1. Energetic ion excited long-lasting “sword” modes in tokamak plasmas with low magnetic shear Speaker:RuiBin Zhang Advisor:Xiaogang Wang School of Physics, Peking University, Beijing In Collaboration with: Theory Xianqu Wang, Chijie Xiao in PKU Experiment Yi Liu, Wei Deng in SWIP

2. Outline  Background of 1/1 mode in tokamak  Linear analysis of Sword Mode – Grow rate and frequency – Mode structure – The role of magnetic shear – Comparison with fishbone  Nonlinear analysis – Prey and predator model – Comparison with fishbone  Sword mode on particle transport  Conclusion

3. Modes of m/n=1 in tokamaks(bursting)  Sawteeth Sawtooth-type SXR,caused by the current driven m=n=1 kink-tearing mode flatten temperature profile expel impurity in core region  Fishbones Fishbone-like dB signals, energetic particle driven m=n=1 rotating internal kink “Sawtooth-like” neutron signals Lead to fast ion transport J A Wesson et al NF 1991 K McGuire et al PRL 1983

4. Modes of m/n=1 in tokamaks(saturated)  Internal kink mainly pressure driven ideal mode in tokamak almost stable in low beta tokamak  LLM Weak shear tokamak Pressure driven ideal mode in high beta Together with high harmonics 2/2 3/3  Sword mode sword-like dB signals, energetic particle driven m=n rotating internal kink together with high harmonics 2/2 3/3 lead to fast ion transport, as fishbone I T Chapman et al, ITPA-MHD-WG 2009 W, Deng, Y. Liu, et al, IAEA, 2012

5. Linear model of sword mode Algebraic equation about the eigenvalue Differential equation about the eigenvector Complex frequency and mode structure are decided in the eigenvalue problem together --- non-perturbative EPM theory Iterative method to obtain the eigenvalue and eigenvector of the system numerically Variational method Energy principal Step function as first order trivial function revised eigenvalue revised eigenvector Convergent to the exact eigenvalue and eigenvector L. Chen, PRL,1984

6. Grow rate and frequency of sword modes As fishbone, sword mode propagates along the ion diamagnetic flow, considering the NBI injection direction, thus 1/1 and 2/2 modes are linear unstable, and 2/2 mode can even obtain a higher growth rate 3/3 and high harmonics are all linear stable, the observed fade spectral line are beats of 1/1 and 2/2.

7. Spatially varied radial mode structure Cell-like displacement vector in the poloidal section, similar to the interchange 1/1 mode 2/2 mode Mode structure

8. Effect of magnetic shear Average shear High n number branches are more sensitive to the shear High n branches are unstable only in sufficiently low shear Shot #16070 with ECRH confirms our analysis, as ECRH will increase the shear in the core

9. Comparison between fishbone and sword mode Gentle slope radial mode structure for sword mode--cell displacement Abrupt slope radial mode structure for fishbone--rigid kind displacement The growth rate of sword mode has a nonlinear dependence on fast ion ’ s gradient, while for fishbone, it ’ s nearly linear † The frequency of sword mode is constant as fast ion ’ s gradient decrease, while for fishbone, it chirps down Fishbone is strongly MHD damping, while sword is marginal MHD stable Mode structure effect -For fishbone, (L.Chen,1984) -For sword,

10. Nonlinear evolution of sword mode and fishbone Nonlinear prey-predator model Reproduce the saturation of sword mode and burst behavior of fishbone Frequency chirping for fishbone and constant frequency for sword mode also explained. L. Chen, PRL,1984 Sword mode may have a remarkable impact on the ITER steady state operation scenario and future fusion reactors !?

11. Sword mode on particle and impurity redistribution  Test particle code to estimate the effect of sword and fishbone mode on energetic particle transport and impurity expel  Simulation model Equilibrium field Perturbed field ideal MHD Parallel Ohm’s law Particle motion (no gyro average)

12. Perturbed field structure  Perturbed field is limited in the core region  Resonance with q=1 magnetic surface to create magnetic island  Different mode structure for sword and fishbone Sword fishbone

13. Particle redistribution  Normalized parameters -  Single partilce results benchmark with ORBIT  Uniform initial radial distribrition  Uniform velocity distribution in pitch angel space(α-particle)  Particles moves outwards according to our simulation

14. Conclusion  Fishbone will transform into saturated mode in weak shear tokamak, we define this mode as sword mode  Both spatial and temporal strucutres of sword mode vary slowly and gently compared to fishobne  Sword mode perturbation can push the particles moving outwards.

15. Thank you for your attention!