WAVE TURBULENCE is a state of a system of many simultaneously excited and interacting waves characterized by an energy distribution which is not in any sense close to thermodynamic equilibrium. Such situations in a choppy sea, in a hot plasma, in dielectrics under arise, for example, a powerful laser beam, in magnets placed in a strong microwave field, etc. Among the great variety of physical situations in which wave turbulence arises, it is possible to select two large limiting groups which allow a detailed analysis. The first is fully developed wave turbulence arising when energy pumping and dissipation have essentially different space scales. In this case there is a wide power spectrum of turbulence. This type of turbulence is described in detail e. g. in Zakharov et al. 1 In the second limiting case the scales in which energy pumping and dissipation occur are the same. As a rule, in this case a narrow, almost singular spectrum of turbulence appears which is concentrated near surfaces, curves or even points in k-space. One of the most important, widely investigated and instructive examples of this kind of turbulence is parametric wave turbulence appearing as a result of the evolution of a parametric instability of waves in media under strong external periodic modulation (laser beam, microwave electromagnetic field, etc. ). The present book deals with parametric wave turbulence.

Klappentext

Wave turbulence is a state far from (thermodynamic) equilibrium. It can be observed in a stormy sea, a hot plasma, a dielectric in a powerful laser beam, in magnets exposed to strong microwave fields, etc. A distinction has to be made between fully developed turbulence and parametric turbulence. The latter is the subject of the present book.Addressing not only the expert but also the graduate student it gives a comprehensive review covering developments both in the West and in Eastern Europe where major research into this field has been done. Special attention is paid to the Hamiltonian formalism, multi-wave processes, modulation instabilities, self-focusing, wave collapses, S-theory, the mean-field approximation, chaos, Feynman diagrams, and comparison with experiments (magnons, spin waves).

Inhalt
1 Introduction to Nonlinear Wave Dynamics.- 1.1 Hamiltonian Method for Description of Waves in a Continuous Medium.- 1.2 Dimensional Estimation of Hamiltonian Coefficients.- 1.3 Dynamic Equations of Motion for Weakly Non-Conservative Wave Systems.- 1.4 Three-Wave Processes.- 1.5 Four-Wave Processes.- 2 The General Properties of Magnetodielectrics.- 2.1 Classification of Substances by Their Magnetic Properties.- 2.2 Nature of Interaction of Magnetic Moments.- 2.3 Energy of Ferromagnets in the Continuum Approximation.- 2.4 Magnetic and Crystallographic Structure of Some Magnets.- 3 Spin Waves (Magnons) in Magnetically Ordered Dielectrics.- 3.1 Hamiltonian of Magnons in Ferromagnets (FM).- 3.2 Hamiltonian Function of Magnons in Antiferromagnets.- 3.3 Comments at the Road Fork.- 3.4 Calculation of Magnon Hamiltonian.- 4 Nonlinear Dynamics of Narrow Packets of Spin Waves.- 4.1 Elementary Processes of Spin Wave Interaction.- 4.2 Self-Focusing of Magnetoelastic Waves in Antiferromagnets (AFM).- 4.3 Methods of Parametric Excitation of Spin Waves.- 5 Stationary Nonlinear Behavior of Parametrically Excited Waves. Basic S-Theory.- 5.1 History of the Problem.- 5.2 Statement of a Problem of Nonlinear Wave Behavior.- 5.3 Phase Relations and Mechanisms for Amplitude Limitation.- 5.4 Basic Equations of Motion in the S-Theory.- 5.5 Ground State of System of Interacting Parametric Waves.- 6 Advanced S-Theory: Supplementary Sections.- 6.1 Ground State Evolution of System with Increasing Pumping Amplitude.- 6.2 Influence of Nonlinear Damping on Parametric Excitation.- 6.3 Parametric Excitation Under the Feedback Effect on Pumping.- 6.4 Nonlinear Theory of Parametric Wave Excitation at Finite Temperatures.- 6.5 Introduction to Spatially Inhomogeneous S-Theory.- 6.6 Nonlinear Behavior of Parametric Waves from Various Branches. Asymmetrical S-Theory.- 6.7 Parametric Excitation of Waves by Noise Pumping.- 7 Non-Stationary Behavior of Parametrically Excited Waves.- 7.1 Spectrum of Collective Oscillations (CO).- 7.2 Linear Theory of CO Resonance Excitation.- 7.3 Threshold Under Periodic Modulation of Dispersion Law.- 7.4 Large-Amplitude Collective Oscillations and Double Parametric Resonance.- 7.5 Transient Processes when Pumping is Turned on.- 7.6 Parametric Excitation Under Sweeping of Wave Frequency.- 7.7 Problems.- 8 Secondary Parametric Wave Turbulence.- 8.1 Instability of Ground State and Auto-Oscillations.- 8.2 Route to Chaos in Dynamic Systems.- 8.3 Geometry of Attractors of Secondary Parametric Turbulence of Magnons.- 8.4 Secondary Turbulence and Collapses in Narrow Parametric Wave Packets.- 9 Experimental Investigations of Parametrically Excited Magnons.- 9.1 Experimental Investigations of Parametric Instability of Magnons.- 9.2 Nonlinear Behavior of Parametric Magnons General Information.- 9.3 Investigations of Stationary State With One Group of Pairs.- 9.4 Electromagnetic Radiation of Parametric Magnons.- 9.5 Collective Resonance of Parametric Magnons.- 9.6 Stepwise Excitation in YIG.- 9.7 Conditions of Excitation of Auto-Oscillations of Magnons.- 9.8 Effect of Radio-Frequency Field Modulation on Parametric Resonance.- 9.9 Double Parametric Resonance and Inhomogeneous Collective Oscillations of Magnons.- 9.10 Parametric Excitation of Magnons Under Noise Modulation of their Frequencies.- 10 Nonlinear Kinetics of Parametrically Excited Waves.- 10.1 General Equations.- 10.2 Limit of the S-Theory.- 10.3 Nonlinear Theory of Parametric Excitation of Waves in Random Media.- 10.4 Consistent Nonlinear Theory for Parametric Excitation of Waves.-References.