# 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

In a toroidally confined plasma, 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 ,
where is the pitch angle of the field line, namely
.
Assuming ,
one has , so that
^{[1]}

where *q* is the safety factor, approximated by
.

## 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.

## References

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