1. TH/3-1Ra Nonperturbative Effects of Energetic Ions on Alfvén Eigenmodes by Y. Todo et al. EX/5-4Rb Configuration Dependence of Energetic Ion Driven Alfven Eigenmodes in the Large Helical Device by S. Yamamoto et al.

2. Nonperturbative Effects of Energetic Ions on Alfvén Eigenmodes Y. Todo, N. Nakajima (NIFS) K. Shinohara, M. Takechi, M. Ishikawa (JAERI) S. Yamamoto (Inst. Adv. Energy, Kyoto Univ.) November 1-6, 2004 20th IAEA Fusion Energy Conference Vilamoura, Portugal TH/3-1Ra

3. Outline Linear properties of an unstable mode in a JT- 60U plasma were investigated. The unstable mode is a nonlocal energetic particle mode (EPM). Linear properties of an unstable mode in a JT- 60U plasma were investigated. The unstable mode is a nonlocal energetic particle mode (EPM). Nonlinear simulation of the frequency sweeping of the nonlocal EPM. Nonlinear simulation of the frequency sweeping of the nonlocal EPM. Extension of the MEGA code to the helical coordinate system. Extension of the MEGA code to the helical coordinate system.

4. Fast Frequency Sweeping Mode observed in the JT-60U plasma with NNB injection K. Shinohara et al., Nucl. Fusion 41, 603 (2001). Frequency sweeping takes place both upward and downward by 10-20kHz in 1-5 ms. Investigations of the spatial profile and the nonlinear evolution of the unstable mode are needed.

5. MEGA: a simulation code for MHD and energetic particles [Y. Todo and T. Sato, Phys. Plasmas 5, 1321 (1998)] 1. Plasma is divided into “energetic ions” + “MHD fluid”. 2. Electromagnetic fields are given by MHD equations. 3. Energetic ions are described by the drift-kinetic equation. 4. MHD equilibria consistent with energetic ion distributions are constructed using an extended Grad- Shafranov equation [E.V. Belova et al. Phys. Plasmas 10, 3240 (2003)].

6. Frequency and location of the unstable mode Frequency and location of the unstable mode Toroidal mode number n=1 q(0)=1.64 q=2.5 at r/a=0.8 The unstable mode is not located at the TAE gap at r/a=0.8. This indicates that the unstable mode is not a TAE.

7. Energetic ion orbit width broadens the spatial width of the unstable mode Energetic ion orbit width broadens the spatial width of the unstable mode

8. Effects of the energetic ion orbit width Effects of the energetic ion orbit width Peak location and radial width of the unstable mode spatial profile versus energetic ion orbit width. Growth rate and real frequency of the unstable mode versus energetic ion orbit width.

9. Nonlocal Energetic Particle Mode 1.The spatial width of the unstable mode with the smallest orbit width gives an upper limit of the spatial width which the MHD effects alone can induce. 2.For the experimental condition of the JT-60U plasma, the energetic ions broadens the spatial profile of the unstable mode by a factor of 3. 3.The major part of the spatial profile of the unstable mode is induced by the energetic ions. 4.It is concluded that the unstable mode is primarily induced by the energetic ions and the name “nonlocal EPM” can be justified.

10. Frequency sweeping of the nonlocal EPM (The initial energetic ion beta value is 2/5 of the classical distribution.) Left: Time evolution of the cosine part of radial magnetic field.  B r, average /B~5  10 -4 Right: Frequency shifts both upward and downward by 9% (~5kHz) in 400 Alfvén time (~0.3ms). Close to the experiment.

11. Comparison with the hole-clump pair creation I For [H. L. Berk et al., Phys. Lett. A 234, 213 (1997); 238, 408(E) (1998)] For  d /  A =0.027,  L /  A =0.040, the hole-clump pair creation theory [H. L. Berk et al., Phys. Lett. A 234, 213 (1997); 238, 408(E) (1998)] predicts frequency shift  =0.44  L (  d t) 1/2 =0.018  A in 400 Alfvén time. This corresponds to 7% of the real frequency and 4kHz. This is consistent with the simulation results. This suggests that the hole-clump pair creation causes the fast frequency sweeping in the JT-60U plasma.

12. Extension of the MEGA Code for Helical Plasmas The interesting experimental results of Alfvén eigenmodes in the LHD and CHS plasmas motivate us to extend the MEGA code for helical plasmas. The interesting experimental results of Alfvén eigenmodes in the LHD and CHS plasmas motivate us to extend the MEGA code for helical plasmas. The MEGA code has been extended to the helical coordinate system (u 1,u 2,u 3 ) which is used in the MHD equilibrium code, HINT. The MEGA code has been extended to the helical coordinate system (u 1,u 2,u 3 ) which is used in the MHD equilibrium code, HINT. Relation between the helical coordinates and the cylindrical coordinates (R, , z): Relation between the helical coordinates and the cylindrical coordinates (R, , z):

13. Investigation of a TAE in an LHD-like plasma ・  h0 =1.3% ・ The initial equilibrium is calculated using the HINT code. ・ TAE with the toroidal mode number n=2 ・  /  A ~0.31,  /  A ~0.028

14. Summary TH/3-1Ra TH/3-1Ra A nonlocal EPM exists near the plasma center in the JT-60U plasma. A nonlocal EPM exists near the plasma center in the JT-60U plasma. The nonlinear simulation demonstrated that the frequency shifts of the nonlocal EPM are close to the experimental results. The nonlinear simulation demonstrated that the frequency shifts of the nonlocal EPM are close to the experimental results. The MEGA code has been successfully extended to the helical coordinate system. The MEGA code has been successfully extended to the helical coordinate system. EX/5-4Rb EX/5-4Rb The Alfvén eigenmodes observed in the LHD plasmas were compared with the CAS3D3 calculation results. The Alfvén eigenmodes observed in the LHD plasmas were compared with the CAS3D3 calculation results. The magnetic shear is the key to control the Alfvén eigenmodes in the LHD plasma. The magnetic shear is the key to control the Alfvén eigenmodes in the LHD plasma. This suggests that the continuum damping is the most important damping mechanism in the LHD plasma. This suggests that the continuum damping is the most important damping mechanism in the LHD plasma. The upper envelope of the fluctuation amplitude scales as 2. The upper envelope of the fluctuation amplitude scales as 2.

15. Configuration Dependence of Energetic Ion Driven Alfvén Eigenmodes in the Large Helical Device S. Yamamoto 1, K. Toi 2, N. Nakajima 2, S. Ohdachi 2, S. Sakakibara 2, C. Nührenberg 3, K.Y. Watanabe 2, S. Murakami 4, M. Osakabe 2, N. Ohyabu 2, K. Kawahata 2, M. Goto 2, Y. Takeiri 2, K. Tanaka 2, T. Tokuzawa 2, K. Narihara 2, Y. Narushima 2, S. Masuzaki 2, S. Morita 2, I. Yamada 2, H. Yamada 2, LHD experimental group 1) Institute of Advanced Energy, Kyoto University, Uji, Japan 2) National Institute for Fusion Science, Toki, Japan 3) Max-Planck-Institute für Plasmaphysik, IPP-Euratom Association, Greifswald, Germany 4) Graduate School of Engineering, Kyoto University, Kyoto, Japan 20th IAEA Fusion Energy Conference November 1 ~ 6, 2004 Vilamoura, Portugal EX/5-4Rb

16. Objective The energetic ion driven Alfvén eigenmodes such as the toroidicity-induced Alfvén eigenmmodes (TAE) and the helicity-induced Alfvén eigenmodes (HAE) are observed in the NBI-heated LHD plasmas. The energetic ion driven Alfvén eigenmodes such as the toroidicity-induced Alfvén eigenmmodes (TAE) and the helicity-induced Alfvén eigenmodes (HAE) are observed in the NBI-heated LHD plasmas. Clarify the magnetic configuration dependence of Alfvén eigenmodes. The magnetic configuration is controlled by the vacuum magnetic axis position and the plasma beta value. Clarify the magnetic configuration dependence of Alfvén eigenmodes. The magnetic configuration is controlled by the vacuum magnetic axis position and the plasma beta value. Compare the observed Alfvén eigenmodes with the CAS3D3 calculation results. Compare the observed Alfvén eigenmodes with the CAS3D3 calculation results.

17. Profiles of rotational transform and magnetic shear Configuration 1: high magnetic shear Configuration 2: middle magnetic shear Configuration 3: low magnetic shear

18. Alfvén eigenmodes in high magnetic shear (configuration 1) Two bursting Alfvén eigenmodes are observed after t=0.8s. Dotted and dashed curves denote f TAE (m/n=2,3/1) and f TAE (m/n=3,4/2)

19. Comparison of the observed frequencies with the eigenmodes calculated using the CAS3D3 code The n=1 and 2 modes are identified with the core- localized TAE and the global TAE, respectively. N f =1 C-TAE m=2,3 G-TAE m=3,4,5 N f =2

20. Alfvén eigenmodes in middle magnetic shear (configuration 2) A number of bursting global TAEs with n=2-5 are observed. An ellipticity-induced Alfvén eigenmode with n=5 (f=125kHz at t=1.5s) is observed.

21. Comparison of the observed frequencies with the eigenmodes calculated using the CAS3D3 code The global TAE is localized around the TAE gap: “gap localized TAE”. N f =2N f =5

22. Alfvén eigenmodes in low magnetic shear (configuration 3) A number of bursting global TAEs with n=1-5 are observed. Appreciable energetic ion transport [EX/P4- 44]. Helicity-induced Alfvén eigenmode (f~200kHz at t=1.5s).

23. Comparison of the observed frequencies with the eigenmode calculated using the CAS3D3 code The TAE gaps are well aligned due to the low magnetic shear and the large Shafranov shift. The TAE with n=2 extends from the core to the edge. N f =2(n=±2, ±8,.., ± 52) HAE gap AE gap frequency:  = 1, = 0:  (1,0) - TAE  = 2, = 1:  (2,1) - HAE 21

24. Magnetic fluctuation amplitude versus Threshold value in the beam ion beta is lower for the low magnetic shear (right figure) than the high magnetic shear. The upper envelope of the magnetic fluctuation amplitude scales as 2 in the left figure. This suggests the wave- particle trapping. Rax=3.6 m (high magnetic shear)Rax=3.9 m (low magnetic shear)

25. Threshold for each toroidal mode number The threshold in the low magnetic shear plasma is lower than that in the middle and high magnetic shear plasmas. The most unstable mode number is n=2.

26. Summary TH/3-1Ra TH/3-1Ra A nonlocal EPM exists near the plasma center in the JT-60U plasma. A nonlocal EPM exists near the plasma center in the JT-60U plasma. The nonlinear simulation demonstrated that the frequency shifts of the nonlocal EPM are close to the experimental results. The nonlinear simulation demonstrated that the frequency shifts of the nonlocal EPM are close to the experimental results. The MEGA code has been successfully extended to the helical coordinate system. The MEGA code has been successfully extended to the helical coordinate system. EX/5-4Rb EX/5-4Rb The Alfvén eigenmodes observed in the LHD plasmas were compared with the CAS3D3 calculation results. The Alfvén eigenmodes observed in the LHD plasmas were compared with the CAS3D3 calculation results. The magnetic shear is the key to control the Alfvén eigenmodes in the LHD plasma. The magnetic shear is the key to control the Alfvén eigenmodes in the LHD plasma. This suggests that the continuum damping is the most important damping mechanism in the LHD plasma. This suggests that the continuum damping is the most important damping mechanism in the LHD plasma. The upper envelope of the fluctuation amplitude scales as 2. The upper envelope of the fluctuation amplitude scales as 2.