Fundamentals of Charged Particle Transport in Gases and Condensed Matter (Hardcover)

Introduction
Boltzmann’s equation
Solving Boltzmann’s equation
Experiment and simulation
About this book

I KINETIC THEORY FOUNDATIONS
Basic theoretical concepts: Phase and configuration space
Preliminaries
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
Introduction
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
Charge-exchange
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
Introduction
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
Introduction
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
Introduction
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
Introduction
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
Introduction
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
Introduction
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
Introduction
Single, free particle motion in electric and magnetic fields
Transport theory in E and B fields
Symmetries
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
Summary
Further challenges
Unresolved issues