Outside the plasma, the perturbed electric field induced by the tearing mode satisfies
Resistive Wall Physics
Making use of Equations (3.32)–(3.34), as well as the ordering
, the previous three equations imply that
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
Let us adopt the so-called thin-wall 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
is the so-called wall time-constant [4,9]. Here, use has been made of Equations (3.82) and (3.83).
The thin-wall limit is
valid as long as the wall thickness is less than the resistive skin depth in the wall material. In other words, provided
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.