4.3. Liquid Proportional Counters 231
a cylinder with an anode wire stretched across its axis. Such a structure provides
a very high electric field intensity near the anode wire for charge multiplication as
well as better charge collection.
The basic underlying processes for charge multiplication in a liquid are the same
as in the case of a gas. These processes were discussed at length in the chapter on
gas filled detectors and therefore will not be repeated here. However, we will make
references to the equations derived there and modify those accordingly.
The three most important parameters related to charge multiplication are its
threshold voltage (or the electric field intensity), the first Townsend coefficient, and
the gain. We referred to these quantities in the chapter on gas filled detectors
through the termsVt,α,andMrespectively. In gases a gain of 10^4 can be quite
easily achieved but in liquids it has been found that going beyond a few hundred is
extremely difficult even with single wire chambers having very thin anodes. This,
at first sight, may seem counterintuitive since one would expect the higher density
of molecules in a liquid to favor the charge multiplication. However we should keep
in mind that at each interaction not only electrons but also positive charges are
produced. The ions thus produced move much slower than the electrons and produce
a sheath of charges between the anode and the cathode. This cloud of charges
decreases the effective electric field experienced by the electrons, thus suppressing
the charge multiplication after some time.
The reader should note that even though the charge multiplication in liquids is
not as large as in gases, since the initial number of charge pairs in liquids is much
larger, the net effect is to increase the output signal height considerably.
The threshold for avalanche in liquids is higher than in gases, so cylindrical
chambers are generally used to build liquid filled proportional counters. The first
Townsend coefficient, in such a case, is a function of the position because the electric
field intensity has a radial dependence inside the chamber. The growth of electron
population is still exponential, that is
N=N 2 exp[∫
α(r)dr]
, (4.3.1)
whereN 2 is the number of electrons initiating the avalanche andα(r)istheposition
dependent (or more specifically, electric field dependent) avalanche constant or, as
it is generally known, the first Townsend coefficient. The reader can compare this
equation with equation 3.3.3, which represents the avalanche multiplication in a
uniform electric field environment. Here we have deliberately avoided the use ofN 0
to represent the initial number of electrons, which we used in the case of gases. The
reason lies in the fact that in liquids the recombination and parasitic absorption
of electrons is non-negligible. We will therefore represent the initial number of
electrons produced by the incident radiation byN 0 and the number of electrons
that have survived the recombination byN 1. N 1 can be approximately computed
from (see, for example (6))
N 1 =
N 0
1+K/E(r), (4.3.2)
whereKis the recombination coefficient andE(r) is the radial electric field intensity.
We will discuss the process of recombination in the next section.