The DIII-D Map -- An Area-Preserving Map for Trajectories of Magnetic Field Lines in the DIII-D Tokamak

The EFIT data for the DIII-D shot 115467 3000 ms is used to calculate the generating function for an area-preserving map for trajectories of magnetic field lines in the DIII-D. We call this map the DIII-D map. The generating function is a bivariate polynomial in base vectors $\psi^{1/2}$cos($\theta)$ and $\psi^{1/2}$sin($\theta)$. $\psi$ is toroidal flux and $\theta $ is poloidal angle. The generating function is calculated using a canonical transformation from ($\psi $,$\theta )$ to physical coordinates (R,Z) in the DIII-D [1] and nonlinear regression. The equilibrium generating function gives an excellent representation of the equilibrium flux surfaces in the DIII-D. The DIII-D map is then used to calculate effects of the magnetic perturbations in the DIII-D. Preliminary results of the DIII-D map will be presented. This work is supported by US DOE OFES DE-FG02-01ER54624 and DE-FG02-04ER54793. \newline [1] A. Punjabi, H. Ali, T. Evans, and A. Boozer, \textit{Phys Lett A} \textbf{364} 140--145 (2007).