Effective plasma radius: Difference between revisions

Jump to navigation Jump to search

Effective plasma radius (view source)

Revision as of 03:46, 16 July 2011

1,601 bytes removed ,  16 July 2011
→‎Effective radius based on flux
(revert vandalism)
Line 15: Line 15:
where ''&psi;<sub>N</sub>'' is the normalized toroidal flux, such that it is 0 on the magnetic axis and 1 at the Last Closed Flux Surface (LCFS).
where ''&psi;<sub>N</sub>'' is the normalized toroidal flux, such that it is 0 on the magnetic axis and 1 at the Last Closed Flux Surface (LCFS).


== Effective radius based on flux ==
Very true! Makes a change to see smooene spell it out like that. :)
 
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(&psi;)'' enclosed in a flux surface (using ''V'' = 2 &pi;<sup>2</sup>''Rr''<sub>eff</sub><sup>2</sup>)
* Based on the surface area ''S(&psi;)'' of a flux surface (using ''S'' = 4 &pi;<sup>2</sup>''Rr''<sub>eff</sub>)
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 deviates from that of a torus).
One can avoid making an (arbitrary) choice for ''R'' by defining
* ''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.
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:
* ''r''<sub>eff</sub> = ''dV/dS''
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 ==
Anonymous user
Retrieved from "http://wiki.fusenet.eu/wiki/Special:MobileDiff/3363"

Navigation menu