Analysis of the current‐diffusive ballooning mode

The current‐diffusive ballooning mode is analyzed in the tokamak plasma. This mode is destabilized by the current diffusivity (i.e., the electron viscosity) and stabilized by the thermal conductivity and ion viscosity. By use of the ballooning transformation, the eigenmode equation is solved. An analytic solution is obtained by the strong ballooning limit. Numerical calculation is also performed to confirm the analytic theory. The growth rate of the mode and the mode structure are analyzed. The stability boundary is derived in terms of the current diffusivity, thermal conductivity, ion viscosity, and the pressure gradient for the given shear parameter. This result is applied to express the thermal conductivity in terms of the pressure gradient, magnetic configurational parameters (such as the safety factor, shear, and aspect ratio), and the Prandtl numbers.

[1]  J. Connor.  Pressure gradient turbulent transport and collisionless reconnection , 1993 .

[2]  Atsushi Fukuyama,et al.  Self-sustained turbulence and H-mode confinement in toroidal plasmas , 1993 .

[3]  Atsushi Fukuyama,et al.  L-mode confinement model based on transport-MHD theory in tokamaks , 1992 .

[4]  S. Itoh.  Anomalous viscosity due to drift wave turbulence , 1992 .

[5]  A. Lichtenberg,et al.  The role of stochasticity in sawtooth oscillations , 1992 .

[6]  G. Craddock.  Hyperresistivity due to densely packed tearing mode turbulence , 1991 .

[7]  A. Aydemir.  Magnetohydrodynamic modes driven by anomalous electron viscosity and their role in fast sawtooth crashes , 1990 .

[8]  P. Yushmanov,et al.  Electron diffusion in tokamaks due to electromagnetic fluctuations , 1987 .

[9]  H. Strauss.  Hyper-resistivity produced by tearing mode turbulence , 1986 .

[10]  Bhattacharjee,et al.  Self-consistent dynamolike activity in turbulent plasmas. , 1986, Physical review letters.

[11]  Allen H. Boozer,et al.  Ohm's law for mean magnetic fields , 1986, Journal of Plasma Physics.

[12]  T. J. Martin,et al.  The stability of resistive ballooning modes in a high temperature plasma , 1985 .

[13]  J. Meiss,et al.  Shear-Alfvén dynamics of toroidally confined plasmas , 1985 .

[14]  Benjamin A. Carreras,et al.  The effects of compressibility of the resistive ballooning mode , 1984 .

[15]  R. Goldston.  Energy confinement scaling in Tokamaks: some implications of recent experiments with Ohmic and strong auxiliary heating , 1984 .

[16]  Robert Dewar,et al.  Ballooning mode spectrum in general toroidal systems , 1983 .

[17]  V. K. Pare,et al.  Transport effects induced by resistive ballooning modes and comparison with high-. beta. /sub p/ ISX-B tokamak confinement , 1983 .

[18]  A. Mikhailovskii,et al.  Analytical theory of the ideal shear-driven ballooning mode in Tokamak , 1982 .

[19]  H. R. Strauss,et al.  Resistive ballooning modes , 1981 .

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

[21]  P. Rutherford,et al.  Tearing modes in a plasma with magnetic braiding , 1979 .

[22]  D. Lortz,et al.  Ballooning-instability boundaries for the circular tokamak , 1979 .

[23]  R. J. Hastie,et al.  High mode number stability of an axisymmetric toroidal plasma , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  Tihiro Ohkawa,et al.  A transport model for alcator scaling in tokamaks , 1978 .

[25]  H. R. Strauss,et al.  Dynamics of high tokamaks , 1977 .

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

[27]  H. Wilhelmsson,et al.  Review of plasma physics: Vol. 1 (ed. M. A. Leontovich, Consultants Bureau, New York, 1965) pp. 326, $ 12.50 , 1966 .

[28]  Tadashi Sekiguchi,et al.  Plasma Physics and Controlled Nuclear Fusion Research , 1987 .

[29]  H. R. Strauss,et al.  Nonlinear, three‐dimensional magnetohydrodynamics of noncircular tokamaks , 1976 .

[30]  J. Schmidt,et al.  ANOMALOUS VISCOSITY AS A POSSIBLE EXPLANATION FOR AN ANOMALOUS PLASMA SKIN EFFECT. , 1971 .

[31]  J. Heading,et al.  An introduction to phase-integral methods , 1962 .