Electron Acceleration by Beating of Two Intense Cross-Focused Hollow Gaussian Laser Beams in Plasma

This paper presents propagation of two cross-focused intense hollow Gaussian laser beams(HGBs) in collisionless plasma and its effect on the generation of electron plasma wave(EPW) and electron acceleration process,when relativistic and ponderomotive nonlinearities are simultaneously operative. Nonlinear differential equations have been set up for beamwidth of laser beams, power of generated EPW, and energy gain by electrons using WKB and paraxial approximations. Numerical simulations have been carried out to investigate the effect of typical laser-plasma parameters on the focusing of laser beams in plasmas and further its effect on power of excited EPW and acceleration of electrons. It is observed that focusing of two laser beams in plasma increases for higher order of hollow Gaussian beams,which significantly enhanced the power of generated EPW and energy gain. The amplitude of EPW and energy gain by electrons is found to enhance with an increase in the intensity of laser beams and plasma density. This study will be useful to plasma beat wave accelerator and in other applications requiring multiple laser beams.     

Electron focusing in backscattering from single-crystal Si(100)

Diffraction patterns produced by quasi-elastically backscattered electrons focused in a thin single-crystal Si(100)2×1 near-surface layer have been studied. The measurements performed in the 0.6–2-keV range are compared with calculations made in the single-scattering cluster approximation. This model is shown to describe adequately the experiment. An analysis is made of the relation among the diffraction patterns observed for different silicon faces, and of the effect of the primary-electron beam orientation. The relations governing the focusing of quasi-elastically backscattered electrons escaping from the crystal along the main crystallographic directions have been established. The various aspects of the effect for backscattered electrons undergoing inelastic interaction with the electron subsystem of the crystal have been investigated. Fiz. Tverd. Tela (St. Petersburg) 40, 1364–1369 (July 1998)     

The anomalous penetration of intense circularly polarized electromagnetic beam through overdense magnetized plasma

The steady state nonlinear propagation of an intense, circularly polarized electromagnetic beam in an inhomogeneous magnetized plasma has been investigated in paraxial approximation. The laser induces a large oscillatory velocity on electrons, raising their mass and lowering the plasma frequency. Further, rising due to cyclotron resonance effect. The propagation of the electromagnetic waves in magnetized plasma in both the extraordinary and ordinary mode is analyzed. The nonlinearity in dielectric function is considered in presence of external magnetic field due to saturation effects for arbitrary large intensity, which leads to focusing/defocusing of the beam. The focusing effect along with magnetic field helps in the process of anomalous penetration of the beam by enhancing the depletion of the plasma from the axial region. The penetration increases with the incident beam power up to some critical value beyond which it rises abruptly when all electrons have been driven out of the axis. The cyclotron resonance effect awfully supports the laser beam to propagate inside the overdense plasma region. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction applicable for underdense and overdense plasma.     

Picosecond time-resolved two-dimensional ballistic electron transport

Time-resolved transport of ballistic electrons in a two-dimensional electron gas has been measured with a resolution of less than 5 ps. This was accomplished by using picosecond electrical pulses to launch electrons from the emitter of a transverse magnetic focusing structure and optoelectronically sampling the collector voltage. Both plasma resonances and the ballistic transport signal are clearly resolved. The transit time appears to be somewhat longer than expected from simple Fermi velocity considerations.     

Double ionization of Sc<Superscript>+</Superscript>ions by electron impact

Electron impact double ionization cross-sections of Sc⁺ions have been calculated in the binary encounter approximation (BEA). Accurate expression of σ_ΔE(cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Direct double ionization from ejection of 3d and 4s electrons has been investigated in the modified double binary encounter model incorporating the focusing action of the target ion on the incident electron. The identification of the 3p shell whose ionization provides a major contribution to double ionization through ionization-autoionization is an interesting aspect of the present investigation. The theoretical results show satisfactory agreement with the experimental observations.     

Role of the electron forward-focusing effect in the formation of Kikuchi patterns of single-crystal silicon

Kikuchi patterns produced by quasi-elastic backscattering of electrons with energies of 0.6–2 keV from a thin Si(111)7×7 near-surface layer are studied. It is shown that experimental data obtained for silicon, just like those for metals, can be described satisfactorily by calculations made in single-scattering cluster approximation, as well as in terms of a model taking phenomenologically into account the forward-focusing of backscattered electrons as they escape from the crystal. It has thus been demonstrated that the forward-focusing effect at an energy E=2 keV plays a dominant role in the formation of Kikuchi patterns, which permits their use for visualization of the atomic structure of a surface. The dependences of the focusing efficiency on the parameters of the atomic chains along which electrons propagate have been established for the closest-packed crystal directions. Fiz. Tverd. Tela (St. Petersburg) 39, 752–757 (April 1997)     

关于磁聚焦法测定电子荷质比实验中荧光屏上显示的线段与所加励磁电流的关系

磁聚焦法是测定电子荷质比的一种有效方法,本在此实验的基础上,研究了实验测量过程中荧光屏上显示扫描的线段随所加的励磁电流的变化关系,包括线段的旋转角度和长度的变化。     

Cross-focusing of two laser beams in a plasma

Cross-focusing of two copropagating laser beams in a plasma is investigated using paraxial ray theory. If the lasers have a frequency difference equal to the electron plasma frequency, they can drive a large amplitude plasma wave. The ponderomotive force due to the plasma wave forces the plasma electrons outwards thereby generating a parabolic density profile giving rise to cross-focusing. The results show a decrease in threshold for focusing by two orders of magnitude as compared to focusing due to the ponderomotive force of the laser beams.     

Focusing of electrons reflected from layered crystal

The mechanism of the formation of the diffraction patterns upon inelastic reflection of mean-energy electrons from the VSe₂(0001) layered crystal has been investigated. It is found that the strong scattering of electrons by short atomic chains of the Se-V-Se layer triads leads to the weakening of electron focusing and the enhancement of diffraction scattering in deeper layers, which gives rise to the Kikuchi lines. It is demonstrated that, at an energy of 2 keV, the diffraction pattern is adequately described by the cluster model of single scattering. The atomic structure of thin near-the-surface layer of VSe₂ has been investigated by the computer simulation of experimental data.     

Peculiarities of filamentation of sharply focused ultrashort laser pulses in air

Peculiarities of the self-focusing and filamentation of high-power femtosecond laser pulses in air have been experimentally and theoretically studied under conditions of broad variation of the beam focusing parameter. The influence of the numerical aperture (NA) of the initial radiation focusing on the main characteristics of laser-induced plasma columns (characteristic transverse size, length, and concentration of free electrons) is considered. It is established that, for a rigid (NA > 0.05) initial laser beam focusing, the transverse size of the plasma channel ceases to decrease at a level of R _pl ≈ 2–4 μm as a result of strong refraction of radiation on the plasma formed at the focal waist, which prevents further contraction of the laser beam due to its focusing and self-focusing.     

超导透镜及其聚焦行为

 理论上分析了利用高温超导体作为透镜聚焦强流相对论电子束的机理。实验研究中，研制出的YBa₂Cu₃O₇-d 高温超导体作为透镜的传输和聚焦性能被得到验证，结果表明，超导透镜具有明显的聚焦效果，并可有效控制束流强度分布，使被聚焦电子在束横截面上的分布更为均匀。     

Focusing of an intense neutralized proton beam

An intense low-energy (15–20 keV) proton beam is focused in two stages: ballistic focusing is followed by magnetic compression. The beam is formed by an MAIS wide-aperture source, in which a plasma is generated by many discharge elements via a discharge over the polyethylene surface. In the presence of an external magnetic field, the beam turns out to be overneutralized by electrons coming from the cathode grids of the source and from the target. The maximal focusing efficiency (>70%) is observed within 10 μs after the pulse has been applied if the target is negatively biased. The degree of beam compression in terms of cross-sectional area is 1.6×10³. The numerical simulation of the focusing agrees well with the results of measurement.     

Transverse electron focusing as a way of studying surface crystallography

Conduction electrons represent a unique probe for studying surfaces (and interfaces) due to their extremely low excitation energies and to the fact that they impinge upon the surface from inside the sample. Focusing of conduction electrons by means of a transverse homogeneous magnetic field—transverse electron focusing (TEF)—provides a means for probing the atomic structure and composition of surfaces and interfaces, including both regular and irregular roughness. This article explains what TEF is, reviews what has been learned from it about surface structure, and describes what can be learned in the future.     

箔聚焦强流相对论环形束在同轴波导中的传输

 结合箔聚焦和静电线聚焦的特点,对箔聚焦强流相对论环形电子束在同轴波导中的传输进行了研究。通过数值求解电势满足的泊松方程,得到电势、电场分布及系统的空间电荷限制流,并根据电子的运动方程得到包络电子的平衡条件及其运动轨迹。     

Focusing of electrons reflected from a crystal with loss of energy

A study is made of the features arising in the spatial distributions of reflected electrons as a result of a focusing effect. Experiments are conducted on single-crystal Mo (100) with primary electron energies of 0.5–2 keV and detection of electrons which lose fixed amounts of energy up to 300 eV. An analysis of the data establishes the dependence of the electron focusing efficiency on the amount of energy loss. It is shown that when electrons are reflected with single losses through plasmon excitation, the magnitude of the effect is determined mainly by the average number of scattering atoms encountered by an electron along its path to the surface. When the energy losses are high, defocusing owing to multiple elastic and inelastic scattering of the electrons is found to predominate. Zh. Tekh. Fiz. 68, 128–133 (June 1998)     

Analytical Description of Electron Motion in a Three-Dimensional Undulator Field

The motion of relativistic electrons in an ideal three-dimensional magnetic undulator field satisfying the stationary Maxwell equation is considered. The system of nonlinear differential equations of the electron motion is solved analytically using perturbation theory rather than the method for averaging fast oscillations of the electron trajectory (the focusing approximation), as was done in a series of previous studies. The obtained analytical expressions for the trajectories describe the behavior of particles in a three-dimensional magnetic undulator field much more accurately than the formulas obtained within the framework of the focusing approximation. The analysis of these expressions shows that the behavior of electrons in a three-dimensional undulator field is much more complicated than that described by equations obtained using the averaging method. In particular, it turns out that the electron trajectories in the undulator have a cross dependence; in this case, variations in the initial trajectory parameters in the vertical plane cause changes in the horizontal trajectory components, and vice versa. The results of calculations of the trajectories carried out using analytical expressions are close to those of numerical calculations using the Runge-Kutta method.     

Time resolution of the bunch-shape detector with a thin-wire emission target

The time resolution of a new bunch-length detector based on the radio frequency (RF) scanning of the produced secondary electrons is calculated. A dedicated Monte-Carlo code by means of SIMION software is developed for accurate simulation of spread in the investigated secondary electrons transit times and image width. In calculation the initial energy distribution of electrons and the actual structure of accelerating and focusing electric fields were considered. It is shown that by using a thin-wire emission target a femtosecond time precision could be achieved using moderate applied voltages.     

Influence of angles of incidence of laser radiation on the generation of fast ions

It was established experimentally that the number and energy of fast ions in laser plasma increased with increasing angle of focusing laser radiation onto a flat target. Numerical calculations showed that the increase in angle of focusing brought the mean angle of incidence of laser radiation closer to the optimal angle corresponding to the maximal efficiency of the resonance absorption mechanism and, as a result, increased the fraction of absorbed laser energy in the energy of fast electrons and increased the number of fast electrons. In turn, the increase in the energy and number of fast electrons resulted in an increase in the number of fast electrons involved in the formation of a self-consistent electric field at the target edge and led to the growth of the field strength, which, eventually, was the reason for the increase in the number and energy of fast ions.     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.