Physics and Engineering of Radiation Detection

3.5. Proportional Counters 183

Vout

+

−

Eb

Ea

a r b

E

(a)

a

b

Cathode

Anode

(b)

(c)

Figure 3.5.1: (a) Schematic of a cylindrical proportional counter.

(b) Cross-sectional view of a cylindrical proportional counter. The

thin central wire acts as the anode while the outer wall acts the

cathode. (c) Radial electric field intensity profile inside a cylindrical

chamber.

as compared to parallel plate geometry. The electric field intensity at any radial
distancerin such a cylinder of radiusbhaving center wire of radiusais given by

E(r)=

1

r

V 0

ln(b/a)

. (3.5.1)

HereV 0 is the applied voltage. aandbare the radii of the anode wire and the
cylinder respectively. This implies that the electric field intensity in radial direction
has a 1/rbehavior (see Figs.3.5.1(b and c)).
As stated earlier, the high electric field intensity in the vicinity of the anode
ensures better electron collection efficiency. There is however another more profound
effect of this, that is, the high field enables the electrons to initiate the process
of avalanche multiplication, which we discussed earlier in the Chapter. For every
counter geometry there is a unique range of applied voltage in which the number of
charges produced in the avalanche is proportional to the number of primary charges
produced by the incident radiation, that is

N=MN 0