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Register a new userContributions of plasma physics to chaos and nonlinear dynamics
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Dominique Escande
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This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016]
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Laser-generated plasma gratings are dynamic optical elements for the manipulation of coherent light at high intensities, beyond the damage threshold of solid-stated based materials. Their formation, evolution and final collapse require a detailed understanding. In this paper, we present a model to explain the nonlinear dynamics of high amplitude plasma gratings in the spatially periodic ponderomotive potential generated by two identical counter-propagating lasers. Both, fluid and kinetic aspects of the grating dynamics are analyzed. It is shown that the adiabatic electron compression plays a crucial role as the electron pressure may reflect the ions from the grating and induce the grating to break in an X-type manner. A single parameter is found to determine the behaviour of the grating and distinguish three fundamentally different regimes for the ion dynamics: completely reflecting, partially reflecting/partially passing, and crossing. Criteria for saturation and life-time of the grating as well as the effect of finite ion temperature are presented.
These lecture notes were presented by Allan N. Kaufman in his graduate plasma theory course and a follow-on special topics course (Physics 242A, B, C and Physics 250 at the University of California Berkeley). The notes follow the order of the lectures. The equations and derivations are as Kaufman presented, but the text is a reconstruction of Kaufmans discussion and commentary. The notes were transcribed by Bruce I. Cohen in 1971 and 1972, and word-processed, edited, and illustrations added by Cohen in 2017 and 2018. The series of lectures are divided into four major parts: (1) collisionless Vlasov plasmas (linear theory of waves and instabilities with and without an applied magnetic field, Vlasov-Poisson and Vlasov-Maxwell systems, WKBJ eikonal theory of wave propagation); (2) nonlinear Vlasov plasmas and miscellaneous topics (the plasma dispersion function, singular solutions of the Vlasov-Poisson system, pulse-response solutions for initial-value problems, Gardiners stability theorem, gyroresonant effects, nonlinear waves, particle trapping in waves, quasi-linear theory, nonlinear three-wave interactions); (3) plasma collisional and discreteness phenomena (test-particle theory of dynamic friction and wave emission, classical resistivity, extension of test-particle theory to many-particle phenomena and the derivation of the Boltzmann and Lenard-Balescu equations, the Fokker-Planck collision operator, a general scattering theory, nonlinear Landau damping, radiation transport, and Duprees theory of clumps); (4) nonuniform plasmas (adiabatic invariance, guiding center drifts, hydromagnetic theory, introduction to drift-wave stability theory).
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological phase can also be fruitfully applied to plasmas. Here, the theory of topological phase is introduced, including a discussion of Berry phase, Berry connection, Berry curvature, and Chern number. One of the clear physical manifestations of topological phase is the bulk-boundary correspondence, the existence of localized unidirectional modes at the interface between topologically distinct phases. These concepts are illustrated through examples, including the simple magnetized cold plasma. An outlook is provided for future theoretical developments and possible applications.
The radiation reaction radically influences the electron motion in an electromagnetic standing wave formed by two super-intense counter-propagating laser pulses. Depending on the laser intensity and wavelength, either classical or quantum mode of radiation reaction prevail, or both are strong. When radiation reaction dominates, electron motion evolves to limit cycles and strange attractors. This creates a new framework for high energy physics experiments on an interaction of energetic charged particle beams and colliding super-intense laser pulses.
We consider the general problem of charged particle motion in a strong electromagnetic field of arbitrary configuration and find a universal behaviour: for sufficiently high field strengths, the radiation losses lead to a general tendency of the charge to move along the direction that locally yields zero lateral acceleration. The relativistic motion along such a direction results in no radiation losses, according to both classical and quantum descriptions of radiation reaction. We show that such a radiation-free direction (RFD) exists at each point of an arbitrary electromagnetic field, while the time-scale of approaching this direction decreases with the increase of field strength. Thus, in the case of a sufficiently strong electromagnetic field, at each point of space, the charges mainly move and form currents along local RFD, while the deviation of their motion from RFD can be calculated in order to account for their incoherent emission. This forms a general description of particle, and therefore plasma, dynamics in strong electromagnetic fields, the latter can be generated by state-of-the-art lasers or in astrophysical environments.
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