Space-charge waves of periodic-electrostatically focused electron beams

Space-charge wave propagation for periodic-electrostatically focused electron beams with nonuniform radial beam density distributions is the subject of this paper. The dispersion equation is obtained by solving a differential equation for the ac electric potential inside the electron beam and by matching the solution at the boundaries. An approximate analytic solution and a digital computer treatment are described. The reduced plasma frequency obtained is expressed in terms of the focusing parameters and is compared with that of a Brillouin beam. A study of the differential equation involved suggests that there are certain ranges of system parameters ("forbidden" zones) for which no wave propagation is possible, that is, no space-charge mode can be supported there.     

Azimuthally periodic electrostatically focused electron ribbon beams

Methods of enhancing transmission of ribbon-shaped electron beams undergoing circular motion in azimuthally periodic cylindrical electrostatic lenses are treated. Lens forces add to the naturally occurring curvature focusing to achieve this increase in beam transmission. Three basic configurations, differing only in the method of applying lens voltages, are treated: symmetrical focusing, deflection focusing, and asymmetric focusing (including inner and outer electrode segmentation). Expressions for beam perveance and rippling are derived from the paraxial-ray equation for thin electron ribbons advancing along a two-dimensional curved optical axis. The stiffness of azimuthally periodic electrostatically focused electron ribbons (i.e., the immunity of the beam to transverse disturbing forces) also receives attention. Mathematical extensions of the analysis to ribbon beams undergoing helical motion are discussed, and numerical results applicable to selected values of lens parameters are presented. Experimental results for an azimuthally periodic lens, constructed to test the analysis, are discussed in light of the theory developed.     

Measurement of noise along electrostatically focused electron beams

Noise along periodic-electrostatically focused electron beams have been measured. The noise variation is periodic with the wavelength of the reduced plasma frequency. It is concluded that electrostatic focusing exhibits similar noise properties as magnetic focusing.     

Aperture lens formula corrected for space charge in the electron stream

The aperture lens formula of Davisson and Calbick is rederived to include the effect of space charge forces. The correction is applied to a parallel flow Pierce gun, leading to the focal length reduction as a function of perveance, e.g., 30 per cent reduction at perveance 3 × 10^-6.     

Influence of space charge on lux-ampere characteristics of high-resistivity CdTe

The concentrations of defects forming at near-midgap level in high-resistivity CdTe were estimated on the basis of room-temperature lux-ampere characteristics. A simple model explaining their sublinear dependence based on the presence of discrete levels near the midgap is presented. It is shown that accumulation of space charge in the sample can explain the observed experimental data. Theoretical calculations show that a maximum concentration of the midgap level leading to the observed slope α of lux-ampere characteristic, I_ph=C×I^α, is less than 10¹³ cm⁻³ for a wide range of capture cross sections of electrons and holes. This result supports models that assume formation of a high-resisitivity state with a minimum deep-level doping.     

Linearly focused acoustic beams for acoustic microscopy

A linearly focused acoustic beam is investigated to be introduced into acoustic microscopy for characterising materials in the nonscanning version. The new acoustic beam enables us to detect acoustic anisotropies of materials to be measured successfully. For forming the acoustic beam, an acoustic sapphire lens with a cylindrical concave surface of 1.0 mm in radius is made and the acoustic field distributions are investigated at 200 MHz.     

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.     

The effects of initial electron velocities and space charge in secondary emission

This paper treats a secondary emitter as a fixed-temperature thermionic emitter with an equivalent work function which depends for its value upon the current density of the incident primary electrons. This permits Langmuir's treatment of the parallel-plane thermionic diode to be applied to secondary emission. The resulting equations account quantitatively for observed secondary-emission effects caused by space charge and initial electron velocities. The paper concludes with a discussion of three specific electron devices in which secondary-emission effects due to space-charge and initial electron velocity are important.     

Orthogonal waves on electron beams

The propagation of slow electrokinetic waves on finite electron beams which fill a conducting tunnel is discussed for modes of axial symmetry. In addition to the familiar space-charge modes, a pair of modes exists which are related to the vortex frequency (omega_{upsilon} = omega_{c} - 2theta_{0}). The finite magnetic field introduces a coupling between these modes. A set of four orthogonal modes can be derived by the use of matrix transformations, thus eliminating the necessity of solving a complicated characteristic equation. For infinitely high magnetic fields, the two additional modes disappear and the four modes reduce to the fast and slow space-charge waves.     

Use of the BFCPIC and BFCRAY codes to describe space charge limited emission in electron guns for gyrotrons

Numerical modelling of an electron gun in the space charge limited regime requires determining the current density distribution as well as the electric fields and electron trajectories. This is a rather complicated self-consistent problem, since the space charge influences the electric field, which in turn influences the electron trajectories. Previous simulations of magnetron electron guns using the BFCPIC and BFCRAY codes used a simple emission model (constant current density) that is approximately valid for thermionic emission. The code has been modified to include space charge limited emission. Several different ways of doing this are considered. One of the models considered uses Gauss’s law to force the electric field on the emitter to vanish; it was used in the original version of BFCPIC for the simulation of ion diodes. A second is based on the use of Child’s law (locally), which may be more appropriate for extension to fully electromagnetic particle-in-cell (PIC) codes. Calculations were performed with both models, and the results compared with each other and with experiments performed at FZK.     

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.     

Microwave deflection of electron beams

When an electron beam interacts with a time-varying electric field, it is usual to ignore the effect of the induced magnetic field. It is shown that this may cause errors at microwave frequencies even for slow electrons. The particular case of electrons traversing a microwave cavity is examined in detail.     

Air core coils for deflecting micron-size electron beams

Bobbin-type air core coils have been designed and experimentally evaluated for astigmatic properties in line scan operation over deflection angles of ± 20°. The approximate design technique is successful in specifying the proper operating focal distance when this is comparable to the coil length. Line fields in excess of 20 000 spot diameters have been measured using a 10 kV beam having a 5 × 10-³radian convergence half-angle.     

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.     

Parallel-wire meander line deflection circuit for electron beams

A broadband parallel-wire meander line deflection circuit has been devised. It has relatively flat deflection characteristics in the range 4?17.5 GHz. A dispersion equation for this circuit is derived by considering the phase delay at the bend of the wire, which can estimate the experimental results fairly well.     

Conservation principles for plasmas and relativistic electron beams

Many useful conservation theorems are derived for relativistic electron beams and anisotropic plasmas. All these theorems are valid for confined-flow and irrotational-flow devices, and cold, collisionless plasmas. All the theorems are derived in a similar way, and a generalization of this method, using linear operators, is given. Among the power theorems discussed are: Tonks' theorem, the instantaneous and sinusoidal small-signal theorems, the energy theorem, a large-disturbance theorem, the Manley-Rowe formulas, an ac power theorem, and a cross-correlation theorem. Contributions to power and energy from surface waves are included. Allowing for relativistic flow and writing all equations in the laboratory frame does not significantly complicate the theorems, and in fact clarifies them somewhat. Many simple applications are discussed, although not in detail. Among these are: small-signal energy, power, and passivity; energy velocity in electron beam and plasma wave-guides; and a conservation theorem for multiple electron beams and electron beam-plasma interactions.     

In-the-lens secondary electron analyser for IC internal voltage measurements with electron beams

A new analyser scheme for voltage measurements on integrated circuits is described. The analyser is built into the objective lens of a scanning electron microscope. It features small working distances, high voltage resolution capability, high transmission, and reduced sensitivity to measurement errors.