Prof. Franco Porcelli, Polytechnic University of Turin, Italy

“Vertical displacements, axisymmetric modes and X-point resonances in tokamak plasmas”

Abstract: The magnetic field line going through the X-point(s) of a magnetic divertor separatrix in a tokamak plasma is resonant to axisymmetric MHD perturbations with toroidal mode number n=0. Yet, it appears that the impact of X-point resonances on axisymmetric modes has not been considered so far.

In this talk, the focus is on vertical displacement perturbations. Three main conclusions are drawn:

1) The ideal-MHD model becomes inadequate for the treatment of the vertical instability when the plasma density is non-vanishing at the magnetic X-points. In other words, if the ideal-MHD flux-freezing condition is implemented, the singularity associated with the X-point resonance cannot be resolved by plasma inertia, unless the unrealistic constraint of vanishing perturbed magnetic flux at the magnetic separatrix is imposed.

2) Localized perturbed current density peaking near the magnetic separatrix is the natural consequence of the resonant X-point nature. This current density is modulated along the separatrix as a function of the poloidal angle.

3) The relevant vertical plasma displacement is constant (i.e., rigid) in the plasma core, but it becomes progressively non-rigid as the X-point is approached. Indeed, within the ideal-MHD model, the plasma displacement diverges at the X-points.

These statements may lead to the overall conclusion that previously published work on the vertical stability problem has to be reconsidered when the plasma extends to the X-point(s) of a magnetic divertor separatrix. Indeed, the failure of the ideal-MHD model indicates that the proper treatment of axisymmetric perturbations that are non-vanishing at the magnetic X-points requires a more refined model (such as resistive-MHD) for the plasma response. This will be the subject of future work.

This work in carried out in collaboration with Richard Fitzpatrick at IFS.