EULERIAN CODES FOR THE NUMERICAL SOLUTION OF THE KINETIC EQUATIONS OF PLASMAS -- EULERIAN CODES FOR THE NUMERICAL SOLUTION OF THE KINETIC EQUATIONS OF PLASMAS -- CONTENTS -- EDITOR'S FOREWORD -- DEDICATION -- Chapter 1 SPLITTING METHODS FOR VLASOV-MAXWELL EQUATIONS IN PLASMA SIMULATIONS -- Abstract -- IntroductiON -- Splitting Scheme -- Langmuir Soliton -- A. Electron Heating by Langmuir Soliton -- B. Propagation of Langmuir Soliton -- Electron Cyclotron Wave -- Conclusion -- References -- Chapter2AVLASOVAPPROACHTOCOLLISIONLESSSPACEANDLABORATORYPLASMAS -- Abstract -- 1. Introduction -- 2. The Vlasov-Maxwell Equations as a Hamiltonian Flow onPhase Space -- 3. Commonly Used Numerical Schemes -- 3.1. Particle Methods -- 3.3. A Comparison between Numerical Techniques -- 4. The Vlasov Equation -- 4.1. A Multi-advection Equation -- 4.2. The Particles Motion, Electrostatic Limit -- 4.3. Splitting Scheme -- 4.4. Discrete Representation of the Distribution Function on FunctionalSpaces -- 4.5. Discontinuous Galerkin Schemes -- 4.6. Van Leer Interpolation -- 4.7. Splines Interpolation -- 4.8. Fourier Decomposition -- 4.9. Semi-Lagrangian Methods -- 5. An Application: The Weibel Instability -- Acknowledgements -- References -- Chapter3EULERIANCONSERVATIVEADVECTIONSCHEMESFORVLASOVSOLVERS -- Abstract -- 1. Introduction -- 2. 1D Electrostatic Problems -- 2.1. The Codes Tested -- 2.2. 1D Electrostatic Test Problems -- 2.3. Summary of 1D Electrostatic Tests -- 3. Electromagnetic Problems -- 3.1. 1D Relativistic EM Vlasov Solvers -- 3.2. 2D Relativistic EM Vlasov Solvers -- 4. Solving Amp`ere instead of Poisson -- 5. Electrostatic Problems with Dissipation, Krook Collisionsand a Particle Source -- 6. Conclusion -- References -- Chapter4EULERIAN-LAGRANGIANKINETICSIMULATIONSOFLASER-PLASMAINTERACTIONS -- Abstract -- Introduction.

2. ELVIS Equations and Numerical Method -- 2.1. Model and Geometry -- 2.2. Structure of the Timestep -- 2.3. f Advection: Cubic Splines -- 2.4. Krook Operator -- 2.5. Solving for Ex -- 2.6. Advance of Transverse Fields E±, vys -- 3. Electrostatic Application: Langmuir-Wave Dispersion -- 4. Application to Raman Scattering -- 4.1. Kinetic Inflation and Electron Acoustic Scatter (no Krook Operator) -- 4.2. Inclusion of a Krook Operator -- 4.3. Inclusion of Seed Bandwidth -- 5. Conclusion -- Acknowledgments -- References -- Chapter5GYROKINETICVLASOVSIMULATIONSFORTURBULENTTRANSPORTINMAGNETIZEDPLASMAS -- Abstract -- 1. Introduction -- 2. Vlasov Simulation Methods Based on Symplectic Integrators -- 2.1. Generalization of Splitting Scheme -- 2.2. Verification of Generalized Splitting Scheme -- 2.3. Application to Drift Kinetic System -- 2.4. Verification of Nondissipative Scheme for Drift Kinetic Systems -- 3. Turbulent Transport and Fine-Scale Distribution Functions -- 3.1. Steady and Quasisteady States of Plasma Turbulence -- 3.2. Generation of Fine Structures of Distribution Function -- 3.3. Relation to Kinetic-Fluid Closure Model -- 4. Gyrokinetic Vlasov Simulations of Toroidal Plasmas -- 4.1. Gyrokinetic Vlasov Simulation Code GKV -- 4.2. Collisionless Damping of Zonal Flows and Geodesic Acoustic Mode -- 4.3. Entropy Balance in Toroidal ITG Turbulence -- 4.4. Application to ITG Turbulent Transport in Helical Systems -- 5. Conclusions -- Acknowledgments -- References -- Chapter 6 NUMERICAL SOLUTION OF THE RELATIVISTIC VLASOV-MAXWELL EQUATIONS FOR THE STUDY OF THE INTERACTION OF A HIGH INTENSITY LASER BEAM NORMALLY INCIDENT ON AN OVERDENSE PLASMA -- Abstract -- 1. Introduction -- 2. The Relevant Equations -- 2.1. The 1D relativistic Vlasov-Maxwell Model -- 2.2. The Numerical Scheme.

3. A Circularly Polarized Laser Wave Incident on an OverdensePlasma (n/ncr=25) -- A. Case with 4 0 a = -- 4. A Circularly Polarized Laser Wave Incident on a ModeratelyOverdense Plasma (n/ncr=1.731) -- 5. A Circularly Polarized Laser Wave Incident on a ModeratelyOverdense Plasma (n/ncr=1.6) -- A. Case with 0 ~ λ edge L -- B. Case with 0λ -- 6. A linearly Polarized Laser Wave Incident on an OverdensePlasma (n/ncr=25): Harmonics Generation -- 7. Conclusion -- Acknowledgments -- References -- Chapter 7 SEMI-ANALYTICAL ADAPTIVE VLASOV - FOKKER-PLANCK - BOLTZMANN METHODS -- Abstract -- 1. Introduction -- 2. Comparison of PIC-DSMC and Vlasov-Boltzmann Methods -- 2.1. Collisionless Plasma -- 2.2. PIC-Vlasov Hybrid for Collisionless and Collisional Plasma -- 2.3. Direct Simulation of Coulomb Collisions in PIC Method -- 2.4. Coulomb Collisions with Averaged Potential Functions -- 2.5. Non-linear Coulomb Collisions in PIC and Fokker-Planck Method -- 2.6. Phase Resolution of the Energetic Part of the DF -- 3. Continuous Fokker-Planck Method for Quasineutral Systems -- 3.1. Splitting Scheme for Electron-Ion Plasma with Coulomb Interaction -- 3.2. Semi-analytical and Finite-Volume Approximation of DifferentOperators in the FP Kinetic Equation -- 4. Continuous Boltzmann Method for Neutral Particles -- 4.1. Splitting Scheme for Gas with Boltzmann Collisions -- 4.2. Use of Analytical Solutions for Sub-steps -- 4.3. Benchmarking of the Method -- Conclusion -- Acknowledgments -- Appendix A. Conservative Kinetic Method for Collisional Gasand Plasma -- Appendix B. Transformation from Cartesian to AxiallySymmetric Spherical System of Coordinates -- References -- Chapter 8 THE BUMP-ON-TAIL INSTABILITY -- Abstract -- 1. Introduction -- 2. The Relevant Equations -- 3. The Bump-on-Tail Instability -- 4. Excitation of a Fundamental Mode with k=0.3.

5. Excitation of a Harmonic Mode n=3 with k=0.3 -- 6. Conclusion -- Acknowledgments -- References -- INDEX -- Blank Page.