Rotational transform

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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

  1. K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171