Studies on magnetic surface structures and basic magnetic field properties in 'Ultimate' configurations of the L=1, m=13 torsatron and the 'Vint-20' torsatron

The paper is concerned with numerical investigations of various magnetic configurations of a single-pole toroidal L=1, m=13 'ultimate' torsatron having a low aspect ratio Ah=4.345 and the modulation factors (-0.23) ≤ α ≤ 0.71 (K=1, β=0) of the helix law -mφ=Θ-αK SinΘ-βK sin2Θ. The extremums of the basic properties of closed magnetic surfaces as functions of the coefficient α in the neighborhood of α ∼ 0.4, as well as the structures of the edge magnetic field (substructures of virtual current) and the separatrix have been first determined for the L=1, m=13 'ultimate' torsatron and the 'Vint-20' torsatron. Unusual positions of the separatrix X-points in the cross sections for 1/4- and 3/4-magnetic field periods have been identified. The formula that takes into account the modulation factor α of the helix law was first derived to determine the average vertical magnetic field on the geometrical axis of the torus.