3.3. Regions of Operation of Gas Filled Detectors 163
of charges occurs in such a way that the output pulse remains proportional to the
deposited energy. That is why these detectors are called proportional detectors.
From figures such as Fig.3.3.1 it is sometimes concluded that in proportional coun-
ters the output pulse height is proportional to the applied bias. This is correct only
up to an approximation, though. The correct reason for calling these devices pro-
portional counters is that the total number of charges produced after multiplication
is proportional to the initial number of charges. Let us now have a closer look at
the process of charge multiplication.
C.1 AvalancheMultiplication
For a detector working in the proportional region, an electric field as high as several
kV/cmis not uncommon. This high electric field not only decreases the charge col-
lection time but also initiates a process calledavalanche multiplication,whichisa
rapid multiplication of charges by primary charges produced from the incident radi-
ation. This charge multiplication results in the increase in output pulse amplitude.
Up to a certain bias voltage, the output pulse amplitude remains proportional to the
bias voltage. A detector working in this region is therefore known as aproportional
counter.
Due to the high electric field between the electrodes, the charges quickly gain
energy between collisions. If the total energy of an electron or an ion becomes
higher than the ionization potential of the gas atoms, it can ionize an atom, thus
creating another charge pair.
If all of the conditions, such as electric field, temperature, and pressure remain
constant and the electric field is uniform, then the change in the number of charge
pairs per unit path length is simply proportional to the total number of charge pairs,
that is
dN
dx
=αN. (3.3.1)HereN represents the total number of charge pairs andαis known as thefirst
Townsend coefficient. The first Townsend coefficient represents the number of col-
lisions leading to ionization per unit length of the particle track and is simply the
reciprocal of the mean free path for ionization
α=1
λ. (3.3.2)
Hereλ=Nmolσis the mean free path for ionization withNmolbeing the number of
gas molecules per unit volume andσthe total ionization cross section. αdepends
on the energy that an electron gains in a mean free path and the ionization potential
of the gas. Solution of 3.3.1 as obtained by simple integration is
N=N 0 eαx. (3.3.3)Ifα>0 this equation guarantees exponential growth of number of charge pairs
with distance. The multiplication of charges can be quantitatively described by
multiplication factorMas follows.
M =N
N 0
= eαx (3.3.4)