Rotational transform

The rotational transform (or field line pitch) ι/2π is defined as the mean number of toroidal transits (n) divided by the mean number of poloidal transits (m) of a field line on a toroidal flux surface. The definition can be relaxed somewhat to include field lines moving in a spatial volume between two nested toroidal surfaces (e.g., a stochastic field region).

Assuming the existence of toroidally nested magnetic flux surfaces, the rotational transform on such a surface may also be defined as [1]

where ψ is the poloidal magnetic flux, and φ the toroidal magnetic flux.

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: [2]

 

where φ and θ are the toroidal and poloidal angles, respectively. Thus q = m/n = <dφ/dθ> can be approximated by

 

See also

References

  1. A.H. Boozer, Physics of magnetically confined plasmas, Rev. Mod. Phys. 76 (2004) 1071
  2. K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171