Chaotic electron trajectories in a circular free electron laser

The motion of a relativistic electron is analyzed in the field configuration consisting of a circular wiggler magnetic field, an axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron ring. By generating Poincare surface-of-section maps, it is shown that when the equilibrium self-fields is strong enough, the electron motions become chaotic. Although the realistic circular wiggler magnetic field destroys the integrability of the electron motion as the equilibrium self-fields do, the role the latter plays to make the motions become chaotic is stronger than the former. In addition, the axial magnetic field can restrain the occurrence of the chaoticity.     

CHAOTIC ELECTRON TRAJECTORIES IN A CIRCULAR FREE ELECTRON LASER

The motion of a relativistic electron is analyzed in the field configuration consisting of a circular wiggler magnetic field, an axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron ring. By generating Poincare surface-of-section maps, it is shown that when the equilibrium self-fields is strong enough, the electron motions become chaotic. Although the realistic circular wiggler magnetic field destroys the inte-grability of the electron motion as the equilibrium self-fields do, the role the latter plays to make the motions become chaotic is stronger than the former does. In addition, the axial magnetic field can restrain the occurrence of the chaoticity.     

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.     

在环型自由电子激光器中电子运动的混沌特性

本文分析了相对论性电子在环型摆动器磁场,轴向磁场和由非中性电子束产生的平衡自电场和自磁场中的运动。通过数值计算画出Poincare截面映射图,表明当自场足够强时,这种运动变成混沌的。虽然现实的环型摆动器场和自场一样使电子运动方程成为不可积的,但自场使运动产生混沌的作用要比摆动器场强。轴向磁场有抑制混沌发生的作用。     

Transport of electron beams in periodic permanent-magnet focusing systems with nonharmonic distribution of the magnetic field

The results of the study of the transport of electron beams in periodic magnetic fields are presented for the case when the distribution of the magnetic field is essentially different from a sinusoidal distribution in different parts of the drift channel. An easy-to-implement nonharmonic distribution of the magnetic field is found. This distribution ensures a small ripple of the envelope of a high-intensity electron beam. The results of application of combined periodic permanent-magnet (PPM) focusing systems in high-powered pulse travelingwave tubes (TWT) are presented for the TWTs having a slow-wave structure that is superposed with the pole pieces of the PPM focusing systems.     

A small-signal analysis of the electron cyclotron backward-wave oscillator

In an earlier report on the construction and performance of the electron cyclotron backward-wave oscillator, it was shown, through physical arguments, that in an unloaded waveguide supporting the dominant mode, an electron having transverse rotation at its cyclotron frequency will interact with RF fields of approximately equal frequency. This transverse motion will deliver energy to the RF E fields and interact with the RF H fields, thus producing longitudinal bunching. A small-signal analysis is presented in this paper. With the use of the normal mode expansion analysis, the circuit equation is obtained by considering the normal mode in approximate synchronism with the beam. The RF current is computed by considering electron motion under the dc and circuit fields, but neglecting RF space-charge fields. Combining these equations leads to a sixth-order equation of propagation constants. Two waves are far from synchronism and are therefore neglected; the remaining four are two waves which originate from the "fast cyclotron waves" and two waves which originate from the forward and reflected circuit waves. The "fast cyclotron wave" so obtained has a different meaning from the usual definition and is discussed in detail. Theoretical start-oscillation current is found to depend critically on the reflection coefficient at the electron gun end. Proper adjustment of this parameter leads to excellent agreement between the theoretical and experimental start-oscillation currents.     

High precision phase-shifting electron holography

Today's information-oriented society requires high density and high quality magnetic recording media. The quantitative observation of fine magnetic structures by electron holography is greatly anticipated in the development of such new recording materials. However, the magnetic fields around particles <50 nm have not been observed, because the fields are too weak to observe in the usual way. Here we present a highly precise phase measurement technique: improved phase-shifting electron holography. Using this method, the electric field around a charged polystyrene latex particle (100 nm in diameter) and the magnetic field around iron particles (30 nm in diameter) are observed precisely. A precision of the reconstructed phase image of 2pi/300 rad is achieved in the image of the latex particle.     

The electron density of semiconductors with charged dislocations placed in external fields

Variations in the electron density due to variations in the capture cross section and the thermal ionization upon application of an external electric field and a quantizing magnetic field are considered. Analytical expressions for the electron density in arbitrary electric and quantizing magnetic fields and also in crossed electric and quantizing magnetic fields are obtained. It is assumed that the electrons relax in energy as a result of interacting with acoustic phonons. Calculations for a quantizing magnetic field in the ultraquantum limit are presented. Fiz. Tekh. Poluprovodn. 33, 1300–1302 (November 1999)     

Scanning electron mirror microscopy and scanning electron microscopy of integrated circuits

The recently developed scanning electron mirror microscope (SEMM) is compared with other types of electron microscopes, such as the electron mirror microscope (EMM) and the scanning electron microscope (SEM), for examining integrated circuits. Potential advantages of the SEMM include high resolution, elimination of electron bombardment damage, and high sensitivity of voltage gradients, magnetic fields, and topography. Preliminary observations of integrated, circuits obtained with the feasibility SEMM at various specimen potentials are discussed.     

Measurements of the noise parameters of an electron beam

Measurements of the noise parameters S and II for an electron beam are described. Observations of the standing-wave pattern of noise on the beam show that at high axial magnetic fields the noise space-charge waves decay.     

Effect of a magnetic field on the structure of a high-current electron beam with a compensated charge

A mathematical model of a high-current electron beam with a compensated charge is developed. The effect of the 3D axially symmetric magnetic field induced by the beam current is taken into account. The model is based on the method of current tubes, which makes it possible to calculate electron trajectories in the presence of an external axially symmetric magnetic field. It is demonstrated that, in the presence of an external axially symmetric magnetic field, the beam rotates around its axis and the azimuthal current is induced. The shapes of electron trajectories are strongly affected by the magnetic field of the azimuthal current. The electron trajectories are calculated for various beam currents and external magnetic fields. It is shown that a significant nonlinearity leads to crossing of the trajectories of the initially laminar beam, sheath formation after passing the crossover, and collisionless thermalization of the beam. The boundary of the region inside which the beam can stably overcome the first crossover is determined.     

激光功率密度对自生磁场和电子热传导的影响

为了理解超强激光与等离子体相互作用中产生的自生磁场形成机制和电子热传导特性,采用相对论电磁粒子模拟程序,估算了不同激光功率密度下,在等离子体表面所形成的电磁不稳定性产生的自生磁场大小和空间分布,得到了超热电子和经典Spitzer-Harm理论描述的电子热流随激光功率密度的演化情形.结果表明,非Maxwell速度分布的等离子体,由于电子初始时刻的无规则热运动,在等离子体上激发电磁不稳定性,而不稳定性激发的强电磁场使电子束在非常短的距离内沉积能量,同时对在激光有质动力推开电子时形成的超热电子能量输运产生抑制作用.这一研究结果对更好理解惯性约束核聚变快点火过程中自生磁场的产生、电子热传导等方面有帮助的.     

The oblique electron lens

An oblique electron lens is described that is especially applicable to image converters and camera tubes employing flat opaque photocathodes. The use of optical lenses, corrector plates, and/or mirrors (often employed in other electron lenses designed for use with opaque photocathodes) are eliminated. The oblique electron lens is well suited to ultraviolet and vacuum ultraviolet image converters, and to image converters employiug opaque negative electron affinity photocathodes. It is also possible to use this oblique electron lens for electronography. Measurements on an experimental tube show that a limiting resolution of 50 line pairs/mm is possible, but the intrinsic lens quality is believed to approach that of a conventional electromagnetic lens having uniform and colinear electric and magnetic fields.     

Hot electron energy relaxation in quantizing magnetic fields

A systematic study of the radiative recombination of hot electrons between Landau levels in several n-InSb samples has been carried out as a function of the free electron concentration and the applied electric and magnetic fields (E ～ H). The magnetic field range investigated was 0.5 to 3.0 T. Electron temperatures are derived in dependence of the total electric and the magnetic field applied. The carrier heating is impeded with increasing electron concentration and also with increasing magnetic field. From the direct observation of the recombination radiation intensity on electric field response the electron lifetime in the first Landau level is found to be less than 10^?8. The results obtained are discussed in light of a new theoretical approach. We give evidence that electron-electron scattering plays an important role both for the carrier distribution established and for the electron lifetime in the first Landau level.     

Elimination of integration truncation errors in electron ray calculations

A method for the computation of electron trajectories in arbitrary static electromagnetic fields, which eliminates a major source of error, is given. Under certain conditions the equations of motion are shown to yield analytic solutions that are expressible in terms of the matrix exponential function exp (At).     

Beam‐Induced Fe Nanopillars as Tunable Domain‐Wall Pinning Sites

Focused‐electron‐beam‐induced deposition (FEBID) is employed to create freestanding magnetic nanostructures. By growing Fe nanopillars on top of a perpendicular magnetic domain wall (DW) conduit, pinning of the DWs is observed due to the stray fields emanating from the nanopillar. Furthermore, a different DW pinning behavior is observed between the up and down magnetic states of the pillar, allowing to deduce the switching fields of the pillar in a novel way. The implications of these results are two‐fold: not only can 3‐dimensional nano‐objects be used to control DW motion in applications, it is also proposed that DW motion is a unique tool to probe the magnetic properties of nano‐objects.     

Laminar flow in magnetically-focused cylindrical electron beams

The behavior of a cylindrical electron beam in a magnetic field is discussed in terms of a laminar-flow model. By numerical integration of the equations of motion, the maximum and minimum radii of excursion and the wavelength of the undulations for each electron are presented in graphical form for various boundary conditions on the electron beam. By the proper selection of the boundary conditions, e.g., magnetic field strength at the cathode, the graphs are utilized to describe Brillouin flow, space-charge-balanced flow, immersed flow, confined flow, and, in fact, any electron flow which satisfies the laminar flow criterion. The perturbations introduced by improper injection conditions for any of the flows mentioned can be read directly from the graphs. A study of the wavelength and the amplitude of such perturbations as a function of radial position in the beam determines if a given type of flow with given injection conditions satisfies the laminar flow criterion. The sensitivity of the various types of electron flow to misadjustments of the boundary conditions is clearly revealed by the graphs; e.g., the amplitude of the undulations in Brillouin flow is very sensitive to the adjustment of the magnetic field strength whereas, for immersed flow, a similar deviation in magnetic field strength has very little effect on the amplitude of the undulations.     

Application of a nonharmonic magnetic-field distribution for focusing of intense electron flows in magnetic periodic focusing systems

The results of theoretical and experimental investigation of focusing of intense extended electron flows in periodic magnetic fields with a nonsinusoidal distribution are presented. An easily realizable nonharmonic distribution that has three local maxima on the magnetic-field half-period and ensures small fluctuations of the boundary of an intense electron flow at high values of the field parameter is found. The results of application of magnetic periodic focusing systems (MPFSs) with the obtained distributions in pulsed traveling-wave tubes with a slow-wave structure integrated with the MPFS pole pieces are presented.     

The effect of crossed fields on the velocity distribution of hollow electron beams

An analysis of the effect of radial electric and longitudinal magnetic fields on the axial velocity distribution of electrons in a hollow beam was carried out on a simplified model. Two results, both consistent with experimental observations, were obtained. First, the longitudinal velocity spread (or equivalent temperature) increases with distance from the axis. Second, the retarding potential at which all electrons are collected also increases with distance from the axis; this indicates that the energy of the slowest electrons at the beam edge is decreased as a result of the crossed fields. The radial electric field, which is greatest near the beam edge and zero on the axis, converts some of the longitudinal energy of the electrons into rotational energy. This kind of scattering is analyzed by a perturbation method whereby the transverse motion of the incident beam is considered harmonically bound by the magnetic field. The spectrum of the energy absorbed in the rotational mode is shown to be velocity dependent and thus to give rise to distortion in the Maxwellian distribution of the incident beam.     

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.