elscande. microscopic dynamics of plasmas and chaos

[...]... effects like trapping or chaos for the electrons and fluctuating growth or damping for the waves In order to understand this interaction, fundamental concepts and methods must be introduced These are concepts of nonlinear dynamics and Hamiltonian chaos, relevant to all of classical mechanics, celestial mechanics, non-dissipative hydrodynamics, condensed matter and other fields of physics These concepts... why the Structure of the book xvii Hamiltonian character of the dynamics forbids Landau damping to correspond to an eigenmode and that even the Landau instability involves, backstage, analogues of van Kampen–Case eigenmodes The mechanical approach unifies the Landau theory, the van Kampen–Case theory, their simple physical description, the theory of spontaneous emission and the theory of cold beam–plasma... Benefits of modern tools The approach presented in this book is a direct consequence of this long-lasting controversy about quasilinear equations Indeed this controversy appeared in the 1980s in parallel with the development of nonlinear dynamics and chaos which involved, in particular, plasma physics An intuitive description of chaos and new tools were introduced especially for finite-dimensional dynamics. .. Kampen (1955, 1957) and Case (1959), and shows this damping to be the result of the phase mixing among a continuum of modes with the same wavenumber and a broad frequency spectrum—which questions the meaning of a dispersion relation for Langmuir waves However, even in one space dimension, both Landau and van Kampen–Case approaches fail to unveil the intuitive physical nature of the Landau effect (what... chapter apply to issues as different as the chaos of magnetic field lines, the heating of particles by cyclotronic waves, and chaos of rays in geometrical optics Chapter 7 shows how these ideas can be used to solve the warm beam–plasma instability and to hopefully close the previously mentioned quasilinear controversy; the theory of this chapter and the related part of the preceding one were found while this... wave, and one may consider it as a test particle subjected to it We now consider this test-particle dynamics, and we consider the motion of one particle in the presence of a static electrostatic potential which oscillates sinusoidally in the direction of a coordinate1 q (the analysis is performed in the rest frame of a Langmuir wave) With an appropriate choice of units and origin for q, the equation of. .. typical of energetic particles in tokamaks Structure of the book This book aims at a pedagogical presentation of these theoretical developments with the double concern of understanding and of computing It uses classical mechanics and introduces statistical averages only when they are necessary to obtain analytical results The outcome for the neophyte reader should be both to master the physical aspects of. .. 256 256 257 258 E Probability and stochastic processes E.1 General random variables and vectors E.2 Gaussian distributions E.3 Fokker–Planck equation 261 261 262 263 F Estimates for chapter 6 F.1 n-time correlation function of C(τ ) and S(τ ) F.2 Estimate of the mean number of visited boxes F.3 Initial Brownian motion F.4 Dependence of an orbit on one phase F.5 Estimate of non-quasilinear terms 268... introduces some basic tools of Hamiltonian chaos needed to understand the chaotic regime of wave–particle interactions Chapter 6 extends this introduction to the case of chaotic diffusion in a prescribed set of waves, with both its physical explanation and its analytical computation In fact this dynamics is a good approximation to that occurring in many Hamiltonian systems The concepts and techniques described... character of Landau’s theory It is worth recalling that even for specialists, the reality of collisionless Landau damping was fully recognized only after its experimental observation (Malmberg and Wharton 1964), almost two decades after its prediction (Landau 1946) Finally, when trying to make a complete analogy with the interaction of atoms and light, the student finds that the computation of the spontaneous . concepts of nonlinear dynamics and Hamiltonian chaos, relevant to all of classical mechanics, celestial mechanics, non-dissipative hydrodynamics, condensed matter and other fields of physics. These. Plenty Cover Design: Victoria Le Billon Marketing: Nicola Newey and Verity Cooke Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics. Physics of Hot Plasmas H Wilhelmsson and E Lazzaro The Plasma Boundary of Magnetic Fusion Devices P C Strangeby Non-Linear Instabilities in Plasmas and Hydrodynamics S S Moiseev, V N Oraevsky and