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Rotational transform: Difference between revisions
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<ref>[http://link.aps.org/doi/10.1103/RevModPhys.76.1071 A.H. Boozer, ''Physics of magnetically confined plasmas'', Rev. Mod. Phys. '''76''' (2004) 1071]</ref> | <ref>[http://link.aps.org/doi/10.1103/RevModPhys.76.1071 A.H. Boozer, ''Physics of magnetically confined plasmas'', Rev. Mod. Phys. '''76''' (2004) 1071]</ref> | ||
:<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \ | :<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \Phi}</math> | ||
where ''ψ'' is the poloidal magnetic flux, and | where ''ψ'' is the poloidal magnetic flux, and Φ the toroidal magnetic flux. | ||
== Safety factor == | == Safety factor == | ||
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<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>\frac{r d\theta}{B_\theta} = \frac{Rd\varphi}{B_\ | :<math>\frac{r d\theta}{B_\theta} = \frac{Rd\varphi}{B_\varphi}</math> | ||
where | where <math>\phi</math> and ''θ'' are the [[Toroidal coordinates|toroidal and poloidal angles]], respectively. | ||
Thus | Thus <math>q = m/n = \left \langle d\varphi /d\theta \right \rangle </math> can be approximated by | ||
:<math>q \simeq \frac{r B_\varphi}{R B_\theta}</math> | :<math>q \simeq \frac{r B_\varphi}{R B_\theta}</math> | ||