Intro -- Contents -- Foreword -- In memory of ... -- 1. Prof. Masahiro Wakatani and Fusion Research in His Days K. Itoh -- 1.1 Research period of Prof.Wakatani -- 1.2 Research on nonequilibrium systems -- 1.3 Wakatani-sensei's gifts to scientists -- 1.4 Closing words -- Acknowledgements -- References -- Magnetic relaxation and self-organization in astrophysical and laboratory plasmas -- 2. An Introduction to Mean Field Dynamo Theory D.W. Hughes and S.M. Tobias -- 2.1 Introduction -- 2.2 KinematicMean Field Theory -- 2.2.1 Formulation -- 2.2.2 Calculation of the transport coefficients -- 2.2.3 Linear mean field dynamo models -- 2.3 Incorporating Nonlinear Effects -- 2.3.1 The nonlinear behaviour of the transport coefficients -- 2.3.2 Other nonlinear effects -- 2.3.3 Nonlinear mean Field Models -- 2.3.3.1 Nonlinear Travelling Waves -- 2.3.3.2 Nonlinear Dynamos in Finite Cartesian and Spherical Domains -- 2.4 Discussion -- References -- 3. Origin, Structure and Stability of Astrophysical MHD Jets P.-Y. Longaretti -- 3.1 Introduction -- 3.2 Generalities on astrophysical jets -- 3.2.1 Accretion -- 3.2.1.1 Active Galactic Nuclei -- 3.2.1.2 Young stellar objects -- 3.2.2 Magnetic fields in jets -- 3.2.3 Relativistic vs non-relativistic jets in AGNs -- 3.3 Origin of jets -- 3.3.1 Central object -- 3.3.2 Disk/central-object interaction region -- 3.3.3 Disk -- 3.4 MHD jet structure -- 3.4.1 Jet launching and magnetic surface opening -- 3.4.2 Current structure, and jet acceleration and collimation -- 3.5 Stability of MHD jets -- 3.5.1 Global disk-jet stability and stationarity -- 3.5.2 Motion driving: the Kelvin-Helmholtz instability -- 3.5.3 Magnetic driving: the current and pressure instabilities -- 3.5.3.1 Current-driven instabilities -- 3.5.3.2 Pressure-driven instabilities -- 3.6 Summary and open issues -- Appendices.

3.A A brief compendium of relevant astrophysical facts -- 3.A.1 Mostly AGNs -- 3.A.2 Origin of magnetic fields -- 3.A.3 On the MHD approximation in astrophysics -- 3.B MHD axisymmetric steady-state equations -- 3.B.1 General form -- 3.B.2 IdealMHD form -- 3.C The Kelvin-Helmholtz instability of a single vortex sheet layer -- 3.D MHD stability and the energy principle -- 3.E Pressure-driven instabilities asymptotic limit -- Acknowledgments -- References -- Turbulence and turbulent transport - the agents of relaxation and structure formation -- 4. A Tutorial on Basic Concepts in MHD Turbulence and Turbulent Transport P.H. Diamond, S.-I. Itoh and K. Itoh -- 4.1 Introduction -- 4.2 K41 beyond dimensional analysis - revisiting the theory of hydrodynamic turbulence -- 4.3 Kraichnan-Iroshnikov, Goldreich-Sridhar and all that: a scaling theory of MHD turbulence -- 4.4 Steepening of nonlinear Alfven waves - a little compressibility goes a long way... -- 4.5 Turbulent flux diffusion in 2D MHD - a 'minimal' problem which is not so simple... -- 4.6 Conclusion -- Acknowledgments -- References -- 5. Intermittency Like Phenomena in Plasma Turbulence A. Das, P. Kaw and R. Jha -- 5.1 Introduction -- 5.2 Concept of intermittency in hydrodynamic fluids -- 5.3 Evidence for intermittency in plasmas -- 5.3.1 Laboratory fusion plasma -- 5.3.2 Space plasmas -- 5.3.3 Remarks -- 5.4 Plasma intermittency: fluid approach -- 5.5 Alternative approach for plasma turbulence -- 5.6 Summary and conclusion -- References -- 6. Nonlinear Cascades and Spatial Structure of Magnetohydrodynamic Turbulence W.-C. Müller and R. Grappin -- 6.1 Introduction -- 6.2 Magnetohydrodynamics -- 6.3 Basic concepts -- 6.4 Phenomenologies of turbulent cascades -- 6.4.1 Kolmogorov phenomenology -- 6.4.2 Iroshnikov-Kraichnan phenomenology -- 6.4.3 Goldreich-Sridhar phenomenology -- 6.5 Numerical simulation.

6.5.1 Pseudospectralmethod -- 6.6 Nonlinear energy dynamics -- 6.6.1 Isotropic energy spectra -- 6.6.2 Anisotropic energy spectra -- 6.6.3 Residual energy spectra -- 6.6.3.1 Closure theory -- 6.6.3.2 A phenomenology for the residual energy -- 6.7 Spatial structure -- 6.7.1 Intermittency modelling -- 6.7.1.1 Hydrodynamics -- 6.7.1.2 Isotropic MHD -- 6.7.1.3 Anisotropic MHD -- 6.8 Conclusion -- Acknowledgements -- References -- 7. Scale Covariance and Scale-ratio Covariance in Turbulent Front Propagation A. Pocheau -- 7.1 Introduction -- 7.2 Turbulent front and scale symmetries -- 7.3 From scale invariance to scale covariance -- 7.3.1 Single variable relationship -- 7.3.2 Geometry -- 7.3.3 Equilibrium systems -- 7.3.4 Out-of-equilibrium -- 7.4 On the scale-ratio invariance -- 7.4.1 The meaning of scale-ratio invariance -- 7.4.2 Single variable function -- 7.4.3 Multivariable function -- 7.4.4 Front propagation -- 7.5 Front propagation laws both scale covariant and scale-ratio covariant -- 7.6 Experimental evidence of scale covariance in turbulent front propagation -- 7.6.1 Experimental set-up and data processing -- 7.6.2 Integral analysis -- 7.6.3 Local analysis -- 7.6.4 Sensitivity of scale covariance -- 7.7 Scale construction of turbulent fronts -- 7.7.1 Deterministic construction of front geometry in scale space -- 7.7.2 "Apparent" fractal dimensions -- 7.7.3 An artifact of finite size: the variation of "fractal dimensions" with turbulence intensity -- 7.8 Conclusion -- References -- Transport bifurcations and relaxation -- 8. Transport Barrier Relaxations in Tokamak Edge Plasmas P. Beyer -- 8.1 Introduction -- 8.2 Model for resistive ballooning turbulence -- 8.3 Formation of a transport barrier -- 8.4 Appearance of relaxation oscillations -- 8.5 Low dimensional model and non-linear short-term dynamics of shear flow stabilization -- 8.6 Conclusions.

References -- 9. Dynamics of Edge Localized Modes X. Garbet, P. Ghendrih, Y. Sarazin, P. Beyer, G. Fuhr-Chaudier and S. Benkadda -- 9.1 Introduction -- 9.2 An introduction to edge localized modes -- 9.2.1 Tokamak geometry -- 9.2.2 A brief description of edge localized modes -- 9.2.3 MHD stability -- 9.3 Dynamical models of edge localized modes -- 9.3.1 Minimal model -- 9.3.2 Quasi-linear MHD model -- 9.3.3 Status of the modelling of ELM's based on the MHD quasi-linearmodel -- 9.4 L-H transition and edge localized modes -- 9.4.1 Models based on a subcritical bifurcation -- 9.4.2 Models based on shear flow stabilization -- 9.4.3 Models based on shear flow generation -- 9.5 Conclusion -- Acknowledgments -- References -- 10. On the Onset of Collapse Events in Toroidal Plasmas Turbulence Trigger K. Itoh, S.-I. Itoh, M. Yagi, S. Toda and A. Fukuyama -- 10.1 Introduction -- 10.2 Phenomenological observations and problem definition -- 10.2.1 Onset of collapse and topological change of magnetic surfaces -- 10.2.2 Approaches for bifurcation phenomena -- 10.3 Theoretical Framework -- 10.3.1 Model -- 10.3.2 Stochastic equation -- 10.3.3 Statistical properties -- 10.3.3.1 Nonlinear dissipation function -- 10.3.3.2 Rate of transition -- 10.3.3.3 Phase boundary and the rule for selection of the state -- 10.3.3.4 Life time near phase boundary -- 10.3.3.5 Short summary -- 10.4 Example of Neoclassical Tearing Mode -- 10.4.1 Description of nonlinear instability and stochastic equation -- 10.4.2 Nonlinear instability, subcritical excitation and cusp catastrophe -- 10.4.3 Statistical property -- 10.4.3.1 Nonlinear dissipation function -- 10.4.3.2 Statistical average and phase boundary -- 10.4.3.3 Life time -- 10.5 Conclusion -- Acknowledgements -- References.

Key Features:Provides an extremely pedagogical reference text for PhD studentsSuitable for more experienced physicists by presenting an up-to-date and comprehensive overview of the present theories on the subjectWell-known authors and active contributors in the field who regularly share and confront their views in high-level publications and conferences, while continuously training young researchers.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.