Fundamentals of Charged Particle Transport in Gases and Condensed Matter  book cover
1st Edition

Fundamentals of Charged Particle Transport in Gases and Condensed Matter

ISBN 9781498736367
Published September 12, 2017 by CRC Press
426 Pages 74 B/W Illustrations

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Book Description

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

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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.