The design and performance of a magnetron-injection gun

The space-charge flow solutions described by Kino and others in connection with the crossed-field carcinotron gun can be generalized to form the basis of a magnetron-injection gun design suitable for the production of hollow electron beams. In the first part of the paper this generalization is described. From the resulting flow it is possible to determine by an approximate method the electrodes to produce a gun of desired perveance with nearly uniform current density at the cathode. This technique has been used to design guns having ratios of cathode length to a diameter considerably greater than unity. The close agreement between the results obtained on several experimental guns and the theoretical predictions is described, along with the effect of departures from the prescribed fields given by the design method.     

A new type of cathode-ray tube with a crossed-field gun

This paper introduces a new type of cathode-ray tube with a crossed-field electron gun which produces an electron beam in a region where a nonuniform magnetic field and an electric field cross perpendicularly. The new configuration gives increased freedom in the design of crossed-field guns. As a result, a long, directly heated cathode can be readily applied to a gun structure which makes high perveance and instant operation possible with much improved cathode heating efficiency. The new gun provides ion trap action by virtue of a magnetic field which separates ions from electrons due to the difference in their masses. A new type of cathode-ray tube using this gun not only demonstrates these features but also requires relatively low operational voltages for beam acceleration and control electrodes. The paper includes an analysis of electron motion in a crossed field with a nonuniform magnetic field. It also shows practical configuration of electrodes and current characteristics of the gun.     

The experimental characteristics of a wide dynamic range crossed-field gun

This paper briefly describes the experimental verification of the properties of a wide dynamic range crossed-field gun [1]. This gun, which is a combination of a Kino short gun (or it could be a Kino long gun) and a two-section transformer region, can be used to inject electron beams (with cathode current density varying over a wide range) into the interaction region under optimum conditions and under conditions of a fixed magnetic field. The beam injection level and its injection velocity can also be varied over a wide range by suitably adjusting the electric fields in the two sections of the transformer. The fabrication of the experimental tube is also briefly described.     

Amplitude and frequency modulation using a wide dynamic range injected-beam crossed-field gun†

Methods for amplitude modulation and frequency modulation of injected beam crossed-field tubes using a wide dynamic range crossed-field gun (Sidhu and Wadhwa 1967) are described. This gun has the property that by properly adjusting the electric fields in the two regions of the transformer section, the electron beam can be injected into the interaction region at any desired level, with a fixed injection velocity or the velocity of injection can be varied over a wide range at a fixed injection level. The properties of injection level variations and injection velocity variation can be utilized to produce amplitude modulation and frequency modulation in injected beam crossed-field tubes.

The beam is injected optimally into the interaction region as desired, without any cycloid formation under conditions of fixed magnetic field. The flexibility of the gun to give variable current and inject the beam optimally into the interaction region under the conditions of fixed magnetic field, can also be used for amplitude modulation purposes.     

A gun and focusing system for crossed-field traveling-wave tubes

A problem encountered in the design of crossed-field traveling-wave tubes (particularly M-type amplifiers or backward-wave oscillators) is a limitation on current due to the restricted cathode size in the usual gun systems. The scheme considered here incorporates into a crossed-field device the techniques commonly used in O-type devices for designing converging Pierce-type strip-beam guns, which can increase the effective cathode area by perhaps ten times. A design procedure is presented for getting a well-formed beam from such a gun, which is magnetically shielded, through a fringing crossed-field region into the uniform-field region of interaction. An analysis of electron flow through the fringing-field region, including the effect of space charge, is presented. A trajectory equation, solved on a digital computer, yields trajectories for the beam and design curves for various values of the important parameters. The results show the scheme to be feasible. Results are also presented from tests on an experimental, demountable tube used to test the focusing scheme. About 90 to 95 per cent of the current entering the crossed-field region could be focused to the collector, and the system behaved generally as the design predicted. An evaluation of the experimental data showed the scheme to be useful.     

A design method for crossed-field electron guns

A design method for crossed-field guns based on a space-charge-flow solution in crossed fields is given. By using the method of analytic continuation in the complex plane, it is shown that it is possible to find the exact form of the electrodes required The design results in a gun similar to the French "short gun" with the great advantage that the current emitted from the gun and the current density at the cathode can be predicted. It is also shown that by making certain approximations to the exact space-charge-flow solution, a new type of gun can be designed, a "long gun" which can have extremely high convergence. The theory for this latter gun is extremely simple and the electrode shapes can be given entirely in analytic form.     

Investigation of a Convergent Flow Crossed-field Gun†

An abbreviated version of the Kino short gun has been developed for use as a crossed-field beam injection system. The gun is terminated at a plane where the theoretical average space-charge density, beam location and beam thickness are approximately equal to the corresponding Brillouin quantities for the given anode-sole region conditions. The theoretical design was subjected to a digital computer analysis with the results indicating some intersection of the electron trajectories, although the beam configuration was essentially as predicted. Modification of the cathode ramp electrodes resulted in either laminar flow or uniform cathode emission, but not simultaneously. Experimental investigations carried out in a beam analyser indicated better than 90% transmission of cathode current to the collector for theoretical operating conditions. Beam profile measurements verified that the beam entered the anode-sole region with the desired thickness and at approximately the Brillouin beam location. Furthermore, the undulation of the beam in the anode-sole region was minimal when the magnetic field was set at the optimum value. In general, the abbreviated Kino gun was demonstrated to be a good beam-launching system for crossed-field injected-beam devices.     

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.     

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.     

Noise-figure calculations for crossed-field forward-wave amplifiers

The problem of finding an adequate model for derivation of noise-figure expressions for crossed-field forward-wave amplifiers is investigated. The modified Llewellyn-Peterson equations are used for the portion of the beam near the cathode. Four waves, two cyclotron waves and two space-charge waves, are used for the space connecting the gun and interaction region. Noise-figures are found by considering five waves in the interaction region. The results are very close to those found when only the space-charge waves are considered in the development of the equations for both drift and interaction regions. A matrix, like the space-charge-wave matrix for O-type beams, giving the transformation of beam fluctuations along a drifting, crossed-field stream including the effects of four waves is presented. Expressions for fluctuations of transverse velocity and beam center of gravity are derived to account for all the excitation quantities which are believed to be important in crossed-field amplifiers. The transformation of fluctuations of beam position, or center of gravity, along an accelerating stream is derived. Calculated values of noise figures are far in excess of experimental values. The reasons for the discrepancies are discussed.     

Weak magnetic-field expansion for the self-consistent steady-state potential in a planar crossed-field diode

In a planar crossed-field diode, the steady-state flow in the space-charge-limited régime is governed by a nonlinear integrodifferential equation. We have derived a generalized Fry-Langrnuir equation for the potential which is self-consistent to second order in the normalized magnetic field µ. The small-µ crossed-field potential may be considered as the Fry-Langmuir potential of the corresponding unmagnetized diode, i.e., with the same diode parameters but with zero magnetic field, plus the steady-state second-order perturbation produced by the magnetic field. Owing to the symmetry of the unbounded, planar geometry, there is no first-order perturbation. From four universal functions (the Fry-Langrnuir function and three additional functions we have derived), one can determine the potential and density profiles of any space-charge-limited planar crossed-field diode for which µ is small. It is shown that the crossed-field potential minimum is deepened and shifted toward the anode with respect to the unmagnetized potential minimum.     

Experiments with a new type adiabatic crossed-field gun

In this paper experiments with a "long" crossed-field gun, designed by a method given by Kino, are described. This gun yielded the predicted value of current, but the other characteristics of the beam were not in accordance with the results of the theory. Experiments were carried out from which it may be concluded that there are RF instabilities present in the beam, instabilities which grow in the drift region and are generated at the cathode. The rate of growth of these instabilities is of the same order as the rate of growth of RF fields given by the theory of McFarlane and Hay.     

A small-signal field theory analysis of crossed-field amplifiers applicable to thick beams

Various authors have presented analyses of crossed-field amplifiers. Generally, these analyses have dealt with very thin electron beams in the presence of crossed-fields or with beams in which the bulk ac charge density within the beam has been neglected. It is the purpose of this paper to develop a field-theory analysis which is applicable to both thick or thin beams and which includes the effect of space charge. In place of the usual approximate match at the input boundary plane, a rigorous variational technique is presented, which considers the effect of the cutoff waves on the amplitudes of the propagating waves. This enables one to solve the input boundary problem for the first time insofar as the amplitudes of the propagating waves are concerned, without determining the individual amplitudes of the cutoff waves implicitly. As opposed to the usual approximate match, which is only valid for a thin, unmodulated entering electron stream, this variational method is valid for both thick and thin beams, as well as unmodulated or modulated beams entering a crossed-field slow-wave interaction region or entering a crossed-field drift region. The paper presents propagation constants obtained for thick beams based on the author's model. The variational procedure, which is a valid technique for other models as well as other types of beam devices, has been applied to one numerical case involving a thin beam and the results are compared with the results of the usual approximate match. A modification of the complex amplitudes of the excited waves, even in the case of thin beams, is noted.     

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.     

关于磁控注入式电子枪的噪声问题

磁控注入式电子枪能提供高导流系数的电子注,可应用于大功率微波管中。但是,通常认为这种电子枪属于交叉场型的,具有交叉场器件固有高噪声的特性。这使它的应用受到了限制。 有两个实验打破了上述这种看法。1962年C波段低噪声行波管应用磁控注入式电子枪获得了3.1dB的噪声系数。1965年S波段中功率前向波放大器获得了3.5dB的噪声系数。但这些器件均限于中小功率范围,阴极长度很短,即阴极长径比很小的情况;而对于大功率管中使用的磁控注入式电子枪,能否获得足够小的噪声系数的问题,尚有待于进一步深入研究。 本文简要讨论了影响大功率微波管中磁控注入式电子枪噪声的主要因素以及通过改变阴极区磁场分布的方法来减小噪声的实验结果。     

Transformation of fluctuations along accelerating crossed-field beams

Equations are derived to express the ac potential difference and the transformation of fluctuations of velocity and current between two arbitrary planes along an accelerating crossed-field electron stream. The system of equations, after being simplified by the assumption of zero total ac current, is applied to the special cases of the temperature-limited diode, the space-charge-limited diode, and a diode in which the beam enters with appreciable average velocity. Finally, the open-circuit equations are applied to an approximate model of a beam in a crossed-field electron gun. A new mechanism of growth, peculiar to the crossed-field beam, is discussed as a possible explanation of the observed large sole current in beam-type magnetron amplifiers and related devices.     

Some considerations for reduction of noise and instability improvement in high-power crossed-field devices

The maximum potential of the high-power crossed-field devices has been restricted because of the presence of instability in these devices without any RF drive. The experimental investigation of the crossed-field instability as found from various tubes is briefly reviewed. It is believed that this instability is due to interaction of the slow cyclotron wave with the fast forward circuit wave. The theoretical work presented here refers to the interaction of both the slow and fast cyclotron waves with either of the circuit waves. The tuning characteristics of the interacting (oscillating) frequency due to slight changes in beam velocity resulting from changes in sole-to-anode voltage or magnetic field are derived. It is found that there is a good correlation between the theoretical and experimental results only for the case of interaction of the slow cyclotron wave with the fast forward circuit wave. For other interactions the tuning characteristics have opposite signs. In order to achieve a stable and less noisy operation of the device it is necessary to avoid the interaction of the cyclotron modes with the circuit wave. This limits the usable bandwidth which is plotted for different operating parameters. The electronic efficiency depending upon these operating parameters is also discussed. The problems in the gun design are reviewed. It is estimated that the conventional Kino gun may be used without any loss in bandwidth and efficiency up to frequencies in L band provided design procedures outlined in the paper are followed. For higher frequencies one has to use modified guns unless a reduction in bandwidth and efficiency can be tolerated.     

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.     

Gridded Electron Guns and Modulation of Intense Beams

Gridded guns are useful for producing modulated electron beams. This modulation is generally limited to simple gating of the beam but may be used to apply structure to the beam pulse shape. In intense beams, this structure spawns space-charge waves whose dynamics depend in part on the relative strengths of the velocity and density variations which comprise the initial current modulation. In this paper, the strengths of beam current and velocity modulation produced in a gridded electron gun are calculated, and it is shown that under normal conditions, the initial modulation is dominated by density variation rather than velocity variation     

On the performance of high perveance electron guns

A design of high perveance electron gun has recently been proposed by Müller. An experimental investigation has been made of the electron beams produced from: 1) a gun designed directly from Müller's charts, and 2) a gun whose design is a modification of the Müller design to make it more suitable for high-voltage operation. The perveance in each case was about 2 × 10^-6. The distribution of the current density and the profile of the beam were examined, either by allowing the beam to fall on a plate coated with carbon, or by measuring the current passing through a pinhole in a screen which could be moved across the beam at a number of axial positions. Electrostatic experiments showed that the beams were initially annular, but further along the axis the current density became highest at the center. This is attributed to crossing trajectories resulting from lens aberrations in an anode aperture whose diameter is comparable with the cathode-anode spacing. With magnetic focusing, the current density distribution across the beam varied periodically along the axis to an extent which depended critically on the magnetic field conditions in the accelerating region of the gun.