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Table of Contents
Intro
Preface
Acknowledgements
Editor biographies
Gianpiero Colonna
Antonio D'Angola
List of contributors
Chapter 1 Boltzmann and Vlasov equations in plasma physics
1.1 Fundamentals
1.1.1 The convection operator
1.1.2 The collisional operator
1.1.3 Boltzmann's H-theorem
1.1.4 Vlasov equation
1.2 Cross sections
1.3 Solution of the Boltzmann equation
1.4 Plasma modeling numerical codes
References
Chapter 2 Two-term Boltzmann Equation
2.1 Two-term distribution
2.2 Differential equations
2.3 Quasi-stationary approximation
2.4 Rapidly varying oscillating field
2.4.1 Case B = 0
2.4.2 Generalization to independent frequencies
2.4.3 Matrices for single frequency
2.4.4 Some considerations
2.4.5 Power absorbed by electrons
2.4.6 Mean magnetic dipole moment
2.4.7 Perpendicular energy equation
2.5 Electrons in flow
2.6 Electron energy distribution
2.6.1 Current anisotropy
2.6.2 Transport properties
2.6.3 Nozzle flow
2.7 The collision integral
2.7.1 Elastic collisions with heavy species
2.7.2 Electron-electron collisions
2.7.3 Inelastic and superelastic collisions
2.7.4 Chemical processes
2.8 The numerical solution
2.9 Appendix: angle integrals
2.9.1 Type (a)
2.9.2 Type (b)
References
Chapter 3 Multiterm and non-local electron Boltzmann equation
3.1 Introduction
3.2 Basic relations
3.2.1 Boltzmann equation of the electrons
3.2.2 Expansion of the velocity distribution
3.2.3 Macroscopic balances
3.3 Numerical treatment
3.3.1 Solution method for time-dependent conditions
3.3.2 Multiterm solution for space-dependent plasmas
3.4 Concluding remarks
References
Chapter 4 Particle-based simulation of plasmas
4.1 Types of interacting systems
4.1.1 Strength of interaction.
4.2 Computer simulation of interacting systems
4.3 Particle-in-cell method
4.3.1 Mathematical formulation of PIC
4.3.2 Selection of the particle shapes
4.3.3 Derivation of the equations of motion
4.4 Coupling with the field equations: spatial discretization on a grid
4.5 Temporal discretization of the particle methods
4.5.1 Explicit temporal discretization of the particle equations
4.5.2 Explicit PIC cycle
4.5.3 Electrostatic explicit methods
4.5.4 Stability of the explicit PIC method
4.6 Implicit particle methods
4.7 Annotated python code
4.7.1 Initialization
4.7.2 Particle initialization
4.7.3 Grid initialization
4.7.4 Main cycle
References
Chapter 5 The ergodic method: plasma dynamics through a sequence of equilibrium states
5.1 Introduction to the ergodic method
5.2 Expansion of spherical nanoplasmas
5.3 Electron dynamics in a Penning trap for technology applications
References
Chapter 6 Fluid models for collisionless magnetic reconnection
6.1 Two-fluid model
6.1.1 Normalization
6.2 Collisionless plasmas
6.3 Linear dispersion relation
6.3.1 The ρs→0 case
6.3.2 The ρs⩾de case
6.4 Hamiltonian formulation
6.5 Numerical simulations of collisionless reconnection
6.5.1 The ρs→0 limit
6.6 Shear flow effects on the reconnecting instability
References
Chapter 7 Magnetohydrodynamics equations
7.1 MHD models
7.1.1 Model foundation
7.1.2 MHD approximation
7.1.3 Non-equilibrium conditions
7.1.4 Magnetoquasistatics
7.1.5 General model
7.1.6 Ideal MHD
7.1.7 Low magnetic Reynolds number model
7.2 Numerical model
7.3 Applications
References
Chapter 8 Drift-diffusion models and methods
8.1 Drift-diffusion transport equations
8.1.1 Drift-diffusion model in the absence of magnetic field.
8.1.2 Boundary conditions at solid surfaces
8.2 Stiffness and why it needs to be overcome
8.3 Block-implicit schemes
8.4 Why the drift-diffusion system is particularly stiff
8.5 Overcoming the drift-diffusion stiffness
8.5.1 Ohm-based potential equation
8.5.2 Modified ion transport equation
8.5.3 Ambipolar form of the electron transport equation
8.6 Generalized recast of the drift-diffusion system
References
Chapter 9 Self-consistent kinetics
9.1 The state-to-state approach
9.2 Collisional-radiative model
9.3 Vibrational kinetics
9.4 The self-consistent approach
9.5 High enthalpy ionized flows
9.6 The self-consistent approach for CO2 plasmas
9.6.1 CO2 vibrational levels
9.6.2 CO2 state-to-state kinetics
9.6.3 Results
References
Chapter 10 Hypersonic flows with detailed state-to-state kinetics using a GPU cluster
10.1 Physical model
10.1.1 Governing equations
10.1.2 Transport properties
10.1.3 Multi-temperature Park model
10.1.4 State-to-state model
10.2 Numerical scheme
10.2.1 Finite-volume approach
10.2.2 Convective fluxes discretization
10.2.3 Diffusive fluxes discretization
10.2.4 Time integration
10.2.5 Evaluation of source terms: splitting approach
10.3 GPU clustering
10.3.1 CUDA environment
10.3.2 Kernel development
10.3.3 MPI-CUDA environment
10.3.4 Kernel examples
10.4 Results
10.4.1 High enthalpy flow over a double-wedge
10.4.2 Scalability performance
References
Chapter 11 Hybrid models
11.1 Basic assumptions and governing equations
11.2 Numerical implementation
11.2.1 Time-advance algorithm
11.2.2 Initialization and boundary conditions
11.3 Applications
11.3.1 Electrostatic case: plasma plume expansion and Langmuir probes
11.3.2 Magnetostatic case: E × B field devices.
11.3.3 Electromagnetic case: fusion and space plasmas
11.3.4 Spatially hybrid simulation: streamers and laser-plasma interaction
References
Chapter 12 On the coupling of vibrational and electronic kinetics with the electron energy distribution functions: past and present
12.1 H2 plasma
12.2 N2 plasma
12.3 O2 plasma
12.4 CO plasma
12.5 Nozzle flows
12.6 Conclusions
References
Chapter 13 Atmospheric pressure plasmas operating in high frequency fields
13.1 Atmospheric pressure plasmas modelling in high frequency fields
13.1.1 Transport properties of electrons in non-magnetized and partially ionized gases
13.1.2 Treatment of ions and neutral species
13.1.3 Macroscopic equations for the weakly ionized gas flow
13.1.4 Electrodynamics
13.2 Application-contraction of an argon discharge
13.3 Conclusion
References
Chapter 14 Direct current microarcs at atmospheric pressure
14.1 Introduction
14.2 Unified fluid modelling of microarcs
14.3 Transport quantities, thermodynamic and transport properties
14.4 Plasma chemistry
14.5 Boundary conditions
14.6 Realization and selected results
14.7 Conclusion
References
Chapter 15 Multiscale phenomenona in a self-organized plasma jet
15.1 Introduction
15.2 Setup and discharge behaviour
15.3 Model equations
15.3.1 Gas dynamics
15.3.2 Plasma description
15.3.3 Argon plasma chemistry
15.3.4 Solution method
15.4 Plasma jet models
15.4.1 Single filament model
15.4.2 Period-averaged plasma jet model
15.5 Concluding remarks
References
Chapter 16 High-enthalpy radiating flows in aerophysics
16.1 Fluid dynamic model
16.2 Radiative gas dynamics of re-entry space vehicles
16.2.1 Fire-II
16.2.2 Stardust
16.2.3 RAM-C-II
16.2.4 ORION
16.2.5 PTV
16.2.6 MSL
16.3 Conclusions
References.
Chapter 17 Simulating plasma aerodynamics
17.1 Background and levels of modeling
17.2 Flow control via plasma heating
17.3 Flow control via magnetic forces
17.4 Flow control via electrical forces
17.5 Summary and paths forward
References
Chapter 18 Dust-plasma interaction: a review of dust charging theory and simulation
18.1 Introduction
18.2 Basics of dust-plasma interaction
18.2.1 Repelled species (qατ̔̈”Γ͵·d&
#62
0)
18.2.2 Attracted species (qατ̔̈”Γ͵·d<
0)
18.2.3 Summary of OML theory
18.2.4 Some important considerations
18.3 A note on the numerical solution of dust-plasma interaction problems
18.4 Dust electron emission
18.4.1 The OML approach
18.4.2 Transition from negatively- to positively-charged states
18.5 Final remarks
References
Chapter 19 Magnetic confinement for thermonuclear energy production
19.1 Ideal magnetostatic equilibrium
19.1.1 First principles and topological properties
19.1.2 General representations of the magnetic field
19.1.3 Specific curvilinear flux coordinate system
19.2 Grad-Shafranov equation
19.2.1 Figures of merit of the tokamak equilibria
19.2.2 Large aspect ratio limit
19.2.3 Plasma confined within a conducting shell
19.2.4 Radial and vertical equilibrium
19.2.5 Shape of plasma meridian cross-section
19.2.6 Shape and boundary conditions
19.3 Direct and inverse problems
19.3.1 Tokamak equilibrium with flow
19.4 Principal technical elements of a tokamak
19.5 Plasma formation
19.5.1 Poynting theorem
19.5.2 Start-up and current ramp-up
19.5.3 Toroidal coils
19.6 Similarity principles applied to tokamaks
References
Chapter 20 Verification and validation in plasma physics
20.1 Introduction
20.2 The validation and verification methodology
20.2.1 Code verification methodology.
20.2.2 Solution verification methodology.
Preface
Acknowledgements
Editor biographies
Gianpiero Colonna
Antonio D'Angola
List of contributors
Chapter 1 Boltzmann and Vlasov equations in plasma physics
1.1 Fundamentals
1.1.1 The convection operator
1.1.2 The collisional operator
1.1.3 Boltzmann's H-theorem
1.1.4 Vlasov equation
1.2 Cross sections
1.3 Solution of the Boltzmann equation
1.4 Plasma modeling numerical codes
References
Chapter 2 Two-term Boltzmann Equation
2.1 Two-term distribution
2.2 Differential equations
2.3 Quasi-stationary approximation
2.4 Rapidly varying oscillating field
2.4.1 Case B = 0
2.4.2 Generalization to independent frequencies
2.4.3 Matrices for single frequency
2.4.4 Some considerations
2.4.5 Power absorbed by electrons
2.4.6 Mean magnetic dipole moment
2.4.7 Perpendicular energy equation
2.5 Electrons in flow
2.6 Electron energy distribution
2.6.1 Current anisotropy
2.6.2 Transport properties
2.6.3 Nozzle flow
2.7 The collision integral
2.7.1 Elastic collisions with heavy species
2.7.2 Electron-electron collisions
2.7.3 Inelastic and superelastic collisions
2.7.4 Chemical processes
2.8 The numerical solution
2.9 Appendix: angle integrals
2.9.1 Type (a)
2.9.2 Type (b)
References
Chapter 3 Multiterm and non-local electron Boltzmann equation
3.1 Introduction
3.2 Basic relations
3.2.1 Boltzmann equation of the electrons
3.2.2 Expansion of the velocity distribution
3.2.3 Macroscopic balances
3.3 Numerical treatment
3.3.1 Solution method for time-dependent conditions
3.3.2 Multiterm solution for space-dependent plasmas
3.4 Concluding remarks
References
Chapter 4 Particle-based simulation of plasmas
4.1 Types of interacting systems
4.1.1 Strength of interaction.
4.2 Computer simulation of interacting systems
4.3 Particle-in-cell method
4.3.1 Mathematical formulation of PIC
4.3.2 Selection of the particle shapes
4.3.3 Derivation of the equations of motion
4.4 Coupling with the field equations: spatial discretization on a grid
4.5 Temporal discretization of the particle methods
4.5.1 Explicit temporal discretization of the particle equations
4.5.2 Explicit PIC cycle
4.5.3 Electrostatic explicit methods
4.5.4 Stability of the explicit PIC method
4.6 Implicit particle methods
4.7 Annotated python code
4.7.1 Initialization
4.7.2 Particle initialization
4.7.3 Grid initialization
4.7.4 Main cycle
References
Chapter 5 The ergodic method: plasma dynamics through a sequence of equilibrium states
5.1 Introduction to the ergodic method
5.2 Expansion of spherical nanoplasmas
5.3 Electron dynamics in a Penning trap for technology applications
References
Chapter 6 Fluid models for collisionless magnetic reconnection
6.1 Two-fluid model
6.1.1 Normalization
6.2 Collisionless plasmas
6.3 Linear dispersion relation
6.3.1 The ρs→0 case
6.3.2 The ρs⩾de case
6.4 Hamiltonian formulation
6.5 Numerical simulations of collisionless reconnection
6.5.1 The ρs→0 limit
6.6 Shear flow effects on the reconnecting instability
References
Chapter 7 Magnetohydrodynamics equations
7.1 MHD models
7.1.1 Model foundation
7.1.2 MHD approximation
7.1.3 Non-equilibrium conditions
7.1.4 Magnetoquasistatics
7.1.5 General model
7.1.6 Ideal MHD
7.1.7 Low magnetic Reynolds number model
7.2 Numerical model
7.3 Applications
References
Chapter 8 Drift-diffusion models and methods
8.1 Drift-diffusion transport equations
8.1.1 Drift-diffusion model in the absence of magnetic field.
8.1.2 Boundary conditions at solid surfaces
8.2 Stiffness and why it needs to be overcome
8.3 Block-implicit schemes
8.4 Why the drift-diffusion system is particularly stiff
8.5 Overcoming the drift-diffusion stiffness
8.5.1 Ohm-based potential equation
8.5.2 Modified ion transport equation
8.5.3 Ambipolar form of the electron transport equation
8.6 Generalized recast of the drift-diffusion system
References
Chapter 9 Self-consistent kinetics
9.1 The state-to-state approach
9.2 Collisional-radiative model
9.3 Vibrational kinetics
9.4 The self-consistent approach
9.5 High enthalpy ionized flows
9.6 The self-consistent approach for CO2 plasmas
9.6.1 CO2 vibrational levels
9.6.2 CO2 state-to-state kinetics
9.6.3 Results
References
Chapter 10 Hypersonic flows with detailed state-to-state kinetics using a GPU cluster
10.1 Physical model
10.1.1 Governing equations
10.1.2 Transport properties
10.1.3 Multi-temperature Park model
10.1.4 State-to-state model
10.2 Numerical scheme
10.2.1 Finite-volume approach
10.2.2 Convective fluxes discretization
10.2.3 Diffusive fluxes discretization
10.2.4 Time integration
10.2.5 Evaluation of source terms: splitting approach
10.3 GPU clustering
10.3.1 CUDA environment
10.3.2 Kernel development
10.3.3 MPI-CUDA environment
10.3.4 Kernel examples
10.4 Results
10.4.1 High enthalpy flow over a double-wedge
10.4.2 Scalability performance
References
Chapter 11 Hybrid models
11.1 Basic assumptions and governing equations
11.2 Numerical implementation
11.2.1 Time-advance algorithm
11.2.2 Initialization and boundary conditions
11.3 Applications
11.3.1 Electrostatic case: plasma plume expansion and Langmuir probes
11.3.2 Magnetostatic case: E × B field devices.
11.3.3 Electromagnetic case: fusion and space plasmas
11.3.4 Spatially hybrid simulation: streamers and laser-plasma interaction
References
Chapter 12 On the coupling of vibrational and electronic kinetics with the electron energy distribution functions: past and present
12.1 H2 plasma
12.2 N2 plasma
12.3 O2 plasma
12.4 CO plasma
12.5 Nozzle flows
12.6 Conclusions
References
Chapter 13 Atmospheric pressure plasmas operating in high frequency fields
13.1 Atmospheric pressure plasmas modelling in high frequency fields
13.1.1 Transport properties of electrons in non-magnetized and partially ionized gases
13.1.2 Treatment of ions and neutral species
13.1.3 Macroscopic equations for the weakly ionized gas flow
13.1.4 Electrodynamics
13.2 Application-contraction of an argon discharge
13.3 Conclusion
References
Chapter 14 Direct current microarcs at atmospheric pressure
14.1 Introduction
14.2 Unified fluid modelling of microarcs
14.3 Transport quantities, thermodynamic and transport properties
14.4 Plasma chemistry
14.5 Boundary conditions
14.6 Realization and selected results
14.7 Conclusion
References
Chapter 15 Multiscale phenomenona in a self-organized plasma jet
15.1 Introduction
15.2 Setup and discharge behaviour
15.3 Model equations
15.3.1 Gas dynamics
15.3.2 Plasma description
15.3.3 Argon plasma chemistry
15.3.4 Solution method
15.4 Plasma jet models
15.4.1 Single filament model
15.4.2 Period-averaged plasma jet model
15.5 Concluding remarks
References
Chapter 16 High-enthalpy radiating flows in aerophysics
16.1 Fluid dynamic model
16.2 Radiative gas dynamics of re-entry space vehicles
16.2.1 Fire-II
16.2.2 Stardust
16.2.3 RAM-C-II
16.2.4 ORION
16.2.5 PTV
16.2.6 MSL
16.3 Conclusions
References.
Chapter 17 Simulating plasma aerodynamics
17.1 Background and levels of modeling
17.2 Flow control via plasma heating
17.3 Flow control via magnetic forces
17.4 Flow control via electrical forces
17.5 Summary and paths forward
References
Chapter 18 Dust-plasma interaction: a review of dust charging theory and simulation
18.1 Introduction
18.2 Basics of dust-plasma interaction
18.2.1 Repelled species (qατ̔̈”Γ͵·d&
#62
0)
18.2.2 Attracted species (qατ̔̈”Γ͵·d<
0)
18.2.3 Summary of OML theory
18.2.4 Some important considerations
18.3 A note on the numerical solution of dust-plasma interaction problems
18.4 Dust electron emission
18.4.1 The OML approach
18.4.2 Transition from negatively- to positively-charged states
18.5 Final remarks
References
Chapter 19 Magnetic confinement for thermonuclear energy production
19.1 Ideal magnetostatic equilibrium
19.1.1 First principles and topological properties
19.1.2 General representations of the magnetic field
19.1.3 Specific curvilinear flux coordinate system
19.2 Grad-Shafranov equation
19.2.1 Figures of merit of the tokamak equilibria
19.2.2 Large aspect ratio limit
19.2.3 Plasma confined within a conducting shell
19.2.4 Radial and vertical equilibrium
19.2.5 Shape of plasma meridian cross-section
19.2.6 Shape and boundary conditions
19.3 Direct and inverse problems
19.3.1 Tokamak equilibrium with flow
19.4 Principal technical elements of a tokamak
19.5 Plasma formation
19.5.1 Poynting theorem
19.5.2 Start-up and current ramp-up
19.5.3 Toroidal coils
19.6 Similarity principles applied to tokamaks
References
Chapter 20 Verification and validation in plasma physics
20.1 Introduction
20.2 The validation and verification methodology
20.2.1 Code verification methodology.
20.2.2 Solution verification methodology.