Nonconstant Linear Resonant Response Regimes
Suppose that
and
. It follows that , , , and

(5.103) 
Hence, we deduce that

(5.104) 
This response regime is known as the inertial regime, because the layer response is dominated by
ion inertia [2,13]. Note that the plasma response in the inertial regime is
equivalent to that of two closelyspaced shearAlfvén resonances that straddle the rational surface [4].
In fact, it is easily demonstrated that in real space,

(5.105) 
which suggests that the resonances lie at
.
The characteristic layer width is
,
which implies that the regime is valid when , , , and
.
Suppose that
and
. It follows that , , , and

(5.106) 
Hence, we deduce that

(5.107) 
This response regime is known as the viscousinertial regime, because the layer response is dominated by
ion perpendicular viscosity and ion inertia [13].
The characteristic layer width is
,
which implies that the regime is valid when ,
,
, and
.
Suppose, finally, that
and
. It follows that , , , and

(5.108) 
Hence, we deduce that

(5.109) 
This response regime is known as the diffusiveinertial regime, because the
layer response is dominated by perpendicular energy diffusivity and ion inertia [15]. The characteristic layer width is
, which implies that the regime is valid when ,
,
, and
.