Electron Beam Focusing System Research Articles

Design of a compact coaxial distributed intense relativistic electron beam focusing system

In order to achieve the objectives of compactness and miniaturization in high-power microwave systems, along with reducing system energy consumption, this paper presents a design of a compact coaxial distributed intense relativistic electron beam (IREB) focusing system based on the transit time oscillator. The design methodology integrates theoretical analysis with a 2.5-dimensional particle simulation method. The entire IREB focusing system is composed of three sets of distributed magnetic rings and front-end focusing structures. The layout of this magnetic system is optimized based on periodic permanent magnets, leading to the formation of a quasi-trapezoidal wave magnetic field configuration. This optimization reduces the required number of magnetic rings while ensuring the efficient transmission of the IREB. To prevent the breakdown of the loaded magnetic rings and to optimize the radial electric field in the diode region, an additional front-end focusing structure was added. Based on the aforementioned structural configuration, a 100% electron beam transmission rate was achieved within a 150 mm range.

Twist periodic solutions of the electron beam focusing system with unshielded cathode

In this article, we consider the electron beam focusing system guided by an axially symmetric periodic magnetic field with unshielded cathode. Based on the third‐order approximation method and some quantitative methods, we establish two different sufficient conditions for the existence of twist periodic solutions of the system. Such twist periodic solutions are stable in the sense of Lyapunov. Some results in the literature are generalized and improved.

Development of the sheet electron beam focusing system based on thermionic and field emission cathodes

Synthesis method has been developed for modeling the electron-focusing systems formed compressed sheet electron beam with a field emission cathode. The results of modeling by synthesis of a convergent sheet electron beam with a cross section of 0.15·0.8 mm2 and a current of 100 mA with magnetic shielding of the thermionic and field emission cathodes are presented. The estimated electric field on the cathode is 0.2·105 V/cm at the anode voltage of 20 kV. Experimental investigations of the current-voltage characteristic of an electron gun with impregnated flat cathode in a pulsed mode are conducted, where the collector current is 100 mA.

New results for Brillouin electron beam focusing system

An experimental conjecture on the existence of positive periodic solutions for the Brillouin electron beam focusing system x''+a(1+cos 2t)x=frac{1}{x} for ain(0,frac{1}{2}) is proved by applications of the Manasevich-Mawhin theorem.

Electrostatic-focusing image sensor with volcano-structured Spindt-type field emitter array

The authors have developed a highly sensitive, compact image sensor comprising a field emitter array (FEA) and a high-gain avalanche rushing amorphous photoconductor (HARP) target with the ultimate aim of developing an ultrahigh sensitivity, compact, high-definition television camera. Double-gated field emitters have the advantage of a compact electron beam focusing system; however, image intensities reproduced by a sensor with the double-gated, Spindt-type field emitter array with the focusing electrode stacked 1.5 μm above the gate electrode were nonuniform owing to low electron beam current. The minimum required electron beam current extracted from the double-gated field emitter array is considered for possible use with the sensor. Furthermore, a suitable field emitter array pitch to balance the electron beam current and the electrostatic-focusing lens strength was simulated. For the sensor's design guidelines, a field emitter array pitch of approximately 3 μm would be reasonable in the case of employing the volcano-structured, double-gated, Spindt-type field emitter array with the focusing electrode placed 0.2 μm below the gate electrode hole. Based on simulation results, an image sensor with the volcano-structured, Spindt-type, 3.1-μm-pitch FEA with the focusing electrode placed 0.2 μm below the gate electrode hole was fabricated. It was confirmed that the minimum electron beam current extracted from the volcano-structured FEA was approximately 2 μA/pix, and the sensor could obtain images with improved image intensity uniformity by utilizing the electrostatic-focusing effect. These results indicate that the volcano-structured, double-gated, Spindt-type FEA is potentially suitable for high-definition television FEA-HARP image sensors.

Double-Gated, Spindt-Type Field Emitter With Improved Electron Beam Extraction

We have developed a highly sensitive, compact image sensor that comprises a field emitter array (FEA) and a high-gain avalanche-rushing amorphous photoconductor target, with the ultimate aim of developing an ultrahighly sensitive, compact, high-definition television camera. Double-gated FEs have an advantage of having a compact electron beam focusing system; however, image intensities reproduced by the sensor were nonuniform due to low electron beam current. Furthermore, the simulated electron beam current disagreed with the measured current. The electron beam current characteristics of two types of double-gated, Spindt-type FEs (both with improved electron beam current extraction) are discussed for possible use within the sensor: convex-structured and volcano-structured. A highly accurate simulation model of the image sensor using a double-gated, Spindt-type FE has been examined; the simulated electron beam currents extracted from the double-gated, Spindt-type FE are in agreement with the measured electron beam currents when the initial electron velocity is assumed, thus suggesting that the simulated anode current–anode voltage characteristic conforms to the measured one. For example, the electron beam currents extracted from the convex-structured and volcano-structured FEs when the focusing electrode is placed 0.2 $\mu \text{m}$ below the gate electrode opening at a focusing electrode voltage of 15 V are, respectively, 1.8 and 1.9 times larger than that extracted from the previously used FEs when the focusing electrode is stacked 1.5 $\mu \text{m}$ above the gate electrode. The results show potential for reducing the degradation of the uniformity of the reproduced image’s intensity, and show that the highly accurate simulation model of the sensor is valid to design the double-gated FEAs for the sensor.

Study of Electron Beam Space Charge Effect of Electrostatic Focusing

The influence of space charge in the space electron beam focusing system is introduced.Then charge-quantity distribution method which is used to calculate the density of space charge and the Computer Aided Design (CAD) method are put forward The result by programming calculation shows that the method is correct.

An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system

In this paper, we point out an error in the paper: Positive periodic solution for Brillouin electron beam focusing system, Discrete Contin. Dyn. Syst. Ser. B, 16(2011), 385-392. Meanwhile, it is pointed out that, for $0 < a < 1$, the conjecture that the Brillouin electron beam focusing system $x''+a(1+\cos 2t)x=1/x$ admits positive periodic solutions is still an open problem.

Positive periodic solution for Brillouin electron beam focusing system

An experimental conjecture on the existence ofpositive periodic solutions for the Brillouin electron beam focusingsystem $x''+a(1+\cos2t)x=\frac{1}{x}$for $0 < a < 1$ is proved, using a topological degree theorem by Mawhin.

Research and development of an electron beam focusing system for a high-brightness X-ray generator

A new type of rotating anticathode X-ray generator, where an electron beam of up to 60 keV irradiates the inner surface of a U-shaped Cu anticathode, has achieved a beam brilliance of 130 kW mm(-2) (at 2.3 kW). A higher-flux electron beam is expected from simulation by optimizing the geometry of a combined-function-type magnet instead of the fringing field of the bending magnet. In order to minimize the size of the X-ray source the electron beam has been focused over a short distance by a new combined-function bending magnet, whose geometrical shape was determined by simulation using the Opera-3D, General Particle Tracer and CST-STUDIO codes. The result of the simulation clearly shows that the role of combined functions in both the bending and the steering magnets is important for focusing the beam to a small size. FWHM sizes of the beam are predicted by simulation to be 0.45 mm (horizontal) and 0.05 mm (vertical) for a 120 keV/75 mA beam, of which the effective brilliance is about 500 kW mm(-2) on the supposition of a two-dimensional Gaussian distribution. High-power tests have begun using a high-voltage 120 kV/75 mA power supply for the X-ray generator instead of 60 kV/100 mA. The beam focus size on the target will be verified in the experiments.

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

We study the existence of spatial periodic solutions for nonlinear elliptic equations −∆u + g(x,u(x)) = 0 ,x ∈ R N where g is a continuous function, nondecreasing w.r.t. u .W e give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonin- creasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations.

磁界集束系を備えた１インチ２５６×１９２画素冷陰極ＨＡＲＰ撮像板

We have been developing a new image sensor with a field emitter array and a high-gain avalanche rushing amorphous photoconductor (HARP) target, with the aim of using it in ultrahigh-sensitivity, high-resolution compact TV cameras. We fabricated and tested 256 × 192 pixel sensor with a pixel size of 50 × 50μm and its electron-beam focusing system consisting of permanent magnets. Experiments showed that the prototype sensor has both enough resolution for its pixel size and high sensitivity due to the HARP target, thus demonstrating its potential as a practical image sensor.

Existence of positive periodic solution for the electron beam focusing system

AbstractIn this paper, we study the mathematical model of electron beam focusing system where a&gt;0,b⩾0 are constants, find conditions for the existence of positive π‐periodic solution of the above equation by using analytical method and comparison theory, and prove the existence of positive π‐periodic solution by the continuously dependent theory of initial value problem. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Differential algebraic method for arbitrary order curvilinear-axis combined geometric–chromatic aberration analysis

The principle of differential algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric–chromatic aberrations of electron optical systems. Expressions of differential algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric–chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well.

Compact focusing system for ion and electron beams

A compact ion and electron beam focusing column design has been developed in Plasma and Ion Source Technology Group at Lawrence Berkeley National Laboratory. The electrostatic ion beam-focusing column was simulated using 2D IGUN [R. Becker and W. B. Herrmansfeldt, Rev. Sci. Instrum. 63, 2756 (1992)] ion extraction and beam transport code. A new method has been developed to include finite ion temperature to the IGUN simulation (Reijonen et al., Proceedings of the LINAC Conference, 2000). The focused ion beam system includes an ion temperature collimator, which eliminates the large angle beam trajectories resulting in a small beam spot size. The small holes in the column electrodes are laser drilled, and are aligned by an optical comparator. Simulations show that focused beam spot size as small as 147 nm is achievable for a 40 keV argon beam. The compact electron beam focusing system consists of three elements: the plasma cathode, an electron temperature collimator (similar to the ion beam temperature collimator), and the focusing electrode elements. The total length of the system is less than 10 mm. The column design is performed using EGUN (W. B. Herrmansfeldt, Slac Report No. 331, 1988), electron beam computation code, and IGUN. Space charge effects as well as the electron temperature are incorporated in the computation. The simulations show that focused beam spot size of 60 nm can be achieved. Both columns use similar type rf-induction plasma generator. P+, BF2+, and O2+ ion species production by such source is also demonstrated.

Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system

We find conditions for the existence of an elliptic periodic solution of a singular equation that governs the motion of a magnetically focused axially symmetric electron beam with Brillouin flow by using a monotone iterative scheme starting from a couple of upper and lower solutions on the reversed order. Also, a uniqueness result is proved by using Brouwer degree and index of solutions. Copyright © 2000 John Wiley & Sons, Ltd.

Periodic Solutions of Liénard Equations with Singular Forces of Repulsive Type

In this paper we will use the coincidence degree to give an existence result of periodic solutions for the scalar Liénard equations with singular forces of repulsive type. The main result of this paper clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution. As an application, we will improve the results of Ding, Ye, and Wang for the Brillouin electron beam focusing system.

Asymmetry aberrations and tolerancing of complete systems of electron lenses and deflectors*

The computation of asymmetry aberrations in electron-beam focusing and deflection system is discussed. The aberrations caused by the asymmetry errors (misalignment, tilt, and ellipticity) in magnetic and electrostatic defectors are especially emphasized. First, the method for evaluating the perturbations of electrostatic and magnetic fields due to the asymmetry errors are described; then the formulas for computing the asymmetry aberration coefficients are derived. A set of computer programs based on this paper and also our previous work [X. Zhu and H. Liu, in Proceedings of the International Symposium on Electron Optics, Beijing, 1986 (Institute of Electronics, Academia Sinica, Beijing, 1987), p. 309; E. Munro, J. Vac. Sci. Technol. B 6, 941 (1988); and H. Liu and X. Zhu, Optik 84, 123 (1990)] has been developed, which can handle the tolerancing of complete columns containing any combination of electrostatic and magnetic lenses and deflectors, such as are required for electron-beam lithography and inspection systems.