Equilibrium orbit analysis in a free-electron laser with a coaxial wiggler

An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and trajectories in the radially dependent wiggler. Simple analytical solutions are obtained in the radially-uniform-wiggler approximation and a formula for the derivative of the axial velocity $v_{\|}$ with respect to Lorentz factor $\gamma$ is derived. Results of numerical computations are presented and the characteristics of the equilibrium orbits are discussed. The third spatial harmonic of the coaxial wiggler field gives rise to group $III$ orbits which are characterized by a strong negative mass regime.Comment: 13 pages, 9 figures, to appear in phys. rev.

Studies of a Terawatt X-Ray Free-Electron Laser

The possibility of constructing terawatt (TW) x-ray free-electron lasers (FELs) has been discussed using novel superconducting helical undulators [5]. In this paper, we consider the conditions necessary for achieving powers in excess of 1 TW in a 1.5 {\AA} FEL using simulations with the MINERVA simulation code [7]. Steady-state simulations have been conducted using a variety of undulator and focusing configurations. In particular, strong focusing using FODO lattices is compared with the natural, weak focusing inherent in helical undulators. It is found that the most important requirement to reach TW powers is extreme transverse compression of the electron beam in a strong FODO lattice. The importance of extreme focusing of the electron beam in the production of TW power levels means that the undulator is not the prime driver for a TW FEL, and simulations are also described using planar undulators that reach near-TW power levels. In addition, TW power levels can be reached using pure self-amplified spontaneous emission (SASE) or with novel self-seeding configurations when such extreme focusing of the electron beam is applied.Comment: 10 pages, 12 figure

Two-Dimensional Ultrathin Silica Films

Two-dimensional (2D) ultrathin silica films have the potential to reach technological importance in electronics and catalysis. Several well-defined 2D-silica structures have been synthesized so far. The silica bilayer represents a 2D material with SiO2 stoichiometry. It consists of precisely two layers of tetrahedral [SiO4] building blocks, corner connected via oxygen bridges, thus forming a self-saturated silicon dioxide sheet with a thickness of ∼0.5 nm. Inspired by recent successful preparations and characterizations of these 2D-silica model systems, scientists now can forge novel concepts for realistic systems, particularly by atomic-scale studies with the most powerful and advanced surface science techniques and density functional theory calculations. This Review provides a solid introduction to these recent developments, breakthroughs, and implications on ultrathin 2D-silica films, including their atomic/electronic structures, chemical modifications, atom/molecule adsorptions, and catalytic reactivity properties, which can help to stimulate further investigations and understandings of these fundamentally important 2D materials

Branching Instabilities in Rapid Fracture: Dynamics and Geometry

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.Comment: 9 pages, 11 figure

Elucidating Surface Structure with Action Spectroscopy

Surface Action Spectroscopy, a vibrational spectroscopy method developed in recent years at the Fritz Haber Institute is employed for structure determination of clean and H2O-dosed (111) magnetite surfaces. Surface structural information is revealed by using the microscopic surface vibrations as a fingerprint of the surface structure. Such vibrations involve just the topmost atomic layers, and therefore the structural information is truly surface related. Our results strongly support the view that regular Fe3O4(111)/Pt(111) is terminated by the so-called Fetet1 termination, that the biphase termination of Fe3O4(111)/Pt(111) consists of FeO and Fe3O4(111) terminated areas, and we show that the method can differentiate between different water structures in H2O-derived adsorbate layers on Fe3O4(111)/Pt(111). With this, we conclude that the method is a capable new member in the set of techniques providing crucial information to elucidate surface structures. The method does not rely on translational symmetry and can therefore also be applied to systems which are not well ordered. Even an application to rough surfaces is possible

Learning from Minimum Entropy Queries in a Large Committee Machine

In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization error decreases exponentially with the number of training examples, providing a significant improvement over the algebraic decay for random examples. The connection between entropy and generalization error in multi-layer networks is discussed, and a computationally cheap algorithm for constructing queries is suggested and analysed.Comment: 4 pages, REVTeX, multicol, epsf, two postscript figures. To appear in Physical Review E (Rapid Communications

Statistical Mechanics of Linear and Nonlinear Time-Domain Ensemble Learning

Conventional ensemble learning combines students in the space domain. In this paper, however, we combine students in the time domain and call it time-domain ensemble learning. We analyze, compare, and discuss the generalization performances regarding time-domain ensemble learning of both a linear model and a nonlinear model. Analyzing in the framework of online learning using a statistical mechanical method, we show the qualitatively different behaviors between the two models. In a linear model, the dynamical behaviors of the generalization error are monotonic. We analytically show that time-domain ensemble learning is twice as effective as conventional ensemble learning. Furthermore, the generalization error of a nonlinear model features nonmonotonic dynamical behaviors when the learning rate is small. We numerically show that the generalization performance can be improved remarkably by using this phenomenon and the divergence of students in the time domain.Comment: 11 pages, 7 figure