  We analyse the two-dimensional MHD configurations characterising the steady
state of the accretion disk on a highly magnetised neutron star. The model we
describe has a local character and represents the extension of the crystalline
structure outlined in Coppi (2005), dealing with a local model too, when a
specific accretion rate is taken into account. We limit our attention to the
linearised MHD formulation of the electromagnetic back-reaction characterising
the equilibrium, by fixing the structure of the radial, vertical and azimuthal
profiles. Since we deal with toroidal currents only, the consistency of the
model is ensured by the presence of a small collisional effect,
phenomenologically described by a non-zero constant Nernst coefficient (thermal
power of the plasma). Such an effect provides a proper balance of the electron
force equation via non zero temperature gradients, related directly to the
radial and vertical velocity components.
  We show that the obtained profile has the typical oscillating feature of the
crystalline structure, reconciled with the presence of viscosity, associated to
the differential rotation of the disk, and with a net accretion rate. In fact,
we provide a direct relation between the electromagnetic reaction of the disk
and the (no longer zero) increasing of its mass per unit time. The radial
accretion component of the velocity results to be few orders of magnitude below
the equatorial sound velocity. Its oscillating-like character does not allow a
real matter in-fall to the central object (an effect to be searched into
non-linear MHD corrections), but it accounts for the out-coming of steady
fluxes, favourable to the ring-like morphology of the disk.
