A Detailed Study of the Remodulation of an Already Modulated Electron Beam

A theoretical und experimental study of the remodulation of on election beam in the small and large signal region is described. The variation of a.c. current amplitude on the beam with distance as a function of amplitude and phase of two independent modulation signals is shown and the conditions yielding maximum a.c. current are given.

In the theoretical study the problem has been considered as that of velocity modulating a beam which has initial current modulation. The solution includes both space charge and largo signals but loses validity when electron overtaking occurs.     

L波段相对论速调管束流实验研究

介绍在L波段强流相对论速调管研究中,强流相对论短脉冲空心电子束的产生、传输、束流调制及其诊断等方面的初步实验研究情况。在直线感应加速器上,利用66mm、壁厚3mm的石墨空心阴极,加上约5kGs的准直流引导磁场,引出了约500kV、4.5kA、脉宽100ns、54.5mm、厚度4.5mm的空心电子束。注入500kW的微波调制,束流经过输入腔后,得到了约6％的最大基波电流调制深度,经过中间腔后,得到了约23％的基波电流调制深度。     

The radio-frequency current distribution in Brillouin flow

It has been shown that in an electron beam with Brillouin focusing, two pairs of space-charge waves are possible. One pair has the peculiar property of having no RF charge density in the volume of the beam, with most of the current being caused by ripples of the boundary. This paper shows that, in the case of modulation by the gridless gap of a klystron, it is only these space-charge waves which are excited in the electron beam. This result has also been verified elsewhere by experiment. In addition to the detailed calculation, a simple proof is given which demonstrates why one gets the particular behavior predicted by the detailed theory, namely, a modulated beam with no RF charge density in the volume. This effect arises from the fact that the modulation is produced by an electric field with zero divergence, and therefore the RF velocity produced also has zero divergence. Zero divergence of the velocity is the condition for an incompressible fluid; i.e., constant density. In the case of modulation by a grid, the electric field does not have zero divergence and this kind of behavior does not occur.     

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.     

Influence of space charge on the Langmuir limit for focused electron beams

A theoretical investigation of the validity of Langmuir's expression for the limiting current density in a focused electron beam when space-charge forces are significant was carried out by computing the performance of a series of simple electron tubes, each consisting of a Pierce gun coupled by a thin lens to an equipotential drift space. The analyses show that, while the cathode current density and the peak current density in the spot are related, they are not directly proportional as stated in Langmuir's expression which, therefore, does not give an accurate prediction of the current density that can be obtained in the spot. The dimensions of the tubes were chosen such that this conclusion is also valid in the case of television picture tubes. It is also shown that thermal velocities have only a minor influence on the lens strengths required to focus beams, and that the focused spots havea Gaussian distribution of current density even though the emission density in a Pierce gun is uniform.     

Radial and axial RF current and velocity distributions in large-signal velocity-modulated electron beams

Measurements of the amplitude and the phase of the current density in a Brillouin beam modulated at large signal levels were made at 1940 MHz and at harmonics of 1940 MHz as a function of the amplitude of the modulating signal. In addition to a surface current similar to that reported for small-signal Brillouin beams, current existed along the axis of the beam that was very large and often 180° out of phase with the surface current. Thus, at some axial positions, a cavity surrounding the beam would detect practically none of the current in the beam. At some drive levels above the point where electron overtaking occurred, it is shown that the RF current in the beam disappeared completely in both the radial and axial directions after the beam drifted approximately one plasma wavelength from the modulating cavity. Explanations based on measurements of the velocity distribution of the current are given for the unusual behavior of the current in the Brillouin beam. The distribution of the second and third harmonic currents in the beam were similar to the fundamental current distribution. One of the implications of this result is that it is probably not possible to use the second harmonic current in klystrons utilizing Brillouin beams for efficiency enhancement.     

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.     

Simulation of electron-optical forming systems with highly compressed electron beams

A method of synthesis is developed, equations are derived, and the results are obtained via this method for the simulation of systems that form high-intensity electron beams with a high compression. The relatively high compression of a beam is realized owing to both a faster (in comparison with a variation in the accompanying magnetic field) increase in the axial component of the magnetic field at a certain plane in the gun region and to selection of the length of the region in the gun where the potential increases. Electron-optical systems with beams whose structure is substantially affected by electron thermal velocities are considered. Relationships that allow determination of the initial parameters of the beam and the focusing magnetic field during the synthesis of such systems are presented.     

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.     

Magnetic focusing of electron beams in the presence of transverse velocity components

The behavior of nonlaminar electron beams having an originally Gaussian current density distribution in a uniform magnetic field is studied by analytical and numerical methods. The effects of transverse velocity components vTin the beam are described by a fictitious, equivalent perveance which is proportional to the square ofbar{v}_{T}, the rms value of vT. Simple expressions are given for the magnetic field required to achieve a certain beam transmission through a tunnel of given diameter, and for the optimum beam filling factor. In the Appendix a simple experimental method for the determination ofbar{v}_{T}is descried.     

The traveling-wave phototube part I: Theoretical analysis

The traveling-wave phototube (TWP) is a broad-band photodetector which is useful for demodulation of light that has been amplitude-modulated at a microwave frequency, and for optical heterodyning of coherent light signals with microwave difference frequencies. In either application the light beam(s) results in the emission of a current-modulated electron beam from a photocathode; interaction between this beam and a slow-wave circuit such as a helix is employed for broad-band detection of the microwave modulation. Part I of this paper presents a detailed analysis of the TWP beam-circuit interaction process, including the effects of loss, space charge and asynchronism. Computer results are given for both current modulation and velocity modulation excitations, since the latter can be important under certain operating conditions. Conclusions regarding the effects of beam current, circuit length and circuit loss are drawn which are important in the design, understanding and use of TWP's. The results of this analysis are also generally applicable to other cases where a slow-wave circuit is excited by an electron beam. In Part II of this paper, a detailed experimental analysis of the TWP will show good agreement with the predictions of this theoretical treatment.     

Limiting current of helical electron beams in gyrotrons

Potential depression (PD) and limiting current (LC) of helical electron beams (HEB) are investigated. Nonneutral electron beams and two velocity distributions: uniform and Rayleigh distribution are taken into account. For Rayleigh distribution electron reflection from magnetic mirror is taken into account. It is shown that velocity spread may lead to substantial reduction of LC for real values of the mean pitch-factors of helical trajectories. PD and LC are an unmonotonous functions of the velocity spread for Rayleigh distribution. A connection of PD with the change of gyrofrequency and with the beam broadening in gyrotron operating space is retraced.     

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.     

The effect of beam cross-sectional velocity variation on backward-wave-oscillator current

Low-voltage helix-type backward-wave oscillators require a starting current that rises to infinity toward the low-frequency end of the tuning range. The effect has been attributed to the raising of the space-charge parameter QC by the dc space-charge-induced velocity spread. H. R. Johnson has calculated the velocity-spread effect on starting current qualitatively, but the predicted nonoscillation frequency is generally much lower than the observed one. As a further analysis, space-charge wave propagation in an electron beam having an actual cross-sectional variation of dc velocity is investigated. It is shown that the RF current modulation in the slow space-charge wave is concentrated in the region of the slowest-moving electrons. In a helix-type backward-wave oscillator using a hollow beam, the slower electrons are farther away from the RF circuit, so that the effective impedance for the slow space-charge wave may be considerably reduced. The use of an impedance reduction factor therefore provides better agreement between theory and experiment with regard to the starting-current phenomenon. Theoretical and experiment results of the investigation are presented.     

Excitation of microwave by an annular electron beam in a plasma-filled dielectric lined waveguide

An axial relativistic electron beam passing through a slow wave structure is unstable to an electromagnetic perturbation whose phase velocity equals the velocity of the beam. This phenomenon of Cherenkov emission is the basis of all traveling wave tubes. In this paper an excitation of Cherenkov radiation by a thin annular relativistic electron beam in a plasma-filled dielectric-lined waveguide is analysed by use of the self-consistent linear theory. The effect of the thin annular electron beam on the beam-wave interaction is completely described by a jump condition. The dispersion equation and the simultaneous condition of the beam-wave interaction are derived. Finally, the growth rate of the wave is obtained, and the effect of the background plasma density and the electron beam radius on the growth rate of the wave are presented.     

Spatial structure of the light beam diffracted in a one-dimensional photonic crystal

The spatial structure of narrow optical beams whose frequency is close to the region of the first forbidden band of a 1D photonic crystal is considered. Various distortions of the beam profile (from bifurcation near the left edge of the band to diffraction broadening near the right edge) are demonstrated with the help of numerical modeling performed for a semiinfinite periodic structure. Features of diffraction of the beams with modulation of the initial profile are analyzed.     

Analog computer solutions for correction of ripple in magnetically-collimated electron beams

Analysis of the dynamics of an electron beam in a magnetic collimating field leads to formulas which can be processed conveniently in an analog computer to obtain individual solutions. This technique is applied to the problem of correcting the ripple which is generally imposed upon the envelope of the beam after passage through a spatial variation or reversal of the collimating field. However, a relatively general viewpoint is retained in developing methods and formulas for studying the motion of an outermost electron of a relatively uniform, round, straight electron beam. Fer this reason the results can be applied to beams from shielded or unshielded cathodes, passing through uniform, periodic, or nonperiodic reversing magnetic collimating fields. A simplified development of the mathematical theory of magnetically confined electron beams is presented, including the effects of spatial variations and reversals in the collimating magnetic fields. Formulas are developed for the equilibrium electron beam radius, and for the ripple frequency, axial wavelength, amplitude, and phase of the outermost electrons, in terms of the field parameters and the initial beam conditions. Analog computer solutions for an electron beam with various collimating magnetic fields serve to illustrate and confirm the developed formulas. From these computer solutions, suggestions are derived for guidance in shaping collimating magnetic fields so that electron beam ripple will be prevented or reduced.     

Triode electron injection systems for hollow beams

Novel electron guns, in which a conical hollow electron beam is projected at a large angle to the axis into a coaxial deflection region, were tested. The guns have a triode structure so that the perveance can be varied easily. The strong deflection increases the effective perveance of the beam and makes the trajectories insensitive to current variations. In the form of a device with the gun at a large radius and projecting the beam inward, the electron paths are sensitive to scattering in the gun. The inverted gun, projecting the beam outward, is relatively free from this difficulty. The systems generally behave as expected, and should be quite useful for initiating variable-current hollow electron beams in various available focusing arrangements.     

边射波束和锥状波束可重构的微带贴片天线

本文提出了一种边射波束和锥状波束可重构的新型微带贴片天线,该天线在锥状波束模式下具有圆度较好、锥角可设计的优点。首先,在贴片的中间引入一排短路孔,当短路孔两侧的探针反相馈电时,贴片上两侧电流同向,辐射边射波束;而当两个探针同相馈电时,贴片上两侧电流反向,辐射锥状波束。接着,对短路排孔与贴片边缘之间的间距进行了优化设计,调整电流分布,从而改善锥状波束在方位面上的圆度。最后,在贴片的对角线上额外引入了四个短路孔,通过控制其位置和大小来调节固定频率下贴片的尺寸,从而设计出不同锥角的锥状波束。通过全波仿真,设计了三个边射波束和锥状波束可切换的贴片,锥状波束的锥角分别为55°、50°和45°,均具有较好的圆度。     

Ka波段高压缩比电子光学系统的分析与设计

微波电真空器件向高功率、高频率、宽频带、高效率和小型化方向发展,对电子光学系统的要求也日益增高。文中设计了工作于Ka 波段的扩展互作用速调管(Extended Interaction Klystron, EIK)高压缩比电子枪,利用二维仿真软件E-GUN 和三维仿真软件Opera-3D 对轴对称电子束在均匀永磁聚焦磁场内运动状态进行建模并仿真计算。相关结果表明,在阳极电压25 kV、注电流2.5 A、阴极面电流密度不超过12A/cm2 的条件下,面压缩比约为85,电子注以良好的刚性通过互作用区域。