Variational derivation of the dispersion relation of kinetic coherent modes in the acoustic frequency range in tokamaks

Nguyen, C.; Garbet, X.; Smolyakov, A. I.
November 2008
Physics of Plasmas;11/1/2008, Vol. 15 Issue 11, p112502
Academic Journal
In the present paper, we compare two modes with frequencies belonging to the acoustic frequency range: the geodesic acoustic mode (GAM) and the Beta Alfvén eigenmode (BAE). For this, a variational gyrokinetic energy principle coupled to a Fourier sidebands expansion is developed. High order finite Larmor radius and finite orbit width effects are kept. Their impact on the mode structures and on the Alfvén spectrum is calculated and discussed. We show that in a local analysis, the degeneracy of the electrostatic GAM and the BAE dispersion relations is verified to a high order and based in particular on a local poloidal symmetry of the two modes. When a more global point of view is taken, and the full radial structures of the modes are computed, differences appear. The BAE structure is shown to have an enforced localization, and to possibly connect to a large magnetohydrodynamic structure. On the contrary, the GAM is seen to have a wavelike, nonlocalized structure, as long as standard slowly varying monotonic profiles are considered.


Related Articles

  • Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks' [Phys. Plasmas 18, 092103 (2011)]. Goedbloed, J. P. // Physics of Plasmas;Jun2012, Vol. 19 Issue 6, p064701 

    It is shown that some of the main results of the recent paper by Lakhin and Ilgisonis [Phys. Plasmas 18, 092103 (2011)], viz. the derivation of the equations for the continuous spectra of poloidally and toroidally rotating plasmas and their special solution for large aspect ratio tokamaks with...

  • Effect of toroidal rotation on the geodesic acoustic mode in magnetohydrodynamics. Ren, Haijun // Physics of Plasmas;Sep2012, Vol. 19 Issue 9, p094502 

    Theoretical research on the geodesic acoustic mode (GAM) induced by equilibrium toroidal rotation flow in the tokamak plasmas is approached by using ideal magnetohydrodynamic model. The dispersion relation of the GAM is presented by taking into account magnetic field perturbations. It is shown...

  • Length spectra and degeneration of flat metrics. Duchin, Moon; Leininger, Christopher J.; Rafi, Kasra // Inventiones Mathematicae;Nov2010, Vol. 182 Issue 2, p231 

    In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat...

  • Velocity fluctuation analysis via dynamic programming. Schlossberg, D. J.; Gupta, D. K.; Fonck, R. J.; McKee, G. R.; Shafer, M. W. // Review of Scientific Instruments;Oct2006, Vol. 77 Issue 10, p10F518 

    A new method of calculating one-dimensional velocity fluctuations from spatially resolved density fluctuation measurements is presented. The algorithm uses vector-matching methods of dynamic programming that match structures, such as turbulent fluctuations, in two data sets. The associated time...

  • The effect on stellarator neoclassical transport of a fluctuating electrostatic spectrum. Mynick, H. E.; Boozer, A. H. // Physics of Plasmas;Jun2005, Vol. 12 Issue 6, p062513 

    A study is presented of the effect on neoclassical transport of a fluctuating electrostatic spectrum, such as produced either by plasma turbulence, or imposed externally. For tokamaks, it is usually assumed that the neoclassical and “anomalous” contributions to the transport roughly...

  • Once more: The continuous spectrum of ideal magnetohydrodynamics. Goedbloed, J.P. // Physics of Plasmas;Sep98, Vol. 5 Issue 9, p3143 

    Examines the existence of the continuous spectrum of ideal magnetohydrodynamics. Study of the Hain-Lust equation; Demonstration of the three-dimensional dyadic; Description of the local dynamics on the magnetic surfaces by the classical continua.

  • Numerical Study of the Parametric Excitation of the Geodesic Acoustic Mode Continuum by Drift Wave. Jun Yu; Wenlong Shi // Applied Physics (21607567);Jul2012, Vol. 2 Issue 3, p98 

    The geodesic acoustic modes continuum excitation by the drift waves are numerically studied as a parametric process in the tokamak plasmas with a non-uniform ion temperature profile for which the non-uniform part of the inherent geodesic acoustic mode frequency takes the form of sin function. It...

  • Effect of impurity ions on the geodesic acoustic mode. Guo, Wenfeng; Wang, Shaojie; Li, Jiangang // Physics of Plasmas;Nov2010, Vol. 17 Issue 11, p112510 

    A dispersion relation of the geodesic acoustic mode with the effect of impurity ions is systematically derived. It is found that the frequency of the geodesic acoustic mode for a plasma with impurity ions is lower than that without impurity ions, which are mainly due to the polarization of...

  • Electromagnetic effects on geodesic acoustic modes. Bashir, M. F.; Smolyakov, A. I.; Elfimov, A. G.; Melnikov, A. V.; Murtaza, G. // Physics of Plasmas;2014, Vol. 21 Issue 8, p1 

    By using the full electromagnetic drift kinetic equations for electrons and ions, the general dispersion relation for geodesic acoustic modes (GAMs) is derived incorporating the electromagnetic effects. It is shown that m = 1 harmonic of the GAM mode has a finite electromagnetic component. The...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics