Vacuum stellarator: direct approach

It’s well known that rotation transform ι produce a poloidal flux. Here I consider such φ, in the next paper the calculation of ι. In any toroidal vacuum field B¯ = Δ¯f. We call S1 the equipotential surfaces. In the axisimmetric case there are the S1 on the meridional half planes, the B¯‐lines are circulars, and B is constant on each line. There is toroidal flux Φ, but no poloidal flux Φp. It is supposed that a suitable toroidal arrangement of external coils generates inside a toroidal volume V1, limited by a toroidal surface S3(w1) a magnetic field B¯ having the following properties.