Erratum: Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets (Phys. Plasmas (2015) 22 (090704) DOI: 10.1063/1.4931094)

In Ref. 1, we demonstrated that three-dimensional, ideal magnetohydrodynamic (MHD) equilibria with continuously nested fluxsurfaces and with discontinuous rotational transform across the resonant rational surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium codes such as the stepped-pressure equilibrium code (SPEC).2 This seemingly rescued the possibility of constructing MHD equilibria with current sheets and smooth pressure profiles. For the construction to be possible, we derived a criterion for the minimum jump in rotational transform, Eq. (4) of Ref. 1, which we called the sine qua non condition for the existence of equilibria. However, Zhou et al.3 showed that equilibria with continuous rotational transform and resonant rational surfaces can also be obtained (approached numerically, with arbitrary accuracy) by using non-perturbative methods such as the one proposed by Rosenbluth et al.4 More recently, Huang et al.5 have confirmed that such equilibrium states can be computed with the SPEC code without requiring discontinuities in the rotational transform, provided that the Newton method is initialized with care and provided that the magnetic helicity, and not the rotational transform, is constrained.