Mode Competition and Self-Consistent Simulation of a Second Harmonic Gyrotron Oscillator

A nonlinear numerical simulation of a second harmonic gyrotron oscillator is presented in this paper. Mode competition from a competing fundamental mode is investigated. In addition, a self-consistent nonlinear theoretical model, including the effect of velocity spread, is applied to analyze the second harmonic gyrotron. A series of numerical calculations is carried out for different electron beam parameters. The results are compared with that of calculations using the cold-cavity, fixed field approximation and with experiments. Good agreement is found between our calculations and an experiment at Fukui University. The azimuthal polarization of the field and the choice of the electron beam radius are also discussed.     

Design of a 24 GHz, 25-50 kW Technology Gyrotron Operating at the Second Harmonic

The preliminary design of a moderate (25-50 kW) gyrotron operating at the ISM (industrial, scientific, medical) frequency of 24.1 GHz is presented. Operation at the second harmonic is considered so that one can obtain radiation at the given frequency with only half the magnetic field required.     

Properties of a Second Harmonic Gyrotron Cavity with Internal Blazed Grating

Spectral domain analysis, scattering matrix analysis and PIC simulations are used here to design a second harmonic gyrotron cavity with an internal blazed grating which favors operation at the second harmonic of the electron cyclotron frequency rather than operation at the electron cyclotron frequency itself. Based on these simulations, the cavity design is optimized. The results show that a new gyrotron with higher power and higher frequency can be achieved by incorporating such a blazed grating.     

Self-Consistent Effects on the Starting Current of Gyrotron Oscillators

Self-consistent effects on the starting current of gyrotron oscillators are examined. Field profiles in the open cavity are shown to be sensitive to the interaction dynamics. This can either significantly raise or lower the oscillation threshold, particularly for the low-Q modes. The transition from resonant-mode oscillations at the low magnetic field to backward-wave oscillations at the high magnetic field is demonstrated.     

Simulation of a High Harmonic Gyrotron with Axis-Encircling Electron Beam and Permanent Magnet

A computer code for simulation of beam-field interaction in a resonant cavity of a gyrotron has been developed. It is based on a self-consistent, time-independent, single-mode physical model. The code has been applied to the analysis of the electrodynamical system of a novel high-harmonic gyrotron with axis-encircling beam and a permanent magnet. In this paper both the physical model and numerical techniques used are outlined. Some results of the numerical experiments are presented and discussed.     

Particle Simulation of a 35-GHz Third-Harmonic Low-Voltage Complex Cavity Gyrotron

A self-consistent particle simulation code has been developed for the research of a 35-GHz third-harmonic Low-voltage complex cavity gyrotron. Aided with microcomputer we use FORTRAN to simulate the process of interaction between electron beam and electromagnetic field. About 7000 macro particles are included at the same time. In the program many useful physical graphs are accessible for the further research of this kind of gyrotron such as the field profile, electrons distribution in various spaces, output power, efficiency and et al. Such simulation results may be helpful to the optimization of devices operation parameters     

Design of Cavities for a Short Pulse Powerful Large Orbit Gyrotron

Designs of cavities for fundamental and high harmonic operation in Large Orbit Gyrotron (LOG) are discussed. The fundamental operation allows one to use beam currents in the range from 200 A to 300 A achieve output power of the order of 9–10 MW at frequency 143.6 GHz. Mode competition calculations show that stable oscillations in the TE^1,4 mode using high beam currents are possible even with the pitch factor 1.3 which is significantly lower than the design value 1.55. For the second harmonic operation, the maximum current used for excitation of the TE^2,4 mode is 60 A and the optimum magnetic field is 7.6 T. A cavity design for fourth harmonic operation using the TE^4,4 mode is also presented.     

高数值孔径二次谐波显微术的分子取向探测

基于矢量衍射理论和格林函数法,利用坐标变换分析高数值孔径条件下二次谐波强度随胶原纤维取向的变化规律.研究结果表明,当胶原纤维垂直于z轴时,聚焦光场Ey、Ez分量的增强导致二次谐波相对强度极小值的上升；随着胶原纤维极角的改变,二次谐波强度的整体变化趋势发生变化,同时前向和后向二次谐波之间的强度变化也出现明显差异.     

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.     

Higher Harmonic Operations of Submillimeter Wave Gyrotrons (Gyrotron FU Series)

Higher harmonic operation of gyrotrons is necessary to obtain high frequencies. Some gyrotrons included in the Gyrotron FU series developed at Fukui University have achieved operation at the third and even fourth harmonics of the electron cyclotron frequency. The output lies in the millimeter to submillimeter wavelength range and the output powers are several watts to several tens of watts. In this paper, the gyrotrons and the conditions under which they operate are described in detail.     

An Introduction to p-adic Fields,Harmonic Analysis and the Representation Theory of SL2

In this expository article, we develop in considerable detail harmonic analysis on p-adic fields. This harmonic analysis is distinctly different from that on the real and complex numbers due to the nature of the underlying topology.     

High Frequency and High Mode Purity Operations of Gyrotron FU IVA

The cavity of the newest gyrotron, Gyrotron FU IVA in the high frequency series of Fukui University gyrotrons (the Gyrotron FU series) is designed to minimize the mode conversion from the main cavity mode to the higher modes. In this paper, the experimental results are compared with simulations for the complete gyrotron oscillator. The gyrotron has an additional advantage to cover the wide frequency range in submillimeter wave region.     

TDLAS波长调制法中调制深度与高次谐波中心幅值关系的研究

可调谐半导体激光光谱技术（TDLAS）是近年来发展十分迅速的光谱检测技术,相较于其他光谱检测技术,它具有高灵敏度、高分辨率、实时监测、便携性好、小型化等优点,在工业环保、医疗检测、气象监测等领域得到了广泛的应用。TDLAS波长调制法中谐波信号易受气压影响,经研究发现气压的影响是调制深度对谐波信号的影响,基于TDLAS技术谐波法的原理,研究了各次谐波与调制深度的关系,通过计算四次谐波与二次谐波中心幅值比,利用调制深度函数推算当前气压环境的调制深度,调整调制频率幅度,使得调制深度接近各次谐波最佳调制深度值,使谐波信号信噪比最佳,提高检测精度。实验通过国瑞智GRZ5031湿度发生器产生固定为1 000 ppm的水汽,调节气阀控制密封箱内不同的气压环境,采用TDLAS水汽检测系统获得了10.2~177.9 kPa气压条件下的二次谐波和四次谐波信号,并进行了仿真与实验分析。仿真结果显示：四次谐波与二次谐波中心幅值比的理论值和仿真值最大相对误差为-1.44%,调制深度的理论值与仿真值最大相对误差为1.78%,说明了仿真下的调制深度函数曲线与理论一致。实验结果显示：根据调制深度函数推算调制深度值,当m=2.226 7时,实测的二次谐波中心频率幅值达到最大值,当m=4.061 0时,实测的四次谐波中心频率幅值达到最大值,与理论结果一致;在30.2 kPa<p<177.9 kPa时,调制深度与气压乘积mp值相对误差较小,最大相对误差不超过±3.2%,说明了此气压条件下的mp值波动不大,通过调制深度函数推算的调制深度值与实际值近似,验证了调制深度函数理论的准确性。     

Observation of Mode Patterns for High Purity Mode Operation in the Submillimeter Wave Gyrotron FU VA

Operation tests of a cavity designed for high purity mode operation of the submillimeter wave gyrotron FU VA has been carried out successfully. The observed emission patterns of several cavity modes appear very pure and are compared with calculated results. High purity mode operation has the advantage of making the conversion to Gaussian-like beams more efficient.     

Observation of Mode Patterns for High Purity Mode Operation in the Submillimeter Wave Gyrotron FU VA

Operation tests of a cavity designed for high purity mode operation of the submillimeter wave gyrotron FU VA has been carried out successfully. The observed emission patterns of several cavity modes appear very pure and are compared with calculated results. High purity mode operation has the advantage of making the conversion to Gaussian-like beams more efficient.     

Ka波段二次谐波损耗波导回旋行波管非线性分析

建立了由损耗段和铜段组成的波导结构的Ka波段二次谐波回旋行波放大器理论模型,并进行了非线性理论研究。基于稳定性分析,确定35 GHz TE02模二次谐波回旋行波放大器的基本工作参数:波导半径为1.02 cm,电子注工作电压为90 kV,工作电流为25 A,工作磁场为0.642 6 T,横纵速度比为1.2;然后通过模拟详细分析了工作电流、波导损耗和速度零散等因素对该放大器性能的影响。研究表明：在该结构中损耗段可以有效地抑制模式竞争从而提高输出功率和带宽;工作电流对输出功率的影响存在最大值;速度零散对输出功率有很大的影响。     

Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators

In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ∂/∂λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.     

非线性光学晶体铌酸钾锂的二次谐波产生

研究铌酸钾锂晶体的近经这过光谱：利用铌酸钾锂晶体对８９０￣９６０ｎｍ的Ｔｉ：ｓａｐｐｈｉｒｅ近红外激光进行倍频,获得蓝得蓝绿光输出;研究了晶体的倍频特性,探讨了提高晶体倍频效率的方法。     

Harmonic Maps as a Subclass of Isometric Embeddings of the Spacetime in Five Dimensions

In the light of the Campbell-Magaard embedding theorem we demonstrate that it is always possible to harmonically and isometrically embed any n-dimensional space into a (n + 1)-dimensional Ricci-flat space. We work out an example to illustrate the results.     

Some New Features of Linear Theory for Describing Non-linear Diffusion

The non-linear flux equation, the non-linear Fokker-Planck equation （or Smoluchowski equation）, and the non-linear Langiven equation are the basic equations for describing particle diffusion in non-ideal system subjected to time-dependent external fields. Nevertheless, the exact solution of those equations is still a challenge because of their inherent complexity of the non-linear mathematics. Li et al. found that, based on the defined apparent variables, the nonlinear Fokker-Planck equation and the non-linear flux equation could be transformed to linear forms under the condition of strong friction limit or loeal equilibrium assumption. In this paper, some new features of the theory were found： （i） The linear flux equation for describing non-linear diffusion can be obtained from the irreversible thermodynamic theory; （ii） The linear non-steady state diffusion equation for describing non-linear diffusion of the non-steady state, which was described by the non-linear Fokker-Planek equation, can be derived more consistently from the microscopic molecular statistical theory; （iii） In the theory, the non-linear Langiven equation also bears a linear form; （iv） For some special cases, e.g. diffusion in a periodic total potential system, the local equilibrium assumption or the strong friction limit is not required in establishing the linear theory for describing non-linear diffusion, so the linear theory may be important in the study of Brown motor.