Numerical Simulation of Plasmas

Numerical Simulation of Plasmas

Paperback(Softcover reprint of the original 1st ed. 1986)

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Product Details

ISBN-13: 9783642825941
Publisher: Springer Berlin Heidelberg
Publication date: 12/21/2011
Series: Scientific Computation
Edition description: Softcover reprint of the original 1st ed. 1986
Pages: 304
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Controlled Fusion and Numerical Simulation.- 1.1 Controlled Fusion.- 1.1.1 The Lawson Criterion.- 1.1.2 Magnetic and Inertial Confinement of Plasma.- 1.1.3 The Role of Numerical Simulation in Fusion Research.- 1.2 Tokamaks.- 1.2.1 Design and Principle of Operation.- 1.2.2 The Current Status of Tokamak Research.- 1.2.3 Mathematical Models of Plasma in Tokamak Devices.- 1.3 Motion of Charged Particles in Tokamaks.- 1.3.1 Drift Equation of Motion.- 1.3.2 Tokamak Magnetic Field with a Circular Cross Section.- 1.3.3 The Motion of Charged Particles in the Tokamak Magnetic Field.- 2. Simulation of Kinetic Processes Involving Coulomb Interaction.- 2.1 Operator of Coulomb Collisions.- 2.1.1 Coulomb Collision Operator.- 2.1.2 Properties of Coulomb Operator.- 2.1.3 Coulomb Collision Operator for Axisymmetric Velocity Distributions.- 2.1.4 Coulomb Collision Operator for Isotropic Velocity Distribution of ? Particles.- 2.2 Cauchy Problem. Characteristic Relaxation Times.- 2.2.1 Cauchy Problem.- 2.2.2 Collisions Between Particles of the Same Species. The Simplest Relaxation Time.- 2.2.3 Relaxation of Relative Motion of Electrons and Ions.- 2.2.4 Energy Exchange and Temperature Equalization in Nonisothermal Plasma.- 2.2.5 Qualitative Description of the Behavior of the Cauchy Problem Solution for Two-Component Plasma.- 2.3 Linear Problem on the Interaction Between Fast Ions and Maxwellian Plasma.- 2.3.1 Mathematical Formulation.- 2.3.2 Isotropic Problem.- 2.3.3 Two-Dimensional Problem.- 2.3.4 Difference Scheme for the Solution of a Linear Kinetic Equation.- 2.4 Electric Field Effects.- 2.4.1 Critical Electric Field.- 2.4.2 Runaway Electrons.- 2.4.3 Effective Electric Field Acting on Ions.- 2.4.4 Interaction of Fast Ions with Plasma in the Presence of an Electric Field.- 2.5 The a).- b) Internal Modes (rs < a).- c) Dissipative Modes (? ? ?).- d) Effect of Toroidicity on the Helical Mode Stability (R/a ? ?).- e) Local Stability Criteria (m ? 1, n ? 1).- 3.3.4 Numerical Solution of Stability Problems.- a) Time Evolution of Solutions of System (3.3.1).- b) Investigation of the Potential Energy Sign.- c) Minimization of Functional (3.3.13) to Obtain the Natural Frequency Spectrum.- d) Examples.- 3.4 Nonlinear Problems.- 3.4.1 Nonlinear Evolution of External Modes.- 3.4.2 Evolution of the Internal Mode m/n =1/1 and Reconnection of Magnetic Surfaces.- 3.4.3 Nonlinear Evolution of Modes m ? 2 and Growth of Islands.- 3.4.4 Helical Modes with Two Resonant Surfaces (“Double Tearing Modes”).- 3.4.5 Interaction Between Helical Modes.- 4. Transport Models.- 4.1 Physical Grounds of Transport Models.- 4.1.1 Basic Equations.- 4.1.2 Neoclassical Fluxes of Particles and Energy.- 4.2 Development of the Transport Model.- 4.2.1 Model of Classical Energy Balance.- 4.2.2 Anomalous Thermal Conductivity of Electrons.- 4.2.3 Particle Flux.- 4.2.4 Model for Neutrals.- 4.2.5 The Effect of Magnetic Field Rippling.- 4.2.6 Compression of Plasma by a Magnetic Field.- a) Compression Along the Minor Radius.- b) Compression Along the Major Radius.- 4.3 Impurities.- 4.3.1 Influx of Impurities into Plasma.- 4.3.2 Basic System of Equations.- 4.3.3 Atomic Processes.- 4.3.4 Particle Fluxes.- 4.3.5 Approximate Solutions of System (4.3.1).- 4.3.6 Comparison with Experiments.- 4.3.7 Radiation of Impurities in Energy Balance Models.- 4.4 Numerical Solution of Systems (4.1.1, 3.1).- 4.4.1 Linear Implicit Scheme.- 4.4.2 Nonlinear Implicit Scheme.- 4.4.3 Gear’s General Methods for Stiff Systems.- 4.5 Appendix.- 5. Hybrid Models.- 5.1 Models of Plasma Heating by High-Energy Neutral Injection.- 5.1.1 Ionization and Capture of Energetic Neutrals.- a) Narrow-Beam Model.- b) Wide-Beam Model.- 5.1.2 Simple Model of Energy Balance with Neutral Injection.- 5.1.3 Hybrid Model of Energy Balance with Neutral Injection.- 5.1.4 Effect of Multiple Charge Exchange on Energy Transfer from Fast Ions to Bulk Plasma Particles.- 5.2 Effect of MHD Mixing on Energy and Particle Balance.- 5.2.1 Experimental Data on Mixing.- 5.2.2 Structure of the Hybrid Model.- 5.2.3 The Kadomtsev Model of Internal Mixing for Tearing Mode m/n = 1/1.- 5.2.4 Mixing for Nonmonotonic Current Profile.- 5.2.5 Electric Field in Mixing.- 5.2.6 Properties of the Hybrid Model and Its Application to the Experiment Description.- 5.3 Kinetic Convective Transport of Ions in Longitudinal Magnetic Field Ripples.- 5.3.1 Diffusive and Convective Transport.- 5.3.2 Basic Equations.- 5.3.3 Solution of Systems (5.3.5-10) and (5.3.18-21).- 5.3.4 Numerical Solution of Systems (5.3.5-10), (5.3.28-32).- References.

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