Nonlinear dynamics of Joule heated toroidal discharges

Starting from the complete MHD system (D), it has been possible in the present analysis to reduce this very large system to its dominant subpart (Ds), which drives to first order its dynamics, splitting apart the equilibrium and cinematics of the magnetic surfaces, the impurity cascade dynamics and the ions dynamics, to be analyzed separately. To study the system (Ds) which is yet a complicated nonlinear one, a specific way has been proposed. Instead of using as elsewhere the approximation or expansion techniques which could very well apply to (Ds), due to its parabolic nature, useful for convergence, it has been remarked that (Ds) possesses invariance property through the group of similarities (S0). During the first phase of the discharge when the temperature profile-concentrates and shrinks whereas the temperature rises up, the boundary effects, as verified on the datas, are not felt by the solution which follows the group invariance property