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Lecture Series in Energetic Particle Physics of Fusion Plasmas Guoyong Fu Princeton Plasma Physics Laboratory Princeton University Princeton, NJ 08543, USA IFTS, Zhejiang University, Hangzhou, China, Jan. 3-8, 2007

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A series of 5 lectures (1) Overview of Energetic Particle Physics in Tokamaks (Jan.3) (2) Tokamak equilibrium, shear Alfven wave equation, Alfven eigenmodes (Jan. 4) (3) Linear stability of energetic particle-driven modes (Jan. 5) (4) Nonlinear dynamics of energetic particle-driven modes (Jan. 6) (5) Summary and future direction for research in energetic particle physics (Jan. 8)

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Outline Kinetic/MHD hybrid model TAE stability: energetic particle drive and dampings EPM stability: fishbone mode Summary

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Kinetic/MHD Hybrid Model

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Quadratic form G.Y. Fu et al. Phys. Fluids B5, 4040 (1993)

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Drift-kinetic Equation for Energetic Particle Response

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A simple w k for passing particles

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Perturbative Calculation of Energetic Particle Drive G.Y.Fu and J.W. Van Dam, Phys. Fluids B1, 1949 (1989) R. Betti et al, Phys. Fluids B4, 1465 (1992).

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Finite Orbit Width Effects on Energetic Particle Drive G.Y. Fu et al, Phys. Fluids B4, 3722 (1992)

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Dampings of TAE Ion Landau damping Electron Landau damping Continuum damping Collisional damping “radiative damping” due to thermal ion gyroradius G.Y.Fu and J.W. Van Dam, Phys. Fluids B1, 1949 (1989) R. Betti et al, Phys. Fluids B4, 1465 (1992). F. Zonca and L. Chen 1992, Phys. Rev. Lett. 68, 592 M.N. Rosenbluth, H.L. Berk, J.W. Van Dam and D.M. Lindberg 1992, Phys. Rev. Lett. 68, 596 R.R. Mett and S.M. Mahajan 1992, Phys. Fluids B 4, 2885

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Ion Landau Damping

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“Radiative” damping The damping comes from coupling to kinetic Alfven waves due to thermal ion gyroradius effects. R.R. Mett and S.M. Mahajan 1992, Phys. Fluids B 4, 2885

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TAE Stability in ITER N.N. Gorelenkov, H.L. Berk, R. Budny, et al. 2003, Nucl. Fusion 43, 594

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Example of EPM: fishbone instability Mode structure is of (m,n)=(1,1) internal kink; Mode is destabilized by energetic trapped particles; Mode frequency is comparable to trapped particles’ precessional drift frequency K. McGuire, R. Goldston, M. Bell, et al. 1983, Phys. Rev. Lett. 50, 891 L. Chen, R.B. White and M.N. Rosenbluth 1984, Phys. Rev. Lett. 52, 1122

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Fishbone dispersion relation L. Chen, R.B. White and M.N. Rosenbluth 1984, Phys. Rev. Lett. 52, 1122

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Summary For discrete modes such as TAE, the stability can usually be calculated perturbatively. For EPM, a non-perturbative treatment is needed. For TAE, there are a variety of damping mechanisms. For instability, the energetic particle drive must overcome the sum of all dampings. For EPM to be unstable, the energetic particle drive must overcome continuum damping.

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