Resistive Wall Physics
Outside the plasma, the perturbed electric field induced by the tearing mode satisfies

(3.91) 
which yields
Making use of Equations (3.32)–(3.34), as well as the ordering
, the previous three equations imply that
where
.
Here, we have assumed that
, where is the radial thickness of the wall. We have
also made use of the fact that
outside the plasma.
Inside the wall,
where is the wall's electrical resistivity.
Making use of Equations (3.37), (3.38), (3.96), and (3.97), as well as the fact that
, both of the previous two equations reduce to

(3.101) 
Let us adopt the socalled thinwall limit, according to which
is assumed to vary
only weakly in across the wall. In this limit, integration of the previous equation across the wall yields

(3.102) 
where

(3.103) 
is the socalled wall timeconstant [4,9]. Here, use has been made of Equations (3.82) and (3.83).
The thinwall limit is
valid as long as the wall thickness is less than the resistive skin depth in the wall material. In other words, provided
that

(3.104) 
In the thin wall limit, Equations (3.82) and (3.95)–(3.100) yield
inside the wall. Note that
, as is required by charge conservation.