Institute for Fusion Theory and Simulation, Zhejiang University

IFTS Intensive Course on Advanced Plasma Physics-Spring 2014 Nonlinear dynamics of phase-space zonal structures and energetic particle physics in fusion plasmas. Announcement

Lecture Plan and Teaching Material

Abstract: This Lecture series addresses the importance of phase-space zonal structures for the investigation of nonlinear Alfvénic fluctuation behaviors in fusion plasmas and related transport phenomena. A general introduction is devoted to explaining the concept of phase space zonal structures and fluctuation induced transport processes, which generally occur on the same spatial and temporal scales. The role of wave-particle resonances is analyzed, with emphasis on the importance of equilibrium magnetic field geometry and nonuniformity in the onset of nonlocal behaviors. The concepts of resonance detuning, radial decoupling and phase-locking are introduced and explained within this framework. In the uniform plasma limit, the nonlinear dynamics of beam-plasma interaction is adopted as paradigm for understanding saturation by wave-particle trapping and to illustrate the calculation of renormalized particle distribution function as solution of the corresponding Dyson equation. The standard quasilinear plasma description is also derived from these results. For nonuniform toroidal plasmas of fusion interest, the general governing equations for the nonlinear dynamics of phase-space zonal structures are derived and discussed, including renormalized particle response and Dyson equation. Actual solutions for phase-space zonal structures in cases of practical interest are discussed in detail for the cases of fishbone fluctuations and Energetic Particle Modes, for which the self-consistent interplay between mode structure nonlinear dynamics and energetic particle transport is of crucial importance. Prerequisite of the course is a preliminary knowledge of general plasma physics, fluid description of magnetized plasmas and kinetic theory, including linear gyrokinetic equations, which are briefly reviewed in this Lecture series.
 

Main areas that will be explored are:
i) General introduction and background: the concept of phase space zonal          structures. (Lecture 1)
ii) The role of wave-particle resonances: onset of nonlocal behaviors.           (Lecture 2)
iii) The uniform plasma limit: the nonlinear beam-plasma system. (Lecture 3)
iv) Nonlinear dynamics of phase-space zonal structures: governing equations,            renormalized particle response and Dyson equation. (Lecture 4)
v) Nonlinear description of fishbones: nonlinear evolution (mode-particle           pumping) and reduced (predator-prey) equations. (Lecture 5)
vi) Energetic Particle Modes: solitons in active media and modulation of            the radial envelope. (Lecture 6)

Sources: Portions of these lecture notes are based on Lectures I gave for the IFTS Intensive Courses on Advanced Plasma Physics-Spring 2011 and 2012 at the Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, China. These Lecture Notes are all available online.
 
Lecture Notes: Available in electronic form following the hyperlinks above. At the end of each lecture, a list of specific reading material is given explicitly. Should you have difficulty in finding literatures and papers, please contact me at fulvio.zonca@enea.it.
 
Exercises and Research Projects: In the Lectures, both Exercises (E) and Research Projects (RP) of various difficulty levels are suggested.
 

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