Construction of three-dimensional vacuum magnetic fields with dense nested flux surfaces

Toroidal vacuum magnetic fields are analyzed by the surface of section technique and noncanonical perturbation theory. The surface of section analysis shows that it is easy to find magnetic fields with an outermost flux surface of relatively small aspect ratio. However, as the aspect ratio is decreased, so is the rotational transform of the outermost flux surface. A new method of averaging combined with noncanonical perturbation theory shows that island overlap can account roughly for this loss of rotational transform. Finally, it is shown that one can significantly decrease the stochasticity and island structure by making small modifications to the magnetic field.