Plasma physics focuses on the most abundant state of matter in the universe, corresponding to ionized gas comprising ions and electrons. It can be created artificially and has a huge range of technological applications, from television displays to fusion energy research. Every application of plasma technology requires its own numerical solution to the complex physical and mathematical equations which govern the research field of plasma physics.
Modelling and Simulation in Plasma Physics for Physicists and Mathematics offers an introduction to the principles of simulating plasma physics applications. It provides knowledge not only of the fundamental algorithms in computational fluid mechanics, but also their specific role in a plasma physics context. In addition, the book dissects the challenges and advancements, unveiling the delicate balance between accuracy and computational cost.
Modelling and Simulation in Plasma Physics for Physicists and Mathematics readers will also find: - Cutting-edge computational insights where powerful simulations meet theoretical complexities, providing physicists and mathematicians a gateway to cutting-edge research. - An overview of programming language-agnostic code generation and the construction of adaptable models that resonate with the intricate dynamics of plasma physics, ensuring precision in every simulation. - Advanced simplification strategies, including time splitting, analytic models, averaged rates, and tabular material, offering scientists and engineers a roadmap to balance computational demands with scientific rigor.
Modelling and Simulation in Plasma Physics for Physicists and Mathematics is ideal for plasma physicists, students, and engineers looking to work with plasma technologies.
Table of Contents
Preface
1 Foundations of Computational Fluid Mechanics
1.1 Basic Concepts of Finite Difference Integration
1.2 Basic Concepts of Fluid Mechanics
1.3 The Basic Equations of Fluid Mechanics
1.4 Ideal (Dissipationless) Flow - Hyperbolic Equations
1.5 Formal Solution
1.6 Discontinuities
1.7 Plasma Fluid Dynamics
1.8 Basic Principles of Finite Differencing
1.9 Numerical Fluid Approximations
1.10 Grid Geometry
1.11 Control Volume Differencing
1.12 Mesh types
2 Analytic and Quasi-Analytic Approximations
2.1 Analytic and Quasi-Analytic Methods
Appendix 2.A The Nemchinov conjecture
Appendix 2.B The energy integral
3 Numerical Fluid Dynamics
3.1 Eulerian Schemes
3.2 Steady State Problems
3.3 Spatial Differencing
3.4 Generalised Euler Schemes
4 Lagrangian Systems
4.1 Lagrangian Fluid Dynamics
4.2 One Dimensional von Neumann-Richtmyer Algorithm
4.3 Multi-Dimensional Lagrangian Schemes
4.4 Choice of Method
5 Arbitrary Lagrangian-Eulerian Schemes
5.1 Introduction
5.2 Step 1: The Lagrangian Stage
5.3 Step 2: The Iteration Stage
5.4 Step 3: Mesh generation
5.5 Step 4: Rezoning
6 Hybrid or 1 1/2 d Schemes
6.1 Introduction
7 Magneto-hydrodynamics
7.1 Introduction
7.2 The MHD Equations
7.3 Self-generated Fields
8 Monte Carlo Schemes
8.1 Monte-Carlo methods
8.2 Monte Carlo Integration
8.3 Random Walks
8.4 Nuclear Reactor Criticality
8.5 Thermodynamic Properties and Equation of State
Appendix 8.A Kinematics of Elastic Scattering
9 Particle transport
9.1 Particle transport
10 Numerical Diffusion Schemes
10.1 Introduction
10.2 Split time step and ADI Methods for Solving Diffusion Problems in Orthogonal Cartesian Grid Systems
10.3 The Diffusion Matrix
Appendix 10.A Thomas algorithm -Tri-diagonal matrix equation solver
11 Particle path tracking
11.1 Introduction
Appendix 11.A Bunemann-Boris algorithm
Appendix 11.B Stability of the 1d electrostatic model
11.B.1 Time step limitation
11.B.2 Space step limitation
11.B.3 Stability of the 1D electro-magnetic model
12 Ion-electron equilibration
13 Ionisation-recombination Models
13.1 Introduction
13.2 Collisional-radiative model
13.3 Two stage model
Appendix 13.A Solution of the Collisional radiative equations
Appendix 13.B A theorem on determinants
Appendix 13.C An algorithm using the exact solution
Supplement M.1 Partial Differential Equations
M.1.i General Form of First-Order Partial Differential Equations
M.1.ii Linear second order partial differential equations
M.1.iii Separation of variables
M.1.iv Boundary conditions
Supplement M.2 Stiff Equations
Supplement M.3 Weak solutions
Supplement M.4 Operator Splitting
M.4.i Split time step
Supplement M.5 Statistics Primer
M.5.i Basic stochastic nomenclature and results
M.5.ii Moments
M.5.iii Covariance, Correlation and Regression
M.5.iv Elementary Statistical Results
M.5.v Variance of a Sum of Samples
M.5.vi Variance of the mean
M.5.vii Weighted averaging
Supplement M.6 Numerical Solution of Poisson’s Equation
M.6.i One dimension
M.6 .ii Two dimensions 223
Supplement M.7 Compressible Gas Potential Flow
M.7.i Compressible Gas Potential Flow
M.7.ii Perturbation Flow
M.7.iii The General Solution
Supplement M.8 Viscous Incompressible Flow
M.8.i Introduction
M.8.ii Marker-in-Cell
