Toroidal coordinates: Difference between revisions

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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]] (''&epsilon;''), [[triangularity]] (''&kappa;''), etc. (to account for non-circular flux surface cross sections)
* adding [[ellipticity]] (''&kappa;''), [[triangularity]] (''&delta;''), and squareness (''&zeta;'') 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 ==

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