Flux coordinates: Difference between revisions

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Different flux surface labels can be chosen like toroidal <math>(\Psi_{tor})</math> or poloidal <math>(\Psi_{pol})</math> magnetic fluxes or the volume contained within the flux surface <math>V</math>. By single valued we mean to ensure that any flux label <math>\psi_1 = f(\psi_2)</math> is a monotonous function of any other flux label  <math>\psi_2</math>, so that the function  <math>f</math> is invertible at least in a volume containing the region of interest. We will denote a generic flux surface label by <math>\psi</math>.
Different flux surface labels can be chosen like toroidal <math>(\Psi_{tor})</math> or poloidal <math>(\Psi_{pol})</math> magnetic fluxes or the volume contained within the flux surface <math>V</math>. By single valued we mean to ensure that any flux label <math>\psi_1 = f(\psi_2)</math> is a monotonous function of any other flux label  <math>\psi_2</math>, so that the function  <math>f</math> is invertible at least in a volume containing the region of interest. We will denote a generic flux surface label by <math>\psi</math>.
To avoid ambiguity in the sign of line and surface integrals we impose <math>d\psi(V)/dV > 0</math>, the toroidal angle increases in the clockwise direction when seen from above and the poloidal angle increases such that <math> \nabla\psi\cdot\nabla\theta\times\nabla\xi > 0</math>.
   
   
=== Flux Surface Average ===
=== Flux Surface Average ===
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