4,427
edits
Effective plasma radius: Difference between revisions
Jump to navigation
Jump to search
→Effective radius based on flux
| Line 14: | Line 14: | ||
== Effective radius based on flux == | == Effective radius based on flux == | ||
To obtain the dimensional effective radius ''r''<sub>eff</sub> (in meters) of a flux surface, several possibilities exist | To obtain the dimensional effective radius ''r''<sub>eff</sub> (in meters) of a flux surface, it is common to make the assumption that the shape of the flux surface does not deviate much from a [[:Wikipedia:Torus|torus]]. In this case, several possibilities exist to define a radius: | ||
* | * Based on the volume ''V(ψ)'' enclosed in a flux surface (using ''V'' = 2 π<sup>2</sup>''Rr''<sub>eff</sub><sup>2</sup>) | ||
* | * 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 is not close to a toroid). | 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 is not close to a toroid). | ||
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'' (still implicitly assumes the surfaces are near toroids) or | * ''r''<sub>eff</sub> = 2''V/S'' (this still implicitly assumes the surfaces are near toroids) or | ||
* ''r''<sub>eff</sub> = ''dV/dS'' (more general, assumes that ''S'' is linear in ''r''<sub>eff</sub>) | * ''r''<sub>eff</sub> = ''dV/dS'' (more general, assumes only that ''S'' is linear in ''r''<sub>eff</sub>) | ||
== Effective radius based on field lines == | == Effective radius based on field lines == | ||