3D MHD Equilibrium with Externally Applied Perturbations in Tokamaks and Stellarators

Free boundary magnetohydrodynamic tokamak equilibrium states

with spontaneous three dimensional deformations of the plasma

vacuum interface are computed with the 3D VMEC solver¹. The

structures we have obtained have the appearance of saturated ideal

external kink/peeling modes. Large edge pressure gradients yield

toroidal mode number n = 1 corrugations when the edge bootstrap

current is large and n = 4 distortions when this current is

small. The deformations of the plasma boundary region induces a

nonaxisymmetric Pfirsch-Schluter current that drives a field-aligned

current ribbon which is consistent with experiment.

We claim that the equilibrium states we compute model

the Edge Harmonic Oscillation² observed on DIII-D and the Outer

Mode3 found in JET during Quiescent H-mode operation. The

application of an external perturbation of the n = 1 family of

toroidal Fourier modes to a fixed 10-field period Heliotron boundary

with magnitudes below 1mm up to 1cm produce saturated ideal

m/n = 1/1 interchange-like MHD equilibrium structures. The deformed

internal structures triggered by the weak external pertubations

are amplified in the core of the plasma and are observed well within the

rotational transform ι = 1 surface with a peak distortion near the ι = 1/2 flux

contour.

¹S.P. Hirshman, W.I. van Rij and P. Merkel, Comput. Phys. Commun. 43 (1986) 143.

²K.H. Burrell et al., Phys. Plasmas 22 (2005) 021805; W.M. Solomon et al., Phys. Rev. Lett. 113 (2014) 135001.

³E.R. Solano et al., Phys. Rev. Lett. 104 (2010) 185003.