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This report studies "saturated" MHD instabilities in terms of stable non linear solution branches of weakly dissipative MHD equations. Starting from an exact representation of MHD by scalar functions, reduced MHD equations are desired for helically symmetric cylindrical geometry and for toroidal geometry, including resistivity, parallel and perpendicular heat conductivity, and viscosity. Using given external sources (mass, heat, electric field) and appropriate boundary conditions, the equilibrium solutions and nonlinear solution branches are found which correspond to kink, quasi-interchange and tearing instabilities. Two particular cases are described. The first is a helically symmetric cylindrical plasma possessing an equilibrium with flat current profile, from which solution branches of the kink type (helical equilibria) and branches of quasi-interchange type (stationary convective states) bifurcate. The second is a toroidal plasma possessing an axisymmetric equilibrium from which stationary solution branches of the internal kink type bifurcate. This is discussed in relation to the problem of sawtooth oscillations with m = 1 precursor in tokamaks.

Additional information

Authors: MASCHKE E, CEA sur la Fusion, DRFC, CEN Cadarache, Saint-Paul-lez-Durance (FR);MORROS TOSAS J, CEA sur la Fusion, DRFC, CEN Cadarache, Saint-Paul-lez-Durance (FR)
Bibliographic Reference: Paper presented: The Annual Controlled Fusion Theory Conference, The International Sherwood Theory Meeting, San Antonio, Texas (US), April 3-5, 1989 Text not available
Availability: Available from (1) as Paper EN 34603 ORA
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