Periodic Electrostatic Focusing Research Articles

INVESTIGATION AND OPTIMIZATION OF LOW-ENERGY HEAVY-ION BEAM DYNAMICS IN PERIODIC AXISYMMETRICAL STRUCTURES WITH DC FOCUSING

It is well-known that nonsynchronous harmonics of a RF field can focus particles. In order to focus ultra-low energy beam particles, a spatially periodic electrostatic field can be used, too. In this case the transverse focusing is provided by a periodic array of electrostatic lenses. This article is dedicated to questions of two high-current low-energy beam focusing types used in an injector-buncher of an ion linear accelerator, an application of a spatially periodic electrostatic focusing being examined for the first time. A two-dimensional nonlinear motion equation is derived in the Hamiltonian form in a smooth approximation. It allows us to study a correlation between the longitudinal and transverse ion beam dynamics at low energies. An investigation of the phase and transverse beam dynamics stability conditions in the initial part of the linac are given consideration. Conditions of the beam dynamics stability are found and analyzed. An approach to the field optimization problem is described. A method of the geometric parameter choice is worked out for a realization of the required field distributions in each structure. To verify the results of the beam dynamics stability analysis and optimized structure parameter choice, numerical simulations of low-energy heavy-ion beams are carried out.

Computer Simulation of the Periodic Electrostatic Focusing Converter

A computer study was made of the various physical processes that take place in the periodic electrostatic focusing, direct energy converter. Computer simulation techniques are described and the results are presented. The effect that space charge, secondary electrons, beam size, charge exchange, and ionization have on conversion efficiency is examined. The results are applied to the design of a reactor. Finally, future plans for studies of direct converters are discussed.

Surface requirements for electrostatic direct energy converters

There are two major electrostatic direct energy converter concepts which will be discussed from the point of view of the surfaces. One is the Venetian blind concept and the other is the periodic electrostatic focusing concept. They are both of the direct collector type. Fluxes of D +, T +, He ++, electrons, and X-rays are given. Design consideration due to thermionic emission, secondary electron emission, and radiation cooling are discussed. A detailed discussion is devoted to breakdown physics, the voltages and electric field strengths that can be employed, and how surface deterioration may affect voltage holding due to He ++ bombardment blistering.

Periodic electrostatic focusing of abeam of elliptical cross section

An exact analytic solution has been given [1] for the shaping of a flat beam with a nonmonotonic potential variation at the boundary. It has been shown that construction of a periodic focusing system amounts to calculation of the equipotentials in a part with a potential distribution symmetric about the center and to coupling of two such elements via sufficiently thick screening grids whose charge density varies in a definite way. Here I derive a simple analytic solution for the shaping of a beam of elliptical cross section by approximating the potential at the boundary via a quadratic parabola [2].

Theory of periodic electrostatic focusing of electron beams

A general theory of periodic electrostatic focusing structures in micowave tubes is presented. A general method for evaluating the properties of focusing systems is developed. The method is based on the use of the Action Function and is applicable to structures whose potential distribution can be found by the method of separable variables. It is shown that this approach can yield results similar to, but more exact, than those obtained by the classical paraxial ray equation. The basic and double-ring structures have been examined in detail. Parameters describing these structures are presented in graphical and tabular form. It is shown that for irrotational flow, a specific current distribution is required. The use of computer techniques for the solution of electron flow problems is discussed. A computer analysis has been developed and results obtained are discussed. The accuracy of the Action Function and the computer analyses has been verified experimentally. It has been shown that the focusing potentials predicted by the Action Function analysis are in good agreement with the experimental values. The computer analysis has also been shown to give results comparable with those obtained practically. Hollow beams of 3.85, 5.4, and 15.6 µP have been focused using the basic ring structure. In order to investigate the effect of unbalance of focusing and defocusing forces at the inner beam boundary, pinhole measurements have been made. It is shown that the ring structure focuses a hollow beam with some change in the beam cross section. The effect of the unbalance of forces is to transform the current density profile. Results indicate that the transformation is desirable since a beam of constant current density may be transformed to a distribution which approaches that required for irrotational flow.

1285. Some results of experimental investigation of combined centrifugal and periodic electrostatic focusing: A A Boridin and Yu N Pchel'nikov,Radiotekh Elektron, 13 (4), April 1968, 719–724 ( in Russian)

1285. Some results of experimental investigation of combined centrifugal and periodic electrostatic focusing: A A Boridin and Yu N Pchel'nikov,Radiotekh Elektron, 13 (4), April 1968, 719–724 ( in Russian)

Periodic electrostatic focusing of a ribbon beam

Obtaining a solution of the equations of a beam satisfying certain conditions at the emitter is, as is known, only part of the problem. Any such solution determines the flow in an unbounded region, whereas actual beams have finite dimensions. To realize the flow described by the solution obtained, we must consider the problem of a system of focusing electrodes capable of producing a beam of given configuration. The solution of this problem reduces to the problem of analytic continuation of the potential given at the beam boundary together with its normal derivative into the charge-free region, i . e . , to the Cauchy problem for the Laplace equation. The problem was first formulated and solved in [1] in relation to a space-charge beam. In [2-4], the concepts of [1] were generalized to the case of plane curved trajectories. The mathematical bases of the method of e lectrostatic focusing were considered in [5] (problems of existence, uniqueness, and correctness). For a number of flows, a solution was obtained in terms of contour integrals which are very difficult to evaluate [6]. In [7], an analytic solution of the problem of the formation of arbitrary axially symmetric beams is given, Transition to ~he complex domain and transformation of the Laplace equation to hyperbolic form made it possible to give the solution in a form more convenient for obtaining final results. Only a few analytic solutions in elementary functions and closed form are known for the problem of focusing stationary flows [1, 4, 8-15] (plane diode [1, 13, 15], plane magnetron [4, 8, 9], hyperbolic [10] and elliptic [11, 12] beams, flow along circles and spirals in some nonuniform magnetic fields [14]). In [I6] electrodes were determined for several nonstationary beams.

A periodically focused backward-wave oscillator

The application of some new periodic focusing techniques to the backward-wave oscillator is discussed. An oscillator utilizing a hollow electron beam was constructed at S-band. A periodic electrostatic focusing method was used with considerable success, and an octave tuning range was obtained. A periodic magnetostatic focusing method was attempted with less encouraging results. Some interesting effects were observed when the periodic focusing techniques were applied and some of these are described.

An electrostatically focused high power traveling-wave tube

Previous work on periodic electrostatic focusing of the electron beam in traveling-wave tubes was confined primarily to bifilar helices. Most structures of the helical type, however, are severely limited in their power-handling capabilities. This paper discusses the application of periodic electrostatic focusing to high-power slow-wave structures to allow the development of extremely light-weight, high power amplifiers. It has been shown recently that a solid beam of high perveance can be focused by the use of a prescribed potential distribution between alternating focusing electrodes. Two slow-wave structures, a crossed-bar type and a folded-line type, were developed which incorporate the required focusing-electrode arrangement without impairing the rf properties of the basic slow-wave circuit. Hot-test results are presented for a crossed-bar structure designed for operation at X-band with a peak power output of five kilowatts. To date, a relatively short structure without attenuator, tested in a continuously pumped bell jar system, has given a peak power of six kilowatts with an efficiency of 17 percent. The tests proved the feasibility of incorporating electrostatic focusing into high power, periodic, slow-wave structures.

Relaxation instabilities in high-perveance electron beams

Spurious low-frequency oscillations similar to those reported by Cutler have been observed in the form of large amplitude modulation of both the RF output and the collector current of klystrons utilizing high-perveance electron beams. This modulation, which appears typically as sawtooth-like relaxation oscillations with frequencies ranging from 10 cps to 100 kc, was observed to occur spontaneously only if the operating pressure was lower than a critical threshold ( \approx 1 \times 10^{-7} mm Hg). Experiments are described which were designed to investigate this phenomenon using dc beam testers. Evidence is presented which indicates that the oscillations are due to a relaxation back and forth between two possible solutions to Poisson's equation which both satisfy all boundary conditions. One of the possible solutions corresponds to the existence of a virtual cathode within the beam, resulting in a partial reflection of electrons. Experimental evidence indicates that positive ions play an important role in triggering the relaxation. Both theoretical and experimental evidence are presented which point to relaxation instabilities of the type described as a potential hazard in utilizing depressed collector operation for improved efficiency of high-perveance microwave tubes. The same potential hazard exists in the use of periodic electrostatic focusing.

Balanced Acceleration and Deflection Electrostatic Focusing†

have the following property: as the strength of the focusing field is increased from zero, the system is initially stable but subsequently passes through alternate bands of stability and instability, of which the former are normally the narrower. In consequence, operation of a given system must usually be restricted to the first band. A suitable combination of acceleration focusing and deflection focusing leads to a model for a periodic electrostatic focusing system that is free from instabilities. Convenient electrode structures are shown which will approximate the required field; the resulting system should have only narrow bands of instability. Such structures are similar to the Slalom configuration with the important difference being that the beam travels on one side only of the central electrodes. This scheme has the following characteristics that should make it suitable for incorporation in a tape-helix travelingwave tube: the beam velocity varies in such a way that electrons spend more time between the central electrodes, and the beam thickness varies in such a way that the beam is thinnest where it passes the central electrodes. (auth)

A method of constructing tubes employing planar periodic electrostatic focusing of sheet beams

One of the main reasons why tubes employing planar periodic electrostatic focusing of electron sheet beams have not been used more widely is that extremely precise alignment of tube parts is required in order to achieve good beam transmission. A simple technique for achieving this precise alignment has been developed. This technique, in brief, consists of the assembly of the tube electrodes in two separate halves, the surfaces of which are then ground simultaneously with an abrasive wheel. Finally, the two halves are bolted together at each end. This technique has been employed successfully in the construction of a tube containing a 2.1 in. long electrostatic focusing structure consisting of 19 pairs of plates having a separation of 0.025 in. In this tube, 99.8% of the 0.005 in. thick, 28 µ amp. electron beam was transmitted through the structure with no increase of beam width. This technique can be applied to the construction of any device employing planar periodic electrostatic focusing of a sheet beam. Two possible applications are a transverse-field traveling-wave tube and a parametric amplifier. This technique may also be used for constructing well-aligned electron guns for generating well-collimated sheet beams to be used for other applications, such as slalom focusing and E-type devices.

Periodic electrostatic focusing of a hollow electron beam

A method of focusing a long hollow electron beam is described in which beam space-charge fields are balanced against uniform radial electric fields and periodic radial and longitudinal electric fields. There is no magnetic field associated with this focusing method. Elimination of the usual large axial magnetic-field requirement of "confined flow" focusing allows the tube system employing the electrostatically focused hollow beam to be lighter in weight, more compact, and to enjoy an enhancement of over-all efficiency. A physical description of the focusing mechanism is given, followed by a mathematical treatment which yields conditions for stable beam flow. Expressions are derived for electrode voltages required to focus a given hollow beam, as well as for velocity variation and beam deflection. A comparison of beam "stiffness" is made with a conventional "confined flow" beam. Beam stability is investigated under various "overfocusing" conditions and imperfect entrance conditions. Finally, this focusing method is compared with other purely electrostatic methods. An experimental program was carried out which demonstrated the usefulness of this type of focusing. Results indicate that good beam definition and transmission coefficients can be obtained with some insensitivity to entrance conditions.

Focusing of a Long Cylindrical Electron Stream by Means of Periodic Electrostatic Fields

This paper presents a theory of focusing long cylindrical electron streams by means of electric fields which vary periodically along the stream. The use of a bifilar helix or a series of annular rings to produce periodic electric fields is considered. The potential distribution at the position of the electrons is expanded in a power series, and an equation of electron motion is written. The solutions obtained indicate that the flow of electrons is essentially parallel, provided that the electrons enter the focusing structure practically without transverse velocities and are distributed across the stream such that the space charge fields decrease radially toward the axis in a manner similar to that of the periodic electric fields. The method of periodic electrostatic focusing is of particular interest in connection with traveling wave tubes. The possibility of using a bifilar helix as both the slow wave and the focusing structure is discussed.