Computer experiments on electron guns

Computer techniques for analyzing an axially symmetric or two-dimensional electrode system with an emitting surface can be used to obtain cathode current density distribution, beam minimum radius and its location, as well as possible electrode current interception. Here, comparison is made of available experimental data from two axially symmetric Pierce-type guns. The choice of the two axially symmetric Pierce-type guns was made for their different value of PV/T ratio, an invariant for transverse scaling. One of them has a low ratio of PV/T(approx 0.1 times 10^{-6}), which signifies considerable beam spread due to the effects of the Maxwellian velocity distribution of the thermal electrons leaving the cathode. The other gun has a high perveance of2 times 10^{-6}, and thus relatively high PV/T ratio where beam spreading is mainly due to space-charge forces alone. Good agreement with experimental data is shown. Computer techniques of this type can be a valuable tool for diagnostic purposes of any type of space-charge-flow devices (e.g., electron guns, ion guns for space propulsion, linear accelerators, etc.) and enable the engineer-designer to arrive quickly and cheaply at an optimum configuration.     

Digital computer simulation of crossed-field electron guns

A digital computer program for the simulation of crossed-field electron guns is described. The program simulates the electrodes and fields within the gun on a matrix of up to 10 000 points. The program, written in FORTRAN II for the IBM 7090, is generally executed in six minutes or less. It is shown to produce results within four percent of theory and experiment for two different cases.     

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.     

Gridded electron guns for high average power

The design and performance of electron guns producing high-average-power beams which are controlled by an intercepting-type grid are described. The design consists of a modification of the design of Pierce-type electron guns to allow for the effect of grid insertion, and calculation of the amplification factors based on the potential distribution. The performance is evaluated in terms of the beam shapes and average beam powers obtainable. Measured amplification factors are compared with calculated values. Factors influencing the measured beam shapes are discussed. Trajectories of electrons emitted as secondaries from the grid and those of electrons deflected by the lens effect of the grid wires were plotted using an analog computer and electrolytic tank. The shapes and focusing properties of electron beams from similar gridded and nongridded guns are compared. Expressions relating the average beam power capability to the gun and grid dimensions are developed. The calculated average beam power capabilities are compared with measured values. Average beam power as high as 8 kw has been obtained with electron guns of a size suitable for use in X-band twt's.     

Digital computer analysis of axially symmetric electron guns

A digital computer program written in the IBM 7090 FORTRAN programming system is described and then employed in the analysis of several axially symmetric electron guns. The digital program employs relaxation techniques while alternately computing electric fields and trajectories. One cycle through the program consists of three parts. 1) Calculation of the voltages within the electron gun by solving Poisson's equation, in difference form, on a matrix containing a maximum of 10 000 points on which electrode potentials are laid out. 2) Calculations of new current densities along the cathode and the setting up of new trajectory starting points along the cathode to simulate these current densities. 3) Calculations of trajectories, including magnetic fields and relativistic effects if desired, and comparison of the new beam with the previous one. Thermal effects and direct particle-particle interaction effects are ignored although space-charge effects, introduced through the field calculations, tend to prevent excessive or usual trajectory crossings. Execution time for the entire program is between 4 and 12 minutes, although for most guns 5 to 7 minutes is usually sufficient. Results produced by the program are presented and compared with experimental and analytical results.     

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.     

Numerical computation of the emission current in electron guns

 A computer program for evaluating the emission current in electron guns has been developed, and good agreement between evaluations and experiments has been achieved. The computational model is based on the statistical theory of thermal electron emission, and the potential distribution in front of the cathode is equivalent to that of an infinite planar diode in which the longitudinal ther- mal velocity effect (LTVE)is taken into account. From the results evaluated by the computer for several different cases, the conclusions are shown as follows: 1. In cathode ray tube (CRT) guns, the LTVE must be taken into account. The emission current values estimated by the program are greater than those calculated by the 3/2 power law. The former values are closer to the measured values than the latter ones. 2. In high perveance guns, the LTVE is noticeable when the operating potentials are low, but this influence of the LTVE is much smaller than in CRT guns. 3. The LTVE becomes significant as the ratio of the saturated emission current density de- livered from the cathode to the actual emission current density increases, and remains unchanged when the ratio is beyond a certain value.     

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.     

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.     

Experiments on high-perveance electron guns with a subfocusing electrode

High-perveance electron guns with a subfocusing electrode were designed analytically, produced, and tested. The experiments are carried out to evaluate the design method. Perveance of guns are 1.7 to 1.3 × 10^-6A/V^3/2, convergence angles being 30°. The results confirmed that it was possible to design electron guns of perveance up to 3.0 × 10^-6A/V^3/2.     

Transit-time effects on noise in planar crossed-field electron guns

A theory is developed for the noise in an unbounded parallel-plate crossed-field diode. The high-frequency regime is studied, where transit-time effects must be included. The diode is assumed to be operating in the space-charge-limited regime. Maxwell's equations and the Vlasov equation are expanded to first order. A key consideration in this expansion is the fluctuation in the boundaries of velocity space appearing in the integrals for the charge and current density. The first-order terms describe the linear response of the electric field and transmitted current resulting from the injection of a small additional cathode emission composed of electrons of a specified velocity. Using a statistical approach, these perturbations are combined to determine the noise factor. The special case of a parabolic average-potential distribution in space is considered.     

Analysis of the role of high-brightness electron guns in lithography

The development of reliable, high-brightness, temperature-field (TF) emission electron guns promises greater flexibility in electron-beam lithography. Detailed pattern analysis of two IC mask sets was performed for the purpose of identifying those areas of electron-beam lithography where high-brightness guns could be applied to advantage. Potential exists for throughput improvement in both Variable Shaped Spot (VSS) Vector Scanning Systems and in ultra-high-speed Raster Scanning Systems.     

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.     

Beam transmission in electron guns having a single-apertured control grid

The ratio of target current to cathode current (beam transmission) has been studied for a number of vidicons and scan converters. These are high-resolution electron tubes that characteristically have a control grid with a single aperture. The results, as anticipated, show that beam transmission is affected much more than total cathode emission by tube aging processes. The transmission was determined by direct beam current measurement and the cathode condition recorded by the cathode imaging technique. Because of the centralized area in which the loss of emission occurred, beam transmission was reduced much more than total cathode current. In vidicons, the decreasing beam transmission was correlated with increasing residual signal after erasure and with saturation of the gamma transfer characteristics at lower light levels. In practice, beam current rather than cathode current, should be monitored.     

Sources of velocity spread in electron beams from magnetron injection guns

Calculated trajectories for the electron beam of a known gyrotron have been analysed to determine the relative importance of some of the contributions to velocity spread. For the geometry analysed, space-charge and thermal velocities at the cathode produced only a small part of the calculated velocity spread; much more was generated by the variation of electric field over the length of the cathode surface. The total range of transverse velocity was substantially reduced by adjustment of the shape of one electrode.     

The effect of space charge on shot noise in crossed-field electron guns

The two-dimensional electronic behavior of the crossed-field potential minimum is analyzed by means of a feedback network which provides a vehicle for understanding the complex phenomena, while allowing quantitatively accurate numerical calculations. The solutions, limited to the low-frequency range where transit time may be neglected, Show shot-noise smoothing as a function of magnetic field and cathode length. For low magnetic fields and short cathodes, the smoothing approaches the results of the North theory for zero magnetic field. It is also shown that if the cathode length is greater than about 11 normalized (Kino) units or 0.55 of the cycloid length for the existing field conditions, an initial perturbation of the emission current will lead to growing fluctuations of the beam current. This instability is considered to be responsible for the observation, in some crossed-field tubes, that the output noise increases when the cathode is heated sufficiently to form a potential minimum in front of the cathode. This criterion for the existence of excess noise is applied to all the experiments for which sufficient data have been published and no disagreement is found.     

Effect of surface roughness on the velocity spread in electron guns for gyrotrons

The effects of the roughness of the cathode surface on the emittance of an electron beam in a gyrotron gun are investigated. Parameter studies using a very simple model are performed in order to determine a reasonable parametrization of the effect for use in the BFCPIC and BFCRAY codes. Calculations are then performed for a gun in use at FZK.     

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.     

Analysis of a frequency-modulated reflex klystron with minimum incidental amplitude modulation

Simultaneous modulation of the reflector and beam voltages of a reflex klystron will produce frequency modulation with minimum incidental amplitude modulation. The required variation of reflector voltage with beam voltage, for constant output power, is derived from the fundamental equations of the reflex klystron. Experimental verification of this analysis is presented. Reflex klystron oscillators which can be frequency modulated with minimum incidental amplitude modulation find application in FM Doppler radars, communications systems, and as signal sources for microwave testing.     

Free electron laser spectral dynamics with a modulation of electron beam energy

Recent experimental and theoretical works on free electron laser spectral dynamics have pointed out the difficulty to obtain a narrow and stable spectrum operation. This goal can only be achieved by avoiding the sideband generation leading to a broadband and unstable spectrum. Tapered wiggler and two-frequency wiggler are well suited for combining sharp spectrum and high efficiency but are not really compatible with a wide tunability of laser light. Filtering sidebands is a good way for lower power experiments but it seems to be difficult to conceive wideband filters, specially in the far-infrared region. Modulation of electron energy is a new potential soft way for controlling the spectral dynamics of longpulse free electron laser. Spectral dynamics under the modulation is investigated in the linear and non-linear regimes in the far-infrared region. Simulations show that a pulsed and sharp spectrum behavior can be obtained by optimizing the modulation parameters. The interest of such a method for the far-infrared experiments is discussed.