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Toroidal coordinates: Difference between revisions
→Simple toroidal coordinates
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<ref>[http://link.aip.org/link/?PHPAEN/5/973/1 R.L. Miller et al, ''Noncircular, finite aspect ratio, local equilibrium model'', Phys. Plasmas '''5''' (1998) 973]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/5/973/1 R.L. Miller et al, ''Noncircular, finite aspect ratio, local equilibrium model'', Phys. Plasmas '''5''' (1998) 973]</ref> | ||
* letting ''R<sub>0</sub>'' depend on ''r'' (to account for the [[Shafranov shift]] of flux surfaces) <ref>R.D. Hazeltine, J.D. Meiss, ''Plasma confinement'', Courier Dover Publications (2003) ISBN 0486432424</ref> | * letting ''R<sub>0</sub>'' depend on ''r'' (to account for the [[Shafranov shift]] of flux surfaces) <ref>R.D. Hazeltine, J.D. Meiss, ''Plasma confinement'', Courier Dover Publications (2003) ISBN 0486432424</ref> | ||
* adding [[ellipticity]] (''& | * adding [[ellipticity]] (''κ''), [[triangularity]] (''δ''), and squareness (''ζ'') 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)\\ | |||
Z(r,\theta) = Z_0(r) + \kappa(r) r \sin(\theta + \zeta \sin 2 \theta) </math> | |||
== Toroidal coordinates == | == Toroidal coordinates == | ||