development of micro-pattern gaseous detectors – gem - LMU

18 Chapter 1 Interactions of Charged Heavy Particle and Photons in Matter
Figure 1.8: Elastic cross section with Ramsauer minimum for electrons in Argon as a function of the electron’s
energy. [Saul 77]
1.2.4 Gas Amplification
In order to readout the total charge created by primary ionization, the amount has to be multiplied,
since it is usually too small to be detected. This feature makes the gas amplification to the key
principle in gaseous detectors.
Applying high electric fields accelerates the electrons along the field lines and they gain enough
energy between two collisions to ionize other gas molecules, whose liberated electron also gains
energy in the field to ionize more molecules and so on. This avalanche of ions and electrons has
drop-like shape, due to the difference in the drift velocity and the diffusion of migrating charges in
the gas (cf. Fig. 1.9). One of the most important properties of a gaseous detector is the one associated
with the gas amplification, the so-called gas gain G and is defined as:
n(x)
G = = e αx
(1.36)
n0
with n0 and n(x) the number of ion-electron pairs before and after an amplification along the path x.
The total number of ionized electrons generated by one primary electron per unit length of drift is
called first Townsend coefficient α. The exponential rise of liberated charge is only valid as long as
recombination and attachment are negligible and no ionization due to UV-photons takes place. The
multiplication factor cannot be increased in any order. The Raether condition gives a phenomenological
limit for the gas amplification:
αx ≈ 20 or G ≈ 10 8 . (1.37)
From Eq. 1.37 it is obvious that for increasing path length, i.e. gap thickness in the GEM detector (cf.
Ch. 3), the Raether limit will be met at decreasing values of α. Therefore the breakdown probability
increases for a given field strength with the gap size. The Townsend coefficient, normalized to the
applied pressure, for Ar/CO2 mixtures in several percentages can be seen in Fig. 1.10.