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With a view to studying non-linear saturation of the magnetohydrodynamic instabilities of a plasma using a bifurcation theory, an exact general representation of the MHD equations is put forward, in the form of equations bearing on scalar functions. It is characterised by the introduction of a stationary magnetic reference field and by a new expression of the velocity field, making it possible to write equations for scalar functions in a form which facilitates physical interpretation. An approximation method is then described, which would give systems of reduced equations suitable for studying particular instabilities. The problem of bifurcation of non-linear solutions is studied in connection with cylindrical or toroidal plasmas. In the case of a cylindrical plasma, this representation leads to a reduced system which allows analytical calculations to be made. Two very different types of stationary bifurcated solutions are found. In the case of a toroidal plasma, a system of equations particularly well adapted to that geometry is obtained; a qualitative approach is then made to bifurcation of a stationary solution of the kink type in toroidal geometry.

Additional information

Authors: MORROS TOSAS J, CEA, Département de Recherches sur la Fusion Contrôlée, CEN/Cadarache, 13108 Saint-Paul-lez-Durance (FR)
Bibliographic Reference: Report: EUR-CEA-FC-1372 FR (1989)
Availability: Available from CEA, Département de Recherches sur la Fusion Contrôlée, Saint-Paul-lez-Durance (FR)
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