Three-dimensional equilibrium reconstruction on the DIII-D device

The presence of toroidal variation in diagnostic measurements indicates that the two-dimensional (2D) symmetry of tokamak equilibria can be violated when resonant magnetic perturbations (RMPs) are applied to suppress edge localized modes. While tokamak control is still possible with a 2D model, questions arise regarding the applicability of 2D equilibria when performing detailed analysis. In particular, questions regarding edge physics would benefit from equilibrium calculations which are consistent with measurements indicating toroidal variations. The ability to fit three-dimensional (3D) equilibria to diagnostic measurements has long been a challenge for stellarators, non-axisymmetric devices with an inherently 3D field structure. The STELLOPT code provides a solution to such a challenge by fitting 3D VMEC equilibria to magnetic, Thomson, motional Stark effect (MSE) and charge-exchange diagnostics. The plasma of the DIII-D tokamak with applied n = 3 RMP is reconstructed with STELLOPT (shot number 142603). The reconstruction is governed by fit to magnetic diagnostics, measured vacuum coil currents, Thomson scattering, charge-exchange spectroscopy and MSE polarimetry. The reconstructed equilibria possess features where pressure gradients become vanishingly small at low-order rationals. Such features can be associated with the applied RMP spectrum, indicating mode penetration for this shot. Boundary displacements on the order of 0.5 cm peak-to-peak were present. This suggests that while the 3D effect was small relative to the plasma minor radius, resonant mode penetration occurred, indicating the ability of 3D reconstructions to resolve small key features in the plasma.