  We analyze an axisymmetric magnetohydrodynamics configuration, describing the
morphology of a purely differentially rotating thin plasma disk, in which
linear and non-linear perturbations are triggered associated with microscopic
magnetic structures. We study the evolution of the non-stationary correction in
the limit in which the co-rotation condition (i.e., the dependence of the disk
angular velocity on the magnetic flux function) is preserved and the poloidal
velocity components are neglected. The main feature we address here is the
influence of ideal (finite electron inertia) and collisional (resistivity,
viscosity, and thermal conductivity) effects on the behavior of the flux
function perturbation and of the associated small-scale modifications in the
disk. We analyze two different regimes in which resistivity or viscosity
dominates and study the corresponding linear and non-linear behaviors of the
perturbation evolution, i.e., when the backreaction magnetic field is
negligible or comparable to the background one, respectively. We demonstrate
that when resistivity dominates, a radial oscillating morphology (crystalline
structure) emerges and it turns out to be damped in time, in both the linear
and non-linear regimes, but in such a way that the resulting transient can be
implemented in the description of relevant astrophysical processes, for
instance, associated with jet formation or cataclysmic variables. When the
viscosity effect dominates the dynamics, only the non-linear regime is
available and a very fast instability is triggered.
