Relativistic surface-wave oscillators with 1D and 2D periodic structures

A nonlinear nonstationary theory of surface-wave oscillators with 1D and 2D periodic structures is constructed in terms of a quasi-optical approach. The radiation field is represented as a superposition of quasi-optical wave beams coupled on a corrugated surface and forming a self-consistent structure. Synchronous interaction with rectilinear relativistic ribbon and cylindrical electron beams is observed when the surface wave slows down. The results obtained in terms of the average approach are compared with those obtained by direct numerical particle-in-cell simulation. The feasibility of creating small-size millimeterwave gigawatt power supplies based on 2D planar and cylindrical surface-wave oscillators is demonstrated.     

Three-dimensional electromagnetic PIC model of a compact ECR plasmasource

A three-dimensional electromagnetic particle-in-cell (PIC) model is developed and used to model a compact ECR plasma source. The finite-difference time-domain (FDTD) technique is used to model the microwave fields which excite the plasma at 2.45 GHz. The PIC technique is used to model the dynamics of both the electrons and ions in the plasma. The grid structure used is constructed using the cylindrical coordinate system. Techniques which permit stable numerical solutions in the cylindrical coordinate system are developed and described. The electromagnetic fields and the plasma dynamics are solved in a self-consistent manner. A compact ECR (electron cyclotron resonance) plasma source used for the generation of ions for materials processing is simulated. This source has a plasma size of 3.6 cm in diameter and 3 cm in height. Simulation results of microwave power absorption, plasma potential, and microwave electric fields are presented. Distributed computing techniques are explored to handle the large computer memory requirements and the long computer simulation times associated with the three-dimensional particle-in-cell plasma model     

Ring microresonator as a photonic structure with complex eigenfrequency

For the analysis of light propagation in photonic guided-wave ring microresonators, leaky-mode solvers for bent channel waveguides are often used. In the analytical approach, the leaky mode field is expressed in terms of cylindrical functions of complex arguments and a complex order which plays a role of the (azimuthal) propagation constant. In this contribution we present a modified approach which takes into account the circular symmetry of the structure. We calculate the eigenmodes of a lossy microresonator as modes with complex eigenfrequencies. In this approach, the eigenmodes are described by cylindrical functions of an integer order and a complex argument. Similarities and differences of both approaches are demonstrated using simple examples of 2D (planar) structures.     

Theory of high-harmonic gyrotron oscillators with slottedcross-section structure

A linear-theory analysis of gyrotron oscillators with slotted cross section is used to calculate the net change in beam energy. In this formalism, geometric factors are clearly distinguished from the geometry-independent harmonic resonance terms due to the fundamental electron cyclotron maser and peniotron interactions. This separation of the interaction terms from the geometric factors simplifiers the physical analysis, and leads to a very compact form for the net change in beam energy. The theory is applied to slotted rectangular oscillators and to slotted cylindrical oscillators to show that a unified expression can be obtained for the start-oscillation condition. In sample applications of the theory, it is demonstrated that slots lower the start-oscillation condition in both cylindrical and rectangular geometries, and can lead to a decrease in this condition as harmonic number is increased in the rectangular geometry. It is also found that the peniotron interaction, which is easily identified in this formalism, may be very strong in slotted cavities     

无箔二极管电磁PIC模拟空间电荷限制发射模型比较

 为了在无箔二极管电磁PIC模拟中采用与电磁场自洽的空间电荷限制发射模型，对查尔特定律模型、高斯定律模型和一维二极管模型进行了理论分析和实例模拟比较。模拟结果表明，三种模型都能与电磁场自洽并反映外加磁场对发射电流的影响，但高斯定律模型受网格剖分粗细程度的影响较大且容易产生振荡，一维二极管模型在网格参数合理的情况下结果与查尔特定律模型基本接近，但需要求解超越方程，花费时间多。通过对模拟结果进行分析和比较，认为外加磁场对电子发射模型本身的影响很小，在电磁PIC数值模拟中可以不考虑，因此，查尔特定律模型更适合用于无箔二极管的电磁PIC模拟。     

Theoretical and Numerical Investigation of a Four-cavity TE021-Mode Gyroklystron

Using self-consistent field theory and PIC simulation, the interaction of electron flow with HF fields in a four-cavity Gyroklystron with TE₀₂₁-mode has been analyzed. Self-consistent field theory includes both linear theory and nonlinear theory. Optimized parameters and their corresponding efficiency, gain and bandwidth of the optimized Gyroklystron have been found. Numerical investigation using PIC simulation is also given. Parameters of the cavities which are operating in TE₀₂₁ mode are optimized to minimize TE₀₁₁ mode and to suppress parasitic self-oscillations. The results of theory are in good qualitative agreement with PIC simulation. This work is supported by the Chinese Natural Science Foundation under Contract 60532     

Stable 1 MW, third-harmonic gyro-TWT amplifier

The concept that the relatively weak harmonic gyro-TWT interactions allow high values of electron beam current for stable operation has been extended to design two extremely high power, 140 GHz, third-harmonic TE₃₁ gyro-TWT amplifiers. One device is driven by an axis-encircling electron beam from a cusp gun and the other employs a magnetron injection gun (MIG). These devices are predicted by a self-consistent nonlinear numerical simulation code to yield, respectively, output powers of 775 kW and 937 kW with 15.5% and 18.7% efficiency, saturated gains of 27 dB and 30 dB, and saturated bandwidths of % and 6.5%. The stability of the amplifiers is ensured by limiting the length of the interaction section(s) to the shortest starting oscillation length as determined by linear theory. The cylindrical waveguide circuits of both amplifiers have been sliced to suppress modes without a threefold azimuthal symmetry. The amplifier utilizing a MIG yields superior performance because the dominant competing interaction is minimized for the choice of the beam's guiding center radius. The advantages as well as limitations of this approach for high power microwave generation are also addressed     

Electromagnetic Field and Cutoff Frequencies of the Azimuthally Rippled Wall Waveguide

The cylindrical waveguide with azimuthally periodic corrugations described by a sinusoidal function is analyzed. Relevant to magnetron and gyrotron interactions, TE-mode oscillations are treated by deriving a dispersion relation—linking the cut-off frequency and corrugation parameters—upon expansion of the field quantities in terms of space harmonics. From numerical examples, the present paper examines how the geometrical properties (area and perimeter) of the corrugated cross section relates with the cutoff frequencies of 2 and modes having one radial variation. The waveguiding system studied here with continuously corrugated azimuthal profile looks attractive to relativistic, slow-wave electron devices for it is more resistant to RF breakdown in comparison with traditional magnetron cavities with vane-type side resonators.     

基于描述函数方法的神经群自激振荡特性分析

在无外界刺激时神经群表现为节律性自激振荡,自激振荡是非线性系统特有的一种运动形式.在非线性描述函数法理论框架下,对神经群模型自激振荡特性进行分析,并揭示其产生机理.神经群模型的sigmoid非线性函数(简称为S函数)是其自激振荡的根源.首先,求解S函数的描述函数;然后,基于S函数的描述函数得到神经群模型正反馈回路S函数和负反馈回路S函数的等效增益,在此基础上将神经群模型转化为可用描述函数法分析的典型结构形式;最后,应用描述函数法理论对神经群模型自激振荡特性进行理论分析,得到自激振荡特性的定量描述,并通过仿真分析对理论分析结果进行了验证.理论分析及仿真分析结果表明基于描述函数方法的神经群自激振荡特性分析方法是正确有效的.S函数是神经系统的典型非线性环节,S函数的处理方法及神经群自激振荡特性分析方法对于其他神经模型的自激振荡特性分析具有参考价值.     

同轴慢波结构相对论高功率微波产生器理论分析

 推导了同轴波导的空间电荷限制流,其值大于圆波导的空间电荷限制流。因此在阴极电势和束流相等的情况下,同轴波导中的束流具有更高的动能,同轴器件有可能获得更高的微波转换效率。理论推导出同轴慢波结构中考虑束流空间电荷影响的色散方程,利用Matlab进行了编程求解。不考虑束流空间电荷影响时,编程计算结果与Superfish模拟结果一致。由考虑束流空间电荷影响的色散方程数值计算结果,可知文献中提出的同轴慢波结构相对论高功率微波产生器工作在准TEM模的π模,频率为7.67 GHz,峰值时间增长率较高,电子束损失的能量与其初始能量之比为34%。这些结果均与文献中的数值模拟结果一致。同时理论分析说明该种器件无论在能量转换效率,还是在产生微波脉冲的上升时间上均具有优势。     

同轴波纹返波管色散特性研究及粒子模拟

 计算了同轴波纹慢波结构的色散特性,分析了波纹周期长度、波纹幅值大小以及同轴内导体半径对慢波结构色散特性的影响。研究表明内导体的存在使系统截止频率升高,系统尺寸可比普通波纹波导慢波系统更大, 并且可以采用大半径电子注并工作在低磁场状态。运用Magic软件对同轴波纹返波管进行了数值模拟, 发现同轴波导内场分布有利于注波互作用,在数值模拟基础上设计出高效率、低磁场的非均匀同轴波纹返波管,互作用效率达60%,聚束磁场小于1 T。     

Finite element approach for radiative transfer in multi-layer graded index cylindrical medium with Fresnel surfaces

Because the optical plane defined by the incidence and reflection direction at a cylindrical surface has a complicated relation with the local azimuthal angle and zenith angle in the traditional cylindrical coordinate system, it is difficult to deal with the specular reflective boundary condition in the solution of the traditional radiative transfer equation for cylindrical system. In this paper, a new radiative transfer equation for graded index medium in cylindrical system (RTEGCN) is derived based on a newly defined cylindrical coordinate system. In this new cylindrical coordinate system, the optical plane defined by the incidence and reflection direction is just the isometric plane of the local azimuthal angle, which facilitates the RTEGCN in dealing with cylindrical specular reflective boundaries. A least squares finite element method (LSFEM) is developed for solving radiative transfer in single and multi-layer cylindrical medium based on the discrete ordinates form of the RTEGCN. For multi-layer cylindrical medium, a radial basis function interpolation method is proposed to couple the radiative intensity at the interface between two adjacent layers. Various radiative transfer problems in both single and multi-layer cylindrical medium are tested. The results show that the present finite element approach has good accuracy to predict the radiative heat transfer in multi-layer cylindrical medium with Fresnel surfaces.     

风成海面的极化辐射

采用几何光学模型和统计的方法研究了风成海面的极化辐射特性.本文假设海面由一系列随 机分布的小镜面组成，海面对电磁波的散射可看作镜面的反射，风成海面的辐射是小镜面辐 射的统计平均.计算了前三个Stokes 参数，结果表明辐射亮温随方位的变化关系为余弦函数 ，周期为π；辐射亮温随方位角的变化幅度为几个Κ.风成海面的极化辐射特性提供了利用 被动微波遥感手段反演海洋风场的途径. 关键词： 极化 辐射 亮温 风成海面     

Trajectories of Charged Particles in Radial Electric and Uniform Axial Magnetic Fields

The trajectories of charged particles were determined over a wide range of parameters characterizing the motion in cylindrical low-pressure gaseous discharges and plasma-heating devices which have steady radial electric fields E perpendicular to uniform steady magnetic flelds B. Three radial distributions of E were considered: E ? r, constant E, and E ? r-1. These distributions are characteristic of the fields measured in a modified Penning discharge, in two NASA Lewis Bum-out-type plasma-heating devices, and that estimated for the Ixion device, respectively. The plasmas of such ? × B? devices are often characterized by their high ratios of drift energy to mean particle energy, finite gyroradius effects, and sizeable electric field changes in the distance covered by a cyclotron radius. Such particle motions are not amenable to simple guiding center theory. From numerical calculations of the actual trajectories it was concluded that the differences between cyclotron frequency and qB/m, and between azimuthal drift and a guiding center approximation (including ? × B? and centrifugal force terms) are appreciable. The net cyclotron motion obtained by subtracting the actual drift from the trajectories, however, has a nearly circular contour over which the speed is quite constant.     

An energy- and charge-conserving,implicit, electrostatic particle-in-cell algorithm

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov–Poisson formulation), ours is based on a nonlinearly converged Vlasov–Ampére (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant–Friedrichs–Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier “energy-conserving” explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton–Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.     

高增益自由电子激光饱和态分析的三维统计理论

考虑电子束横向发射度和电子β振荡,将2005年国际上提出的单通过高增益自由电子激光饱和状态分析的统计物理方法发展到三维情形。首先建立一种描述电子三维运动的归一化简化模型,推导了一维光场下包含电子横向运动的Vlasov方程。在螺旋型波荡器情形下通过引入横向运动守恒量发展了三维统计物理分析方法,并编写了相应计算程序,计算自由电子激光达到饱和时系统的光强增益、聚束因子。作为对比验证,编写包含N个电子自由电子激光系统的三维直接数值模拟程序,结果表明数值模拟和统计计算结果相一致。对比文献中一维模拟和一维统计理论计算结果,所得结果反映了电子束横向发射度以及电子在波荡器中的横向β振荡对饱和点参数的影响。     

Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmodial slime mold

Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems.     

波瓣波导谐振腔太赫兹回旋管的研究

以电子回旋脉塞非线性理论为基础, 结合三维电磁仿真软件, 通过导入高频场数值解替代理论解析的方法, 对波瓣波导谐振腔高次谐波太赫兹回旋管进行了理论和模拟研究. 给出了该类回旋管的起振电流、耦合系数以及注波互作用效率等重要参数, 并在此基础上设计了一只工作频率为0.4 THz, 工作模式TE₃₃模三次谐波波瓣波导谐振腔回旋管, 其电子注参数为1.0 A, 40.5 kV, 横纵速度比1.5,互作用区引导磁场为5.09 T, 输出功率达到3.3 kW.     

粒子模拟中激励源的一种等效设置方法

 基于计算电磁学中对强迫激励源消除虚假反射的算法分析,提出了用等效电流和等效磁流在FDTD公式中引入电场激励源和磁场激励源的方法。从粒子模拟方法的基本方程和迭代公式出发,分析了激励源的引入过程,推导出激励源所等效的电流项和磁流项表达式,实现了新的激励源设置方法,并进行了数值验证和结果讨论。研究表明：这类等效模型与标准FDTD公式能紧密结合,引入非常方便;不必专门设置一个附加的散射场区来处理散射场的计算,大大节省了计算时间和计算内存,比常规总场/散射场体系方法的效率高20%以上,对粒子模拟这类耗时的计算较为适用。通过对2维柱坐标系下相对论速调管放大器(RKA)的模拟,证明了此类激励源设置方法的实用性。     

压缩态光场的四阶量子干涉

采用半经典理论讨论了同一抽运源抽运的两个独立光学参量振荡腔(OPO)所产生的压缩态光场的四阶量子干涉效应．结果表明：在OPO振荡阈值处,输出光场压缩度最高但四阶量子干涉最弱,条纹可见度为33.3%,远离阈值时干涉越来越强. 关键词：