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Effective plasma radius: Difference between revisions
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→Effective radius based on flux
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* Based on the surface area ''S(ψ)'' of a flux surface (using ''S'' = 4 π<sup>2</sup>''Rr''<sub>eff</sub>) | * Based on the surface area ''S(ψ)'' of a flux surface (using ''S'' = 4 π<sup>2</sup>''Rr''<sub>eff</sub>) | ||
Here, ''R'' is the [[Toroidal coordinates|major radius]] of the [[:Wikipedia:Torus|torus]]. | Here, ''R'' is the [[Toroidal coordinates|major radius]] of the [[:Wikipedia:Torus|torus]]. | ||
Particularly in helical systems, choosing a value of ''R'' may be inappropriate (since the magnetic axis is not a circle, and the shape of the flux surfaces | Particularly in helical systems, choosing a value of ''R'' may be inappropriate (since the magnetic axis is not a circle, and the shape of the flux surfaces deviates from that of a torus). | ||
One can avoid making an (arbitrary) choice for ''R'' by defining | One can avoid making an (arbitrary) choice for ''R'' by defining | ||
* ''r''<sub>eff</sub> = 2''V/S'' | * ''r''<sub>eff</sub> = 2''V/S'' | ||
This still implicitly assumes the surfaces are very similar to a torus. | |||
A different approach is offered by recognizing that the flux surfaces are topological toroids of a single parameter. | A different approach is offered by recognizing that the flux surfaces are topological toroids of a single parameter. | ||
Then, the surface area and volume corresponding to such surfaces are related. | Then, the surface area and volume corresponding to such surfaces are related via a differential equation. | ||
Assuming only that ''S'' is linear in ''r''<sub>eff</sub> (or ''V'' is cuadratic in ''r''<sub>eff</sub>), it follows that: | Assuming only that ''S'' is linear in ''r''<sub>eff</sub> (or ''V'' is cuadratic in ''r''<sub>eff</sub>), it follows that: | ||
* ''r''<sub>eff</sub> = ''dV/dS'' | * ''r''<sub>eff</sub> = ''dV/dS'' | ||
This definition is more general. | |||
== Effective radius based on field lines == | == Effective radius based on field lines == | ||