Connection length

The connection length is understood to be the distance between two points, measured along a magnetic field line passing through these points.

In the fusion context, a distinction is made between closed field lines (inside the Last Closed Flux Surface) and open field lines (outside).

Closed field lines

Inside the Last Closed Flux Surface, the connection length is commonly defined as the length, measured along the magnetic field, to complete a poloidal turn.

In a circular tokamak, the poloidal circumference is 2πr. The connection length is L = 2πr/sin(α), where α is the pitch angle of the field line, namely tan(α) = B_θ/B_φ. Assuming B_φ >> B_θ, one has sin(α) ∼ tan(α), so that

$L=2\pi r{\frac {B_{\phi }}{B_{\theta }}}=2\pi Rq$

where q is the safety factor, approximated by q = r B_φ / R B_θ.

Open field lines

Outside Last Closed Flux Surface, the connection length associated with a given point is defined as the shortest distance from that point to any material surface measured along the field line through that point.