov instabilities which are driven when a linear electron beam is injected into a dielectric-loaded waveguide immersed in an axial magnetic field. In the analysis we consider azimuthally symmetric TM_0n modes. We derive dispersion relations for three types of waveguide, and compare computationally obtained linear growth rates of both instabilities. For the type A, which consists of a metallic cylinder with dielectric liner on its inner surface, the growth rate of the Cherenkov instability is larger than that of the cyclotron-Cherenkov instability. For the type B, which consists of a dielectric core and an outer metallic cylinder, both growth rates are comparable. And for the type C, which consists of a metallic core with dielectric liner on its surface and an outer metallic cylinder, the growth rate of the latter instability is higher than that of the former instability. Finally, for the type C, obtained are dependences of the oscillation frequency and the growth rates of both instabilities on the following parameters: the beam energy, the beam current, the axial magnetic field, the dielectric constant, and the thickness of the dielectric.     

TE03 to TE01 mode converters for use with a 150 GHz gyrotron

Two-step high-power TE03-to-TE01 mode transducers (TE02 is the intermediate mode) were designed to transform the TE03 output mode of the 150 GHz KfK gyrotron into the fundamental circular symmetric TE01 mode for low-loss propagation and further conversion into the linearly polarized quasioptical HE11 mode. The advanced perturbation structures of the ruppled-wall mode converters (with input- and output-diameter D=27.8 mm) were optimized by numerically solving the proper coupled-wave differential equations. The overall TE03-to-TE01 conversion efficiency at 150 GHz was calculated to be ₀=99.1% for a long converter (total length L=2.67 m) and ₀=97.8% for a short converter (L=1.07 m); ohmic attenuation is included. The corresponding theoretical bandwidth (for 95%) is ±1.4 GHz and ±2 GHz, respectively. Low-power experimental data are in excellent agreement with these computed values.     

离子通道电子束回旋脉塞的等离子体波效应

 研究了离子通道回旋电子束脉塞（ICECM）中的等离子体波非线性效应。利用流体理论与自洽非线性理论方法对ICECM中等离子体波效应的微观机理进行了分析。研究发现，等离子体波加强了电子束的纵向群聚，束-波互作用的能量交换效率及系统增益得到明显提高。数值模拟计算表明，对于中等等离子体密度、1.5kA电流和1MV加速电压的电子束，系统能够获得的脉冲功率和频率分别为200MW和280GHz的毫米波束。     

Computer-aided analysis and design of corrugated TE11 to HE11 mode converters in highly overmoded waveguides

A theoretical and experimental study of TE11-to-HE11 mode conversion in highly oversized waveguides is given. The balanced HE11 hybrid mode propagating in a circumferentially corrugated circular waveguide is in many respects ideal for effective electron cyclotron resonance heating of fusion plasmas with high-power gyrotrons. At an aperture antenna it exhibits desirable radiation characteristics such as linear polarization with very low cross polarization and axisymmetric power distribution with low sidelobe levels. This Gaussian-like mode can be generated from a TE11 mode by means of a corrugated mode converter in which the depth of the annular slots is tapered gradually from one-half to one-quarter wavelength. Computer-aided optimization of converter length, shape of corrugations, and of non-linear slot depth variation for 28 GHz- and 70 GHz-transducers was achieved with a scattering matrix formalism employing the modal field expansion technique (Modular Analysis Concept). In both cases the measured conversion efficiency of (98.5±0.5)% and the experimental values of the maximum cross polarization (below –28 dB) are in very good agreement with the predicted values. High-power operation was successfully demonstrated using pulsed 28 GHz- and 70 GHz-VARIAN gyrotrons (200 kW).     

Excitation of microwave by an annular electron beam in a plasma-filled dielectric lined waveguide

An axial relativistic electron beam passing through a slow wave structure is unstable to an electromagnetic perturbation whose phase velocity equals the velocity of the beam. This phenomenon of Cherenkov emission is the basis of all traveling wave tubes. In this paper an excitation of Cherenkov radiation by a thin annular relativistic electron beam in a plasma-filled dielectric-lined waveguide is analysed by use of the self-consistent linear theory. The effect of the thin annular electron beam on the beam-wave interaction is completely described by a jump condition. The dispersion equation and the simultaneous condition of the beam-wave interaction are derived. Finally, the growth rate of the wave is obtained, and the effect of the background plasma density and the electron beam radius on the growth rate of the wave are presented.This work is supported by National Natural Science Foundation of China.     

Cross-sectional analysis of the graded microstructure in an AISI D2-steel treated with low energy high-current pulsed electron beam

A detailed analysis from cross-section of the rapidly solidified layer of a steel formed by low energy high-current pulsed electron beam (LEHCPEB) treatment has been successfully carried out. The results of electron backscattering diffraction (EBSD) measurements revealed that the microstructures and phase components vary dramatically through the melted layer and the heat-affected zone. The exact nature of such a graded structure also changes with the number of pulses. The phase transformation paths vary at different depth and different areas (close to or far away from the carbides). They are determined both by (i) the temperature gradients and (ii) the composition gradients in the surface layers induced by the LEHCPEB treatment.     

The Investigation of Thermal Plasma-Loaded Free-Electron Laser: Linear Analysis

The dispersion equation of thermal plasma-loaded FEL is derived employing linear fluid theory. The characteristic of this thermal plasma FEL is analyzed in detail. FEL growth rate varying with plasma density and plasma temperature is investigated. We find there is an optimum plasma temperature where FEL growth rate can be enhanced considerably. The FEL growth rate is decreased accompanying plasma density raising.     

Renormalization group study of Mullins' equation for molecular beam epitaxy with conserved noise

The dynamics of driven interfaces under conserved noise in a continuum model of growth by a molecular beam has been studied by means of the Noziéres-Gallet dynamic renormalization group technique, using the results of Sun and Plischke for the case of non-conserved noise. Relaxation of the growing film is due to both surface tension and surface diffusion. In (1 + 1) dimensions, four growth regimes have been found. None of these are purely diffusive. One of these fixed points has negative surface tension and is stable with respect to renormalization group flow. This is an unstable growth state in which the creation of large slopes in the interface configuration is expected. In (2 + 1) dimensions, seven growth regimes have been found, in which three are purely diffusive. There is also one fixed point with a negative surface tension. However, this fixed point is unstable with respect to renormalization group flow, and is therefore expected to crossover into the other growth regimes at large system size and long times.