16.3 Cylindrical tokamak

For a large aspect-ratio, circular cross section tokamak, the R on a magnetic surface is nearly constant, R R0. The poloidal angle dependence of the magnetic field can be neglected, i.e., Bϕ(r,𝜃) Bϕ(r), and Bp(r,𝜃) Bp(r), where r is the minor radius of the relavent magnetic surface. Using these, the safety factor in Eq.  (37) is approximated to

    1 ∮  1B        1 B  (r) 1 ∮        1 B (r)1        r B (r)
q =---   ---ϕdℓp ≈ ----ϕ-----   dℓp = ----ϕ-----2πr = ----ϕ---,
   2π    R Bp      2πBp (r)R0         2π Bp(r)R0      R0 Bp(r)
(488)