Advances in Imaging and Electron Physics

Advances in Imaging and Electron Physics, 1st Edition

Selected Problems of Computational Charged Particle Optics

Advances in Imaging and Electron Physics, 1st Edition,Dmitry Greenfield,Mikhael Monastyrskii,ISBN9780123747174

Advances in Imaging and Electron Physics


P Hawkes   

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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. This 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.

This monograph summarizes the authors' knowledge and experience acquired over many years in their work on computational charged particle optics. Its main message is that even in this era of powerful computers with a multitude of general-purpose and problem-oriented programs, asymptotic analysis based on perturbation theory remains one of the most effective tools to penetrate deeply into the essence of the problem in question.


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

Information about this author is currently not available.
Information about this author is currently not available.

Advances in Imaging and Electron Physics, 1st Edition

Chapter 1. Integral equations method in electrostatics
1.1. Statement of the problem
1.2. Boundary surface approximation
1.3. Surface charge density approximation
1.4. Interface boundary conditions for dielectric materials
1.5 Reducing the integral equations to the finite-dimensional linear equations system
1.6. Accuracy benchmarks for numerical solving the 3D electrostatic problems
1.7. More complicated examples of 3D field simulation
1.8 The cases of planar and axial symmetries
1.9 Calculation of potential and its derivatives near the boundary
1.10. Acceleration of field calculation. Finite-difference meshes and calculation domain decomposition
1.11. Microscopic and averaged fields of periodic structures

Chapter 2. Surface charge singularities near irregular surface points
2.1. Two-faced conductive wedge in vacuum
2.2. Two-faced conductive wedge in the presence of dielectrics
2.3. The transfer matrix method
2.4. The case of pure dielectric vertex
2.5. Upper boundaries for the singularity index in 2D case
2.6. Variational approach to the spectral problem
2.7. Three-dimensional corners
2.8. Variational method in the case of dielectrics
2.9. Reduction to the 2D case
2.10. On-rib singularities near three-dimensional corner
2.11. The cases allowing separation of variables
2.12. Numerical solution of the Beltrami-Laplace spectral problem
2.13. Cubical and prism corners

Chapter 3. Geometry perturbations
3.1. Integral variational equations and conjugate integral equation for the Green function
3.2. 3D perturbations in axisymmetric systems
3.3 Some examples of 3D perturbations in axisymmetric systems
3.4. 3D perturbations in planar systems
3.5. Locally strong 3D perturbations in axisymmetric systems
3.6. 3D fringe fields in planar systems

Chapter 4. Some aspects of magnetic field simulation
4.1. Vector and scalar potential approaches
4.2. Direct integration over the current contours
4.3. The current contours in the presence of materials with constant permeability
4.4. Variational principle in three-dimensional, planar, and axisymmetric cases
4.5. Finite-element modeling of magnetic systems with saturable materials
4.6. Second-order FEM and the use of curvilinear elements
4.7. Magnetic superelements
4.8. The boundary element approach in magnetostatics
4.9. Hybrid computational methods

Chapter 5. Aberration approach and the tau-variation technique
5.1. A brief excursion to the history of aberration theory
5.2. The essence of the tau-variation technique
5.3. The tau-variation equations in tensor form
5.4. Arrival time variations and contact transformation
5.5. Jump condition for aberration coefficients
5.6. Multiple principal trajectories approach
5.7. Tolerance analysis using the aberration theory
5.8. Tracking technique
5.9. Charged particle scattering

Chapter 6. Space charge in charged particle bunches
6.1. Self-consistent simulation of thermionic electron guns
6.2. Cold-cathode approximation: semi-analytical approach
6.3. Coulomb field in short bunches. The technique of tree-type pre-ordering
6.4. Exclusion of the external field in space charge problems
6.5. Some examples of ion beam simulation

Chapter 7. General properties of emission-imaging systems
7.1. Charged particle density transformations and electron image
7.2. Spatial/temporal spread function. Isoplanatism condition
7.3. Modulation and phase transfer functions (MTF and PTF). Spatial and temporal resolution

Chapter 8. Static and time-analyzing image tubes with axial symmetry
8.1. Spatial aberrations of the electron image formed by electrostatic systems
8.2. Temporal aberrations in streak image tubes
8.3. High-frequency asymptotics of OTF in image tubes
8.4. Examples of the spread functions and OTF in the image tubes
8.5. The boundary-layer effect in cathode lenses and electron mirrors

Chapter 9. Spatial and temporal focusing of photoelectron bunches in time-dependent electric fields
9.1. Two different jobs that ultrashort electron bunches can do
9.2. The master equation of first-order temporal focusing
9.3. Moving potential well as a simple example of temporal focusing
9.4. Thin temporal lens approximation
9.5. Second-order aberrations and quantum-mechanical limitations
9.6. Approximate estimation of the space charge effects contribution
9.7. Simulation of a photoelectron gun with time-dependent electric field and some experimental results

Appendix 1. Some Gauss quadrature formulas
Appendix 2. Numerical integration of the Green functions with Coulomb singularities in the coincidence limit
Appendix 3. First variation of a functional upon the equality-type operator constraints (R.P. Fedorenko’ variational scheme)
Appendix 4. Jump condition for variations of the ordinary differential equations with non-smooth right part
Appendix 5. Some general properties of linear systems
Appendix 6. The probability density transformations
Appendix 7. The multidimensional stationary phase method

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