3.4. Ionization Chambers 177
To determine the total change in potential we must addV−andV+together.
V = V−+V+= −Q
2 πl
ln[
a+r 0
a]
+−
Q
2 πl
ln[
b
a+r 0]
= −
Q
2 πlln[
b
a]
(3.4.14)
Since the capacitance per unit lengthClfor a cylindrical chamber is given by
Cl=2 π
ln(b/a), (3.4.15)
therefore the total potential changeVin equation 3.4.13 can also be written as
V=−
Q
lCl. (3.4.16)
This result clearly shows that for a cylindrical chamber the pulse height is indepen-
dent of the point of charge generation, which proves its advantage over the parallel
plate geometry. However, since the parallel plate chambers are easier to build as
compared to the cylindrical chambers, therefore they are still widely used. The
true advantage of the cylindrical geometry lies in its ability to produce radially
non-uniform electric field and high field intensity near the anode wire, thus greatly
enhancing the probability of gas multiplication. The process of gas multiplication is
exploited in proportional and GM counters which we will visit later in the Chapter.
3.4.C ChoiceofGas...........................
Since the average energy needed to produce an ion pair in a gas (W-value) depends
very weakly on the type of gas, therefore, in principle, any gas can be used in an
ionization chamber. Ion chambers filled with air are also fairly common. However
when it comes to precision detectors, theW-value is not the only factor that has to
be considered since the precision of a detector depends heavily on the efficiency of
charge collection. The charge collection efficiency depends not only on the detector
geometry and the bias voltage but also on the drift and diffusion properties of
the electrons and ions in the gas. Furthermore, small amounts of contaminants in
the filling gas can severely deteriorate the performance of the chamber. The most
troublesome of these contaminants are the so calledelectronegative gases,which
parasitically absorb the electrons and produce non-linearity in detector’s response.
Since this effect is extremely important for the operation of a gas filled detector,
we will revisit it in some detail later in the Chapter when we discuss the sources of
errors in gaseous detectors.
The reader should again be pointed to the fact that the choice of gas is highly
application dependent. For low resolution detectors where we are not concerned with
fluctuations of a few percent in signal height, we can use any available gas. In fact,
it is also possible to operate an ionization chamber filled with air. Such detectors
are widely used in laboratories for educational purposes and generally consist of a
cylindrical chamber with one end open.