4 Gaseous Detectors
111
Fig. 4.11 Pulse-height transition from limited proportionality to limited streamer mode [41]
examples of measurements [42]; it shows the strong increase of α with electric field
in the region of interest to gas detectors, up to about 250 kV/cm. No simple relation
exists for α as function of electric field E, but Monte Carlo simulation has been used
to evaluate α. Figure 4.13 shows an example [27]. For the lower field values there
is reasonable agreement with measurement. The discrepancy at the highest fields is
attributed to photo-and Penning-ionization not being included.
The amplification A in the detector is obtained by integration
A = n/n 0 = exp
α(s) ds = exp
α(E)/ (dE/ds) dE,
(4.45)
from E min , the minimum field to start the avalanche, to the field E(a) on the wire.
E min e is equal to the ionization energy of the gas molecules divided by the mean
free path between collisions. Near the wire and far from other electrodes, the field
is
E(r) = q s / (2πrε 0 ) ,
(4.46)
111
Fig. 4.11 Pulse-height transition from limited proportionality to limited streamer mode [41]
examples of measurements [42]; it shows the strong increase of α with electric field
in the region of interest to gas detectors, up to about 250 kV/cm. No simple relation
exists for α as function of electric field E, but Monte Carlo simulation has been used
to evaluate α. Figure 4.13 shows an example [27]. For the lower field values there
is reasonable agreement with measurement. The discrepancy at the highest fields is
attributed to photo-and Penning-ionization not being included.
The amplification A in the detector is obtained by integration
A = n/n 0 = exp
α(s) ds = exp
α(E)/ (dE/ds) dE,
(4.45)
from E min , the minimum field to start the avalanche, to the field E(a) on the wire.
E min e is equal to the ionization energy of the gas molecules divided by the mean
free path between collisions. Near the wire and far from other electrodes, the field
is
E(r) = q s / (2πrε 0 ) ,
(4.46)