Alfvén modes and wave-particle interaction in a tokamak
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This work is motivated by the nonlinear wave-particle interaction problems. To build a self-consistent theory, we consider eigenmodes of the bulk plasma as well as the dynamics of the energetic particles. The modes of our particular interest are the Alfvén Cascades and the Toroidicity Alfven Eigenmodes (TAE), which we describe using Magnetohydrodynamic(MHD) analysis and the AEGIS codes. We investigate the stabilizing effect for the Alfvenic waves from continuum damping, especially near the TAE gap. For the kinetic description of the energetic particles, we propose new canonical straight field line coordinates to model the guiding center motion. We then formulate wave-particle interaction problem using the action-angle variables. In Chapter 2, we interpret Alfvén Cascades observed in Madison Symmetric Torus (MST). We do linear MHD calculations and find the mode frequency, structure, and stability boundary. We then perform MHD simulation using the AEGIS code, with the equilibrium reconstructed from experiment. The result is discussed and compared with the experimentally observed features. In Chapter 3, we analyze continuum damping for Alfvénic waves, especially in the extreme situation near the TAE gap. We find that the continuum tip absorption feature is actually related to the existing of TAEs in the gap. On the technical level, we improve the numerical scheme of AEGIS and resolve two closely-spaced singularities. As a result, the absorption features observed in the simulation show good agreement with our analytical calculation. In order to simulate the energetic particle guiding center motion in the Hamiltonian form, we propose a new set of straight magnetic field line coordinates. The new coordinates exist for general tokamak devices and facilitate both MHD calculations and energetic particles. The new coordinate system makes it very convenient to take the advantage of the Hamiltionian structure of the guiding center motion. We use a canonical transformation to action-angle variables to formulate the interaction model for particles. The action-angle variables allow us to resolve wave-particle resonances and describe the conserved quantities for resonance particles. The model can give us a complete picture for nonlinear stage of wave-particle interaction.