Analytical Solutions for Geodesic Acoustic Eigenmodes in Tokamak Plasmas

Authors: Victor I. Ilgisonis, Ludmila V. Konovaltseva, Vladimir P. Lakhin, Ekaterina A. Sorokina

Abstract:

The analytical solutions for geodesic acoustic eigenmodes in tokamak plasmas with circular concentric magnetic surfaces are found. In the frame of ideal magnetohydrodynamics the dispersion relation taking into account the toroidal coupling between electrostatic perturbations and electromagnetic perturbations with poloidal mode number |m| = 2 is derived. In the absence of such a coupling the dispersion relation gives the standard continuous spectrum of geodesic acoustic modes. The analysis of the existence of global eigenmodes for plasma equilibria with both off-axis and on-axis maximum of the local geodesic acoustic frequency is performed.

Keywords: Tokamak, MHD, geodesic acoustic mode, eigenmode.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337303

References:

[1] N. Winsor, J. L. Johnson, J. M. Dawson, Phys. Fluids, vol. 11, p. 2448, 1968.
[2] G. R. McKee, R. J. Fonck , M. Jakubowski et al, Phys. Plasmas, vol. 10. p. 1712, 2003.
[3] A.V. Melnikov, V.A. Vershkov , L.G. Eliseev et al, Plasma Phys. Control. Fusion, vol. 48, p. S87, 2006.
[4] T. Ido, Y. Miura, K. Hoshino et al, Nucl. Fusion, vol. 46, p. 512, 2006.
[5] A. Kr¨amer-Flecken , S. Soldatov , H.R. Koslowski , O. Zimmermann and TEXTOR Team, Phys. Rev. Lett., vol. 97, p. 045006, 2006.
[6] G. D. Conway, C. Tr¨oster, B. Scott et al, Plasma Phys. Control. Fusion, vol. 50, p. 055009, 2008.
[7] C. Silva, G. Arnoux, M. Groth et al, Plasma Phys. Control. Fusion, vol. 55, p. 025001, 2013.
[8] T. Ido, Y. Miura, K. Kamiya et al, Plasma Phys. Control. Fusion, vol. 48, p. S41, 2006.
[9] A.V. Melnikov, L.G. Eliseev, S.V. Perfilov et al, 40th EPS Conf. Plasma Physics, p. 2.178, 2013.
[10] Z. Huang, C. A. de Meijere, S. Coda et al, 40th EPS Conf. Plasma Physics, p. 2.175, 2013.
[11] H. L. Berk, C. J. Boswell, D. N. Borba, Nucl. Fusion, v. 46, p. S888, 2006.
[12] V. P. Lakhin, E. A. Sorokina, Phys. Lett. A, vol. 378, p. 535, 2014.
[13] V. I. Ilgisonis, I.V. Khalzov, V. P. Lakhin et al, Plasma Phys. Control. Fusion, vol. 56, p. 035001, 2014.