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…mehr
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.
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.
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.
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