Physics and Engineering of Radiation Detection

172 Chapter 3. Gas Filled Detectors

vn

vp

V 0 Veff

C R

− +

t

t

x

− +

Incident

Radiation

d

Figure 3.4.3: Simple parallel plate ionization chamber. In

this geometry the output voltageVef fdepends on the point

where charge particles are generated. Electrons owing to

their small mass move faster than ions and therefore the

distribution of electrons is shown to have moved a larger

distance as compared to that of ions.

If we haveN 0 ion pairs at any instantt, then the kinetic energy possessed by the
electrons having average velocityvnis given by

Tn(t)=N 0 eEvnt

=

V 0

d

N 0 evnt,

where we have assumed that the electric field intensityE, under whose influence
the electrons move, is uniform throughout the active volume and can be written as
E=V 0 /d,dbeing the distance between the electrodes. Similarly the kinetic energy
of ions having average velocityvpcan be written as

Tp(t)=N 0 eEvpt

=

V 0

d

N 0 evpt.

The potential energy contained in the chamber volume having capacitanceCcan be
written as

Uch=

1

2

CVnp^2 ,

while the total energy delivered by the applied potentialV 0 is

Utotal=

1

2

CV 02.