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Effective plasma radius: Difference between revisions
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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 via a differential equation. | Then, the surface area and volume corresponding to such surfaces are related via a differential equation (''dV = S dr''). | ||
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 | ||
''dr = (dS/S) dV/dS = dr/r dV/dS'', so: | |||
* ''r''<sub>eff</sub> = ''dV/dS'' | * ''r''<sub>eff</sub> = ''dV/dS'' | ||
This definition is more general. | This definition is more general, although its validity is subject to the mentioned assumption. A fully general definition follows from | ||
* <math>r_{\rm eff} = \int_0^V{dV'/S(V')}</math> | |||
but it requires knowledge of the full equilibrium in terms of the function ''S(V)''. | |||
== Effective radius based on poloidal cross sections == | == Effective radius based on poloidal cross sections == | ||
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== See also == | == See also == | ||
* [[: | * [[:Media:Surf_vol.pdf|Comments on the use of the minor radius for stellarators]], where it is argued that it is preferable to use the Volume or Surface directly, instead of the effective radius, in view of the ambiguities in the definition of the latter - at least when making comparisons between different machines, e.g., in the framework of [[Scaling law]]s. | ||
== References == | == References == | ||
<references /> | <references /> | ||