Smoothing properties of transition semigroups in hilbert spaces

The paper gives conditions under which the transition semigroup corresponding to a large class of semilinear equations on a Hilbert space transforms Borel functions onto Frechet differentia hies ones.     

Optimal resolution with extreme depth of focus

When the focal depth is required to be much larger than the wavelength, λ, the effective NA of the beam with optimal resolution is much less than unity. An aperture that is much larger than this beam's footprint is then of no consequence. Such beams that maximize the mean encircled energy fraction within a cylindrical focal region are shown to depend on only a single parameter, ω, that is proportional to the ratio of the square of the cylinder's radius to the product of its length and λ. A linear combination of Hermite– or Laguerre–Gaussian modes is used to represent these fields in two and three dimensions, respectively. For small ω, the results are compared both to asymptotic expansions and to optimal Gaussian and Bessel–Gauss beams.     

New expressions for field distribution in the focal region

In an earlier paper dealing with the flat-topped light beams [Y. Li, Opt. Lett. 27 (2002) 1007], it is shown that the flat-topped beams can be expressed as 1 − [1 − exp(−ξ²)]^M, where ξ is a dimensionless parameter and M is a non-negative number. The binomial expansion of this express contains only lowest-order Gaussian modes; this situation makes it possible to develop a new formulation of diffraction of converging spherical wave at an aperture in a plane opaque screen if the Gaussian mode expansion is employed to describe the boundary values of the screen.     

Interaction of He Atoms with XeF2 Observed in Crossed Molecular Beams

The interactional shape of XeF₂ with respect to energy and distance was observed by He atom scattering in molecular beam experiments. The heterogeneous second virial coefficient and the binary coefficient of diffusion were calculated from the resulting interaction potential.     

Electron acceleration using two crossed Bessel beams in vacuum

The direct acceleration of electrons by using two crossed linearly polarized Bessel beams with equal frequency and amplitude in vacuum is studied and compared with the case of single linearly polarized Bessel beam. It is found that two zeroth- and first-order Bessel beams with π-rad phase difference have a nonvanishing longitudinal electric field on the z-axis, which can be maximized under certain conditions and used to accelerate electrons. Two crossed zeroth- and first-order Bessel beams have a larger maximum longitudinal electric field on the z-axis than that of a single first-order Bessel beam, and are suited for laser electron acceleration.     

Optimum design of vibrating cantilevers: A classical probem revisited

Optimum design of vibrating cantilevers is a classical problem widely used in the literature and textbooks in structural optimization. The problem, originally formulated and solved by Karihalloo and Niordson (Ref. 5), was to find the optimal beam shape that will maximize the fundamental vibration frequency of a cantilever. Upon reexamination of the problem, it has been found that the original analysis and solution procedure can be simplified and improved substantially. Specifically, the time-consuming inner loop devised for solving the Lagrange multiplier in the original work has been proved to be tolally unnecessary and thus should not be considered in the problem solution. This conclusion has led to a new set of simplified equations for the construction of iteration schemes. New asymptotic expressions for the optimum design solution have been obtained and verified by numerical results. Numerical analysis has shown a significant improvement in convergence rate by the proposed new procedure. Also some obvious numerical errors in the original paper have been identified and corrected.This work was suppoted in part by the University of Arizona Foundation and the Office of the Vice President for Research. The author is grateful to the reviewers for their valuable comments.     

Irradiance map of an apertured Gaussian beam affected by coma

The Gaussian amplitude of a laser beam incident on an optical system affected by coma is expanded until the fourth order. This expansion is included in the Huygens-Fresnel integral calculation to obtain the amplitude and irradiance distribution on the focal plane of an optical system affected by coma. The analytical results obtained here are compared with a previous model of a comatic Gaussian beam. Appropriateness of the analytical model is also validated by the fitting with experimental data.     

A method for predicting the deflection of reinforced concrete beams strengthened with carbon plates

For strengthening bent beams, plates of reinforced plastics are glued to their tensioned surface. As s result, the beam becomes layered, and it is possible to control its rigidity and deflection. Based on the methods of structural mechanics of layered media, a method is elaborated for determining the deflection of such beams on the entire range of loading up to their ultimate failure. A comparison between the theoretical and experimental results is carried out. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 45–60, January–February, 2006.     

氨对硅基铁纳米薄膜高温重凝核的影响

采用弧过滤离子沉积系统（arc filtered deposition，AFD）在纯硅表面制备铁纳米薄膜。研究了750℃下铁纳米薄膜在氢气氛围以及氨气氛围中重凝核的规律。研究表明，在氢气氛围中，铁纳米薄膜重凝核以后形成的铁纳米颗粒随薄膜的厚度增加以及保温时间的延长而增大；但在氨气氛围中，铁纳米薄膜重凝核后形成的纳米颗粒的尺寸随保温时间的变化更为复杂：在氨气作用的初始阶段，铁颗粒的尺寸随氨气作用时间的延长而逐渐变大，但一段时间以后，铁颗粒的尺寸又随氨气作用时间的延长而变小，直到铁颗粒平均直径达到一个最小值（大约在氨气介入后的12min），随后铁颗粒的尺寸又逐渐变大，并最终达到一稳定值。     

Plasma Photocathodes

Plasma wakefield accelerators offer accelerating and focusing electric fields three to four orders of magnitude larger than state-of-the-art radiofrequency cavity-based accelerators. Plasma photocathodes can release ultracold electron populations within such plasma waves and thus open a path toward tunable production of well-defined, compact electron beams with normalized emittance and brightness many orders of magnitude better than state-of-the-art. Such beams will have far-reaching impact for applications such as light sources, but also open up new vistas on high energy and high field physics. This paper reviews the innovation of plasma photocathodes, and reports on the experimental progress, challenges, and future prospects of the approach. Details of the proof-of-concept demonstration of a plasma photocathode in 90° geometry at SLAC FACET within the E-210: Trojan Horse program are described. Using this experience, alongside theoretical and simulation-supported advances, an outlook is given on future realizations of plasma photocathodes such as the upcoming E-310: Trojan Horse-II program at FACET-II with prospects toward excellent witness beam parameter quality, tunability, and stability. Future installations of plasma photocathodes also at compact, hybrid plasma wakefield accelerators, will then boost capacities and open up novel capabilities for experiments at the forefront of interaction of high brightness electron and photon beams.