Generalised zonal modes in stationary axisymmetric plasmas

The MHD model enables derivation and analysis of the rich structure of geodesic acoustic modes (GAMs) and zonal modes in axisymmetric magnetic confined plasmas. The modes are identifiable from a single dispersion relation as two branches of slow magnetosonic continua. The lower frequency branch can be identified as a zonal flow (ZF), which in the simplified limit of static plasmas, has vanishing magnetic component. It is shown in this contribution that axisymmetric, and lesser known non-axisymmetric, zonal modes can be derived from MHD and kinetic models. The work provides a comprehensive derivation of the GAMs and ZF continua in stationary toroidally rotating plasmas, and investigates the exact solution and structure of a generalised family of zonal modes in static equilibria.

[1]  B. McMillan,et al.  Global gyrokinetic simulations with strong flows , 2016 .

[2]  J. Graves,et al.  Magnetohydrodynamic theory of the global structure and magnetic components of the geodesic acoustic continuum modes in tokamaks , 2016 .

[3]  M. Chu,et al.  Axisymmetric electrostatic magnetohydrodynamic oscillations in tokamaks with general cross-sections and toroidal flow , 2016 .

[4]  Fulvio Zonca,et al.  Physics of Alfvén waves and energetic particles in burning plasmas , 2016 .

[5]  H. Grad.  The Guiding Center Plasma , 2015 .

[6]  H. Ren,et al.  Landau damping of geodesic acoustic mode in toroidally rotating tokamaks , 2015, 1501.01750.

[7]  Lei Ye,et al.  Kinetic effect of toroidal rotation on the geodesic acoustic mode , 2015 .

[8]  F. Wagner,et al.  Geodesic acoustic mode investigation in the spherical Globus-M tokamak using multi-diagnostic approach , 2015 .

[9]  T. Lunt,et al.  Impact of magnetic perturbation coils on the edge radial electric field and turbulence in ASDEX Upgrade , 2015 .

[10]  Liu Chen,et al.  Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation , 2014 .

[11]  P. Hennequin,et al.  Complete multi-field characterization of the geodesic acoustic mode in the TCV tokamak , 2014 .

[12]  S. Coda,et al.  Control of magnetohydrodynamic stability by phase space engineering of energetic ions in tokamak plasmas , 2012, Nature Communications.

[13]  J. Goedbloed,et al.  Advanced Magnetohydrodynamics: Computational linear MHD , 2010 .

[14]  I. Chapman,et al.  Importance of centrifugal effects for the internal kink mode stability in toroidally rotating tokamak plasmas , 2009 .

[15]  Christer Wahlberg,et al.  Low-frequency magnetohydrodynamics and geodesic acoustic modes in toroidally rotating tokamak plasmas , 2009 .

[16]  C Wahlberg,et al.  Geodesic acoustic mode induced by toroidal rotation in tokamaks. , 2008, Physical review letters.

[17]  H. Sanuki,et al.  Eigenmode analysis of geodesic acoustic modes , 2008 .

[18]  Fulvio Zonca,et al.  Radial structures and nonlinear excitation of geodesic acoustic modes , 2007 .

[19]  Chengdu,et al.  Electron fishbones: theory and experimental evidence , 2007, 0707.2852.

[20]  P. Diamond,et al.  Physics of zonal flows , 2005 .

[21]  T. S. Hahm,et al.  Zonal flows in plasma—a review , 2005 .

[22]  S. Itoh,et al.  Excitation of geodesic acoustic mode in toroidal plasmas , 2005 .

[23]  J. P. Goedbloed,et al.  FINESSE: axisymmetric MHD equilibria with flow , 2002 .

[24]  K. Hopcraft,et al.  The effects of sheared toroidal plasma rotation on the internal kink mode in the banana regime , 2000 .

[25]  A. Glasser.  Instabilities in a confined plasma , 1999 .

[26]  Marshall N. Rosenbluth,et al.  POLOIDAL FLOW DRIVEN BY ION-TEMPERATURE-GRADIENT TURBULENCE IN TOKAMAKS , 1998 .

[27]  Francois Waelbroeck,et al.  Gyroscopic stabilization of the internal kink mode , 1996 .

[28]  W. Kerner,et al.  Solution of the drift‐kinetic equation for global plasma modes and finite particle orbit widths , 1994 .

[29]  Bondeson,et al.  Effects of trapped thermal particles on the n=1 internal kink mode in tokamaks. , 1993, Physical review letters.

[30]  I. Bernstein,et al.  Ion transport in toroidally rotating tokamak plasmas , 1987 .

[31]  G. Gerdin.  Reviews of Plasma Physics (Vol. 8) , 1982 .

[32]  J. L. Soule,et al.  Internal kink modes in toroidal plasmas with circular cross sections , 1975 .

[33]  J. P. Goedbloed.  Spectrum of ideal magnetohydrodynamics of axisymmetric toroidal systems , 1975 .

[34]  John M. Dawson,et al.  Geodesic Acoustic Waves in Hydromagnetic Systems , 1968 .

[35]  Manuel Rotenberg,et al.  ON HYDROMAGNETIC STABILITY OF STATIONARY EQUILIBRIA , 1960 .

[36]  V. Ferraro.  The non-uniform rotation of the Sun and its magnetic field , 1937 .