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Optics of Charged Particles - 1st Edition - ISBN: 9780127621302, 9780323156783

Optics of Charged Particles

1st Edition

Author: Hermann Wollnik
eBook ISBN: 9780323156783
Imprint: Academic Press
Published Date: 18th March 1987
Page Count: 304
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Optics of Charged Particles describes how charged particles move in the main and fringing fields of magnetic or electrostatic dipoles, quadrupoles, and hexapoles using the same type of formulation and consistent nomenclature throughout.

This book not only describes the particle trajectories and beam shapes, but also provides guidelines for designing particle optical instruments. The topics discussed include Gaussian optics and transfer matrices, general relations for the motion of charged particles in electromagnetic fields, and quadrupole lenses. The sector field lenses, charged particle beams and phase space, and particle beams in periodic structures are also elaborated. This text likewise considers the fringing fields, image aberrations, and design of particle spectrometers and beam guide lines.

This publication is suitable for undergraduate students in physics and mathematics.

Table of Contents


1 Gaussian Optics and Transfer Matrices

1.1 Method of Transfer Matrices

1.2 Transport through an Optical System of One Thin Lens

1.3 Transport through a General Optical System

1.4 Examples for the Use of Transfer Matrices


2 General Relations for the Motion of Charged Particles in Electromagnetic Fields

2.1 Energy, Velocity, and Mass of Accelerated Particles

2.2 Forces on Charged Particles in Magnetic and Electrostatic Fields

2.3 Description of a Chromatic Particle Bundle

2.4 Refractive Index of the Electromagnetic Field

2.5 Euler-Lagrange Equations



3 Quadrupole Lenses

3.1 Particle Trajectories in Quadrupole Lenses

3.2 Design of Quadrupole Multiplets

3.3 Properties of Thin-Lens Quadrupole Multiplets

3.4 How to Calculate Quadrupole Multiplets Numerically

Appendix: Potential Distribution Between Hyperbolic Electrodes


4 Sector Field Lenses

4.1 Homogeneous Magnetic Sector Fields

4.2 Inhomogeneous Magnetic Sector Fields Formed by Inclined Planar Pole Faces (Wedge Magnets)

4.3 Radially Inhomogeneous Sector Fields Formed by Conical Pole Faces or Toroidal Electrodes

4.4 Particle Flight Times in Radially Inhomogeneous Sector Fields, Quadrupoles, and Field-Free Regions



5 Charged Particle Beams and Phase Space

5.1 Liouville's Theorem and First-Order Transfer Matrices

5.2 Phase-Space Areas of Particle Beams Passing through Optical Systems

5.3 Beam Envelopes

5.4 Positions and Sizes of Envelope Minima

5.5 A Minimal Size Beam Envelope at a Postulated Location

5.6 Liouville's Theorem and Its Application to Wide-Angle Beams

5.7 Beams with Space Charge


6 Particle Beams in Periodic Structures

6.1 Single-Particle Trajectories and Beam Envelopes

6.2 Rings of Unit Cells


7 Fringing Fields

7.1 Particle Trajectories in Fringing Fields of Dipole Magnets

7.2 Particle Trajectories in Fringing Fields of Electrostatic Deflectors

7.3 Particle Trajectories in Fringing Fields of Quadrupole Lenses


8 Image Aberrations

8.1 Systematics of Image Aberrations

8.2 Origin of Image Aberrations

8.3 Relations Between Coefficients of Equation (8.2) Due to the Condition of Symplecticity

8.4 Image Aberations of nth Order

Appendix: Coefficients of Image Aberrations of nth Order


9 Design of Particle Spectrometers and Beam Guide Lines

9.1 Dispersion and Resolving Power of Multifield Particle Spectrometers

9.2 An Optical Qx Value for Particle Spectrometers

9.3 A Q1 Value for Time-of-Flight Particle Spectrometers

9.4 Correction of Image Aberrations




No. of pages:
© Academic Press 1987
18th March 1987
Academic Press
eBook ISBN:

About the Author

Hermann Wollnik

Professor Hermann Wollnik’s work has taken him around the world, and includes positions at the Los Alamos and Oak Ridge National Laboratories in the USA, the KEK/RIKEN research center in Tokyo, Japan, and the GSI research center in Darmstadt, Germany. After retiring from Justus Liebig University in Giessen, Germany in 2001, Professor Wollnik took up a position as a professor at the New Mexico State University in Las Cruces, USA in 2002. Additionally, he is a visiting scientist at the RIKEN research center in Tokyo, and since, 2012 has been a visiting professor at the KEK research institute in Tokyo for approximately 4 months every year. Professor Wollnik’s main scientific work has concentrated on the design, building and operation of ion-optical instruments for the mass analysis of short-lived nuclei. Knowing these masses is of key importance in understanding how elements were formed in our universe. Essential for this work was the idea and the design of energy-isochronous time-of flight mass spectrographs, the development of which he started in the mid-1970s.

Affiliations and Expertise

New Mexico State University in Las Cruces, USA

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