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We analyze an axisymmetric magnetohydrodynamics configuration, describing themorphology of a purely differentially rotating thin plasma disk, in whichlinear and non-linear perturbations are triggered associated with microscopicmagnetic structures. We study the evolution of the non-stationary correction inthe limit in which the co-rotation condition (i.e., the dependence of the diskangular velocity on the magnetic flux function) is preserved and the poloidalvelocity components are neglected. The main feature we address here is theinfluence of ideal (finite electron inertia) and collisional (resistivity,viscosity, and thermal conductivity) effects on the behavior of the fluxfunction perturbation and of the associated small-scale modifications in thedisk. We analyze two different regimes in which resistivity or viscositydominates and study the corresponding linear and non-linear behaviors of theperturbation evolution, i.e., when the backreaction magnetic field isnegligible or comparable to the background one, respectively. We demonstratethat when resistivity dominates, a radial oscillating morphology (crystallinestructure) emerges and it turns out to be damped in time, in both the linearand non-linear regimes, but in such a way that the resulting transient can beimplemented in the description of relevant astrophysical processes, forinstance, associated with jet formation or cataclysmic variables. When theviscosity effect dominates the dynamics, only the non-linear regime isavailable and a very fast instability is triggered.

Behavior of thin disk crystalline morphology in the presence of corrections to ideal magnetohydrodynamics