Charged Particle Optics Theory: An Introduction

Description

Charged Particle Optics Theory: An Introduction identifies the most important concepts of charged particle optics theory, and derives each mathematically from the first principles of physics. Assuming an advanced undergraduate-level understanding of calculus, this book follows a logical progression, with each concept building upon the preceding one. Beginning with a non-mathematical survey of the optical nature of a charged particle beam, the text: Discusses both geometrical and wave optics, as well as the correspondence between them Describes the two-body scattering problem, which is essential to the interaction of a fast charged particle with matter Introduces electron emission as a practical consequence of quantum mechanics Addresses the Fourier transform and the linear second-order differential equation Includes problems to amplify and fill in the theoretical details, with solutions presented separately Charged Particle Optics Theory: An Introduction makes an ideal textbook as well as a convenient reference on the theoretical origins of the optics of charged particle beams. It is intended to prepare the reader to understand the large body of published research in this mature field, with the end result translated immediately to practical application. Content: ContentsPrefaceIntroduction: The Optical Nature of a Charged Particle BeamGeometrical OpticsRelativistic Classical MechanicsHamilton's Principle of Least ActionThe Hamiltonian Function and Energy ConservationMechanical Analog of Fermat's PrincipleExact Trajectory Equation for a Single ParticleConservation LawsThe Lagrange InvariantLiouville's Theorem and Brightness ConservationGeneral Curvilinear AxisEquation of Motion in Terms of Transverse Coordinates and SlopesNatural UnitsAxial SymmetryExact Equations of Motion for Axially Symmetric FieldsParaxial Approximation, Gaussian OpticsSeries Solution for the General Ray EquationSpace ChargeThe Primary Geometrical AberrationsSpherical AberrationField AberrationsChromatic AberrationIntensity Point Spread FunctionStochastic Coulomb ScatteringMonte Carlo SimulationAnalytical Approximation by Markov's Method of Random FlightsHamilton-Jacobi TheoryCanonical TransformationsApplications of Hamilton-Jacobi TheoryHamilton-Jacobi Theory and Geometrical OpticsWave OpticsQuantum Mechanical Description of Particle MotionThe Postulates of Quantum MechanicsParticle Motion in a Field-Free SpaceWave Packet Propagation and the Heisenberg Uncertainty PrincipleThe Quantum Mechanical Analog of Fermat's Principle for Matter WavesParticle Motion in a General Electromagnetic PotentialPath Integral Approach for the Time-Dependent Wave FunctionSeries Solution for a Particle in a General Electromagnetic PotentialQuantum Interference Effects in Electromagnetic PotentialsThe Klein-Gordon Equation and the Covariant Wave FunctionPhysical Interpretation of the Wave Function and Its Practical ApplicationDiffractionThe Fresnel-Kirchhoff RelationThe Fresnel and Fraunhofer ApproximationsAmplitude in the Gaussian Image PlaneAmplitude in the Diffraction PlaneOptical Transformation for a General Imaging System with Coherent IlluminationOptical Transformation for a General Imaging System with Incoherent IlluminationThe Wave Front Aberration FunctionRelationship between Diffraction and the Heisenberg Uncertainty PrincipleParticle ScatteringClassical Particle KinematicsScattering Cross Section and Classical ScatteringIntegral Expression of Schrodinger's EquationGreen's Function Solution for Elastic ScatteringPerturbation TheoryPerturbation Solution for Elastic ScatteringInelastic Scattering of a Particle by a Target AtomSlowing of a Charged Particle in a Dielectric MediumSmall Angle Plural Scattering of Fast ElectronsElectron Emission from SolidsThe Image ForceThe Incident Current DensityThermionic EmissionField EmissionEmission with Elevated Temperature and FieldSpace Charge Limited EmissionAppendix A: The Fourier TransformAppendix B: Linear Second-Order Differential EquationBibliographyIndex