Magnetic coordinate systems for helical SHAx states in reverse field pinch plasmas

Single helical axis (SHAx) states are the improved confinement RFP helical states, which have been observed at high plasma currents (beyond 1 MA) in the RFX-mod device. A reconstruction of these equilibrium configurations has been implemented in a code named SHEq, where SHAx states are modelled as pure single helicity (SH) states. We consider the helical flux in this work, which happens to be a good flux function for SH equilibrium, and its contours give the shape of the flux surfaces in the helical equilibrium. New curvilinear and non-orthogonal 'helical' coordinate systems are defined in SHEq, with the fundamental request that angles are defined with respect to the helical axis. We look for helical coordinates beginning from the canonical form of the magnetic field B and the Hamiltonian mechanics theory enables us to obtain straight-field-line helical coordinates computing action-angle coordinates. These coordinate systems are used to determine the helical safety factor q, using the simple formula valid in action-angle coordinates. Very good agreement with the computation of the safety factor using the ORBIT code has been found.