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Toroidal coordinates: Difference between revisions
→Simple toroidal coordinates
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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> | ||
== Toroidal coordinates == | == Toroidal coordinates == | ||