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# Analytical, Approximate-Analytical and Numerical Methods in the Design of Energy Analyzers

- 1st Edition, Volume 192 - October 22, 2015
- Editor: Peter W. Hawkes
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 8 0 2 2 5 2 - 8
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 2 5 1 8 - 5

Advances in Imaging and Electron Physics merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The ser… Read more

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Advances in Imaging and Electron Physics

merges two long-running serials,*Advances in Electronics and Electron Physics*and

*Advances in Optical and Electron Microscopy*.

The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science, and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.

- Contains contributions from leading authorities on the subject matter
- Informs and updates on all the latest developments in the field of imaging and electron physics
- Provides practitioners interested in microscopy, optics, image processing, mathematical morphology, electromagnetic fields, electron, and ion emission with a valuable resource
- Features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science, and digital image processing

Physicists, electrical engineers and applied mathematicians in all branches of image processing and microscopy as well as electron physics in general.

- Foreword
- Preface
- Future Contributions
- Chapter One: Energy Analysis of Charged Particle Flows
- Abstract
- 1 Basic Parameters
- 2 Main Types of Energy Analyzers
- 3 Advanced Energy Analyzers

- Chapter Two: Analytical Design Methods
- Abstract
- 1 Focusing Properties of Electrostatic Mirrors with Ideal Cylindrical Fields
- 2 Focusing Properties of Electrostatic Mirrors with Ideal Hyperbolic Fields

- Chapter Three: Approximate-Analytical Method of Calculating the Charged Particle Trajectories in Electrostatic Fields
- Abstract
- 1 Integro-Differential Equation of Charged Particle Trajectories in the Electrostatic Hexapole-Cylindrical Field U(r,z) = lnr + γU
_{h}(r,z) - 2 Calculation of Charged Particle Trajectories in the Electrostatic Hexapole-Cylindrical Field U(r,z) = lnr + γU
_{h}(r,z) - 3 Electron-Optical Properties of the Hexapole-Cylindrical Energy Analyzer with End-Face Electrodes (γ = − 1)
- 4 Electron-Optical Properties of the Hexapole-Cylindrical Energy Analyzer with γ = 1
- 5 Analysis of Electron-Optical Characteristics of the Energy Analyzer with the Field Distribution U (r,z) = lnr−U
_{h}(r,z)

- Chapter Four: Numerical Methods in the Design of Energy Analyzers
- Abstract
- 1 Methods for Numerical Simulation of Electrostatic Fields
- 2 Main Approaches to Solving the Problems of Potential Theory Using BEM
- 3 General Techniques for Calculating the Integrals of Functions with Singularities
- 4 Using BEM to Solve the Interior Dirichlet Problem
- 5 Exterior Dirichlet Problem and Calculating the Integrals of Functions with Singularities
- 6 Numerical Calculation of Potential Gradient
- 7 Trajectory Analysis Techniques in Corpuscular-Optical Systems
- 8 Correlation Method for Seeking the Conditions of Higher-Order Angular Focusing
- 9 Examples of Numerical Simulation of Energy Analyzers

- Appendices
- Appendix 1 Some Intermediate Mathematical Calculations Relevant to Chapter 3
- Appendix 2 The Relationship Between the Output Parameters of the Energy Analyzers Considered in Chapter 3 and Initial and Boundary Conditions in Different Modes
- Appendix 3 Boundary Element Method (BEM) for Calculating the Potential and Its Gradient in Planar Systems

- References
- Contents of Volumes 151-191
- Index
- Analytical, Approximate-Analytical, and Numerical Methods for Design of Energy Analyzers
- Brief Annotation

- No. of pages: 224
- Language: English
- Edition: 1
- Volume: 192
- Published: October 22, 2015
- Imprint: Academic Press
- Hardback ISBN: 9780128022528
- eBook ISBN: 9780128025185

PH

### Peter W. Hawkes

Peter Hawkes obtained his M.A. and Ph.D (and later, Sc.D.) from the University of Cambridge, where he subsequently held Fellowships of Peterhouse and of Churchill College. From 1959 – 1975, he worked in the electron microscope section of the Cavendish Laboratory in Cambridge, after which he joined the CNRS Laboratory of Electron Optics in Toulouse, of which he was Director in 1987. He was Founder-President of the European Microscopy Society and is a Fellow of the Microscopy and Optical Societies of America. He is a member of the editorial boards of several microscopy journals and serial editor of Advances in Electron Optics.

Affiliations and expertise

Founder-President of the European Microscopy Society and Fellow, Microscopy and Optical Societies of America; member of the editorial boards of several microscopy journals and Serial Editor, Advances in Electron Optics, FranceRead

*Analytical, Approximate-Analytical and Numerical Methods in the Design of Energy Analyzers*on ScienceDirect