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