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Connection length: Difference between revisions
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== Closed field lines == | == Closed field lines == | ||
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 tokamak, the poloidal circumference is ''2πr''. | 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 [[ | 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 == | ||