Finally, there is the resistive wall impedance. The beam pipe wall consists
of an inner layer of thickness t and resistivity 
, and an outer
layer of thickness t' and resistivity 
. For such a pipe,
the resistive wall impedance is given by the formula
where b is the beam pipe radius, and L is the length of the segment in question.
The ring is taken to consist of two sections: the first has an inner
layer of copper, and an outer stainless steel layer. This segment
occupies 90% of the ring, and is kept at at temperature of 20 K. b
is taken to be 19 mm, which is a value that has been corrected taking
into account the beam pipe shape. We take t' to be 10 mm and t to
be 50 
m. At these temperatures,
m, and 
m.
The remaining 10% of the ring is 2 mm thick copper at room temperature,
giving a of 
m. The correct
formula is obtained by taking t'=0. A simplified expression
for the impedance in this case can be given by
where
In both cases, the average 
-function is taken to be 85 m.