Field theory of a traveling wave tube amplifier with a tape helix

A self-consistent relativistic field theory for a helix traveling wave tube (TWT) is presented for a configuration in which a magnetized pencil beam propagates through a tape helix enclosed with a loss-free well. A linear analysis of the interaction is solved subject to the boundary conditions imposed by the beam, helix, and wall. The wave equation for the fields within the electron beam corresponds to the Appleton-Hartree magnetoionic wave modes that are of mixed electrostatic/electromagnetic polarization. Hence, the determinantal dispersion equation that is obtained implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. This dispersion equation includes azimuthal variations and all spatial harmonics of the tape helix. Solutions that correspond to both the extraordinary (X) and ordinary (O ) solutions for the Appleton-Hartree modes are found numerically     

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented.     

The microwave generation mechanism of arelativistic electron beampropagating through the dielectric-loaded cylindrical waveguide

The general dispersion relation is derived for the fundamental transverse magnetic modes driven by a cold relativistic electron beam in a dielectric-loaded cylindrical waveguide using the fluid Maxwell equations. It is then reduced to the algebraic equation for the space charge and cyclotron modes using a tenuous beam approximation. Solutions of the resulting equation are obtained by varying several parameters, such as the external magnetic field the dielectric constant and the thickness of the dielectric material. It is shown that the growth rate of the slow cyclotron instability is greatly increased for the region of B_o≲1000 G to the extent that it becomes comparable to the growth rate of a slow space-charge instability. In this region the magnetic-field effect on the slow space-charge mode is shown to increase the growth rate by up to 10%. In the limit of the critical external magnetic field defined as the field below which no beam equilibrium exists, it is found that two slow modes of cyclotron and space-charge modes become degenerate with a finite value of growth rate     

Small-signal analysis of a rectangular helix structure traveling-wave-tube

This paper investigates the properties of traveling wave-beam interaction in a rectangular helix traveling-wave-tube (TWT) for a solid sheet electron beam. The `hot' dispersion equation is obtained by means of the self-consistent field theory. The small signal analysis, which includes the effects of the beam parameters and slow-wave structure (SWS) parameters, is carried out by theoretical computation. The numerical results show that the bandwidth and the small-signal gain of the rectangular helix TWT increase as the beam current increases; and the beam voltage not obviously influences the small signal gain. Among different rectangular helix structures, the small-signal gain increases as the width of the rectangular helix SWS increases, however, the bandwidth decreases whether structure parameters a and L or ψ and L are fixed or not. In addition, a comparison of the small-signal gain of this structure with a conventional round helix is made. The presented analysis will be useful for the design of the TWT with a rectangular helix circuit.     

螺旋坐标系下考虑厚度的螺旋线行波管小信号研究(英文)

采用螺旋坐标系对有限厚度的螺旋带行波管进行了注波互作用的线性理论分析,利用自洽场理论得出了此结构中引入电子注后的"热"色散方程,数值计算了其小信号增益,分析了电子注参数和螺旋线厚度对于螺旋线慢波系统的色散特性的影响。结果表明:螺旋线厚度的增加,行波管的小信号增益也会增加,且带宽也略有增加。该结论为高增益宽频带的螺旋线行波管放大器的设计提供了理论基础。     

填充等离子体的介质同轴波导中的切伦科夫辐射

 利用自洽线性场理论，导出了薄环形相对论电子注通过填充等离子体的介质同轴波导中的注波互作用色散方程，得到了注波互作用产生切伦科夫辐射的同步条件和波增长率。分析了填充等离子体后的波与电子注之间的能量交换及等离子体密度对色散特性、波增长率和注波能量交换的影响。分析结果表明：切伦科夫辐射是由沿介质同轴波导传播的慢波与沿薄环形相对论电子注传播的负能空间电荷波耦合所致，且其耦合强度与电子注的密度成正比；输出频率和波增长率随着填充等离子体密度的增大而提高；保持一定的输出频率，增大电子注的束流可得到高的微波输出功率。     

A new approach for evaluating the current and charge density distributions in electron guns and beams

Current and space-charge density distribution calculation is of great significance for numerical analysis and design of high-current electron guns and beams. When the electrons’ thermal initial velocities are taken into account, though there have been some numerical methods published, the calculation is very complicated. By introducing equivalent meridional potential and projection trajectory theory, the curvilinear axis trajectory equation for electrons neighboring to a central curved trajectory in rotationally symmetric electro-magnetic fields is derived in first- and second-order approximations. The evolution equation of the current density distribution of toroidal electron sub-beams is derived and it can be used to calculate the current and charge density distribution in electron beams and guns in iteration calculation. A compact numerical algorithm for calculating round high-current electron guns and beams was developed and related program was written as well. As examples, the evolution of the current density distribution of a Pierce gun and a periodic magnetic focusing high-current electron beam is simulated. This proves that this method is effective and practical.     

Effect of longitudinal space-charge waves of a helical relativisticelectron beam on the cyclotron maser instability

The influence of the longitudinal space-charge waves of a coherently gyrophased helical relativistic electron beam on the cyclotron maser instability is investigated in a cylindrical waveguide configuration using a three-dimensional kinetic theory. A dispersion relation that includes waveguide effects is derived. The stability properties of the cyclotron maser interaction are examined in detail. It is shown that, in general, the effects of space-charge waves on a coherently gyrophased beam are suppressed in a waveguide geometry, in comparison with an ideal one-dimensional cyclotron maser with similar beam parameters     

Nonlinear time-dependent simulation of helix traveling wave tubes

A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory.     

基于伽辽金级数的空间电荷场计算模型

利用局部伽辽金矩量法,建立了电子注空间电荷场的2.5维计算模型. 将空间电荷场在径向展开为各个模式的叠加,利用伽辽金级数表示,通过求解其系数方程组, 最终求得空间电荷场.利用本文的模型,计算分析了电子注空间电荷场的特性, 并研究了模型中仿真参量对空间电荷场计算结果的影响.本文的空间电荷场计算模型利用粒子模拟基本方法, 可以应用到速调管注波互作用计算模型中.     

等离子体填充带状螺旋线的色散方程

利用线性场理论和螺旋线的导带模型，对填充等离子体的带状螺旋线进行了严格的场分析.在给出各区域电磁场分量表达式的基础上，利用螺旋带的边界条件，导出了等离子填充带状螺旋线中电磁波传播的色散方程. 关键词： 等离子体 带状螺旋线 色散方程     

Linear Theory of Plasma-Filled Coaxial Cylindrical Cherenkov Maser

Injection of background plasma into the beam-wave interaction region can greatly enhance the beam-wave interaction efficiency and the microwave output power of the device. In this paper, a new type of plasma-filled slow-wave structure, i.e., plasma-filled, dielectric-loaded coaxial cylindrical waveguide with a dielectric ring enclosing tightly the inner conductor, is developed. The Cherenkov radiation excited by the beam-wave interaction in the slow-wave structure is examined by use of the self-consistent linear field theory. The dispersion equation and the synchronized condition of the beam-wave interaction are derived. It's clearly shown that the Cherenkov radiation excited by the beam-wave interaction results from the coupling between the slow electromagnetic wave, TM-modes, propagated along the slow-wave structure and the negative-energy space-charge wave propagated along the relativistic electron beam. And the wave growth rate is solved, and the beam-wave energy exchange in the presence of the background plasma is discussed. Finally, the effects of the background plasma density on the dispersion characteristics, the distribution of the longitudinal fluctuating electric field, the wave growth rate and the beam-wave energy exchange are calculated and discussed.     

The Linear Analysis of Coaxial Helical-Groove Slow-Wave Structure

The coaxial helical-groove slow-wave structure is a new-type high power circuit. The dispersion equation of this circuit with an annular electron beam is obtained according to self-consistent field theory. The computation results of the hot dispersion equation show the relations between electron beam parameters and the small signal gain. The presented analysis will be useful for the design of the TWT with coaxial helical-groove circuit.     

速调型相对论返波管理论研究

对速调型相对论返波管慢波结构色散特性及束波相互作用进行了理论研究。色散特性研究表明:器件工作模式为TM01模,近点,耦合阻抗较高。色散特性预测的工作频率与粒子模拟结果非常接近。慢波结构峰值增长率相对较小,这与电子束与慢波结构相距较大有关,因而器件从起振到饱和的时间较长。在束波相互作用理论中,全面考虑了电子束与慢波结构前向波基波、反向波－1次空间谐波及空间电荷场相互作用、谐振反射器对电子束进行的束流调制和能量调制作用,以及调制腔和提取腔处引入的耦合阻抗及轴向波数突变。稳态和非稳态计算结果均获得了超过40%的束波转换效率。     

A re-examination of the traveling wave interaction

A re-examination of the traveling wave interaction (in the helix traveling wave tube and the free-electron laser) is performed using three-dimensional linear stability analyses for an idealized annular electron beam model in order to investigate the validity of the well-known scaling laws in which the gain varies as the cube (fourth) root of the current when space-charge effects are negligible (dominant). The results indicate that these scaling laws are simplistic generalizations which break down for broad bandwidth interactions, and that the actual variation of the pain, with the current can be more complex. A three-dimensional nonlinear analysis of a free-electron laser using a more realistic electron beam model is also discussed in which these scaling laws are also shown to break down,     

Improved Computer Program for Magnetron Injection Gun Design

Gyrotron has received extensive attention owing to its high-power capability, especially when the wavelength shrinks below the millimeter-wave range. The electron beam of a gyrotron is typically generated by a magnetron injection gun (MIG). For high cathode current density, the MIG may operate in a region that combines temperature limited and space-charge limited emissions. An improved computer program for electron gun design is appropriate for MIGs that operate between space-charge limited and temperature limited emission. Moreover, the initial input formation of the program resembles that of the EGUN code. Analysis of a Pierce electron gun and MIGs reveals that the stimulated beam current appears consistent with the measured results. However, EGUN simulation results in which the cathode emitters of MIGs are chosen for the temperature limited emission differ from those of our simulation results. This difference is most likely owing to that the initial emitting energy can not be completely described in the EGUN simulation. Finally, the improved computer program is used to design a MIG for a Ka-band, TE₀₁ mode gyro-TWT.     

Linear Cold-Fluid Theory of a Free-Electron Laser

The linear cold-fluid theory of a free-electron laser is given where the laser field must be in the two-mode operation. The ration between the two modes of laser field is obtained. The dispersion relation is discussed in the Raman- and Compton-regimes and the space-charge wave theory is worked out.     

Linear Theory of Radially Inhomogeneous, Unneutralized, Relativistic Electron Beams

A set of four, coupled, first-order differential equations describing the normal modes of a cylindrically symmetric, cold fluid, unneutralized, relativistic electron beam of arbitrary radial profile is derived. Effects of beam rotation and equilibrium fields are treated exactly. The differential equations are found to have singular points for a radially inhomogeneous beam wherever the eigenfrequency equals the cyclotron or Doppler resonance frequencies. The resulting branch cuts in the dispersion function give rise to secularly decaying contributions to the initial value problem. The rate of decay and the character of the eigenmode near the singularity are determined from the solution of the corresponding indicial equation. Discrete eigenmodes also exist and are obtained by numerical solution of the differential equations and boundary conditions. For realistic solid-beam equilibria, only one slow cyclotron-mode exists for any given pair of axial and azimuthal wavenumbers, and that mode is localized at the beam edge. Under identical conditions several slow space-charge modes exist and are not so distorted. However, even at the space-charge limit, the phase velocity of long-wavelength slow space-charge waves does not decrease to zero. These results are relevant to the Autoresonant and Converging Guide collective ion acceleration proposals.     

磁化等离子体填充螺旋线的色散方程

利用等离子体流体理论和纵向场分量法，结合螺旋线的导电面模型，对在有限磁场作用下，填充等离子体的螺旋线进行了严格的场分析. 在给出各区域电磁场分量表达式的基础上，利用螺旋线的边界条件，导出了磁化等离子体填充螺旋线中电磁波传播所满足的色散方程，并对所导出的色散方程进行了讨论. 关键词： 有限磁场 等离子体 螺旋线 色散方程     

Higher-order space-charge field effects on the self-deflection of two-photon bright photovoltaic spatial solitons

We investigate numerically the effects of higher-order space-charge field on the self-deflection of bright photovoltaic spatial solitons in two-photon photovoltaic photorefractive crystals under steady-state conditions. The expression for an induced space-charge electric field, including higher-order space-charge field terms is obtained. The dynamical evolution equation is built in which the effects that arise from these higher-order terms are considered. Numerical results indicate that bright photovoltaic solitons can bend towards both the same direction as the crystal's c-axis and the opposite direction, respectively. Specifically, self-deflection cannot occur for bright photovoltaic solitons if the strength of the photovoltaic field and the intensity of the input beam are appropriately selected. Relevant examples are provided.