Rotational transform: Difference between revisions
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In [[Tokamak|tokamak]] research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor"). | In [[Tokamak|tokamak]] research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor"). | ||
In a circular [[Tokamak|tokamak]], ''q'' can be approximated by | In a circular [[Tokamak|tokamak]], | ||
the equations of a field line on the flux surface are, approximately: | |||
<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref> | |||
:<math>\frac{r d\theta}{B_\theta} = \frac{Rd\phi}{B_\phi}</math> | |||
where ''φ'' and ''θ'' are the [[Toroidal coordinates|toroidal and poloidal angles]], respectively. | |||
Thus ''q = dφ/dθ'' can be approximated by | |||
:<math>q = \frac{r B_\phi}{R B_\theta}</math> | |||
== References == | |||
<references /> | |||
Revision as of 15:51, 30 July 2010
Assuming the existence of toroidally nested magnetic flux surfaces, the rotational transform (field line pitch) is defined as
where ψ is the poloidal magnetic flux, and φ the toroidal magnetic flux. Thus, ι/2π is the mean number of toroidal transits (n) divided by the mean number of poloidal transits (m) of a field line on a flux surface.
In tokamak research, the quantity q = 2π/ι is preferred (called the "safety factor"). In a circular tokamak, the equations of a field line on the flux surface are, approximately: [1]
where φ and θ are the toroidal and poloidal angles, respectively. Thus q = dφ/dθ can be approximated by
References
- ↑ K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171