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.