Analytic equilibrium of elongated plasmas bounded by a magnetic separatrix and the problem of resistive axisymmetric X-point modes

Theoretical and experimental considerations suggest that axisymmetric perturbations that are resonant at the X-point(s) of a magnetic divertor separatrix may play a role for the understanding of ELMs in tokamaks and their active control via so-called vertical kicks. The first step in the development of an analytic model for resistive axisymmetric X-point modes is presented, i.e., finding an adequate and relatively simple analytic MHD equilibrium for a plasma column with noncircular cross section bounded by a magnetic separatrix.