Calculation of the magnetic surface function gradient in stellarators with broken stellarator symmetry

The computation of the gradient of the magnetic surface function, ∇ψ, plays an essential role in plasma physics, e.g., for investigations of plasma equilibrium currents or transport fluxes in stellarators. The evaluation of ∇ψ becomes more complicated if the magnetic field B does not exhibit stellarator symmetry. Here, a scheme for computation of ∇ψ for magnetic configurations which do not show stellarator symmetry is presented. The proposed method is based on computations of gradients of integrals of magnetic field line equations. This new technique for ∇ψ calculations is applied to Uragan-2M [O. S. Pavlichenko for the U-2M group, Plasma Phys. Controlled Fusion 35, B223 (1993)]. Taking into account the influence of current feeds and detachable joints of the helical winding the magnetic configuration does not exhibit stellarator symmetry. Computations of ∇ψ, the effective ripple ϵeff, and the geometrical factor λb for the bootstrap current in the 1/ν transport regime are performed.