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Flux coordinates: Difference between revisions
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Flux coordinates in the context of magnetic confinement fusion (MCF) is a set of coordinate functions adapted to the shape of the [[Flux surface|flux surfaces]] of the confining magnetic trap. They consist of one flux label, often termed <math>\psi</math> and two angle-like variables <math>\theta, \phi</math> whose constant contours on the flux <math>(\psi({\mathbf x}) = {\textrm constant})</math> surfaces close either poloidaly (<math>\phi</math>) or toroidallly (<math>\theta</math>). | Flux coordinates in the context of magnetic confinement fusion (MCF) is a set of coordinate functions adapted to the shape of the [[Flux surface|flux surfaces]] of the confining magnetic trap. They consist of one flux label, often termed <math>\psi</math> and two angle-like variables <math>\theta, \phi</math> whose constant contours on the flux <math>(\psi({\mathbf x}) = {\textrm constant})</math> surfaces close either poloidaly (<math>\phi</math>) or toroidallly (<math>\theta</math>). | ||
In this coordinates equilibrium vector fields like the magnetic field <math>{\mathbf B}</math> or current density <math>{\mathbf j}</math> have simplified expressions. A particular kind of flux coordinates, generally called [[Flux_coordinates#Magnetic_coordinates|magnetic coordinates]], simplify the <math>{\mathbf B}</math>-field expression further making field lines straight in the <math>(\theta, \phi)</math> plane. | In this coordinates equilibrium vector fields like the magnetic field <math>{\mathbf B}</math> or current density <math>{\mathbf j}</math> have simplified expressions. A particular kind of flux coordinates, generally called [[Flux_coordinates#Magnetic_coordinates|magnetic coordinates]], simplify the <math>{\mathbf B}</math>-field expression further by making field lines look straight in the <math>(\theta, \phi)</math> plane of that family of coordinates. | ||
== General curvilinear coordinates == | == General curvilinear coordinates == | ||