1. 1 Magnetic components existing in geodesic acoustic modes Deng Zhou Institute of Plasma Physics, Chinese Academy of Sciences

2. 2 Introduction Zonal flows : m/n=0/0 electrostatic modes, with Geodesic Acoustic modes : dominant m/n=0/0 modes with GAMs are characterized by a m=1 poloidal density perturbation; Interaction between poloidal variational magnetic drift and the m=1 poloidal density perturbation results in a m=2 radial drift and a symmetric drift component. => The polarized radial drift is balanced by poloidal symmetric magnetic drift => while the m=2 radial current requires a m=2 parallel current to make total current divergent free, i. e., a m=2 magnetic perturbation.

3. 3 Recent experiment and numerical support Recent experiments have observed magnetic perturbations coexisting with GAMs[1,2]. Numerical simulations based on MHD also reveals that a perpendicular magnetic perturbation with dominant mode number m=2 coexists with GAMs, almost proportional to the electrostatic potential in magnitude[2]. [1]A. V. Melnikov, V. A. Vershkov, L. G. Eliseev, et al., Plasma Phys. Control. Fusion 87, S41 (2006). [2]H. L. Berk, C. J. Boswell, D. Borba, et al., Nucl. Fusion 46, S888 (2006).

4. 4 Physics Model large aspect ratio tokamak with a circular cross section, and the equilibrium magnetic field, The perturbed scalar and vector potentials

5. 5 Expanding the drift kinetic equation order by order Introduce a small parameter

6. 6 Solution to the lowest order Eq. Written as

7. 7 Quasi-neutral condition(1) Quasi-neutral condition Yields

8. 8 Parallel Ampere’s law(1) The parallel current * No m=1 magnetic perturbation presents. Using quasi-neutrality(1) results === 

9. 9 The equation of 2 nd order The same procedure to solve the 2 nd order equation to obtain

10. 10 Quasi-neutrality(2) === 

11. 11 Parallel Ampere’s law(2) The m=2 parallel current == 

12. 12 Simplified forms of current The current expression is written using quasi-neutrality condition(2) Further simplified using quasi-neutrality condition(1)

13. 13 An alternative approach for the current The interaction between magnetic drift and m=1 perturbation causes a m=2 radial current which requires a m=2 parallel current to make total current divergent free. The explicit expression

14. 14 GAM dispersion Balancing the poloidal invariant radial drift current and the polarization current results in the dispersion relation of GAMs Its asymptotic solution for large q is

15. 15 Divergent free of current The relation yields Generally Then this current is equal to that obtained from solving 2th drift kinetic equations The corresponding magnetic perturbation is

16. 16 Conclusion There always exists a m=2 magnetic perturbation components accompanying the GAMS while the m=1 components is 0. The perturbation is caused by the coupling between the m=1 plasma response and the m=1 poloidal variation of magnetic drift, which leads to a m=2 parallel current.