Numerical study of the unstable MHD spectrum of a small aspect ratio, flat current, non-circular tokamak

The Lausanne ideal MHD stability code ERATO is used to investigate spectral properties of Solovèv's equilibrium at small aspect ratios. Two different elongations are considered. Both free and rigid boundary models are computed and compared. Modes characterized by a large radial extension have been found which appear to be due to a coupling ofm=1 andm=2 modes due to toricity. The internal modes spectrum is compared with the predictions of the full mercier criterion, taking into account its spatial dependence, and with the ballooning modes stability criterion.RésuméLes propriétés spectrales des équilibres analytiques de Solov'èv à petit rapport d'aspect sont étudiées à l'aide du code numérique ERATO qui permet de calculer le spectre magnétohydrodynamique d'une configuration Tokomak quelconque. Nous avons examiné deux situations différentes: paroi conductrice collée contre la surface du plasma et vide infini ainsi que deux élongations. Nous avons trouvé que les modes instables ont une grande extension radiale, due au couplage torique entre les modesm=1 etm=2. Le spectre des modes internes est comparé aux prédictions du critère de Mercier, prenant en considération sa dépendance radiale. La limite de stabilité aux modes internes à basn est comprise entre la limite de Mercier correspondante et la limite ballooning.

[1]  E. A. Frieman,et al.  An energy principle for hydromagnetic stability problems , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  A. H. Glasser,et al.  Theory of ballooning modes in tokamaks with finite shear , 1977 .

[3]  J. W. Connor,et al.  Shear, periodicity, and plasma ballooning modes , 1978 .

[4]  K. E. Weimer,et al.  Toroidal effects on magnetohydrodynamic modes in tokamaks , 1973 .

[5]  G. Laval.  Internal kink mode in a diffuse pinch with a noncircular cross section , 1975 .

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

[7]  E. Rebhan.  Stability boundaries of tokamaks with respect to rigid displacements , 1975 .

[8]  W. Schneider,et al.  MHD instabilities as an initial boundary-value problem , 1974 .

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

[10]  John L. Johnson,et al.  Long‐wavelength kink instabilities in low‐pressure, uniform axial current, cylindrical plasmas with elliptic cross sections , 1974 .

[11]  A. Sykes,et al.  Two-dimensional calculation of tokamak stability , 1974 .

[12]  C. Mercier,et al.  A necessary condition for hydromagnetic stability of plasma with axial symmetry , 1960 .

[13]  W. Kerner.  Numerical study of the MHD spectrum in tokamaks with a non-circular cross-section , 1976 .

[14]  R. Gruber,et al.  Continuous Spectra of a Cylindrical Magnetohydrodynamic Equilibrium , 1974 .

[15]  R. Gajewski.  Magnetohydrodynamic Equilibrium of an Elliptical Plasma Cylinder , 1972 .