Electron-beam flow in superimposed periodic and uniform magnetic fields

Theoretical and experimental results are presented on the focusing of an electron beam by means of a magnet structure which produces, along the axis of the beam, a periodic magnetic field superimposed on a uniform field. The relation between space-charge and magnetic-field parameters for minimum ripple is derived. The flow in superimposed uniform and periodic magnetic fields is shown to be degraded from the flow of electrons in a magnetic field which has a sinusoidal variation along the axis. The results indicate the flow conditions to be expected, where such combined fields are unavoidable. The focusing of electron beams in this type of superimposed magnetic field and in Brillouin flow are compared.     

Equilibrium solutions for partially immersed relativistic electron beams

The equations relating the beam radius and axial electron velocity to easily measurable external beam parameters are developed for solid, relativistic beams. The beam parameters are tunnel voltage, beam current, axial magnetic field, cathode magnetic field, tunnel radius, and cathode radius. The equations are sufficiently complex to warrant the use of a digital computer if many cases are to be evaluated. Error indicators are formulated to prevent use of the relations beyond their range of validity. The equilibrium solutions for relativistic electron beams from unshielded cathodes show that the required magnetic focusing field is lower than that computed from nonrelativistic formulas. The angular magnetic field produced by the beam itself aids in focusing the electrons. The potential depression due to space charge is analyzed. Correction curves are given which allow the use of nonrelativistic equations in predicting equilibrium behavior. The maximum possible microperveance of relativistic beams is shown to be lower than the classical value of 25.4.     

Focusing of an Electron Beam from a Low-noise Gun with Different Magnet Systems†* Part IV. Trajectories of the Outermost Electron in a Beam Focused by a Periodic Permanent Magnet

This paper deals with the traces described by the outermost electron in a beam produced by a magnetically immersed electron gun and focused by a periodic permanent magnet in the drift region. The beam profiles have been computed by use of a fast computer for three types of magnetic flux density distribution in the transition interval between the gun and the drift regions.

In the first series of solutions, the uniform magnetic field over the gun region connects directly "with the rising part of the sinusoidally varying magnetic field. With the period of the alternating flux held constant, proper and improper flux densities in the gun and helix regions produce, respectively, acceptable or runaway electron beams. In the second series of computations, a compensating field in the form of a dent is introduced over the intervening space between the gun and drift regions. Variations are made in the magnitude of the gun field and the amplitude and period of the alternating field. Satisfactory profiles are obtained when these parameters have optimum values; incompatibility between high flux densities and large period of the magnets is indicated by the ever-growing beam ripples. In the third series, beam profiles are computed for the cases when optimum spatial period of the magnet is used and the magnitudes of flux densities in the gun, transition, and helix regions are altered. Very high gun fields are not conducive to producing good electron transmission, while judicious choice of compensating field leads to smooth beams even with comparatively low flux densities in both the gun and helix regions.

There are other modes of flux distribution over the gun and the transition regions which also provide both good electron transmission and noise performance, but these are not considered here.     

Electron beams in axially-symmetric crossed fields

M-type traveling-wave tubes use electron beams that drift in crossed electric and magnetic fields. One such tube, the axiotron described by Warnecke and Doehler in 1950, used a hollow beam drifting parallel to the tube axis in a radial electric field crossed by an azimuthal magnetic field. The addition of an axial magnetic field to the azimuthal one adds another degree of complication and flexibility to the beam equations, yet maintains their symmetry about the tube axis. It gives, in effect, a helical magnetic field crossed by a radial electric field. This report examines the behavior of hollow electron beams drifting in laminar flow through fields of the latter configuration. It defines a stability index for electron paths, and four fairly general types of beam. It determines the stability index and the distribution of space charge obtainable in each type as functions of the amplitudes and directions of the fields and drift velocities. In general, the density tends to be greatest at the inner beam radius, but it is possible to approach uniform density in stable beams. This report does not consider beam launching nor the "gun" problem; nor does it consider over-all beam instabilities such as scalloping.     

Periodic focusing of beams from partially shielded cathodes

Using both an analog computer and an approximate analytical method, the equation describing the beam shapes which result from a uniform pencil beam of electrons entering a periodic magnetic field has been studied. The investigation has been primarily directed toward beams emergent from ideal cathodes only partially shielded from the magnetic field. Cases of both small and large scalloping have been considered. Curves relating the magnetic field coefficient α and the space-charge coefficient β are presented. A previously proposed relationship between α and β for small scalloping is shown to be inaccurate for large scalloping. Stable solutions for the motion of an electron beam having no thermal velocities are obtained for values of α less than 0.66 and in addition they are also found for some values of α greater than 0.66.     

Transport of electron beams in periodic permanent-magnet focusing systems with nonharmonic distribution of the magnetic field

The results of the study of the transport of electron beams in periodic magnetic fields are presented for the case when the distribution of the magnetic field is essentially different from a sinusoidal distribution in different parts of the drift channel. An easy-to-implement nonharmonic distribution of the magnetic field is found. This distribution ensures a small ripple of the envelope of a high-intensity electron beam. The results of application of combined periodic permanent-magnet (PPM) focusing systems in high-powered pulse travelingwave tubes (TWT) are presented for the TWTs having a slow-wave structure that is superposed with the pole pieces of the PPM focusing systems.     

Intense Sheet Electron Beam Transport in a Uniform Solenoidal Magnetic Field

In this paper, the transport of intense sheet electron beams in a uniform solenoidal magnetic field in high-power vacuum electronic devices is theoretically examined with the 3-D beam optics code MICHELLE. It is shown that a solenoidal magnetic field can be an effective transport mechanism for sheet electron beams, provided the beam tunnel is matched to the beam shape, and vice versa. The advantage of solenoidal magnetic field transport relative to periodic magnetic transport resides in the feasibility of transporting higher current density beams due to the higher average field strength achievable in practice and the lower susceptibility to field errors from mechanical misalignments. In addition, a solenoidally transported electron beam is not susceptible to voltage cutoff as in a periodic magnetic focusing system; hence, device efficiency is potentially higher.     

Equivalence of periodic magnetic field to uniform magnetic field in electron beam focusing

The general solution of the electron trajectory equation in a periodic magnetic field is derived in the form of series expansion, assuming laminar electron flow and small perturbation. It is concluded that if the cathode is not very heavily immersed in a magnetic field, beam focusing by a periodic magnetic field would be almost equivalent to that by a uniform magnetic field except near the unstable region. Under these restrictions, each focusing system would give almost the same beam ripple (in magnitude and phase) under the same injection conditions into the focusing system. It is also found that the first stable region of beam perturbation in the periodic magnetic field becomes narrower as the flux threading the cathode increases or the period of the magnetic field decreases, as far as linearization of the path equation is possible.     

Solutions in elementary functions obtained for 3D and axisymmetric intense electron flows

Three-dimensional nonrelativistic electron flows in the presence of an arbitrarily oriented uniform magnetic field are considered. The flows are formed by elliptic or hyperbolic current tubes and have a spatial axis. For such flows, a series of new exact solutions in elementary functions are constructed. In the case of nonmonoenergetic beams, a new type of singularities corresponding to the zero-velocity injection is discovered.     

浸没流多透镜多注电子光学系统的模拟研究

该文采用先2维后3维的计算方法,对L波段高峰值功率多注速调管电子光学系统进行了模拟设计。采用均匀场浸没流多透镜聚焦系统对电子注进行聚焦,获得了通过率100%,填充因子55%,特性良好的旁轴电子注。模拟计算表明,多透镜系统可有效调整电子注平衡半径,电子枪区均匀场可有效调整电子注波动性及层流性,聚集系统可在阴极磁感应强度为0.001~0.01 T,主磁场为0.06~0.13 T的范围内实现对旁轴电子注的良好聚焦。     

Magnetic compression of axially symmetric Brillouin-focused electron beams

A study has been made of high-current density Brillouin-focused electron beams formed with magnetic compression. Analysis of the problem was by numerical calculation of electron trajectories using a digital computer. Electrostatic field data were measured using a resistance network analog. The effect of the magnetic field was calculated as an equivalent potential. An experimental system based on the results of the analysis was designed and tested. A Müller-type electron gun was found to provide a more uniform current density than a corresponding Pierce type. Experimental results were in close agreement with design objectives. For an area magnetic compression of 10 to 1, a focused beam approaching ideal Brillouin flow was achieved.     

Instability regions of an electron beam in superimposed periodic and uniform magnetic fields

The stability of an electron beam in a superimposed sinusoidal and uniform magnetic field is theoretically and experimentally investigated. The first instability region degenerates to a point within the first well-known passband for a zero uniform field component, whereas the second instability region coincides with the first stopband of the sinusoidal field. These considerations are of practical significance for periodic magnetically-focused electron beams.     

Performance of magnetically compressed O-type electron beams emitted from nonshielded cathodes

The theory pertaining to the behavior of a cylindrical electron beam emitted from a nonshielded cathode in an axial, monotonically increasing magnetic field is experimentally verified. A convenient technique of measuring the scalloping of electron beams in sealed-off tubes by varying the beam voltage is described. Experimental results include the study of the beam compression and percentage scalloping in several configurations of increasing magnetic fields. It is shown that for such beams the percentage scalloping is fairly independent of the amount of compression.     

均匀磁场聚焦部分屏蔽流电子注的一种设计方法

本文叙述了适用于轴对称强流电子光学系统各种磁结构的部分屏蔽流过渡区的设计方法。通过综合选取磁系统和电子枪参数,实现了磁系统与电子枪的最佳匹配,获得了屏蔽系数大于0.8,波动小于1％的电子注。     

A theory of static deflection in magnetically immersed conical deflectrons

A theory of static deflection is presented for conical deflectrons immersed in a uniform axial magnetic field. Both twisted and untwisted deflectrons are considered. Such arrangements for deflecting low-energy electron beams find applications in vidicons, scan converters, and similar devices. The equations of electron motion are solved analytically. Deflection sensitivity, scan rotation angle, and beam landing angle follow from the solutions. It is shown that beam landing error cannot be eliminated in conical deflectrons as it can be in cylindrical deflectrons. Several numerical examples illustrate the uses of these results.     

Behaviour of Electron Beams in Increasing Magnetic Fields Z α(α><1)†

The behaviour of electron beams in magnetic fields varying as Z ^α ( α><l) is described, both for compression and scalloping, for electrons emitted from completely or partially shielded cathodes. It is shown that the beams emitted from completely shielded cathodes experience a stronger compression with their cross section reducing as the square of the increase in the magnetic field, while this convergence for the electrons emitted from partially shielded cathodes is considerably less, being only proportional to the increase in the magnetic field. From the point of view of scalloping the latter beams are superior, in that their fractional ripple remains constant regardless of the amount of compression, whereas in the former class of beams this parameter increases as the square root of the ratio of the magnetic field to the entrance value. These results are independent of the manner of the increase of magnetic field, making it, therefore, possible to use increasing fields that go over smoothly to the almost constant values, that are needed for r.f. interaction with these compressed, high density, small cross section beams.     

Electron beam characteristics in radially varying periodic magnetic fields

Periodic magnetic fields are being widely used for the light-weight focusing of beams in high-power traveling-wave tubes. In many tube designs, there exists a considerable amount of radial variation in the magnetic focusing field. The effect of this radial field variation is investigated analytically as an extension of the previous work in this field. The usual design curves of α vs β are plotted with three variable parameters: ripple, cathode shielding parameterK, and radial field variation parameter x0. It is noted that it is important to keep the magnetic-field strength constant at the beam edge over a considerable variation of the magnetic-field parameter x0.     

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.     

The Conditions for Stable Sheet Electron Beams Transport in Periodic Permanent Magnet Fields

The stable focusing or transport of sheet electron beams is an essential technology for an emerging class of high-power high-frequency planar-structure microwave devices. This paper, in consideration of space-charge field and cyclotron motion, describes theoretical study and simulation on sheet beams transport in periodic permanent magnetic (PPM) fields. Based on the theoretical study, we obtain the clear conditions for the stable sheet beams transport in PPM field. And the three-dimensional simulations of the sheet beam transport are in good agreement with our theoretical study. Our research will be useful in further study and experimental.     

Propagation and excitation of perturbations in electron beams with velocity shear

A theoretical investigation of the influence of a spatially varying drift velocity on the perturbations in magnetically focused electron beams is presented. The wave propagation on such beams, focused by infinite magnetic fields, is studied under the small-wave assumption. The dispersion relation for slow waves is derived and solved for different transversal boundary conditions. Two sets of infinitely many propagating modes are found in a beam with small velocity shear. In a beam with sufficiently large velocity shear only two eigenfunctions exist. Since it is not possible to match the two eigenfunctions on arbitrary longitudinal boundary conditions, additional solutions (which cannot be written in form of a plane wave) must exist. The excitation of perturbations by ideal grids is solved by introducing the Laplace transform analysis. Additional solutions are ascertained which lead to a spatial decay of the perturbations according to a power law z^-α. This damping, arising from the spatially varying drift velocity, is similar to the Landau damping in electron beams with velocity distribution. Such damping effects are of great practical importance in conjunction with noise reduction in traveling-wave tubes.