  In this paper, we analyze the so-called Master Equation of the linear
backreaction of a plasma disk in the central object magnetic field, when small
scale ripples are considered. This study allows to single out two relevant
physical properties of the linear disk backreaction: (i) the appearance of a
vertical growth of the magnetic flux perturbations; (ii) the emergence of
sequence of magnetic field O-points, crucial for the triggering of local plasma
instabilities. We first analyze a general Fourier approach to the solution of
the addressed linear partial differential problem. This technique allows to
show how the vertical gradient of the backreaction is, in general, inverted
with respect to the background one. Instead, the fundamental harmonic solution
constitutes a specific exception for which the background and the perturbed
profiles are both decaying. Then, we study the linear partial differential
system from the point of view of a general variable separation method. The
obtained profile describes the crystalline behavior of the disk. Using a simple
rescaling, the governing equation is reduced to the second order differential
Whittaker equation. The zeros of the radial magnetic field are found by using
the solution written in terms Kummer functions. The possible implications of
the obtained morphology of the disk magnetic profile are then discussed in view
of the jet formation.
