Electromagnetic geodesic acoustic modes in anisotropic tokamak plasmas

1. Electromagnetic geodesic acoustic modes in anisotropic tokamak plasmas Deng Zhou Institute of Plasma Physics Chinese Academy of Sciences Dec. 08 Hangzhou

2. INTRODUCTION • Two kinds of coherent structure : Low frequency Zonal flows (ZFs) and Geodesic Acoustic Modes (GAMs) exist in tokamaks • It is widely believed that they are electrostatic modes with mode number • They are driven by turbulence, magnetic components are possible to exist since finite Beta effect leads to the magnetic perturbations.

3. Motivation • 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]. • So a magnetic component needs to be included self-consistently to derive the eigenmode from fluid or kinetic equation. [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. Causes leading to magnetic perturbation • The GAM is characterized by a m=1 poloidal density perturbation • The interaction between radial magnetic drift and m=1 distribution perturbation causes a m=2 radial current which requires a m=2 parallel current to make total current divergent free. Then a m=2 perpendicular magnetic component[1] [1] Deng Zhou, Phys Plasmas 14, 104502 (2007).

5. How about an anisotropic plasma • Component of m=1 is almost 0 in an isotropic plasma, both kinetic and MHD description. Is it possible to have a m=1 in an anisotropic plasma? • YES,

6. Physics Model • Consider an anisotropic plasma, two species, electron and ion with unit charge. • Large aspect ratio tokamak with a circular cross section, and the equilibrium magnetic field • Perturbed scalar and vector potentials

7. Two Temperature Bi-maxwellian distribution • Consider the Bi-Maxwellian ion distribution with two temperatures, relevant to ICRF, NBI etc. • Electron has usual single temperature Maxwellian distribution

8. Drift Kinetic Equation If The ratio between 3rd to 4th term Neglect the 3rd term

9. Expanded DKE • DKE (Introduce a small parameter )

10. Solve DKE

11. From m=1 quasi-neutrality condition From the m=1 Ampere’s law parallel components From these 4 equations ( Different from the isotropic cases.)

12. To determine and one more equation is needed The solution to the second order equation

13. The m=0 component of Ampere’ law Then

14. To get m=2 current • Radial drift current • The polarization current

15. From the current continuity equation • Dispersion relation • Parallel current • The eigenfrequency • The magnetic perturbation

16. Conclusion • There always exists a m=2 magnetic perturbation components accompanying the GAMs while the m=1 components is absolutely 0 inan isotropic plasma. • 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. • In a plasma with anisotropic ion distribution a m=1 magnetic is present, proportional to the relative temperature difference, a small relative temperature difference causes the perturbation comparable to the m=2 component. Although it is absolutely 0 in isotropic plasmas. The magnetic perturbation component simulated using MHD ( from Nucl. Fusion, 2006, H L. Berk, et al. )