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E-grāmata: Plasma Simulations by Example

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Lubos Brieda

Formāts: 368 pages
Izdošanas datums: 13-Dec-2019
Izdevniecība: CRC Press
Valoda: eng
ISBN-13: 9780429801068

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Formāts: 368 pages
Izdošanas datums: 13-Dec-2019
Izdevniecība: CRC Press
Valoda: eng
ISBN-13: 9780429801068

Citas grāmatas par šo tēmu:

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"The study of plasmas is crucial in improving our understanding of the universe, and they are being increasingly utilised in key technologies such as spacecraft thrusters, plasma medicine, and fusion energy. Providing readers with an easy to follow set of examples that clearly illustrate how simulation codes are written, this book guides readers through how to develop C++ computer codes for simulating plasmas primarily with the kinetic Particle in Cell (PIC) method. This text will be invaluable to advanced undergraduates and graduate students in physics and engineering looking to learn how to put the theory to the test. Features: Provides a step-by-step introduction to plasma simulations with easy to follow examples Discusses the electrostatic and electromagnetic Particle in Cell (PIC) method on structured and unstructured meshes, magnetohydrodynamics (MHD), and Vlasov solvers Covered topics include Direct Simulation Monte Carlo (DSMC) collisions, surface interactions, axisymmetry, and parallelization strategies"--

The study of plasmas is crucial in improving our understanding of the universe, and they are being increasingly utilised in key technologies such as spacecraft thrusters, plasma medicine, and fusion energy. Providing readers with an easy to follow set of examples that clearly illustrate how simulation codes are written, this book guides readers through how to develop C++ computer codes for simulating plasmas primarily with the kinetic Particle in Cell (PIC) method. This text will be invaluable to advanced undergraduates and graduate students in physics and engineering looking to learn how to put the theory to the test.

Features:

Provides a step-by-step introduction to plasma simulations with easy to follow examples

Discusses the electrostatic and electromagnetic Particle in Cell (PIC) method on structured and unstructured meshes, magnetohydrodynamics (MHD), and Vlasov solvers

Covered topics include Direct Simulation Monte Carlo (DSMC) collisions, surface interactions, axisymmetry, and parallelization strategies.

Lubos Brieda

has over 15 years of experience developing plasma and gas simulation codes for electric propulsion, contamination transport, and plasma-surface interactions. As part of his master’s research work, he developed a 3D ES-PIC electric propulsion plume code, Draco, which is to this date utilized by government labs and private aerospace firms to study plasma thruster plumes. His Ph.D, obtained in 2012 from George Washington University, USA, focused on a multi-scale model for Hall thrusters utilizing fluid-kinetic hybrid PIC codes. He has since then been involved in numerous projects involving development and the use of plasma simulation tools. Since 2014 he has been teaching online courses on plasma simulations through his website: particleincell.com.

Providing the reader with an easy to follow set of examples, this new book guides readers how to develop C++ computer codes for simulating plasmas primarily with the kinetic Particle in Cell (PIC) method. This text would be invaluable to advanced undergraduates and graduate students looking to learn how to put the theory to the test.

Preface

xvii

Chapter 1 Fundamentals

(44)

1.1 Introduction

(1)

1.2 Gas Simulation Approaches

(10)

1.2.1 Direct Method

(1)

1.2.2 Boltzmann Equation

(2)

1.2.3 Maxwell-Boltzmann Distribution Function

(1)

1.2.4 Fluid and Kinetic Methods

(2)

1.2.5 Lagrangian and Eulerian Descriptions

(1)

1.2.6 Comparison of Fluid and Kinetic Approaches

(2)

1.3 Electrostatic Particle in Cell Method

(3)

1.3.1 Lorentz Force

(1)

1.3.2 Maxwell's Equations

(1)

1.3.3 Poisson's Equation

(1)

1.3.4 Simulation Main Loop

(1)

1.4 Single Particle Motion

(27)

1.4.1 Domain Discretization

(4)

1.4.2 Finite Difference Method

(1)

1.4.3 Potential Solver

(1)

1.4.3.1 Tridiagonal Algorithm

(2)

1.4.3.2 Jacobi Iteration

(1)

1.4.3.3 Gauss-Seidel Scheme

(1)

1.4.3.4 Successive Over Relaxation

(1)

1.4.3.5 Convergence Check

(2)

1.4.4 Electric Field

(2)

1.4.5 Particle Motion

(1)

1.4.5.1 Forward Euler Method

(1)

1.4.5.2 Backward Euler

(1)

1.4.5.3 Leapfrog Method

(2)

1.4.5.4 Alternative Approaches

(1)

1.4.6 Interpolation

(2)

1.4.7 Diagnostics

(5)

1.5 Summary

(4)

Chapter 2 Grounded Box

(58)

2.1 Introduction

(1)

2.2 Simulation Setup

(2)

2.2.1 Pseudocode

(1)

2.3 World Object

(7)

2.3.1 Constructor

(1)

2.3.2 Declaration and Implementation

(1)

2.3.3 Multiple Files

(2)

2.3.4 Header Guards

(1)

2.3.5 Implementation

(1)

2.3.6 Mesh Resolution

(1)

2.4 Field Object

(12)

2.4.1 Memory Allocation

(1)

2.4.2 Operator Overloading

(2)

2.4.3 Templates

(1)

2.4.4 Move and Copy Constructors

(1)

2.4.5 Additional Operators

(1)

2.4.6 Output

(1)

2.4.7 Three-Component Vectors

(2)

2.4.8 Adding Fields to World

(1)

2.4.9 Initial Output

(2)

2.4.10 Visualization

(1)

2.5 Potential Solver

(4)

2.6 Electric Field

(2)

2.7 Particles

(9)

2.7.1 Particle Loading

(1)

2.7.2 Random Numbers

(3)

2.7.3 Node Volumes

(1)

2.7.4 Scatter: Particle to Mesh Interpolation

(3)

2.7.5 Number Density

(1)

2.8 Charge Density

(4)

2.8.1 Numerical Noise

(1)

2.8.2 Quiet Start

(2)

2.9 Particle Push

(7)

2.9.1 Gather: Mesh to Particle Interpolation

(1)

2.9.2 Velocity and Position Update

(1)

2.9.3 Particle Boundary Check

(1)

2.9.4 Velocity Rewind

(2)

2.9.5 Time Step

(1)

2.10 Diagnostics

(4)

2.10.1 Elapsed Time

(1)

2.10.2 Particle Counts, Momentum, and Energy

(1)

2.10.3 Animation

(1)

2.11 Main Loop

(1)

2.12 Results

(1)

2.12.1 Convergence Check

(1)

2.13 Summary

(5)

Chapter 3 Flow Around a Sphere

103

(34)

3.1 Introduction

103

(1)

3.2 Simulation Domain

103

(2)

3.3 Potential Solver

105

(7)

3.3.1 Sugarcubing

105

(2)

3.3.2 Neumann Boundaries

107

(1)

3.3.3 Boltzmann Electron Model

108

(1)

3.3.4 Non-Linear Poisson Solver

109

(3)

3.4 Particle Injection and Removal

112

(6)

3.4.1 Cold Beam Source

113

(2)

3.4.2 Particle Removal

115

(2)

3.4.3 Alternate Storage Schemes

117

(1)

3.5 Steady State and Data Averaging

118

(3)

3.6 Potential Solver Revisited

121

(13)

3.6.1 Matrix Representation

122

(2)

3.6.2 Sparse Matrix

124

(3)

3.6.3 Preconditioned Conjugate Gradient Solver

127

(2)

3.6.4 Newton-Raphson Linearization

129

(3)

3.6.5 Quasi-Neutral Approximation

132

(2)

3.7 Summary

134

(3)

Chapter 4 Material Interactions

137

(46)

4.1 Introduction

137

(1)

4.2 Multiple Species

137

(1)

4.3 Surface Interactions

138

(8)

4.3.1 Rebound Algorithm

138

(3)

4.3.2 Diffuse Reflection

141

(2)

4.3.3 Reflection Velocity

143

(1)

4.3.4 Species Change

144

(1)

4.3.5 Sputtering and Surface Emission

145

(1)

4.4 Warm Beam

146

(8)

4.4.1 Velocity Sampling

149

(4)

4.4.2 Particle Merge

153

(1)

4.5 Diagnostics

154

(8)

4.5.1 Macroscopic Properties

154

(4)

4.5.2 Macroparticle Count

158

(1)

4.5.3 Particle Plots

159

(3)

4.6 Collisions

162

(6)

4.6.1 Collision Cross Section

163

(1)

4.6.2 Collision Modeling

164

(1)

4.6.3 Chemistry

164

(2)

4.6.4 Monte Carlo Collisions (MCC)

166

(2)

4.7 DSMC

168

(5)

4.7.1 Particle Sorting

169

(1)

4.7.2 Collision Groups

169

(1)

4.7.3 Collision Probability

170

(1)

4.7.4 Momentum Exchange Collision Handler

171

(2)

4.8 Subcycling

173

(1)

4.9 Dielectric Boundaries

174

(2)

4.10 Discretized Surfaces

176

(4)

4.10.1 Line Triangle Intersection

177

(1)

4.10.2 Particle Impacts

178

(1)

4.10.3 Caveats

179

(1)

4.11 Summary

180

(3)

Chapter 5 Symmetry

183

(22)

5.1 Introduction

183

(1)

5.2 Symmetry

183

(2)

5.2.1 Domain Boundary Condition

183

(1)

5.2.2 Particles

184

(1)

5.2.3 Results

185

(1)

5.3 Periodic Systems

185

(4)

5.3.1 Domain Boundary

186

(2)

5.3.2 Particles

188

(1)

5.3.3 Density Synchronization

188

(1)

5.3.4 Results

189

(1)

5.4 Two-Dimensional Codes

189

(1)

5.5 Planar (XY) Codes

190

(4)

5.5.1 Node Volumes

191

(1)

5.5.2 Data Containers

192

(1)

5.5.3 Scatter and Gather

193

(1)

5.5.4 Output

194

(1)

5.6 Axisymmetric (RZ) Codes

194

(8)

5.6.1 Node Volumes

194

(1)

5.6.2 Finite Volume Method

195

(3)

5.6.3 Particle Source

198

(1)

5.6.4 Scatter and Gather

199

(1)

5.6.5 Particle Rotation

200

(2)

5.6.6 Results

202

(1)

5.7 Summary

202

(3)

Chapter 6 Unstructured Meshes

205

(44)

6.1 Introduction

205

(1)

6.2 Mesh Geometry

205

(10)

6.2.1 Mesh Generation

206

(1)

6.2.2 Mesh Formats

207

(3)

6.2.3 Mesh Import

210

(2)

6.2.4 Cell Volumes

212

(1)

6.2.5 Field Object

212

(1)

6.2.6 Node Volumes

213

(1)

6.2.7 Output

213

(2)

6.3 Particle Injection

215

(2)

6.4 Mesh Interpolation

217

(7)

6.4.1 Shape Factors

218

(2)

6.4.2 Cell Search

220

(2)

6.4.3 Cell Neighbors

222

(1)

6.4.4 Scatter and Gather

223

(1)

6.5 Particle Motion

224

(1)

6.5.1 Number Density

224

(1)

6.5.2 Neutral Results

225

(1)

6.6 Finite Element Method

225

(12)

6.6.1 Strong Form

226

(1)

6.6.2 Weak Form

226

(1)

6.6.3 Galerkin Form

227

(1)

6.6.4 Formulation with Shape Functions

228

(1)

6.6.5 Matrix Form

228

(2)

6.6.6 Element View

230

(1)

6.6.7 Matrix Assembly

231

(1)

6.6.8 Quadrature

231

(2)

6.6.9 Shape Functions

233

(1)

6.6.10 Coordinate Transformation

234

(1)

6.6.11 Single Element Algorithm

235

(1)

6.6.12 Derivatives

236

(1)

6.6.13 Tetrahedral Element

236

(1)

6.7 Putting It all Together

237

(8)

6.7.1 Initialization

237

(1)

6.7.2 Matrix Assembly

238

(2)

6.7.3 Shape Function Derivatives

240

(2)

6.7.4 Nonlinear Solver

242

(2)

6.7.5 Solution Assembly

244

(1)

6.7.6 Electric Field

245

(1)

6.7.7 Results

245

(1)

6.8 Summary

245

(4)

Chapter 7 Electromagnetics

249

(24)

7.1 Introduction

249

(1)

7.2 Classification

249

(1)

7.3 Magnetization

249

(4)

7.3.1 Boris Push

250

(3)

7.4 Magnetostatics

253

(5)

7.4.1 Vector Potential

254

(1)

7.4.2 Scalar Potential

254

(1)

7.4.3 Magnetized Sphere

255

(3)

7.5 Electromagnetic PIC

258

(11)

7.5.1 Curl

259

(1)

7.5.2 Staggered Grid

260

(1)

7.5.3 Time Integration

261

(1)

7.5.4 Boundary Conditions

262

(1)

7.5.5 Gauss' Law

262

(1)

7.5.6 Putting It All Together

263

(1)

7.5.7 Approximations

264

(1)

7.5.8 Relativistic Push

264

(1)

7.5.9 Example

265

(4)

7.6 Summary

269

(4)

Chapter 8 Eulerian Methods

273

(32)

8.1 Introduction

273

(1)

8.2 Magnetohydrodynamics

273

(5)

8.2.1 Conservation Equations

273

(3)

8.2.2 Single Fluid MHD Equations

276

(2)

8.3 Advection-Diffusion Equation

278

(15)

8.3.1 Steady State Form

279

(4)

8.3.2 Unsteady Problem

283

(3)

8.3.3 Stability Analysis

286

(1)

8.3.4 Alternative Time Integration Methods

287

(2)

8.3.5 Example

289

(4)

8.4 Electron Models

293

(3)

8.4.1 Polytropic Relationship

294

(1)

8.4.2 Detailed Electron Model

295

(1)

8.5 Vlasov Solvers

296

(6)

8.5.1 Two-Stream Instability Example

297

(5)

8.6 Summary

302

(3)

Chapter 9 Parallel Programming

305

(34)

9.1 Introduction

305

(1)

9.2 Architectures

305

(6)

9.2.1 Multithreading

307

(1)

9.2.2 MPI

308

(2)

9.2.3 CUDA

310

(1)

9.3 Caveats

311

(6)

9.3.1 Race Condition

311

(1)

9.3.2 Locks

312

(1)

9.3.3 Deadlock

313

(1)

9.3.4 Overhead

314

(3)

9.4 Profiling

317

(1)

9.5 Parallelization Strategies

318

(2)

9.5.1 Domain Decomposition

318

(1)

9.5.2 Ensemble Averaging

319

(1)

9.5.3 GPU Concurrent Computing

319

(1)

9.6 Examples

320

(16)

9.6.1 Multithreaded Particle Push

320

(1)

9.6.1.1 Number of Threads

321

(1)

9.6.1.2 Density Calculation

321

(2)

9.6.1.3 Parallel Efficiency

323

(1)

9.6.2 MPI Domain Decomposition

323

(1)

9.6.2.1 Subdomains

324

(2)

9.6.2.2 Particle Transfer

326

(3)

9.6.2.3 Boundary Update

329

(2)

9.6.2.4 Potential Solve

331

(2)

9.6.3 CUDA Potential Solve

333

(3)

9.7 Summary

336

(3)

Bibliography

339

(6)

Index

345

Lubos Brieda has over 10 years of experience developing plasma and gas simulation codes for electric propulsion, contamination transport, and plasma-surface interactions. As part of his masters research work, he developed a 3D ES-PIC electric propulsion plume code, Draco, which is to this date utilized by AFRL and private aerospace firms to study plasma thruster plumes. His Ph.D, obtained in 2012 from George Washington University, USA, focused on a multi-scale model for Hall thrusters utilizing fluid-kinetic hybrid PIC codes. Recently, after four years working as an engineer at NASA's Goddard Space Flight Centre, he developed a 3D particle-based contamination transport simulation program CTSP for modeling plume impingement, particulate redistribution during launch, and molecular transport in vacuum chambers. Since 2014 he has been teaching online courses on plasma simulations through his website.

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