Symplectic calculation of magnetic footprints in the DIII-D with low mn and magnetic noise and error fields perturbations

The symplectic mathematical maps in natural canonical coordinates for forward and backward integration of magnetic field lines in the DIII-D tokamak [Luxon, J.L.; Davis, L.E. Fusion Technol. 1985,8, 441] are used to calculate the magnetic footprints and their associated parameters on the inboard and outboard collector plates from the low mn magnetic perturbation with and without internal topological noise and magnetic field errors. The Grad-Shafranov solver equilibrium fit (EFIT) results from the experimental data for the DIII-D shot 115467 at 3000 ms [Lao, L.; St John, H.; Peng, Q.; Ferron, J.; Strait, E.; Taylor, T.; Meyer, W.; Zhang, C.; You, K. Fusion Sci. Technol.2005,48, 968] is used to construct an analytic expression for the equilibrium Hamiltonian function for the field line trajectories. The equilibrium Hamiltonian accurately represents the magnetic geometry of the DIII-D. The inboard and outboard footprints consist of a single toroidally winding stripe. Noise and error fields do not change the topology of the footprints, and have a marginal effect on the size of the footprint. Noise and error fields reduce the fraction of poloidal flux connecting the plates, and at the same time enhance the connection length. Noise and error fields reduce the safety factor. Backward trajectories starting close to the X-point have high safety factor. The new approach of symplectic mathematical maps in natural canonical coordinates can give an accurate and realistic picture of footprint reflecting the unique magnetic geometry of device in physical space.