Scaling of the stochastic broadening from low mn, high mn, and peeling-ballooning magnetic perturbations in the DIII-D tokamak

The equilibrium EFIT data for the DIII-D shot 115467 is used to construct the equilibrium generating function for magnetic field line trajectories in the DIII-D tokamak in natural canonical coordinates [A. Punjabi, and H. Ali, Phys. Plasmas \textbf{15}, 122502 (2008)]. A canonical transformation is used to construct an area-preserving map for field line trajectories in the natural canonical coordinates in the DIII-D. Maps in natural canonical coordinates have the advantage that natural canonical coordinates can be inverted to calculate real space coordinates (R,Z,$\phi )$, and there is no problem in crossing the separatrix. This is not possible for magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas \textbf{15}, 072504 (2008)]. This map is applied to calculate stochastic broadening from the low mn (m,n)=(1,1)+(1,-1); high mn (m,n)=(4,1)+(3,1); and the peeling-ballooning (m,n)=(40,10)+(30,10) magnetic perturbations. In all three cases, the scaling of the widths of stochastic layer near the X-point in the principal plane of the DIII-D deviates at most by 6{\%} from the $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ power Boozer-Rechester scaling [A. Boozer, and A. Rechester, \textit{Phys. Fluids }\textbf{21}, 682 (1978)]. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.