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Computational Plasma Science: Physics and Selected Simulation Examples

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The book presents fundamentals of plasma physics with rich references and computational techniques in a concise manner. It particularly focuses on introductions to numerical simulation methods in plasma physics, in addition to those to physics and mathematics in plasma physics. It also presents the fundamentals of numerical methods, which solve mathematical models of plasmas, together with examples of numerical results. A discretization method, the so-called finite difference method, is introduced for particle-in-cell methods and fluid codes, which have been widely employed in plasma physics studies. In addition to the introduction to numerical solutions, it also covers numerical stability. The instabilities and numerical errors significantly influence the results, and for correct results, great efforts are required to avoid such numerical artifacts. The book also carefully discusses the numerical errors, numerical stability, and uncertainty in numerical computations.

Readers are expected to have an understanding of fundamental physics of mechanics, electromagnetism, thermodynamics, statistical physics, relativity, fluid dynamics, and mathematics, but the book does not assume background knowledge on plasma. Therefore, it is a first book of plasma physics for upper undergraduate and early graduate students who are interested in learning it.

Author(s): Shigeo Kawata
Series: Springer Series in Plasma Science and Technology
Publisher: Springer
Year: 2023

Language: English
Pages: 298
City: Singapore

Preface
Contents
1 Introduction to Plasma
1.1 Fourth State of Matter: Plasma
1.2 Brief Introduction to Plasma Physics World
1.3 Collective Motion: The Debye Shielding
1.4 Collective Motion: Plasma Oscillation
1.5 Conditions for Plasma Collective Motion
1.6 Introduction to Mathematical Models for Plasma
1.7 Introduction to Computer Simulation for Plasma
1.7.1 Computer Simulation Power and Uncertainty in Computation
1.7.2 Example Computer Simulation for the Debye Shielding
References
2 Plasma in Equilibrium
2.1 Distribution Function and Plasma
2.2 The Maxwell Distribution
2.3 Plasma Density
2.4 The Coulomb Collision
2.5 Plasma Temperature
2.5.1 Simulation of Temperature Relaxation
References
3 Single Particle Motion
3.1 Equation of Motion
3.2 Cyclotron Motion
3.3 Drift Motion
3.4 Magnetic Moment
3.5 Single Particle Simulations
3.6 Simulation of Electron Motion in Laser Field
References
4 Equations for Electromagnetic Field
4.1 The Poisson Equation
4.2 The Maxwell Equations
4.3 Potential
4.4 Introduction to Kinetic Particle Simulation Model for Plasma
4.4.1 Structure of Particle-in-Cell (PIC) Code
4.4.2 Field Solver
4.4.3 Interaction Between Field and Particles
4.4.4 Simulation of Electron Cloud with Laser Field
References
5 Plasma by Fluid Model
5.1 Basic Fluid Equations
5.2 Introduction to Plasma Simulation by the Euler Fluid Model
5.2.1 Summary of Finite Difference Method (FDM)
5.2.2 Example 2D Simulation for Convection
5.2.3 Numerical Instability and Time Step Control
5.2.4 Numerical Instability and Its Analysis
5.2.5 Example Simulation for Jet Injection
5.2.6 Example Simulation for Diffusion: Heat Conduction
5.3 Introduction to Plasma Simulation by the Lagrange Fluid Model
5.4 Electron Plasma Wave
5.5 Ion Acoustic Wave
5.6 Electromagnetic Wave
5.7 Magnetohydrodynamic Equation
5.8 Frozen Magnetic Flux
5.9 Waves in Magnetized Plasma
References
6 Plasma Treated by Distribution Function: Kinetic Model
6.1 The Vlasov Equation
6.1.1 The Klimontovich Equation
6.1.2 The Liouville Equation
6.1.3 The BBGKY Hierarchy and the Vlasov Equation
6.2 Equilibrium Solution
6.3 The Boltzmann Equation and Collision Effect
6.4 Moment Equations and Fluid Model
6.5 Dielectric Response Function for Unmagnetized Uniform Plasma
6.6 Plasma Oscillation and the Debye Shielding
6.7 Electron Plasma Wave and the Landau Damping
6.8 Electron Wave Propagation in Equilibrium Plasmas
6.9 Physical Meaning of the Landau Damping
6.10 Dispersion Relation for Transverse Electromagnetic Waves
6.11 Dispersion Relation for Magnetized Uniform Plasma
6.12 Waves in Magnetized Uniform Plasma
References
7 Plasma Instability
7.1 Two-Stream Instability
7.1.1 Two-Stream Instability by Fluid Model
7.1.2 Two-Stream Instability by Distribution Function
7.1.3 Example Simulation for Two-Stream Instability
7.2 Ion Acoustic Instability
7.3 Instability of Magnetized Plasma Column
7.3.1 Example Simulation for the Sausage and Kink Instabilities
7.4 Interchange Instability—The Rayleigh-Taylor instability and an Example Simulation
7.5 The Kelvin-Helmholtz Instability and an Example Simulation
7.6 Parametric Instability
7.7 The Weibel Instability
7.8 Filamentation Instability and an Example Simulation
7.9 Tearing Mode Instability and an Example Simulation
7.10 Drift Instability
References
8 Short Introduction to Nonlinear Plasma Physics
8.1 Solitary Wave: The Korteweg-de Vries (KdV) Equation
8.1.1 The Korteweg-de Vries (KdV) Equation for Ion Acoustic Wave
8.1.2 Property of the Korteweg-de Vries (KdV) Equation
8.1.3 Inverse Scattering Transform for the Korteweg-de Vries (KdV) Equation
8.2 The Burgers Equation and Shock Wave
8.3 Plasma Echo
8.4 A Glimpse at Turbulence
References
9 Applications of Plasmas
9.1 Plasma Process
9.2 Electron Temperature Measurement by Single-Probe Method
9.3 Plasma Jet
9.4 Nuclear Fusion
9.4.1 Fusion Reaction
9.4.2 The Lawson Criterion—To Sustain Fusion Reaction
9.4.3 MCF: Magnetic Confinement Fusion
9.4.4 ICF: Inertial Confinement Fusion
9.5 Laser Particle Acceleration
9.6 Cluster Ion Interaction with Plasma
9.7 Control of Plasma: Dynamic Mitigation of Plasma Instabilities and Non-uniformities
9.7.1 Control of Plasma: Theory
9.7.2 Dynamic Control of Plasma Instabilities
References
Appendix A Additional Readings
Appendix B Physical Constants and Mathematical Formulae
B.1 Physical Constants and Relations
B.2 Vector Formulae
B.3 Differential Operators
B.4 Delta Function
B.5 Integral Formulae
Appendix C Complex Analysis: Summary
C.1 Cauchy's Integral Theorem
C.2 Residue Theorem
C.3 Derivation of Eq. (6.90摥映數爠eflinkeq:DebyePotential26.906)
Appendix D Derivation of Ponderomotive Force
Appendix E Parallel Computing by OpenMP
Appendix F Example 3D Pure Euler Fluid Code Structure
Appendix G Derivation of εxx in Eq. (6.151摥映數爠eflinkeqn:EpsilonspsxxForMagnetizedUniformPlasma6.1516) for Magnetized Uniform Plasma
Index