Ideal MHD stability properties of pressure driven modes in low shear tokamaks

The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, the effects of low shear within the plasma upon pressure driven modes are assessed. The standard ballooning theory is shown to break down as the shear is reduced, and the growth rate is shown to be an oscillatory function of n, the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure profile and the safety factor profile. When the shear is sufficiently weak, the oscillations can result in bands of unstable n-values, which are present even when the standard ballooning theory predicts complete stability. These instabilities are named 'infernal modes'. The occurrence of these instabilities at integer n is shown to be a sensitive function of the q-axis, raising the possibility of a sharp onset as the plasma parameters evolve.

[1]  J. Wesson.  Hydromagnetic stability of tokamaks , 1978 .

[2]  J. Taylor.  Some recent Advances in Plasma Stability Theory , 1979 .

[3]  R. Grimm,et al.  Stability of n=1 Kink Modes in Bean-Shaped Tokamaks , 1983 .

[4]  J. Manickam,et al.  Ideal MHD stability calculations in axisymmetric toroidal coordinate systems , 1982 .

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

[6]  L. Bernard,et al.  Systematic optimization of tokamaks for ideal magnetohydrodynamic stability , 1981 .

[7]  J. Taylor,et al.  Validity of ballooning representation and mode number dependence of stability , 1981 .

[8]  Dependence of ideal-MHD kink and ballooning modes on plasma shape and profiles in tokamaks , 1979 .

[9]  R. A. Dory,et al.  Stability study of high-. beta. flux-conserving equilibria , 1979 .

[10]  J. Manickam,et al.  STABILITY OF n= 1 INTERNAL MODES IN TOKAMAKS , 1984 .

[11]  K. Yamazaki,et al.  Ballooning beta limits of Dee- and bean-shaped tokamaks , 1985 .

[12]  J. Freidberg.  Ideal magnetohydrodynamic theory of magnetic fusion systems , 1982 .

[13]  John L. Johnson,et al.  Computation of the Magnetohydrodynamic Spectrum in Axisymmetric Toroidal Confinement Systems , 1976 .

[14]  M. Chance,et al.  The second region of stability against ballooning modes , 1981 .

[15]  W. Schneider,et al.  Erato Stability Code , 1984 .

[16]  S. Jardin,et al.  Ballooning Mode Stability of Bean-Shaped Cross Sections for High-β Tokamak Plasmas , 1983 .

[17]  S. Jardin,et al.  An iterative metric method for solving the inverse tokamak equilibrium problem , 1979 .

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

[19]  A. Ferreira,et al.  Self-Healing of Confined Plasmas with Finite Pressure , 1980 .

[20]  S. Jardin,et al.  Stability of high-beta tokamaks to ballooning modes , 1980 .

[21]  R. Grimm,et al.  n-dependence of ballooning instabilities , 1981 .

[22]  R. Gruber,et al.  Ideal magnetohydrodynamic stability of high-beta, high-current tokamak equilibria , 1981 .