Space and Astrophysical Plasma Simulation. Methods, Algorithms, and Applications

Preface
Contents
Contributors
Acronyms
Part I Introduction to Basic Knowledge—Tutorials
	1 Magnetohydrodynamic Simulations
		1.1 MHD Equations and Properties
		1.2 Basic Considerations for the Numerical Solution of MHD Systems
		1.3 Initial and Boundary Conditions
			1.3.1 Kelvin-Helmholtz Instability
			1.3.2 Fast Shock Simulation
			1.3.3 Magnetotail Simulation
		1.4 Examples of MHD Simulations
			1.4.1 Kelvin-Helmholtz Simulations
			1.4.2 Simulations of Sunward Moving Plasma at the Earth\'s Bow Shock
			1.4.3 Earth\'s Magnetotail Simulations
		1.5 Summary and Conclusions
		References
	2 Hall Magnetohydrodynamics
		2.1 Introduction
		2.2 Hall MHD: Basic Equations and Wave Modes
			2.2.1 Whistler Waves
			2.2.2 Hall Drift Waves
		2.3 Numerical Methods
			2.3.1 Cell Definition
			2.3.2 Time Step Scheme
			2.3.3 Finite Volume Method
			2.3.4 Flux Calculation
				2.3.4.1 High-Order Interpolation Scheme
				2.3.4.2 Partial Donor Cell Method
			2.3.5 Distribution Function Method
			2.3.6 Magnetic Field Evolution
				2.3.6.1 Convective Electric Field
				2.3.6.2 Hall Electric Field
			2.3.7 Courant Condition
			2.3.8 Sub-Cycling the Hall Physics
			2.3.9 Implicit Numerical Scheme
		2.4 Applications
			2.4.1 Linear Hall Waves
				2.4.1.1 Whistler Waves
				2.4.1.2 Hall Drift Waves
			2.4.2 Plasma Opening Switch
			2.4.3 Sub-Alfvénic Plasma Expansions
			2.4.4 Magnetic Reconnection
		2.5 Summary
		References
	3 Hybrid-Kinetic Approach: Massless Electrons
		3.1 Introduction
		3.2 Review of Basic Model and Implementation
		3.3 Examples of Current Hybrid Code Applications
			3.3.1 Planetary Foreshocks and Bow Shocks
			3.3.2 Improved Electron Pressure Closure for Magnetic Reconnection in the Magnetosphere
			3.3.3 Magnetosheath: Effects of the Bow Shock, Turbulence, and Reconnection
		3.4 Other Hybrid Algorithms, Codes, and Applications
		3.5 New Hybrid Algorithms
			3.5.1 An Advanced Hybrid Model
			3.5.2 An Implicit Hybrid Model
			3.5.3 A Brief Note on Comparison of Hybrid Algorithms
		3.6 The Future of Hybrid Codes
		References
	4 Gyrokinetics
		4.1 Effective Kinetic Description of Magnetized, Weakly Collisional Space Plasmas
			4.1.1 Limits of Fully Kinetic and Hybrid Kinetic-Fluid Descriptions
			4.1.2 The New Kid on the Block: Gyrokinetics
			4.1.3 Comparing Gyrokinetic, Hybrid Kinetic-Fluid, and Fully Kinetic Descriptions: Waves and Turbulence in Space Plasmas
			4.1.4 Applications of Gyrokinetics in Space Plasma Physics
		4.2 A Primer on Gyrokinetics
			4.2.1 Guiding Center Dynamics in Given Electromagnetic Fields
				4.2.1.1 A Lagrangian Approach
				4.2.1.2 From Particle Coordinates to Guiding Center Coordinates
				4.2.1.3 Equations of Motion in Guiding Center Coordinates
			4.2.2 Taking into Account Fluctuating Electromagnetic Fields
				4.2.2.1 Gyrokinetic Ordering
				4.2.2.2 Gyrokinetic Equations of Motion
				4.2.2.3 Gyrokinetic Vlasov-Maxwell Equations
			4.2.3 Further Reading
		4.3 Computational Gyrokinetics
			4.3.1 The Lagrangian (Particle-in-Cell) Approach
			4.3.2 The Eulerian (Grid-Based) Approach
		4.4 Applications of Gyrokinetics to Solar Wind Turbulence
			4.4.1 On the Nature of Solar Wind Turbulence at Kinetic Scales
				4.4.1.1 Different Kinetic Descriptions: Advantages and Drawbacks
				4.4.1.2 Gyrokinetic Simulations of Solar Wind Turbulence
				4.4.1.3 Brief Discussion of the Validity of the Gyrokinetic Simulation Results
		4.5 Outlook
		References
	5 Eulerian Approach to Solve the Vlasov Equation and Hybrid-Vlasov Simulations
		5.1 Introduction
		5.2 Numerical Schemes and Hamiltonian Dynamics
		5.3 Models of Different Plasma Regimes
		5.4 Vlasov Equilibrium
		5.5 Basic Applications: Two Textbook Example
			5.5.1 Electrostatic Limit: Landau Damping and Nonlinear Evolution
			5.5.2 Electromagnetic Case: The Current Filamentation (Weibel) Instability
		5.6 Advanced Applications: Recent Progress in Space Plasma Turbulence via Eulerian Vlasov Simulations
			5.6.1 Plasma Turbulence from In situ Measurements in the Solar Wind and in the Earth\'s Magnetosheath: A Brief Overview
			5.6.2 Plasma Turbulence from Kinetic Simulations
				5.6.2.1 Decreasing the Dimensionality of the Problem: Plasma Turbulence via Reduced-Kinetic Eulerian Simulations
		References
	6 Fully Kinetic Simulations: Semi-Lagrangian Particle-in-CellCodes
		6.1 Theoretical Background of Particle-in-Cell Simulations
			6.1.1 Introduction
			6.1.2 Mathematical Description
		6.2 Numerical Implementation
			6.2.1 Field Solvers
			6.2.2 Interpolation
			6.2.3 Particle Motion
			6.2.4 Deposition and Filtering
			6.2.5 Initialization and Particle Handling
			6.2.6 Boundary Conditions
			6.2.7 Parallelization
			6.2.8 Diagnostics
			6.2.9 Test Cases
		6.3 Applications of Particle-in-Cell Simulations
			6.3.1 Turbulence in the Kinetic Regime
				6.3.1.1 Initializing Turbulence
				6.3.1.2 Analyzing Turbulence
				6.3.1.3 Exemplary Results
			6.3.2 Charged Particle Transport
			6.3.3 Instabilities
			6.3.4 Collisionless Shocks
			6.3.5 Reconnection
		References
Part II Introduction to Advanced Simulation Approaches
	7 Adaptive Global Magnetohydrodynamic Simulations
		7.1 Introduction
		7.2 Brief History of Global MHD Simulations of Space Plasmas
			7.2.1 Models of the Solar Corona
			7.2.2 Heliosphere Models
			7.2.3 Geospace Models
		7.3 The Space Weather Modeling Framework (SWMF)
		7.4 BATS-R-US
			7.4.1 Modular Architecture
			7.4.2 Block-Adaptive Mesh Refinement
			7.4.3 Conservation Laws
			7.4.4 BATS-R-US Performance
		7.5 Heliophysics and Planetary Applications
		7.6 MHD-EPIC
			7.6.1 iPIC3D
			7.6.2 Coupling MHD and PiC Simulations
			7.6.3 MHD-EPIC Performance
			7.6.4 MHD-EPIC Applications
		7.7 Summary
		References
	8 Multiscale Kinetic Simulations
		8.1 Plasma Scales and Models
		8.2 Temporal Adaptation
			8.2.1 Implicit Versus Explicit
			8.2.2 Stability of Explicit and Implicit Schemes
		8.3 Spatial Adaptation
			8.3.1 PIC with r-Adaptation
			8.3.2 PIC with h-Adaptation
		8.4 Phase Space Adaptation
		8.5 Model Adaptation
			8.5.1 Linking Kinetic and Fluid States
			8.5.2 One-Way or Two-Way Coupling
		References
	9 Hybrid-Kinetic Approach: Inertial Electrons
		9.1 Introduction
		9.2 Historical Development of Finite-Electron-Mass Hybrid-Kinetic Simulation Models
		9.3 Equations to be Solved
		9.4 Numerical Implementation
			9.4.1 Ions as Particles
			9.4.2 Electron Fluid
			9.4.3 Electromagnetic Fields
			9.4.4 Code Parallelization and Performance
		9.5 Applications
			9.5.1 Magnetic Reconnection
				9.5.1.1 Electromagnetic Fluctuations in Reconnection Regions
				9.5.1.2 EMHD Simulation of Guide Field Magnetic Reconnection with Finite Electron Mass but with Immobile Ions
				9.5.1.3 Hybrid-Kinetic Simulation of Guide Field Reconnection with Finite Electron Mass and Mobile Ions
			9.5.2 Collisionless Plasma Turbulence and Current Sheets
			9.5.3 Collisionless Shocks
			9.5.4 Global Magnetospheric Hybrid Code Simulations
		9.6 Future Possible Improvements of Hybrid Code Algorithms
		References
	10 Generalized Quasi-Neutral Hybrid-Kinetic Simulations
		10.1 Introduction
		10.2 Validity of Quasi-neutrality Assumption
		10.3 Governing Equations
		10.4 Quasi-Neutral Two Fluids Coupled with Kinetic Populations
		10.5 Limiting Cases
			10.5.1 Quasi-Neutral Two-Fluid Model
			10.5.2 Effect of Kinetic Populations
		10.6 Numerical Methods
			10.6.1 Kinetic Part
			10.6.2 Fluid Part
			10.6.3 Ohm\'s Law
			10.6.4 Time Integration
		10.7 Numerical Examples
			10.7.1 Quasi-Neutral Two-Fluid Case
			10.7.2 Hybrid and EP-MHD Hybrid Case
			10.7.3 Fully Kinetic Energetic Electrons
		10.8 Summary and Outlook
		References
	11 Fully Kinetic (Particle-in-Cell) Simulation of AstrophysicalPlasmas
		11.1 Introduction
		11.2 Astrophysical Shock Waves
			11.2.1 Non-relativistic, High-Mach-Number Shocks
			11.2.2 Relativistic Shocks with a Large Bulk Lorentz Factor
		11.3 Magnetic Reconnection in Astroplasma Settings
			11.3.1 Relativistic Magnetic Reconnection with Strong Magnetic Fields
			11.3.2 Magnetic Reconnection in Pulsar Winds
		11.4 Magneto-Rotational Instability (MRI) in Collisionless Accretion Disks
		11.5 Summary
		References
Part III Introduction to Advanced New Algorithms and Developments for Future Simulations
	12 Higher-Order Magnetohydrodynamic Simulations
		12.1 Introduction
		12.2 General Numerical Framework
			12.2.1 Basic Equations
			12.2.2 Motivation for Using Higher-Order Schemes
			12.2.3 Finite-Volume
			12.2.4 Constrained Transport
		12.3 Practical Computation of the Fluxes
			12.3.1 Central Weighted Essentially Non-oscillatory Reconstruction
			12.3.2 Reconstruction of the Magnetic Field Components
			12.3.3 Solving the Riemann Problem
			12.3.4 Passage Through Point Values
			12.3.5 Electric Fluxes on the Edges
			12.3.6 Summary: The Complete Procedure to Determine the RHS
		12.4 Time Integration
		12.5 Strong Shocks and Negative Pressure/Density
		12.6 Numerical Tests
			12.6.1 Verification of the Scheme\'s Order
			12.6.2 Smooth Problems
				12.6.2.1 Circularly Polarized Alfvén Wave
				12.6.2.2 3D MHD Vortex
			12.6.3 Shocked Problems
				12.6.3.1 1D Brio-Wu Riemann Problem
				12.6.3.2 Orszag–Tang Vortex
				12.6.3.3 Decaying Supersonic MHD Turbulence
		12.7 Final Remarks
		References
	13 EMAPS: An Intelligent Agent-Based Technology for Simulation of Multiscale Systems
		13.1 Introduction
			13.1.1 Time Versus Change
			13.1.2 Time-Stepping Approaches to Asynchronous Time Integration
			13.1.3 Asynchronous Time Integration Using Discrete-Event Simulation
		13.2 EMAPS: Event-driven Multi-Agent Planning System
			13.2.1 Basic Algorithm
			13.2.2 Parallelization
		13.3 Early Applications
			13.3.1 Diffusion-Reaction-Advection Equations
			13.3.2 Computational Gas Dynamics
			13.3.3 Hybrid Simulations of Fast Plasma Shocks
		13.4 HYPERS: Hybrid Parallel Event Resolving Simulator
			13.4.1 Magnetic Field Correction
			13.4.2 Simulation Geometry
			13.4.3 Collisions and Resistivity
			13.4.4 Programming Structure
		13.5 Multi-dimensional Simulations of Magnetoplasmas
			13.5.1 Global Magnetospheric Simulations
			13.5.2 Colliding Magnetoplasmas
			13.5.3 Plasma Expansion Across a Transverse Magnetic Field
			13.5.4 Plasma Turbulence
		13.6 Prospective Applications
			13.6.1 Climate Modeling
			13.6.2 Neuromorphic Computing
			13.6.3 Neural Computation
			13.6.4 Next-Generation Multi-Agent Systems
		13.7 Conclusion
		References