doctoral thesis

36 CHAPTER 2. DETECTOR PHYSICS OF RPCS
Average Number of Clusters/mm
16
14
12
10
8
6
4
2
0
10 -1
i-C 4 H 10 100
C 2 F 4 H 2 /i-C 4 H 10 /SF 6 85/5/10
C 2 F 4 H 2 /i-C 4 H 10 /SF 6 96.7/3./0.3
CH 4 100
1 10 10 2
γ-1
Figure 2.2: The average number of ionizing collisions (clusters) per mm (n = 1/λ) as
a function of γ − 1 for different gases as predicted by HEED [25]. T = 296.15 K and
p = 1013 mbar. The solid lines are measurements taken from [75].
2.1.2 Maximum Detection Efficiency
Since the distance between the ionizing collisions is exponentially distributed, the
number of clusters on a distance g follows a Poisson distribution with an average of
n = g/λ. The probability to have n clusters is given by
P (n) = 1
n!
g
n g
−
e λ . (2.5)
λ
The average number of clusters is very different for different gas mixtures. In Table
2.1 we list values of n = g/λ for g = 1 mm for a few common gases.
We assume that all primary clusters in the gas gap are detected, which can only
theoretically be achieved by either an infinite gas gain or a threshold of zero applied to
the signals. With Eq. 2.5 we calculate the maximum detection efficiency ɛmax to be
ɛmax = 1 − e −n , (2.6)