A class of resistive axisymmetric magnetohydrodynamic equilibria in a periodic cylinder

We consider a model of visco-resistive incompressible magnetohydrodynamics in a periodic cylinder, with boundary conditions meant to idealize in a tractable way those of a laboratory plasma. The resistivity is described by a tensor presenting a field dependent anisotropic part suggested by kinetic theory, controlled by a certain anisotropy parameter. An explicit analytical description of the corresponding axisymmetric zero-flow equilibria is given, and it is shown how tokamak-like or paramagnetic-pinch-like field profiles are obtained as the anisotropy parameter is changed. The study of the stability properties of such equilibria is deferred to a later paper.