Connection length: Difference between revisions
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== Closed field lines == | == Closed field lines == | ||
In a toroidally confined plasma, inside the | In a toroidally confined plasma, inside the [[Flux surface|Last Closed Flux Surface]], the connection length | ||
is commonly defined as the length, measured along the magnetic field, | is commonly defined as the length, measured along the magnetic field, | ||
to complete a poloidal turn. | to complete a poloidal turn. | ||
In a circular [[ | In a circular [[tokamak]], the [[Toroidal coordinates|poloidal circumference]] is ''2πr''. | ||
The connection length is | The connection length is <math>L = 2\pi r/\sin(\alpha)</math>, | ||
where | where <math>\alpha</math> is the pitch angle of the field line, namely | ||
<math>\tan(\alpha) = B_\theta/B_\phi</math>. | |||
Assuming | Assuming <math>B_\phi \gg B_\theta</math>, | ||
one has | one has <math>\sin(\alpha) \simeq \tan(\alpha)</math>, so that | ||
<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref> | <ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) {{ISBN|3540242171}}</ref> | ||
:<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math> | :<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math> | ||
where q is the [[Rotational transform|safety factor]], approximated by | where ''q'' is the [[Rotational transform|safety factor]], approximated by | ||
<math>q = r B_\phi / R B_\theta</math>. | |||
== Open field lines == | == Open field lines == | ||
Latest revision as of 12:36, 26 January 2023
The connection length is understood to be the distance between two points, measured along a magnetic field line passing through these points.
In the fusion context, a distinction is made between closed field lines (inside the Last Closed Flux Surface) and open field lines (outside).
Closed field lines
In a toroidally confined plasma, inside the Last Closed Flux Surface, the connection length is commonly defined as the length, measured along the magnetic field, to complete a poloidal turn.
In a circular tokamak, the poloidal circumference is 2πr. The connection length is , where is the pitch angle of the field line, namely . Assuming , one has , so that [1]
where q is the safety factor, approximated by .
Open field lines
Outside Last Closed Flux Surface, the connection length associated with a given point is defined as the shortest distance from that point to any material surface measured along the field line through that point.
References
- ↑ K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171