Field Precision LLC Title

Virtual anode formation Charged Particle Beams

Stanley Humphries
Professor Emeritus
University of New Mexico

Welcome to the Charged Particle Beams download site. The text was originally published by John Wiley and Sons (ISBN 0-471-60014-8, QC786.H86) in 1990.The unabridged book with all illustrations has been converted to PDF format. The conversion was supported by Field Precision LLC. Please send errata and comments to me at

-Stan Humphries

NEW A low-cost printed edition of Charged Particle Beams is now available from Dover Press (0-486-49868-9). The price is $39.95. You can order online at


The copyright (US TX 2 802 132) is held by Stanley Humphries, Jr. The author grants all persons the right to download a single copy of the book in digital format for use on computers and electronic readers. Other modes of reproduction, translation and distribution of any part of this work are unlawful. The PDF file may not be distributed to other individuals or posted on the Internet for download. Any links should be made to this page rather than directly to the download file. Extracts from the book may not be used in other works without permission from the author (

Charged Particle Beams (34.4 MB).

Table of contents

1. Introduction
1.1. Charged particle beams
1.2. Methods and organization
1.3. Single-particle dynamics
2. Phase Space Description of Charged Particle Beams
2.1. Particle trajectories in phase space
2.2. Distribution functions
2.3. Numerical calculation of particle orbits with beam-generated forces
2.4. Conservation of phase-space volume
2.5. Density and average velocity
2.6. Maxwell distribution
2.7. Collisionless Boltzmann equation
2.8. Charge and current density
2.9. Computer simulations
2.10. Moment equations
2.11. Pressure force in collisionless distributions
2.12. Relativistic particle distributions
3. Introduction to Beam Emittance
3.1. Laminar and non-laminar beams
3.2. Emittance
3.3. Measurement of emittance
3.4. Coupled beam distributions, longitudinal emittance, normalized emittance, and brightness
3.5 Emittance force
3.6. Non-laminar beams in drift regions
3.7. Non-laminar beams in linear focusing systems
3.8. Compression and expansion of non-laminar beams
4. Beam Emittance - Advanced Topics
4.1. Linear transformations of elliptical distributions
4.2. Transport parameters from particle orbit theory
4.3. Beam matching
4.4. Non-linear focusing systems
4.5. Emittance in storage rings
4.6. Beam cooling
5. Introduction to Beam-generated Forces
5.1. Electric and magnetic fields of beams
5.2. One-dimensional Child law for non-relativistic particles
5.3. Longitudinal transport limits for magnetically-confined electron beams
5.4. Space-charge expansion of a drifting beam
5.5. Transverse forces in relativistic beams
6. Beam-generated Forces - Advanced Topics
6.1. Space-charge-limited flow with an initial injection energy
6.2. Space-charge-limited flow from a thermionic cathode
6.3. Space-charge-limited flow in spherical geometry
6.4. Bipolar flow
6.5. Space-charge-limited flow of relativistic electrons
6.6. One-dimensional self-consistent equilibrium
6.7. KV distribution
7. Electron and Ion Guns
7.1. Pierce method for gun design
7.2. Medium-perveance guns
7.3. High-perveance guns and ray tracing codes
7.4. High-current electron sources
7.5. Extraction of ions at a free plasma boundary
7.6. Plasma ion sources
7.7. Charged-particle extraction from grid-controlled plasmas
7.8. Ion extractors
8. High-power Pulsed Electron and Ion Diodes
8.1. Motion of electrons in crossed electric and magnetic fields
8.2. Pinched electron beam diodes
8.3. Electron diodes with strong applied magnetic fields
8.4. Magnetic insulation of high power transmission lines
8.5. Plasma erosion
8.6. Reflex triode
8.7. Low-impedance reflex triode
8.8. Magnetically-insulated ion diode
8.9. Ion flow enhancement in magnetically-insulated diodes
9. Paraxial Beam Transport with Space-charge
9.1. Envelope equation for sheet beams
9.2. Paraxial ray equation
9.3. Envelope equation in a quadrupole lens array
9.4. Limiting current for paraxial beams
9.5. Multi-beam ion transport
9.6. Longitudinal space-charge limits in RF accelerators and induction linacs
10. High-current Electron Beam Transport under Vacuum
10.1. Motion of electrons through a magnetic cusp
10.2. Propagation of beams from an immersed cathode
10.3. Brillouin equilibrium of a cylindrical electron beam
10.4. Interaction of electrons with matter
10.5. Foil focusing of relativistic electron beams
10.6. Wall-charge and return-current for a beam in a pipe
10.7. Drifts of electron beams in a solenoidal field
10.8. Guiding electron beams with solenoidal fields
10.9. Electron beam transport in magnetic cusps
11. Ion Beam Neutralization
11.1. Neutralization by comoving electrons
11.2. Transverse neutralization
11.3. Current neutralization in vacuum
11.4. Focal limits for neutralized ion beams
11.5. Acceleration and transport of neutralized ion beams
12. Electron Beams in Plasmas
12.1. Space-charge neutralization in equilibrium plasmas
12.2. Oscillations of an un-magnetized plasma
12.3. Oscillations of a neutralized electron beam
12.4 Injection of a pulsed electron beam into a plasma
12.5. Magnetic skin depth
12.6. Return current in a resistive plasma
12.7. Limiting current for neutralized electron beams
12.8. Bennett equilibrium
12.9. Propagation in low-density plasmas and weakly-ionized gases
13. Transverse Instabilities
13.1. Instabilities of space-charge-dominated beams in periodic focusing systems
13.2. Betatron waves on a filamentary beam
13.3. Frictional forces and phase mixing
13.4. Transverse resonant modes
13.5. Beam breakup instability
13.6. Transverse resistive wall instability
13.7. Hose instability of an electron beam in an ion channel
13.8. Resistive hose instability
13.9. Filamentation instability of neutralized electron beams
14. Longitudinal Instabilities
14.1. Two-stream instability
14.2. Beam-generated axial electric fields
14.3. Negative mass instability
14.4. Longitudinal resistive wall instability
15. Generation of Radiation with Electron Beams
15.1. Inverse diode
15.2. Driving resonant cavities with electron beams
15.3. Longitudinal beam bunching
15.4. Klystron
15.5. Traveling-wave tube
15.6. Magnetron
15.7. Mechanism of the free-electron laser
15.8. Phase dynamics in the free-electron laser