Reusing the analysis of Sections 5.7–5.9, let us again suppose that there are two layers in space (i.e., Fourier space). The
small layer turns out to be of width
, where

(6.4) 
Here, is the hydromagnetic timescale defined in Equation (5.43). Given that we are effectively assuming that
, the condition for the separation of the layer solution into two layers (i.e., that the width of the small layer is less than that of the large layer) is always satisfied. The large layer is governed by the equation

(6.5) 
where
Here, is the normalized diamagnetic frequency [see Equation (5.65)], and
are magnetic Prandtl numbers [see Equations (5.53) and (5.54)], and is the ratio of the electron
to the ion pressure gradient at the rational surface [see Equation (4.5)].
The boundary conditions on Equation (6.5) are
that is bounded as
, and

(6.8) 
as
. Here, is an arbitrary constant.
In the various constant linear growthrate regimes considered in the next section, Equation (6.5) reduces to an equation of the form

(6.9) 
where is real and nonnegative, and is a complex constant. As described in Section 5.8, the solution of this
equation that is bounded as
can be matched to the small asymptotic form (6.8) to give

(6.10) 
where
. The width of the large layer in space is
.