Physics and Engineering of Radiation Detection

3.4. Ionization Chambers 169

where

u ≡ Pd, and

v ≡

A

ln (1 + 1/γ)

The minimum in theVbreak−u(that is,Vbreak−Pd) curve can be obtained by

differentiating both sides of the above equation with respect touand equating

the result to zero.

dVbreak

du

=0

⇒

d

du

[

Bu

ln(v)+ln(u)

]

=0

⇒−

1

[ln(v)+ln(u)]^2

+

1

ln(v)+ln(u)

= 0 sinceB=0

⇒ln(v)+ln(u)=1

⇒ln(uv)=1

⇒uv=e

⇒u=

e

v

This is the value ofuat whichVbreakis minimum. Hence we can substitute

u=(Pd)min and the actual expression forvin this expression to get the

desired result

(Pd)min=

e

A

ln

[

1+

1

γ

]

3.3.F ContinuousDischarge

The breakdown process we studied in the previous section can further advance to the
process of continuous discharge if the high voltage is raised to very high values. This
continuous discharge starts as soon as a single ionization takes place and can not
be controlled unless the voltage is lowered. In this region, electric arcs can produce
between the electrodes, which may eventually damage the detector. It is apparent
that radiation detectors can not be operated at such high voltages and therefore one
must make sure that it remains below the threshold for this process.

3.4 IonizationChambers...........................

Ionization chambers are one of the earliest constructed radiation detectors. Because
of their simplicity in design and well understood physical processes they are still one
of the most widely used detectors.