Rotational transform: Difference between revisions
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Thus ''q = m/n = dφ/dθ'' can be approximated by | Thus ''q = m/n = dφ/dθ'' can be approximated by | ||
:<math>q | :<math>q \simeq \frac{r B_\phi}{R B_\theta}</math> | ||
== References == | == References == | ||
<references /> | <references /> |
Revision as of 06:44, 31 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.
Safety factor
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 = m/n = dφ/dθ can be approximated by
References
- ↑ K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171