Toroidal coordinates: Difference between revisions

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== Magnetic ==
== Magnetic ==


All of the above coordinate systems are ''fixed''.  
All of the above coordinate systems are ''fixed'' and ''axisymmetric'' (except the Cartesian system).  
By contrast, magnetic coordinates ''adapt'' to the magnetic field, and therefore to the [[MHD equilibrium]] (also see [[Flux surface]]). Magnetic coordinates simplify the description of the magnetic field.
By contrast, magnetic coordinates ''adapt'' to the magnetic field, and therefore to the [[MHD equilibrium]] (also see [[Flux surface]]). Magnetic coordinates simplify the description of the magnetic field.
* Hamada coordinates. <ref>S. Hamada, Nucl. Fusion '''2''' (1962) 23</ref><ref>[http://dx.doi.org/10.1063/1.1706651 J.M. Greene and J.L Johnson, ''Stability Criterion for Arbitrary Hydromagnetic Equilibria'', Phys. Fluids '''5''' (1962) 510]</ref> In these coordinates, both the field lines and current lines corresponding to the [[MHD equilibrium]] are straight.  
* Hamada coordinates. <ref>S. Hamada, Nucl. Fusion '''2''' (1962) 23</ref><ref>[http://dx.doi.org/10.1063/1.1706651 J.M. Greene and J.L Johnson, ''Stability Criterion for Arbitrary Hydromagnetic Equilibria'', Phys. Fluids '''5''' (1962) 510]</ref> In these coordinates, both the field lines and current lines corresponding to the [[MHD equilibrium]] are straight.