Charged Particle Optics

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This wikibook will try to explain principles of charged particle optics.

Charged particle usually means ion or electron. Geometrical charged particle optics describes controlling of charged particle trajectories in electric / magnetic fields in order to design some useful devices.

Sample charged particle device are: electron tubes (for example cathode ray tube), ion implanters, charged particle accelerators (the biggest one is famous LHC), numerous electron microscopes, electron spectrometers, electron guns, electron welding machines, some advanced 3D printers, which use electron beam to melt metal powder.

Design of modern charged particle devices requires also focusing on computational techniques, so this book will try to describe computer techniques.

There are some simulation software. These applications are mainly commercial products, however there are some free alternatives.



available at:

keywords: electron optics charged particle optics

There are quite a lot texbooks about this subject. Which book is good - it depends. Here there is sample catalogue of books. There are few areas of interest.

Very general and introductory:

  1. Martin Berz, Kyoko Makino, Weishi Wan, "Introduction to beam physics", CRC Press, 2014

Electron microscopy, spectroscopy etc.

  1. Hawkes, Kasper, "Principles of Electron Optics", Academy Press, 1994
  2. Helmut Liebl, "Aplied Charged Particle Optics", Springer Verlag, Berlin Heidelberg, 2008
  3. D.W.O. Heddle, "Electrostatic Lens Systems", IOP Publishing Ltd, 2000 (introduction to electrostatic lens)
  4. Miklos Szilagyi, "Electron and Ion Optics", Springer US, 1988 (many advanced concepts - optimization etc.)
  5. Harald Rose, "Geometrical Charged Particle Optics", Springer (very advanced and serious)
  6. Jon Orloff (ed.), "Handbook of Charged Particle Optics", CRC Press, 2009 (mainly about SEM/FIB techniques, a lot of references to other publications)

Free courses[edit]

  1. CERN Accelerator School
  2. US Particle Accelerator School

Optics of single lenses[edit]

Motion of charged particle in electric / magnetic field[edit]


The most "brute - force" method of investigating properties of charged particle lens is to calculate charged particle trajectory during passing this lens.

We must "only" know the mathematical model of particle dynamics and some computational methods. Nowadays calculations are done by computer programs, which often simplifies development process.

The equations of particle dynamics can have two forms:

  1. Newton equations
  2. Hamilton equations

This equation enables us to solve single particle trajectory. In fact, there are often repulsive forces between particles. This problem will be described in "Collective Effects" Chapter. However, when current density is low, this problem is not important.

Newton Equations[edit]

Hamilton Equations[edit]

General - purpose charged particle trackers[edit]

There are few computer programs, which can calculate charged particle trajectory in electric / magnetic fields.

The most known is SIMION.

Determination of electric / magnetic fields[edit]

Optics of simple lens systems[edit]


Transfer map method[edit]

Sample devices[edit]

Collective effects[edit]