Numerical simulation and experimental study of magnetron injection guns of high-power shortwave gyrotrons

The results of numerical simulation and experimental study of magnetron injection guns for high-power gyrotrons that form intense helical electron beams are compared. Three types of beams are studied: those with regularly intersecting trajectories, laminar, and mixed (with irregularly intersecting trajectories). The corresponding guns differ in the angle of inclination of the emitting surface to the axis of axial symmetry. Numerical simulation was performed using the ÉPOS program, which takes into account the effect of the space-charge field on the velocity distribution. The experimental studies of the latter were performed by the retarding-field method. It is established that with allowance for temperature deformations of the electrode systems, the experimental data are in satisfactory agreement with the theoretical. It is shown that for a maximal beam current, the best velocity-distribution characteristics (velocity spread and pitch factor) are provided by guns that form laminar and boundary beams (an intermediate case between laminar and regularly intersecting beams).     

Numerical simulation of intense helical electron beams with the calculation of the velocity distribution functions

The method of calculation of intense helical electron beams which allows to find the distribution function of electrons with respect to their transverse (oscillatory) and longitudinal velocities is developed. The initial velocity distribution function can be arbitrary. The data obtained in numerical simulation and experimental measurements for beams with various topologies are compared. The evolution of the transverse velocity distribution function with the beam current growth is traced. It is found that the transformation of the velocity distribution function may indicate a possible instability in a real beam.     

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

The effect of the electron transverse and longitudinal velocity spread at the entrance to the interaction space on wide-band chaotic oscillations in intense multiple-velocity beams is studied theoretically and numerically under the conditions of formation of a virtual cathode. It is found that an increase in the electron velocity spread causes chaotization of virtual cathode oscillations. An insight into physical processes taking place in a virtual-cathode multiple-velocity beam is gained by numerical simulation. The chaotization of the oscillations is shown to be associated with additional electron structures, which were separated out by constructing charged particle distribution functions.     

Inversion of Rayleigh waves using a genetic algorithm in the presence of a low-velocity layer

The shear-wave velocity profile can be obtained by the velocity of Rayleigh waves through the back-calculation based on dispersion curves. However, the dispersion curves obtained in practical application are always discontinuous and correspond to different mode branches due to mode jumping, especially in the presence of low-velocity layer. Mode misidentification may be encountered in inversion based on these jumped dispersion curves. Mode analysis demonstrates that the mode jumping is caused by a different surface displacement distribution with frequency for each mode. This indicates that the surface displacement distribution of the modes should be taken into account for the case of a low-velocity layer. Shear-wave velocity profiles are inversed based on the (possibly discontinuous) dispersion curves of fundamental and/or higher modes using a genetic algorithm (GA). In addition to the dispersion characteristics, the surface displacement distribution is also taken into account for the case of a low-velocity layer; as a result, mode misidentification is avoided. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp 811–824. The text was submitted by the authors in English.     

Study of the magnetic analyzer of relativistic helical electron beams

The paper presents the results of studying the analyzer of helical electron beams experimentally. The analyzer is based on separation of electron velocity fractions in the adiabatically growing magnetic field. Optimization of the analyzer design to minimize the amount of electrons reflected from the analyzer elements made it possible to practically eliminate the systematic error in measurements of the velocity spread and pitch-factor. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 2, pp. 134–140, February 2006.     

8mm波段三次谐波复合腔回旋管的非线性分析

利用含电流的传输线方程,在考虑了诸多实际因素影响的情况下,对三次谐波渐变复合腔回旋管进行了自洽非线性模拟,计算了H₅₁₁-H₅₂₁模式下三次谐波多模注波互作用,分析了电子注的厚度、速度零散、速度比α值及磁场波动对多模注波互作用的影响 关键词： 回旋管 复合腔 多模注波互作用 速度零散 速度比α     

Gyrotron Electron Beams: Velocity and Energy Spread and Beam Instabilities

The stability of the electron beams and maximum share of the electrons oscillatory energy, i.e. finally efficiency, power, and pulse duration of the gyrotron to a considerable extent depend on the velocity and the energy spread (VESP) of the HEB. The basic factors determining VESP in the helical beams are discussed. Among these factors static (initial velocities, cathode heterogeneities, space charge fields) and dynamic (negative mass and diochotron instabilities and a global instability connected with the capture of the electrons in the gyrotron adiabatic trap) factors are considered. Qualitative models of the excitation of the space charge oscillation as well the parasite electromagnetic radiation of the HEB are developed. Some experimental data of the investigation of the parasitic electromagnetic radiation spectrum in one gyrotron are discussed. The methods of the experimental investigation of the VESP are described.     

双注磁控注入电子枪

为了增加回旋管的功率,采用双注磁控注入电子枪产生相对论电子注。与双阳极磁控注入电子枪相比,双注磁控注入电子枪产生双束电子注,在不影响电子注质量的基础上,增加电子枪的电流;电子枪产生相同电流时,双注磁控注入电子枪电子注电流小,电子注电子之间的空间电荷效应小,能够降低电子注的速度零散,提高电子注的质量。采用MAGIC软件数值模拟双注磁控注入电子枪,设计出一支大束流、低速度零散的双注磁控注入电子枪。     

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.     

Improvement of the helical electron beam quality and the gyrotron efficiency by controlling the electric field distribution near a magnetron injection gun

A technique for controlling the electric field distribution near the cathode of a magnetron injection gun is developed. The feasibility of improving the quality of a helical electron beam by optimizing the electric field distribution in a pulsed 4-mm-wave gyrotron is studied theoretically and experimentally. Field distributions are obtained that minimize the electron velocity spread in the beam, coefficient of electron reflection from a magnetic mirror, and intensity of parasitic low-frequency oscillations. It is demonstrated that the gyrotron efficiency can be increased through a rise in the beam quality at the optimized electric field distribution.     

Structure of Electromagnetic Fields in Crossed Gaussian Beams

Expressions for the fields of crossed Gaussian beams with foci shifted relative to the point of intersection of their axes are derived. It is shown that the linear corrections in parameter ε=1/kρ₀ must be taken into account in the crossed-beam intensity distribution (in contrast to the case of a single beam). The interference of crossed Gaussian beams has been investigated based on the intensity calculations taking into account linear corrections to the Poynting vector. The residual electron energy in crossed pulses is multiply increased in comparison with the case of acceleration in a single Gaussian pulse.     

Formation and Diagnostics of Intense Relativistic Helical Electron Beams for Gyrotrons

We develop a magnetron-injection gun for a 1-cm wavelength gyrotron, which allows us to increase the operating current up to 50% of the Langmuir current of the gun by reducing the time required to bring electrons to the high-potential region. To measure the velocity distributions in helical electron beams for energies of several hundreds of keV, we propose, develop, and study a new electron-velocity distribution analyzer based on the phenomenon of electron reflection from an adiabatic magnetic mirror. The results of our study demonstrate that the gun is capable of forming high-quality intense beams suitable for generating microsecond microwave radiation with power higher than 10 MW in gyrotrons.     

Numerical analysis of space charge effects in electron bunches at laser-driven plasma accelerators

Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can reach many kA peak current, over short distances. Space charge issues, even in transport lines as simple as a drift section, have to be carefully taken into account since they can degrade the beam quality, preventing any further application of such electron beams. We analyse the space charge effects within an electron bunch with numerical simulations in order to assess their effect on the beam. We use LPA beam parameters published in previous experimental studies. These studies can give an indication of the working point where space charge can dominate the beam dynamics and has to be taken into account in the application of such beams.     

Computer Simulation of Axis-Encircling Beams Generated by an Electron Gun with a Permanent Magnet System

Results from computer aided design of a novel electron gun generating axis-encircling beams are presented and discussed. Numerical experiments were performed by the new version of the software package GUN-MIG named GUN-MIG/CUSP. It is based on a self-consistent relativistic model and is developed as a problem oriented tool for analysis of electron-optical systems with magnetron injection guns (MIG) and electron guns with field reversal (cusp guns), forming axis-encircling beams. As a result of the simulations an electron-optical design of a novel electron gun with permanent magnet system was accomplished. The gun is expected to form high quality beams with small velocity spread and beam ripple. Parameters of the generated beams are appropriate for a prospective weakly relativistic high harmonic large orbit gyrotron (LOG). The development of such device is in progress now at the Research Center for Development of Far-Infrared Region (FIR Center) at Fukui University.     

Statistical Theory of Two-Sided Multipactor

We develop a statistical theory of secondary-emission discharge (SED) taking the energy distribution of secondary electrons into account. The theory allows one to describe quantitatively the initial stage of development of a two-sided multipactor. For an arbitrary probability density of normal components of the ejection velocity and an arbitrary distance between the walls enclosing the microwave discharge plasma, we construct an analytical solution for the electron distribution function over transit times. The performed analysis is based on the results of a detailed study of conditions under which an electron reaches the opposite side. With allowance for the spread in thermal velocities, we derive a recurrence relation between the electron distribution functions over emission phases and formulate a general integral equation from which the resulting stationary distribution and the threshold of SED onset are determined.     

Advanced Numerical and Experimental Investigation for Gyrotrons Helical Electron Beams

The paper presents a modern approach to studies of characteristics of intense helical electron beams (HEBs) for gyrotrons. The essence of the method consists in finding functions of electron distribution with respect to oscillatory velocities in the beam both by numerical simulation and experimentally. Experimental and calculated data for beams with different topologies were compared in different frequency ranges. Evolution of the electron oscillatory velocities distribution function as the beam current grows has been traced. Influence of the reflected electrons on beam parameters has been simulated numerically.     

Dynamic behaviour of structures in large frequency range by continuous element methods

The continuous element method is presented in the context of the harmonic response of beam assemblies. A general formulation is described from the displacement solution of the elementary problem. A direct computation of elementary dynamic stiffness matrices is presented. In the present formulation, distributed loadings are taken into account. In the case of more complex geometries for which many coupling phenomena occur, an explicit formulation is no more conceivable. In this case, a numerical approach is presented. This approach allows an algorithmic computation of exact dynamic stiffness matrices. This method, called “Numerical Continuous Element”, allows one to consider the coupled vibrations of curved beams and those of helical beams. The validation of this numerical method is achieved by comparisons with the harmonic response of various beams obtained by a finite element approach. Finally, a comparison between eigenfrequencies obtained experimentally and numerically for a straight beam and a helical beam has been made to evaluate the performances of the method.     

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave(SCW) harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability.For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover,we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.     

0.6 THz三次谐波大回旋电子枪设计

基于会切磁场的理论模型,采用粒子模拟软件对0.6 THz三次谐波的太赫兹回旋管所需的大回旋电子光学系统进行研究。通过大量的模拟计算,分析讨论了不同参数对电子注的横向速度离散、纵向速度离散及横纵速度比的影响,优化了电子光学系统的性能参量,得到符合设计要求且具有工程实际应用的电子枪,该电子枪能够产生55 kV,1 A,横向速度离散为3.39%、纵向速度离散为7.10%、横纵速度比为1.53的大回旋电子注。     

Effects of energy spread on brightness and coherence of undulator sources

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free‐electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single‐electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction‐limited rings with ultralow emittance coming on‐line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.