Electron Beam Trajectory Research Articles

Reduction Mechanism for Spherical and Chromatic Aberration Coefficients of Magnetic Lens and Retarding Electric Fields

Aberrations generated by the magnetic lens, the aperture lens and the retarding field lens are calculated separately using the electron beam trajectories. Most of the chromatic aberrations for the magnetic lens and retarding electric field system are generated by the magnetic lens. The chromatic aberration coefficient for the system is reduced by the factor (landing beam energy/initial beam energy), because the beam is not yet retarded in the magnetic lens. The spherical aberration coefficient is reduced because the beam semiangle is increased by the retarding field lens. The aperture lens generates negative-sign aberration and reduced the total aberration for the system; however, its absolute value is the smallest among those generated by the other two lenses.

Simulated electron beam trajectories toward a field ion microscopy specimen

This article explores the conditions under which a directed electron beam originating nearly normal to the specimen axis can be made to impact the near-apex region of a field ion microscopy specimen in a high electric field. Electron trajectories were calculated using a modified Runge-Kutta numerical method. The results indicate that an electron beam can be directed to a specimen under typical field ion microscopy conditions using two methods: by varying initial beam tilt (less than 60 mrad) or by translating the initial beam position relative to the specimen apex (less than 5 mm). The net focusing effect of the high electric field on the electron beam can be treated, to first order, as an astigmatism and may be correctable by a post-lens deflection system.

マスクの磁化による電子ビーム軌道への影響シミュレーション

It is well known that, in a color CRT, color change occurs as a result of the magnetization of the shadow mask and frame in the enviromental magnetic field. In order to clarify the influence of the mask and frame quantitatively, We analyzed the magnetization by integral equation method when a shadow mask and frame were subjected to an ambient field. We calculated the electron beam trajectories by using the derived magnetic field distributions, and computed the miss-landing to evaluate the color change quantitatively. The results of the numerical analysis agree well with experiment, and aid in relating the shielding to the miss-landing.

Error field measurement and analysis for a pure permanent magnet FEL wiggler

Abstract A two meter long pure permanent magnet FEL wiggler with a 4 cm period and a 2.4 kG field on-axis has been fabricated and tested for the random field error parameters which are relevant to high gain FEL performance. The wiggler is part of a submillimeter-wave alpha particle Thomson scattering diagnostic for fusion plasmas. The integrated magnetic field along the electron beam trajectory was measured for each individual wiggler magnet. The magnets were sorted into a configuration which minimizes the random field-error-induced electron beam steering and displacement. A description of the magnetic field error requirements for the FEL, the error field measurement technique, measurement results and magnet sorting algorithms are presented. After sorting, a measured rms field error of less than 0.5% was obtained.

Magnetic Field Distribution of Shadow Mask having a Magnetic Circuit around a Frame Periphery and its Affection to the Electron Beam Trajectory

The shadow mask in a color CRT is a soft thin iron plate which regulates the electron beam path. The mask may be magnetized by ambient magnetic fields, and the magnetization may change the beam path. As a result of the mask magnetization, the CRT screen may show color changes. We introduced magnetic circuits on the periphery of a shadow mask frame in order to decrease the mask and frame magnetization. The magnetic field distribution around the shadow mask was measured, and the effect of the circuits was evaluated through calculations of the change in electron trajectory. The addition of a magnetic circuit may be effective for decreasing the color change in CRT screens.

Proposal of a nanometer beam size monitor for e +e − linear colliders

A new simple method to measure the transverse beam spot size in the nanometer range is proposed for a beam diagnostic system at the collision point in the future TeV region e +e − linear colliders. A high energy electron beam is injected at a rightangle into a photon target of intense laser light, and generates high energy γ-rays by Compton scattering. Since the laser light is stored inside a cavity resonator and forms a standing wave, the γ-ray flux shows periodic variation with the period of the optical wavelength by scanning the electron beam trajectory along the laser beam axis. From this modulation depth, the transverse size of the electron beam can be easily determined by a simple relation. Using the Nd:YAG laser at wavelength 1.06 μm or 532 nm, we can measure the beam spot size of 60 nm in the FFTB experiment [9] with sufficient accuracy. The required laser peak power is about 20 MW to generate 1000 γ-rays per bunch. If we employ a shorter wavelength laser, for example Ar 2 excimer laser at the wavelength of 126 nm, ot will be possible to measure the beam size down to 5 nm, which is almost close to the required beam size in future linear colliders in the TeV region.

Deflection of electron beams by ground planes

Analytic methods are used to determine the effect of a nearby ground plane on the trajectory of a relativistic electron beam passing through dense gas. The beam is shown to respond to the ground plane in one of two distinct modes, determined by beam current and energy. Low-power beams deflect from the ground plane and tear longitudinally. High-power beams do not deflect or tear but tilt, i.e., the beam axis is no longer parallel to the direction of propagation. This conclusion is reached by computing the net beam force as a superposition of the ‘‘bare’’ ground-plane forces, the shielding forces from the beam-generated plasma, the body coupling forces induced by beam tilt, and the force that arises as the beam separates from the plasma. Effects from electromagnetic retardation and ground resistivity are shown to be negligible in typical cases of interest, and the interaction between ground planes and other external forces is discussed as well.

Small signal gain based on analytic models of thin intense electron beams

We develop the free electron laser theory of the effective energy distribution and the small signal gain for a thin electron beam. The assumption of thinness allows us to treat various transverse locations and electron beam trajectory angles as introducing phase shifts that have the same effect as those introduced by a change in energy of the electron. These ideas extend previous work of Colson et al., Dattoli et al., Scharlemann, and others in five important ways. The first is the ability to treat electron beams with three different classes of matching or symmetry conditions: (i) electron beams with separate betatron matching in each plane. (ii) those with aspect ratio matching, and (iii) crossed matched beams. Manifestations of these symmetries include elliptical cross-sections and electron beams that have modulated spatial profiles. For these we derive analytical expressions for effective energy distributions. Second, two emittance parameters for the electron beam are shown to consolidate into a single parameter that describes most of the energy variation of the effective energy distributions. Thus, the effective energy distribution for a 1:4 ribbon electron beam is nearly equivalent to a distribution for a beam of circular cross-section. Third, these calculations extend to energy distributions, angular distributions, and spatial distributions that all follow Gaussian profiles. Fourth, this model incorporates the description of the incident Gaussian optical beam and the above electron beam dynamics into a single influence function kernel. Emittance, energy spread, diffraction, and gain may be interpreted as limiting the length over which the bunching contributions of the propagating electric fields downstream are important. Fifth, three-dimensional profiles of the optical fields are computed. This work is complementary to the recent work of Yu, Krinsky and Gluckstern in that ours always describes the transition from low gain to high gain for a thin beam and not necessarily the high-gain regime itself. Therefore in this work the parameters of the incident optical beam are included, whereas, their work is not concerned with these parameters. The resulting transverse dependence of the fields may be characterized by an optical beam radius. This optical beam width starts out large compared to the thin electron beam and then, in the example given, contracts to a size that becomes so small that the thin-beam assumption is violated.

Undulator fields and electron trajectories at the end of a helical undulator

The magnetic field structure outside the entrance to a bifilar helically wound free electron laser (FEL) undulator is calculated and used to determine the incoming electron beam trajectories. The beam focusing or defocusing effects due to the stray magnetic fields are calculated and compared for different winding configurations to evaluate the optimum design.

Magnetic Field Distribution of Shadow Mask and Its Influence on Electron Trajectory

It is well known that, in a color CRT, color change occurs due to the magnetization of the shadow mask and frame under ambient, e.g., terrestrial, magnetic field. In order to clarify quantitatively the influence of the magnetization of the shadow mask and frame, we measured the magnetic field distribution around the mask and frame, and calculated the change in electron beam trajectory using a slit model to simulate the shadow mask. The results show that remarkable changes in the trajectory and velocity of an electron beam occur in the slit, where the magnetic flux density is high.

Design of a high-field taperable helical wiggler

The advantages of a helical wiggler have long been recognized, but earlier concepts do not meet the taper and field-control requirements of a modern high-gain free electron laser. This work presents a design of an electromagnetic helical wiggler where the field and steering-free taper are completely adjustable. The unique coil and core geometry makes it possible to produce fields over 5 kG in a bore of 2.5 cm. The paper discusses the concept, magnetic-field analysis, electron-beam trajectories and practical considerations of the wiggler.

シャドウマスクの磁界分布と電子軌道への影響

It is well known that, in a color CRT, color change occurs due to the magnetization of a shadow mask and frame under the environmental magnetic field. In order to clarify the influence of the magnetization of a shadow mask and frame quantitatively, we measured the magnetic field distribution around the mask and frame, and calculated the electron beam trajectory change with a slit model to simulate a shadow mask. The results show that the remarkable change of the trajectory and velocity of electron beam occur in the slit region with the high magnetic flux density.

Simulation of a magnetic field correction scheme for a Halbach-type undulator

An electron-beam trajectory in a Halbach-type undulator with simulated magnetization errors in its component magnet blocks has been calculated using a three-dimensional magnetic field calculation program. The errors taken into account were deviations of the magnetization strength from a nominal value and a deviation of the magnetization direction from a nominal axis. Both uniform and Gaussian distributions of the error magnitudes are assumed for the component magnet blocks of an ideal reference undulator. A simple method for rearranging magnet pairs is discovered. The field integrals are reduced by factors of 4–15 on the average with the method, and the local distortion of the trajectory is strongly corrected. It is found that the distortion of the trajectory in the corrected undulator is almost independent of the magnet gap.

Problems in increasing the accuracy of programs for analysing the trajectories of intense electron beams

The problems involved in improving the accuracy of the numerical solution of a boundary value problem for a system of non-linear partial differential equations describing intense electron beams in the hydrodynamic approximation, when part of the boundary of the computed region is a particular surface, are discussed. A new model of the neighbourhood of a cathode is constructed on the basis of antiparaxial theory which is valid at distances comparable with its radious of curvature. Curvilinear orthogonal meshes, which uniformly cover the domain investigated are introduced in the case of flows with substantially different scales.

Improved low-energy diffuse scattering electron-spin polarization analyzer

An improved low-energy diffuse scattering electron-spin polarization analyzer is described. It is based on the low-energy (150 eV) diffuse scattering of polarized electrons from polycrystalline evaporated Au targets. By collecting large solid angles and efficiently energy filtering the scattered electrons, a maximum figure of merit, FOM=S2I/I0=2.3×10−4 is achieved. Maximum measured values of the Sherman function were S=0.15. Further, the instrumental (false) asymmetry due to changes in the trajectory of the incident electron beam has been minimized by balancing the angular and displacement asymmetries. A total residual scan asymmetry as low as 0.0035/mm has been measured over 4-mm scan fields at the Au target in the detector. This instrumental asymmetry would produce a maximum error in the polarization in a SEMPA experiment of less than 0.3% for a 100-μm full-field scan. Details of the design and performance of the new detector are given.

A WIGGLER MAGNET FOR THE UK FREE ELECTRON LASER PROJECT

The design of a 5 m long permanent magnet wiggler is described, a novel feature of which is its construction in four identical sections with independently controllable gaps. The results of magnetic tests on the rare earth cobalt blocks are presented and a method of arranging them in the magnet to reduce errors in the electron beam trajectory is put forward.

Angular distribution and radial profile of a relativistic electron beam in vacuum

The injection of a relativistic electron beam ( nu mod gamma =0.16) into vacuum, results in the formation of a virtual cathode. As a consequence a hollow current density profile is measured beyond the virtual cathode. But the measurement of the angular distribution of the electron velocities indicates that it remains dominated by scattering in the anode foil. Transmitted beam currents are greater than the stationary vacuum limiting current of Bogdankevich, and Rukhadze (1971). Electron beam trajectory calculations, taking into account the electromagnetic beam potential and foil scattering, are capable of describing the virtual cathode. Similar to the calculations of Thode et al. (1979), the hollow profile is steeper than the measured profile and in both cases the calculated limiting current is too small.

The Calculation of the Deflection Magnetic Field and the Electron-Beam Trajectory for Color Television

The practical calculation method for the magnetic field analysis of a saddle-shaped magnetic deflection coil with an iron core has already been reported. The authors used this calculation method to determine the deflection magnetic field. Further, by numerically solving the equation which was derived from the variation principle, the authors developed the program which determined the electron beam trajectory. By using this method, the deflection characteristics can be learned by using only the numerical values which show the physical position and the shape of the picture tube and deflection coils. In the past, the deflection system design was based on experience, but now it will be possible to depend upon theoretical analysis.

3812. Intense relativistic electron-beam trajectories and their effect on beam heating of toroidally confined plasma. (USA): T R Lockner and B R Kusse,J appl Phys, 49 (4), 1978, 2357–2364

3812. Intense relativistic electron-beam trajectories and their effect on beam heating of toroidally confined plasma. (USA): T R Lockner and B R Kusse,J appl Phys, 49 (4), 1978, 2357–2364

Intense relativistic electron-beam trajectories and their effect on beam heating of toroidally confined plasma

The trajectories of an intense relativistic electron beam propagating between a toroidal plasma column and a conducting vacuum wall are calculated theoretically and verified experimentally. Three classes of trajectories are observed, including a set of banana-type orbits. The significance of these trajectories on the ability of the beam to transfer energy to the plasma is discussed.