Plasma Modeling: Methods and applications

PRELIMS.pdf
	Preface
	Acknowledgements
	Editor biographies
		Gianpiero Colonna
		Antonio D’Angola
	List of contributors
CH001.pdf
	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
CH002.pdf
	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
CH003.pdf
	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
CH004.pdf
	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
CH005.pdf
	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
CH006.pdf
	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
CH007.pdf
	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
CH008.pdf
	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
CH009.pdf
	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
CH010.pdf
	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
CH011.pdf
	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
CH012.pdf
	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
CH013.pdf
	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
CH014.pdf
	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
CH015.pdf
	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
CH016.pdf
	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
CH017.pdf
	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
CH018.pdf
	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 (qαϕd>0)
			18.2.2 Attracted species (qαϕd<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
CH019.pdf
	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
CH020.pdf
	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
			20.2.3 Validation methodology
		20.3 A practical example of V…V methodology use
			20.3.1 The TORPEX device, its diagnostics and ancillary systems
			20.3.2 The simulation model
			20.3.3 Code verification
			20.3.4 Solution verification
			20.3.5 Validation
		20.4 Conclusions
		References
CH021.pdf
	Chapter 21 Thermodynamic and transport properties of complex plasmas
		21.1 Partition functions and thermodynamics
			21.1.1 Single species thermodynamics
			21.1.2 Mixture thermodynamics
			21.1.3 Considerations on equilibrium and non-equilibrium plasmas
			21.1.4 Non-ideal corrections
			21.1.5 Fermi–Dirac statistics
		21.2 Lumped level model
			21.2.1 Lumping levels for atoms
			21.2.2 Lumping levels for molecules
		21.3 Equilibrium calculation
			21.3.1 Reaction equilibrium
			21.3.2 Reaction ordering
			21.3.3 Vectorial base of chemical reactions
			21.3.4 State of minimal energy
		21.4 Transport properties
			21.4.1 Viscosity
			21.4.2 Diffusion coefficients
			21.4.3 Thermal conductivity
			21.4.4 Electrical conductivity
			21.4.5 Collision integrals
		21.5 Thermodynamic and transport properties of equilibrium hydrogen plasma
		21.6 EquilTheTA code
		References
CH022.pdf
	Chapter 22 Methods for electron–molecule scattering
		22.1 Simplified approaches
			22.1.1 Simplified approaches for excitation and dissociative excitation
			22.1.2 Classical and binary-encounter approaches for ionization
		22.2 Accurate approaches
			22.2.1 The R-matrix method
			22.2.2 Schwinger multichannel method
			22.2.3 Molecular convergent close-coupling approach
			22.2.4 Other methods
		22.3 Some examples
		22.4 Databases
		References
CH023.pdf
	Chapter 23 Rate coefficients for energy transfer and chemical reactions in heavy particle collisions
		23.1 Semiclassical analytic theory of vibrational energy transfer in molecular collisions
		23.2 Chemical reaction rates for thermally non-equilibrium plasmas
			23.2.1 Non-equilibrium dissociation: classical impulsive theory
			23.2.2 Exchange reactions
		23.3 Quasiclassical trajectory method
			23.3.1 Main features
			23.3.2 The classical S-matrix theory and its relation with QCT
			23.3.3 Some observations about QCT binning
			23.3.4 Cold plasmas and state-to-state data
		References