Trajectories of Magnetic Field Lines in Toroidal Stellarators

Computations are presented to show that in a toroidal ℓ=3 stellarator, in addition to the wellknown inward shift of the magnetic axis the following effects occur: the rotational transform on the last closed surface is substantially less than the winding transform; the closed and open surfaces are separated by a complex region; the shape of the surfaces in the central region is essentially as predicted by Aleksin. The maximum shear available in a feasible stellarator is estimated and compared to that required for stability. The effect of perturbations on the perfect toroidal system is computed.