Fundamentals of Charged Particle Transport in Gases and Condensed Matter: 1st Edition (Hardback) book cover

Fundamentals of Charged Particle Transport in Gases and Condensed Matter

1st Edition

By Robert Robson, Ronald White, Malte Hildebrandt

CRC Press

400 pages | 74 B/W Illus.

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Hardback: 9781498736367
pub: 2017-09-12
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This book offers a comprehensive and cohesive overview of transport processes associated with all kinds of charged particles, including electrons, ions, positrons, and muons, in both gases and condensed matter. The emphasis is on fundamental physics, linking experiment, theory and applications. In particular, the authors discuss:

  • The kinetic theory of gases, from the traditional Boltzmann equation to modern generalizations
  • A complementary approach: Maxwell’s equations of change and fluid modeling
  • Calculation of ion-atom scattering cross sections
  • Extension to soft condensed matter, amorphous materials
  • Applications: drift tube experiments, including the Franck-Hertz experiment, modeling plasma processing devices, muon catalysed fusion, positron emission tomography, gaseous radiation detectors

Straightforward, physically-based arguments are used wherever possible to complement mathematical rigor.

Robert Robson has held professorial positions in Japan, the USA and Australia, and was an Alexander von Humboldt Fellow at several universities in Germany. He is a Fellow of the American Physical Society.

Ronald White is Professor of Physics and Head of Physical Sciences at James Cook University, Australia.

Malte Hildebrandt is Head of the Detector Group in the Laboratory of Particle Physics at the Paul Scherrer Institut, Switzerland.

Table of Contents


Boltzmann’s equation

Solving Boltzmann’s equation

Experiment and simulation

About this book


Basic theoretical concepts: Phase and configuration space


Phase space, kinetic equation

Kinetic equations for a mixture

Moment equations

Concluding remarks

Boltzmann collision integral, H-theorem and Fokker-Planck equation

Classical collision dynamics

Differential cross section

Boltzmann collision integral

Simple gas

Fokker-Planck kinetic equation

Concluding remarks

Interaction potentials and cross sections


Classical scattering theory

Inverse fourth-power law potential

Realistic interaction potentials

Calculation of cross sections for a general interaction potential

Cross sections for specific interaction potentials

Concluding remarks

Kinetic equations for dilute particles in gases

Low density charged particles in gases


Collision term for extremes of mass ratio

Inelastic collisions

Non-conservative, reactive collisions

Two-term kinetic equations for a Lorentz gas

Concluding remarks

Charged particles in condensed matter

Charge carriers in crystalline semiconductors

Amorphous materials

Coherent scattering in soft condensed matter

Kinetic equation for charged particles in soft condensed matter

Concluding remarks


Fluid modelling: foundations and first applications

Moment equations for gases

Constant collision frequency model

Momentum transfer approximation

Stationary, spatially uniform case

Transport in an electric field

Spatial variations, hydrodynamic regime and diffusion coefficients

Diffusion of charge carriers in semiconductors

Fluid models with inelastic collisions


Moment equations with inelastic collisions

Representation of the average inelastic collision frequencies

Hydrodynamic regime

Negative differential conductivity

Fluid modelling with loss and creation processes

Sources and sinks of particles

Reacting particle swarms in gases

Spatially homogeneous systems

Reactive effects and spatial variation

Fluid modelling in condensed matter


Moment equations including coherent and incoherent scattering processes

Structure modified empirical relationships


Strategies and regimes for solution of kinetic equations

The kinetic theory program

Identifying symmetries

Kinetic theory operators

Boundary conditions and uniqueness

Eigenvalue problems in kinetic theory

Hydrodynamic regime

Benchmark models

Numerical Techniques for Solution of Boltzmann’s Equation


The Burnett function representation

Summary of solution procedure

Convergence and the choice of weighting function

Ion transport in gases

Boundary conditions, diffusion cooling and a variational method

Influence of boundaries

Plane-parallel geometry

The Cavalleri experiment

Variational method

Diffusion cooling in an alternating electric field

Concluding remarks

An Analytically Solvable Model


Relaxation time model

Weak gradients and the diffusion equation

Solution of the kinetic equation

Relaxation time model and diffusion equation for an amorphous medium

Concluding remarks


Temporal non-locality


Symmetries and harmonics

Solution of Boltzmann’s equation for electrons in a.c. electric fields

Moment equations for electrons in a.c. electric fields

Transport properties in a.c. electric fields

Concluding remarks

The Franck-Hertz experiment


The experimental and its interpretation

Periodic structures - the essence of the experiment

Fluid model analysis

Kinetic theory

Numerical results

Concluding remarks

Positron transport in soft condensed matter, with application to PET

Why antimatter matters

Positron Emission Tomography (PET)

Kinetic theory for light particles in soft matter

Kinetic theory of positrons in a PET environment

Calculation of the positron range

Transport in electric and magnetic fields and particle detectors


Single, free particle motion in electric and magnetic fields

Transport theory in E and B fields


The fluid approach

Gaseous radiation detectors

Muons in gases and condensed matter

Muon vs electron transport

Muon beam compression

Aliasing of muon transport data

Muon catalyzed fusion

Concluding remarks


Further challenges

Unresolved issues



Comparison of kinetic theory and quantum mechanics

Inelastic and ionization collision operators for light particles

The dual eigenvalue problem

Derivation of the exact expression for ^np(k)

Physical constants and useful formulas

About the Authors

Robert Robson, FAPS, FRMetS, completed a PhD in theoretical physics at the Australian National University in 1972. He has lectured and researched in physics and specializes in electron and positron transport in gases and soft condensed matter. He was Alexander von Humboldt Fellow at the University of Düsseldorf, Germany and held the Hitachi Chair of Electrical Engineering at Keio University, Japan.

Ronald White obtained his PhD in theoretical physics from James Cook University in 1997, and is now Associate Professor and Director of the JCU node of the Australian Research Council’s Centre of Excellence for Antimatter-Matter Studies. He specializes in kinetic theory and fluid modelling of charged particles in gases and soft matter.

Malte Hildebrandt completed his PhD in experimental physics at the University of Heidelberg in 1999, where he worked on the development of particle detectors for high energy particle physics. After a postdoc at the University of Zürich, he joined the Paul Scherrer Institut, and has been head of the detector group in the Laboratory of Particle Physics since 2009.

About the Series

Monograph Series in Physical Sciences

This monograph series brings together focused books for researchers and professionals in the physical sciences. They are designed to offer expert summaries of cutting edge topics at a level accessible to non-specialists. As such, authors are encouraged to include sufficient background information and an overview of fundamental concepts, together with presentation of state of the art theory, methods, and applications. This approach makes these titles suitable for some specialty courses at the graduate level as well. Subject areas covered in this series include condensed matter physics, atomic and molecular physics, plasma physics, particle physics, quantum physics, energy sciences, nanoscience, spectroscopy, mathematical physics, geophysics, environmental physics, and so on, in terms of both theory and experiment.

New books in the series are commissioned by invitation. Authors are also welcome to contact the publisher (Lou Chosen, Executive Editor: to discuss new title ideas.

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics
SCIENCE / Solid State Physics