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Book Cover
E-book
Author Elskens, Y

Title Microscopic Dynamics of Plasmas and Chaos
Published London : CRC Press LLC, 2001

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Description 1 online resource (329 pages)
Series Series in Plasma Physics Ser
Series in Plasma Physics Ser
Contents Cover; Half Title; Title Page; Copyright Page; Permissions; Table of Contents; Preface; Difficulties in the traditional approach; Benefits of modern tools; Structure of the book; Prerequisites and remarks; 1: Basic physical setting; 1.1 The original N-body system; 1.1.1 Physical context; 1.1.2 The plasma model; 1.2 Wave-particle resonance: a paradigm of classical mechanics; 2: From N-body dynamics to wave-particle interaction; 2.1 Intuitive derivation of the self-consistent Hamiltonian; 2.2 Langmuir waves without resonant particles
2.2.1 Decomposition of the field and particle motion-relevant small parameters2.2.2 Collective dynamics; 2.2.3 Bohm-Gross modes; 2.3 Coupled motion of quasi-resonant particles with Bohm-Gross modes; 2.4 Lagrangian formulation*; 2.5 Reference states of the plasma*; 2.5.1 Non-existence of zero-field states; 2.5.2 Thermal distribution of the electric field; 2.6 Physical scalings and error estimates*; 2.7 Final form of the Hamiltonian; 2.8 Historical background and notes; 3: Dynamics of the small-amplitude wave-particle system; 3.1 Reference state with a vanishing electric field
3.2 Small perturbation to the reference state3.3 Ballistic solutions; 3.4 Wavelike solutions; 3.5 Initial value problem; 3.6 Dispersion relation for wavelike modes; 3.7 Physical interpretation: cold beams; 3.7.1 Case of a single beam; 3.7.2 Case of two beams; 3.8 Many cold beams or a warm beam; 3.8.1 Landau unstable mode; 3.8.2 Eigenmodes and initial value problem; 3.8.3 Van Kampen modes*; 3.8.4 Relation with ballistic eigenmodes; 3.8.5 Transition from cold to warm beams; 3.9 Synchronization of particles with a wave; 3.9.1 Synchronization of particles with a wavelike mode
3.9.2 Synchronization of particles during Landau damping*3.9.3 Fate of particles in the presence of many incoherent modes; 3.10 Historical background; 4: Statistical description of the small-amplitude wave-particle dynamics; 4.1 Approach using perturbation expansion; 4.1.1 Second-order perturbation analysis; 4.1.2 Evolution of waves; 4.1.3 Evolution of particles; 4.1.4 Fokker-Planck equation for the particles; 4.2 Approach using Floquet equation*; 4.3 Link with traditional descriptions; 4.3.1 Landau effect from a Vlasovian point of view; 4.3.2 Spontaneous emission; 5: Hamiltonian chaos
5.1 Geometrical tools for Hamiltonian chaos5.1.1 Poincaré surface of section; 5.1.2 Conservation of areas, symplectic dynamics and flux*; 5.1.3 Action-angle variables; 5.2 Motion of one particle in the presence of two waves; 5.2.1 Small resonance overlap and cantori; 5.2.2 Moderate resonance overlap and stochastic layers; 5.2.3 Physical summary; 5.3 Construction of orbits; 5.3.1 Origin of higher-order resonances; 5.3.2 Poincaré and KAM theorems*; 5.3.3 Higher-order resonances from action-angle variables; 5.4 Renormalization for KAM tori; 5.4.1 Simple approach to renormalization
Notes 5.4.2 More explicit derivation*
Print version record
Form Electronic book
Author Escande, D. F
ISBN 9781420033953
1420033956