bluuebunny/crossref_metadata_2025_split huggingface dataset:
Index and anomaly
Authors: Bertlmann Reinhold A. 
Published: January 2010

AbstractThis chapter studies the role of anomaly in the topology of gauge theories. It shows that the anomaly also has a ‘natural’ explanation; it occurs as an obstruction in certain nontrivial bundles and it is determined completely by a topological quantity — the index. Section 11.1 discusses the relation of the single anomaly to the Atiyah–Singer index theorem. Section 11.2 describes the geometric-topological character of the non-Abelian index anomaly in the context of index theorems. Section 11.3 shows the connection between the index of the Weyl operator and the heat kernel of the Laplacian, shedding light on Fujikawa's regularization procedure. Section 11.4 presents the Atiyah–Singer index theorem for the case of YM fields. Section 11.15 introduces a special Dirac operator which is equivalent to the Wely operator, and calculates the non-Abelian anomaly, Bardeen's result, by the path integral method. It also explains the procedure of Alvarez–Gaum é — how to determine the non-Abelian anomaly by a generalized index theorem.
An Introduction to Particle Accelerators
Authors: Wilson Edmund 
Published: January 2010

Abstract
Many scientists and engineers spend their lives designing, constructing, and running accelerators, yet few universities include a study of them in their curricula. This book is a straightforward introduction used by undergraduates and postgraduate students as well as by professional staff attending the summer schools run by the big accelerator laboratories. Research physicists should read it for important background. It covers the essentials of the subject for accelerator physicists and engineers, and is at the level of the introductory courses provided by the CERN and US Accelerator schools. Its style is to give enough information to understand the subject without an excess of mathematics or theory. The text includes exercises and answers to focus the attention of the reader on the calculations necessary to design a new machine. After a chapter on the history of the accelerators, four chapters cover the dynamics of particle beams as they are guided and focused by the magnets of a synchrotron or storage ring and as they are accelerated by rf cavities. Another two chapters cover linear and non-linear effects from imperfect fields. There are chapters on synchrotron radiation, colliders, instabilities, and on future acceleration techniques. A chapter describes the applications of the ten thousand or more accelerators in the world ranging from the linear accelerators used for cancer therapy, through those used in industry and in other fields of research, to the giant ‘atom smashers’ at international particle physics laboratories. A final chapter is to stimulate new ideas for future acceleration techniques.
History of accelerators
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
This chapter is a historical account of the principal kinds of accelerators built in the last century—each with ever-increasing energy to resolve sub atomic physics with ever-increasing resolution. Starting from electrostatic accelerators, it describes the invention of the betatron or ray-transformer, linear accelerators, cyclotrons, and the synchrotrons and storage rings of today. The understanding of phase stability made synchrotrons possible. Later the invention of strong focusing replaced weak focusing and enabled considerable economies in magnet bulk. Finally, the development of superconducting magnets allowed much higher energies to be reached without increasing the ring diameter. Each of these steps played an important part in reaching higher energies. The chapter lists the many applications of accelerators in medicine, industry, and research. It also describes the principle of fixed field alternating gradient accelerators, invented in the 1950s and recently revived for a number of topical applications.
Lattices
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
The lattice described in the chapter is the periodic pattern of focusing and bending magnets that a particle experiences on each turn. Hills Equation describes the vertical and horizontal transverse oscillations of the particle. Its solution is a modified form of the harmonic oscillator. The square of the local amplitude is the product of the beam emittance and the betatron function, beta, which depends on the lattice pattern alone. Beta links to the rate of phase advance of the motion. Two-by-two transport matrices for one turn of the ring have elements that depend on the Twiss parameters, which are the beta amplitude and its derivatives together with the phase advance. They may be computed numerically by multiplying a chain of individual matrices—one for each magnetic element in the ring. The trace of the matrix defines the number of oscillations per turn, Q, which must be real for stability.
Circulating beams
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
This chapter opens with a discussion of Liouville's theorem—a conservation principle that applies to the area of phase space, usually an ellipse, occupied by a beam. In the transverse phase plane, this area—the product of displacement and divergence—is called the emittance. Emittance is strictly conserved only in the canonical coordinates, but we may consider it to be conserved at a particular energy. For a proton beam, we can define a normalised emittance invariant during acceleration to high energy by multiplying it by the Lorenz variables, beta and gamma. A proton beam's emittance shrinks during acceleration and, to economise on magnet aperture, one can design a chain of accelerators, the higher energy rings having smaller aperture. The chapter also describes how emittance and betatron frequency may be measured. Emittance of electron beams is a balance between quantum excitation and damping.
Imperfections and multipoles
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
This chapter discusses the effect of imperfections in magnetic field, gradient, and alignment using a circle diagram in which divergence, weighted by the local value of beta, is plotted against displacement. Plotting the closed orbit when distorted by a field error in this diagram leads to a relation between the amplitude and error. Random errors are discussed, as are their main sources. Azimuthal error patterns contain many Fourier components, the ones closest to the Q value are most important. Closed orbit bumps may be corrected by applying a chain of overlapping triad bumps to a series of correcting magnets around the ring. The corrections are calculated from beam position measurement at each quadrupole. The chapter also treats gradient errors and how these can stimulate resonances in the working diagram of Q(vertical) versus Q (horizontal). Chromaticity—the momentum dependence of focusing—is discussed: its theory, measurement, and correction with sextupoles.
Electrons
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
Electrons behave in the same way as protons in the magnetic guide field of a synchrotron but, being 2000 times lighter than protons, travel much closer to the velocity of light when given the same energy. They emit synchrotron radiation when bent towards the centre of a circle. This chapter describes the power spectrum of this radiation, its distribution, and the energy lost by the particle per turn. The momentum dependence of this loss causes synchrotron radiation damping that continually reduces the emittance of the beam in all three degrees of freedom. At the same time, the quantised nature of the emission stimulates a random walk excitation of the emittances. It is found that there is an emittance where damping and growth are in equilibrium. The chapter describes these physical processes and the mathematics necessary to calculate the emittance.
Cooling
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
Cooling is the way around Liouville's Theorem. The beam is sampled, particles that deviate from the central momentum or betatron amplitude of the beam are selected, and their behaviour corrected. In the stochastic method, samples contain large numbers of particles and the process can only be statistical. This was applied in the Antiproton Accumulator ring at CERN that prepared bunches for the SPS collider. This chapter describes the details of this accumulator. Other methods of cooling have been invented. Electron cooling bathes the hadron beam in an intense co-linear electron beam. The speed of the electrons matches the hadrons while equipartition of energy reduces the hadron emittance at the expense of the electron beam. Yet another method uses lasers to stimulate certain energy levels in an ion beam to mould the bunch to be mono-chromatic. The Muon collider in Chapter 11 relies on ionisation energy loss to do much the same.
Essential Quantum Mechanics
Authors: Finnis Mike 
Published: January 2010

AbstractThis chapter reviews the general concepts in quantum mechanics that are essential for the purpose of deriving models of interatomic forces in condensed matter. It assumes a familiarity with the usual material of a first course in quantum mechanics such as the Hamiltonian in operator notation, and the form of a time-independent Schrödinger equation. The chapter may serve as a guide to most of the notation used in the book, including Dirac notation. There are introductions to periodic boundary conditions, single particle Green functions, densities of states and pseudopotentials, which will be used later in the book.
Exploiting the Variational Principle
Authors: Finnis Mike 
Published: January 2010

AbstractThis chapter begins with a discussion of the ubiquitous theorem that underlies much of the theory of interatomic forces, namely the Hellmann–Feynman theorem, and its derivation from the variational principle. Examples are given, including the description of Van der Waals forces, explaining how the theorem is completely general, but only applicable when the energy functional describing the electrons has been minimized. When this condition is satisfied, the forces on the nuclei can be calculated with classical electrostatics. First and second order perturbation theories are discussed, leading to the second-order Hohenberg–Kohn–Sham functional, and for the first time deriving the errors in it. This in turn leads to the useful functional known as the Harris–Foulkes functional, and variations on it. These functionals do not require time-consuming iteration to self-consistency in the charge density, and are the basis for some simple models.
Quasielastic Neutron Scattering and Solid State Diffusion
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
The book provides an account of quasielastic neutron scattering (QENS) which has made many important contributions to the atomistic elucidation of diffusion processes in solids. The unique feature of QENS is that it probes the diffusion process on atomistic scales of space and time simultaneously. The aim of this book is to inform of the potential of QENS. Chapters 3-6 present the derivation of all equations in great details. Chapter 2 deals with neutron sources, and Chapter 7 with some experimental details of QENS. The second part addresses the expert and summarizes the scientific applications of quasielastic neutron scattering to special solid state material systems, as for example to diffusion in metals or to diffusion in solid state ionic conductors. By far the most favourable element for QENS is hydrogen: hydrogen is very mobile in metals and ceramics, so the restricted energy/time resolution of QENS is no limitation; hydrogen has a huge scattering cross section, so the limited intensity of existing neutron sources is no limitation; hydrogen leads to almost purely incoherent scattering which facilitates the theoretical treatment and interpretation of neutron scattering events appreciably.
Diffusion in solids
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
This chapter starts with a brief history of the science of diffusion. Macroscopically diffusion is characterized by various diffusion coefficients: the self-diffusion coefficient, the tracer diffusion coefficient, the chemical or Fickian diffusion coefficient, and the conductivity diffusion coefficient. Microscopically the gas, liquid-like, and solid state diffusion mechanisms are considered. Solid state diffusion is characterized by the parameters jump rate, jump vector, and coordination number. The stochastic aspects of solid state (jump) diffusion are introduced. Statistical methods (Markov and non-Markov processes) are applied to study the outcome of a sequence of jumps, i.e., the spatial/temporal development of the diffusive process. The nature of the mechanism of a single diffusive event is considered. Topics such as classical jump, phonon-assisted tunnelling, electron-restricted tunnelling, and incoherent tunnelling types, also called hopping, are introduced.
6 Coherent quasielastic neutron scattering
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
QENS on diffusing atoms with a sizable coherent neutron scattering cross section yields information on interference effects and correlated motion contained in the coherent scattering function S(Q, ω). As an introduction to this complex situation, this chapter begins by describing first coherent elastic scattering due to short-range order. The structure factor SSROM(Q) for short-range order of a lattice fluid can be expressed in terms of Cowley's short-range order parameters. For a diffusing lattice fluid, coherent QENS consists of a single Lorentzian: its intensity is given by SSRO and its width Λ and thus the collective diffusion coefficient Dc exhibit the so-called de Gennes narrowing: at the Q value where SSRO has a maximum, Λ and Dc exhibit a minimum. Furthermore, elastic distortion scattering (Huang scattering) and quasielastic scattering on distortions combined with diffusion is dealt with.
Intercalation compounds
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
This chapter discusses the diffusional dynamics in intercalation compounds of graphite with alkali metals. These form two classes: stage 1 compounds like C6Li, and stage 2 compounds like C24Rb. HNO3 has also been intercalated in graphite and studied by QENS. All these systems exhibit interesting transitions between commensurate and incommensurate structures which influences the diffusivity. A two-dimensional Chudley–Elliott model is applied. A few studies in the literature deal with ionic compounds with channels or layers. An example is the Chevrel phase Ni2Mo6S8: the Q dependence of the linewidths establishes fast long-range motion of the intercalated Ni2+ ions.
Quantum-dot edge-emitting lasers
Authors: Ustinov Victor M. , Zhukov Alexey E. , Egorov Anton Yu. , Maleev Nikolai A. 
Published: January 2010

AbstractThis chapter provides an historical overview of the development of quantum dot edge-emitting lasers from their first demonstration to the present status. Issues of gain saturation and temperature instability in initial lasers based on a single plane of self-organized quantum dots are discussed. Several approaches to improve the performance of InGaAs quantum dot lasers are discussed in detail: increase of the QD density of states by stacking of quantum dots; use of matrix material having a higher bandgap energy; seeding of quantum dots to increase their density; and sub-monolayer formation of quantum dots to increase their density and improve uniformity. At the end of the chapter, experimental results for representative quantum-dot lasers grown on non-GaAs substrates are presented.
Historical developments
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter provides a historical introduction to X-ray dynamical diffraction. It starts with an account of Ewald's thesis on the dispersion of light and of the famous experiment of the diffraction of X-rays by crystals by M. Laue, W. Friedrich, and P. Knipping. The successive steps in the development of the theory of X-ray diffraction are then summarized: Laue's and Darwin's geometrical theories; Darwin's, Ewald's, and Laue's dynamical theories; early experimental proofs, the notion of extinction and the mosaic crystal model, observation in the fifties and sixties of the fundamental properties of the X-ray wavefields in crystals (anomalous absorption and the Borrmann effect, double refraction, Pendellösung, bent trajectories in deformed crystals), extension of the dynamical theory to the case of deformed crystals, modern applications for the characterization of crystal defects and X-ray optics for synchrotron radiation.
2 Properties of the electromagnetic field— propagation and scattering
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter gives a theoretical description of the basic properties of electromagnetic radiation. Maxwell's equations are first reviewed; the expressions of electrodynamic potentials in the vacuum and in polarized media are then given. The classic theory of the scattering of X-rays by electrons is described (Thomson scattering). The dielectric susceptibility (polarizability) of matter for X-rays and the Fourier expansions of its real and imaginary parts in a periodic medium (index of refraction, atomic scattering factor, and absorption coefficient) are discussed. A detailed account of Ewald's dispersion theory that is at the base of Ewald's dynamical theory is then presented. The propagation equation of X-rays, which is used throughout the book, is derived from Maxwell's equations according to Laue's basic assumptions. The last part of the chapter is devoted to specular reflection and Fresnel relations.
7 Intensities of plane waves in the reflection geometry
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter calculates the reflected intensity for the reflection, or Bragg, geometry and an incident plane wave. Both the cases of very thick and thin crystals are considered. In each case the boundary conditions are given, the reflectivity and the integrated intensity are determined for absorbing crystals. The shape of the rocking curves is discussed as a function of the absorption coefficient and the ratio between the real and imaginary parts of the index of refraction. The standing wave pattern formed at the surface of the crystal due to the interference of the incident and reflected waves is calculated.
9 n-beam dynamical diffraction
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter is concerned with the cases where several reciprocal lattice points are close to the Ewald sphere and several waves simultaneously excited (multiple-beam or n-beam diffraction). The principle of Renninger-scans is given and it is shown how the solutions of the fundamental equations of the dynamical theory are obtained in the general case. The particular case of the three-beam coplanar case is then considered. One section in this chapter is devoted to the determination of absolute phases using n-beam absorption and its application for structure determinations. The last section explains the enhancement of the anomalous absorption effect (super-Borrmann effect) in specific three-beam cases.
11 Spherical-wave dynamical theory: Ii. Takagi’s theory
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter describes Takagi's dynamical theory of the diffraction of incident spherical waves. It considers the crystal wave to be developed as a sum of modulated waves. The fundamental equations are generalized as a set of partial differential equations (Takagi's equations). Their solutions for an incident spherical wave are first obtained by the method of integral equations for both the transmission and reflection geometries. The hyperbolic nature of Takagi's equations is shown and their solution derived using the method of Riemann functions for a point source located on the entrance surface or away from the incident surface. An appendix describes the properties of hyperbolic partial differential equations.
X-ray optics
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter is devoted to the applications of dynamical diffraction to X-ray optics. After a brief description of X-ray sources (tubes and synchrotron radiation), it gives the principle of the various types of monochromators and of multiple-crystal beam conditioning. It then describes the different devices for beam focusing optics (mirrors, multilayers, curved crystals, Fresnel zone plates, Bragg–Fresnel lenses, refractive lenses, and X-ray waveguides). The last two sections concern the principle and applications of X-ray interferometers (moiré topography, measurement of indices of refraction and anomalous dispersion factors, metrology) and X-ray phase contrast imaging.
Scaling the size of a pendulum
Authors: Matthys Robert James 
Published: January 2010

Abstract
Making a pendulum bigger or smaller involves more than just a linear scaling up or down of the pendulum's dimensions. If you want to make a larger or smaller pendulum than the one you have now, how should the dimensions change? It turns out that not all of the dimensions should change linearly with pendulum length. The free length of the suspension spring should be scaled directly proportional to the pendulum's length. James has shown that the vertical distance from the pendulum's axis of rotation up to the free top edge of the suspension spring is directly proportional to the spring's thickness. So the spring's thickness is then scaled directly proportional to the suspension spring's length (and incidentally, also directly proportional to the pendulum's length also). The suspension spring's width is adjusted to keep the static and bending stresses approximately constant for all pendulum lengths.
Transient response of a pendulum to temperature change
Authors: Matthys Robert James 
Published: January 2010

Abstract
This chapter describes the transient response of a pendulum to a step change in temperature and explains how to eliminate the resulting permanent time error. The permanent time error can be zeroed out by a combination of moving the bob's support point to up near the top of the bob and moving the temperature compensator to a position down below the bob. The pendulum rod must have a little extra length to permit mounting the temperature compensator down below the bob. Supporting the bob at a point above the bob's center reduces the permanent time error, while supporting the bob at a point below the bob's center increases the permanent time error. Two-thirds of the permanent time error can still be eliminated just by moving the temperature compensator down to a position 2-3 inches below the bob. The spacer used to fill the compensator's former space inside the bob should be of the same material as the pendulum rod, so as not to disturb the pendulum's temperature compensation.
Variations on a Riefler bob shape
Authors: Matthys Robert James 
Published: January 2010

Abstract
Riefler's bob shape consists of two truncated cones, back-to-back. It is a shape with low air drag, and works well inside the clock case, where front-to-back space is frequently limited. A 1988 study on the air drag losses of various bob shapes found that the football and oblate spheroid shapes had even less drag than Riefler's two truncated cones. However, they require more front-to-back space, assuming equal volume, and are harder to make. Reducing a bob's air drag is worthwhile for two reasons. First, it reduces the weight needed to drive the escapement's gear train, which in turn reduces the wear on the gearing and the escapement's pallets. Second, the less you disturb a pendulum, the more accurate it becomes. For the lowest air drag, Riefler bobs should have an edge angle of 50-75 degrees and a diameter-to-thickness ratio of 2. Such bobs need 2% less drive force than a sphere of equal volume. This chapter also includes information on bob aerodynamics.