Rotational transform

Assuming the existence of toroidally nested magnetic flux surfaces, the rotational transform (field line pitch) is defined as

${\frac {\iota }{2\pi }}={\frac {d\psi }{d\phi }}$

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:

${\frac {rd\theta }{B_{\theta }}}={\frac {Rd\phi }{B_{\phi }}}$

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

$q={\frac {rB_{\phi }}{RB_{\theta }}}$