Physics and Engineering of Radiation Detection

3.4. Ionization Chambers 175

the electron collection efficiency over the parallel plate geometry. Fig.3.4.6 shows a
typical cylindrical ionization chamber.

Vout

Cathode (Cylinder)

Insulation

Anode Wire

Insulation C

R

HV

− +

Figure 3.4.6: Sketch of a typical cylindrical ionization chamber.

Whenever an ionization interaction takes place inside the chamber, the charge
pairs start moving to the respective electrodes under the influence of the applied
voltage. This inhibits a change in the potential energy inside the chamber and
causes a voltage pulse at the output electrode (generally anode), which can then be
measured. We will now try to analytically study the time evolution of this signal.
For this we first note that the change in the potential energy caused by the movement
of a chargeQin the chamber by a small distancedratrcan be written as

dU=Q

dΦ(r)

dr

dr. (3.4.5)

For a cylindrical chamber the potential Φ(r) can be represented by

Φ(r)=−

ClV 0

2 π

ln

[r

a

]

. (3.4.6)

Hereis the permeability of the gas,Clis the capacitance per unit length of the
chamber,V 0 is the voltage applied across the electrodes,ris the radial distance from
the center of the cylinder, andais the radius of the cylinder.
The reader should note that, due to axial symmetry of the cylinder, the potential
varies only in the radial direction. This is certainly not true for the potential at
the two edges, since there the electric lines of force are no more uniform along the
axial direction. However, the majority of practical ionization chambers have a long
enough length to make this effect negligible.
Differentiating above equation with respect torgives us the required potential
gradient
dΦ(r)
dr

=−

ClV 0

2 π

1

r

. (3.4.7)

Substituting this in equation 3.4.5 gives

dU=−Q

ClV 0

2 π

1

r

dr. (3.4.8)

The potential energyUin the above equation is just the electrostatic energy con-
tained in the electric field inside the chamber. For a cylindrical chamber of lengthl