The effect of tolerances in conical flow Pierce guns II—The perturbed flow in the magnetic field

The first-order perturbations to a beam initially in nonrippling Brillouin flow, which results from several common manufacturing errors in conical flow Pierce guns, are calculated. The manufacturing errors are changes in cathode-anode spacing, changes in cathode curvature, tilt, and transverse displacement of the cathode-focus electrode assembly, and tilt and transverse misalignment of the whole gun to the magnetic field. Errors in cathode-to-focus electrode spacing are not discussed. The tolerances which destroy the rotational symmetry of the gun are shown to cause the smooth beam to perform a helical motion; the tolerances which preserve the symmetry are shown to produce an undulating beam. Using the results of Part I of this paper [1], the magnitudes of individual gun tolerances are related to the effects they produce in the magnetic field. A method of setting limits to the individual gun tolerances is presented and illustrated by calculating tolerances for a gun used in an X-band traveling-wave tube. The calculated tolerances are found to have values which may readily be achieved by careful engineering.     

Beam perturbations in confined flow electron beams with planar symmetry

An analysis of the perturbations in a confined flow beam from a two-anode gun as a result of lens effects at the gun apertures is presented for the case of parallel flow with planar symmetry. The results are presented in the form of plots of the amplitude of the perturbation as a function of the ratio of the final beam voltage at the second anode to the voltage of the first anode. The parameters are the magnetic field and the ratio of spacings between cathode and the first and second anodes. For magnetic fields greater than about twice the Brillouin field corresponding to the first anode voltage, the result is a very broad minimum of perturbation extending over a voltage ratio of the order of thirty to one up to a maximum voltage determined by the spacing ratio. The conditions for exact cancellation of the perturbation introduced at the first anode by the lens action of the second anode are considered, and a convenient chart for determination of these conditions is presented. The lens effect perturbation amplitude is shown to be much greater than that resulting from space charge in the absence of lens effects, except at or very near the voltage and spacing ratio that is correct for cancellation and at relatively low voltages and magnetic fields. It is also shown how these results can be applied to hollow cylindrical beams with and without center conductors.     

用边界元法计算回旋管单阳极磁控注入枪

提出了以边界元法作为理论基础,分析磁控注入枪问题,推导出用边界元法计算这类问题的基本理论方程。并根据整管要求,设计了单阳极磁控注入枪。利用Fortran语言编制了一个模拟计算磁控注入枪的程序,利用计算机辅助设计,给出了电极形状、电子轨迹和电子注参量。理论分析和实际计算结果表明,利用边界元方法分析磁控注入枪是一种有效的方法,具有很好的优点,这为分析电子光学系统提供了一条有效途径。     

Thermal velocity effects in magnetically confined beams

The spreading of magnetically confined electron beams caused by thermal velocities has been investigated theoretically and experimentally. An analysis of the spreading of confined beams of various geometries (strip, rectangular, and cylindrical) is presented. The thermal spreading of a confined cylindrical beam was measured at the anode of a parallel-flow Pierce gun. A transparent fluorescent screen was used for the anode. The spot size at the anode was measured as a function of magnetic field and an attempt made to relate the results to the theory.     

Theory and Operation of a Reciprocal Faraday-Rotation Phase Shifter

The operation of a longitudinally magnetized fully filled square-waveguide reciprocal-ferrite phase shifter is described. The frequency characteristics of the phase shifter are predicted and measured. An error analysis, including rotational errors incurred in wide-band operation and manufacturing tolerances, is used to predict the loss performance of the device. The effect of the ferrite parameters and the waveguide geometry on phase-shifter performance may be calculated using this analysis. The variation of the phase shift with temperature as well as high-power effects are presented, and design considerations, including choice of ferrite saturation magnetization for wide-band performance, are discussed. Experimental results closely confirm the key aspects of this theory.     

Direct synthesis of crossed-field electron guns—A novel gun for producing Brillouin flow

A direct approach to the synthesis of crossed-field electron guns is presented. An iterative approximation to the desired beam form is achieved by application of the paraxial ray equation alternatively solving for potential and curvature along the beam while maintaining certain end-point conditions and the desired convergence pattern. When sufficient accuracy is obtained, polynomial approximations are used to express shapes of the trajectories and the electric fields along the beam edges in analytic form. The electrodes to produce the necessary electric fields along the beam edges are calculated by Kirstein's method. A conformal transformation is used to transform the beam edge into the real axis of a complex plane and analytic continuation of a suitable complex potential function is employed to find equipotential lines. These are transformed back into the plane of real coordinates and are surfaces along which electrodes can be placed. A novel short gun which produces a Brillouin beam has been designed using the iterative approach. The availability of beam curvature as a variable has made it possible to find an electrode system which controls the transition from the cathode-region flow characteristics used in Kino's short gun to a drift Brillouin beam. Detailed experimental evaluation of the gun reveals that the beam characteristics are in good agreement with those predicted theoretically.     

Transport of noise fluctuations in convergent flow crossed-field electron guns

The transport of noise fluctuations in convergent flow or so-called Kino-type crossed-field electron guns is investigated in terms of a two-dimensional computer simulation of the gun by the well-known Monte Carlo method for studying stochastic processes. The exact electrode configurations are simulated in the computer memory. After sufficient time has elapsed for the electron flow to achieve a steady-state condition 2000 additional time intervals are computed and then a statistical analysis is made of the fluctuation quantities. Six emission spots are considered on a finite-width cathode. The analysis is facilitated by the development of a rapid method for the solution of Poisson's equation (two-dimensional). Of particular interest in the results is the improved laminarity of the flow in the KG-M gun and the fact that there is significant space-charge smoothing throughout the gun region in both Kino-type guns. Of greater significance and as yet not explainable is the fact that Ψ versus ωct has local peaks when the space-charge density, which is spatially varying, passes through the Brillouin value (ω_{p}-ω_{c}for this condition). This knowledge could be profitably used in deciding on the location of the gun exit plane. The fact that the laminarity of the flow is sensitive to slight changes in the electric field near the cathode indicates that an absolute evaluation of the noise performance of KG-A and KG-M guns is difficult and may only be obtained through appropriate experiments.     

The grid lens effect in convergent Pierce guns

In a conventional Pierce-type gun, the anode aperture causes a potential reduction in the cathode-anode region from the ideal Langmuir potential distribution. For low-voltage gating of the electron beam, a mesh grid of spherical shape (conforming to an equipotential surface) is used in front of the cathode. When this grid is operated at the Langmuir potential depicted by its relative position, there is a difference in the potential gradients on its two sides. This difference causes a lens action at each mesh element which results in a displacement of the actual electron trajectory from the ideal laminar trajectory in the region beyond the anode. A means for calculating these displacements as a function of distance along the axis is developed. As the grid lenses are divergent, the images of the mesh elements in any plane beyond the anode are larger than those for ideal laminar flow, resulting in a current density distribution which differs from that of the ideal beam. A means of calculating the current density profile by summing the effects of the grid lenses is devised, and the method is applied to a sample gun design to illustrate the effect on the current density distribution.     

场致发射阵列阴极电子枪的设计及模拟研究

讨论了微波管用电子枪的一般参数和要求，对于在微波管中应用场发射阵列阴极电子枪的情况作了分析，表明其中存在的主要问题是电子注散焦。通过比较场发射电子注聚焦的几种方法，利用传统电子枪整体聚焦的思想，初步设计了一个场发射阵列阴极电子枪模型，它包括场致发射阵列阴极，一个Whelnelt电极，一个聚焦电极和一个阳极。通过利用Mafia软件对电子注轨迹的模拟计算，对电子枪的聚焦部分进行了改进。     

W 波段回旋行波管双阳极磁控注入电子枪的设计

回旋行波管是大功率、高频率的微波毫米波器件。根据W波段回旋行波管的要求,设计了双阳级磁控注入电子枪。由电子光学理论,计算得到电子枪的初始参量,然后利用粒子模拟软件MAGIC构造电子枪模型,分析电子枪各个参数对电子注性能的影响,为电子枪设计优化提供了一定的依据。最后优化得到符合设计要求的低速度零散电子枪结构。电子枪阳极电压为70kV,电流10A,电子注速比1.07,电子注横向速度零散0.8%。     

毫米波带状注电子枪的设计方法

利用理论分析和仿真模拟相结合的方法对带状电子注的产生进行了系统的研究,并提出了一种带状注电子枪的设计方法.首先通过理论分析,提出了一种计算带状注电子枪结构参数的迭代算法,即根据注电压、注电流、电子注注腰处半厚度、阴极半厚度和阴极宽度,计算出带状注电子枪的阴极柱面半径、阴阳极间距、阳极柱面半径和射程等主要参数;在此基础上,通过仿真模拟,为毫米波真空电子器件设计了一种带状注电子枪.     

The design and performance of grid-controlled, high-perveance electron guns

The focusing electrode and a probe projecting through the cathode serve as control electrodes for the current from a convergent-beam electron gun. The principal advantage of this type of "grid" is that there is no interception of the high-current-density beam by the probe-grid. This paper presents the design procedure and experimental results for typical probe-gridded guns. The design procedure is used to obtain the desired perveance, beam diameter, and approximate laminar electron flow. The probe geometry that results in a minimum beam distortion is discussed. The range of values of amplification factor obtainable and the influence of probe geometry on this factor are discussed. The magnetic field required for focusing the beam from a probe-gridded gun is compared with that required for perfect laminar flow and for focusing the beam from a nongridded gun of similar design. An electrolytic tank in conjunction with an analog computer was used to plot electron trajectories, with the effect of space charge included, for the probe-gridded gun and a similar nongridded gun. A comparison of the electron optics of the gridded and nongridded gun is made. Electrical breakdown and beam current during the interpulse time are problems considered. Methods used to minimize electrical breakdown and interpulse beam current are presented. Several models of probe-gridded guns were constructed. The measured characteristics of these guns demonstrate that the advantages of grid control can be obtained with only a minor effect on gun perveance and beam focusing.     

Conservation principles in multivelocity electron flow

This paper considers the extension of Poynting's theorem to an electron gas with a continuous distribution of velocities. In particular, an extension of the concept of "kinetic potential" is attempted, since this concept has proved itself very useful in the investigation of single-velocity flow. It is found that in three dimensions the electrokinetic-flow vector cannot be expressed as the product of the convection-current density and a single scalar quantity of the dimension potential. In one-dimensional applications, however, this circumstance is immaterial. Another difficulty is encountered when a small perturbation component on a steady state is considered. The nonlinear Bolzmann transport equation gives a linear equation between the first-order perturbations, but the nonlinearity makes possible a conversion of part of the perturbation power flow to dc power flow. In other words, the power flow associated with a single-frequency perturbation is not necessarily conserved in multivelocity flow, even in the absence of an ac Poynting vector. In the case of space-charge-limited flow in an electron gun, the consequence is that the cooling of an electron stream by adiabatic expansion can proceed beyond the potential minimum and very low noise temperatures are attainable in principle if the accelerating field is maintained small over an appreciable length of the electron gun.     

Tangential magnetic field immersion of a hollow beam electron gun

Harris flow is one of a number of equilibrium electron beams requiring a launching method which imparts angular momentum to the stream. Immersion of the electron gun region in a magnetic field tangent to the cathode and orthogonal to the electron trajectories provides a means of rotation free of the defocusing and discontinuity effects of previous methods. Centrifugal-force spreading is eliminated by electric-field compensation in the gun. This compensation results in field lines at an angle to the stream edges and necessitates gun electrode design by a curvilinear flow method. An immersed gun of this kind has produced a stable Harris flow beam containing 86 per cent of the total energy in rotational motion. Anode transmission is in excess of 95 per cent.     

Quasi-phase-matched second harmonic generation: tuning andtolerances

The theory of quasi-phase-matched second-harmonic generation is presented in both the space domain and the wave vector mismatch domain. Departures from ideal quasi-phase matching in periodicity, wavelength, angle of propagation, and temperature are examined to determine the tuning properties and acceptance bandwidths for second-harmonic generation in periodic structures. Numerical examples are tabulated for periodically poled lithium niobate. Various types of errors in the periodicity of these structures are then analyzed to find their effects on the conversion efficiency and on the shape of the tuning curve. This analysis is useful for establishing fabrication tolerances for practical quasi-phase-matched devices. A method of designing structures having desired phase-matching tuning curve shapes is also described. The method makes use of varying domain lengths to establish a varying effective nonlinear coefficient along the interaction length     

Computer-aided design of electron guns for injected-beam crossed-field amplifiers

A two-dimensional self-consistent computer-aided CFA gun analysis program is discussed which can be used to solve for the characteristics of "long" crossed-field guns with arbitrary electrode shapes and including the effects of space charge. The results of analyzing a "long" Kino gun show excellent agreement between the theoretical gun parameters and those obtained by the computer analysis. The model shows promise of also being useful in the analysis of noise in CFA guns.     

Computation of the average power pattern of a reflector antennawith random surface errors and misalignment errors

To specify manufacturing tolerances of a reflector antenna, various errors such as random surface errors and misalignment errors must be considered at one time because superposition of the effects of those errors may not hold. Based on the Rahmat-Samii's formulation (1983), a method for computing efficiently the average power pattern of a reflector antenna with those errors is presented. Simulation results show that superposition of the effects of errors does not generally hold and demonstrate how those errors degrade the peak-gain and sidelobe levels     

An Iron-Free Magnetron-Injection-Gun for a 28GHz, 200kW Gyroklystron Amplifier

A design study of a double-anode magnetron-injection-gun is performed to incorporate the electron gun into a high power 28GHz gyroklystron amplifier operating at 70kV and 8.2A. The electron gun is designed to be used in a tapered magnetic field in the cathode region produced from an iron-free superconducting magnet. An electron trajectory code predicts a beam axial velocity spread of 5.9% at α = 1.5, 70kV, 8.2A and 10.4kG, which is a high quality electron beam suitable for the high gain, high efficiency, five-cavity gyroklystron amplifier. The successful design of the high quality electron gun is attributed to a longer gap between the modulating anode and the grounded anode compared with the case of the first 28GHz electron gun built with an iron enclosed electromagnet.     

A method of reducing the effects of anode aperture in high-perveance convergent electron guns

A new theoretical method of designing convergent electron guns of high perveance for use in microwave tubes is presented here. A differential equation which represents electron trajectories in a convergent electron stream has been deduced under certain approximations. Electron trajectories in an electron stream and boundary values along its boundary were numerically calculated by solving the differential equation by means of an electronic computer. Boundary values on the virtual anode surface under space-charge-limited conditions were used as the initial values for the calculations. Focusing electrodes were determined to satisfy the boundary conditions on the stream boundary. The design procedure is also shown. The electron guns designed by this method are somewhat different in structure from the conventional ones which are usually designed experimentally rather than theoretically. In these new electron guns, nearly uniform current densities will be obtained over the whole cathode area, while in conventional convergent guns of high perveance, electron emission density near the center of the cathodes is usually reduced due to the influence of the anode aperture. Laminar flow will be obtained at points near the minimum stream diameter also in guns designed by this method. Digital computer experiments were performed and the results proved this hypothesis to be reasonable. An electron gun of 1.72 × 10^-6perveance and area convergence ratio of 70:1 is shown as an example.     

A Y-fed directional coupler modulator with a highly linear transfer curve

We demonstrated a linearized Y-fed directional coupler modulator in Z-cut LiNbO/sub 3/. The proof-of-concept device employed two electrode sections of opposite polarity whose lengths were chosen based on the results of our previous theoretical modeling. A highly linear modulation characteristic and improved tolerance to fabrication errors were achieved with a simple design, in excellent agreement with the theory. The linearity exceeded 90% over a wavelength range of 45 nm, centered around 1530 nm, with a maximum linearity of 97% at 1510 nm and a maximum modulation depth of 98%. By comparison, the linearity of conventional modulators is typically around 70%. Thus the device was proven to have a high linearity with a wide usable spectral range and relaxed fabrication tolerances.