Validation of a NTM model using databases of disruptive plasmas at JET

Pressure-driven instabilities such as the neoclassical tearing modes (NTMs) limit the maximum achievable plasma normalized beta (N) needed for a reliable and efficient tokamak device. For a better understanding of the involved phenomena an almost fully analytic, dynamic, interpretative, multi-mode model describing the evolution of the NTMs is presented. An explicitly derived final formula of the NTM perturbed flux function is provided having a clear time dependent expression. To obtain the latter, the equations the perturbations satisfy are basically solved in the whole space: the ideal plasma perturbed momentum equations, the magnetic island perturbed resistive equations, the perturbed circuit equations in the plasma surrounding resistive wall and coils and finally the perturbed equations in the vacuum between the plasma and the external structures. The external coils play the role of feedback coils and/or error field generating coils. The system of the perturbed equations is completed by all the existing boundary equations across boundaries and the jump equation across the magnetic island that takes into account a heuristic bootstrap term. The assumption of the small perturbations from the equilibrium state is used in order to track the problem analytically, therefore the system of the perturbed equations is a linear one. Obviously the real diagnostic data quantities are not static and cannot be treated as equilibrium quantities from a strict mathematical point of view. This would drive the perturbed system of equations profoundly nonlinear and basically impossible to be analytically treated. Based on the assumption that usually the perturbed quantities have a significantly higher growth rate compared to the diagnostic quantities growth rate, it has been used the approximation that the plasma quantities collected from the diagnostic data behave like equilibrium quantities on the perturbations time scale. This approximation allows us to keep our proposed model linear and to provide a clear, quasi-analytic NTM solution. This solution and therefore the entire model validity have been tested against various discharges at JET.