Magnetic properties of ultimate torsatrons

The nature and properties of the magnetic surface structure of a torsatron plasma confinement device with helical windings designed so as to eliminate the need for vertical compensation coils are investigated. The winding law necessary to produce a zero vertical field component in a toroidal helix is presented, and the vacuum magnetic properties of the ultimate torsatron are calculated numerically based on the modeling of the winding as many small straight segments of filamentary current. The general size and shape of the magnetic surfaces are found to depend on the number of field periods, the poloidal multiplicity and the aspect ratio, while the coil modulation principally determines the magnetic axis radial position. Means for the variation of magnetic properties through the use of small perturbation coils or the choice of the poloidal multiplicity and the number of field periods are indicated, and the effects of a finite conductor size are pointed out.