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Toroidal coordinates: Difference between revisions
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* adding [[ellipticity]] (<math>\kappa</math>), [[triangularity]] (<math>\delta</math>), and squareness (<math>\zeta</math>) to account for non-circular flux surface cross sections. A popular simple expression for shaped flux surfaces is: <ref> R.L. Miller, M.S. Chu, J.M. Greene, Y.R. Lin-Liu and R.E. Waltz, ''Noncircular, finite aspect ratio, local equilibrium model'', [[doi:10.1063/1.872666|Phys. Plasmas '''5''' (1998) 973]]</ref> | * adding [[ellipticity]] (<math>\kappa</math>), [[triangularity]] (<math>\delta</math>), and squareness (<math>\zeta</math>) to account for non-circular flux surface cross sections. A popular simple expression for shaped flux surfaces is: <ref> R.L. Miller, M.S. Chu, J.M. Greene, Y.R. Lin-Liu and R.E. Waltz, ''Noncircular, finite aspect ratio, local equilibrium model'', [[doi:10.1063/1.872666|Phys. Plasmas '''5''' (1998) 973]]</ref> | ||
:<math>R(r,\theta) = R_0(r) + r \cos(\theta + \arcsin \delta \sin \theta) | :<math>R(r,\theta) = R_0(r) + r \cos(\theta + \arcsin \delta \sin \theta)</math> | ||
Z(r,\theta) = Z_0(r) + \kappa(r) r \sin(\theta + \zeta \sin 2 \theta) </math> | :<math>Z(r,\theta) = Z_0(r) + \kappa(r) r \sin(\theta + \zeta \sin 2 \theta) </math> | ||
Warning: there are varying conventions for the directions of <math>\theta</math> and <math>\phi</math>. Which convention is used can depend on the local facility, the software being used, or other context. To help reduce confusion, the different tokamak coordinate conventions have been described and codified in the COCOS system.<ref>O. Sauter and S.Yu. Medvedev, ''Tokamak coordinate conventions: COCOS'', [[doi:10.1016/j.cpc.2012.09.010|Computer Physics Communications '''184''', (2013) 293-302]]</ref> | |||
== Toroidal coordinates == | == Toroidal coordinates == | ||