220
C. W. Fabjan and D. Fournier
Saturation effects are not relevant for electron or photon induced showers (at least
below few TeVs) because the track density remains comparatively low (however,
depending on the technique used for sampling calorimeters, internal amplification—
like in calorimeters with gaseous readout—may saturate for high track density).
Saturation effects do affect hadronic showers because of slow, highly ionizing
fragments from nuclear break-up and slow proton recoils.
The—in general excellent—energy resolution of homogeneous calorimeters used
for electromagnetic showers is affected by several instrumental effects. One of
the most fundamental ones, the existence of a threshold energy E th above which
an electron of the shower does produce a signal will be illustrated in Sect. 6.3.2
when dealing with Cherenkov based electromagnetic calorimeters. Other effects
include:
– longitudinal and transverse shower containment
– efficiency of light collection
– photoelectron statistics
– electron carrier attachment (impurities)
– space charge effects, . . .
These effects will be considered when dealing with examples where they are
particularly relevant. The closer a detector approaches the intrinsic resolution—
like for Ge crystals—the more important are the above limitations. In practice,
large calorimeter systems for high energy showers based on homogeneous semiconductor crystals are unaffordable. Scintillating crystals and pure noble liquids
are the best compromise between performance and cost, but do suffer from other
limitations, as illustrated in examples given below.
6.2.4 Sampling Calorimeters and Sampling Fluctuations
In the simplest geometry, a sampling calorimeter consists of plates of dense, passive
material alternating with layers of sensitive material.
For electromagnetic showers, passive materials with low critical energy (thus
high Z) are used, thus maximizing the number of electrons and positrons in a shower
to be sampled by the active layers. In practice, lead is most frequently used. Uranium
has also been used to optimize the response towards hadrons (Sect. 6.2.7), and
tungsten has been used in cases where compactness is a premium.
The thickness t of the passive layers (in units of X 0 ) determines the sampling
frequency, i.e. the number of times a high energy electron or photon shower is
‘sampled’. Intuitively, the thinner the passive layer (i.e. the higher the sampling
frequency), the better the resolution should be. The thickness u of the active layer
is usually characterized by the sampling fraction f S which is the ratio of dE/dx of a
C. W. Fabjan and D. Fournier
Saturation effects are not relevant for electron or photon induced showers (at least
below few TeVs) because the track density remains comparatively low (however,
depending on the technique used for sampling calorimeters, internal amplification—
like in calorimeters with gaseous readout—may saturate for high track density).
Saturation effects do affect hadronic showers because of slow, highly ionizing
fragments from nuclear break-up and slow proton recoils.
The—in general excellent—energy resolution of homogeneous calorimeters used
for electromagnetic showers is affected by several instrumental effects. One of
the most fundamental ones, the existence of a threshold energy E th above which
an electron of the shower does produce a signal will be illustrated in Sect. 6.3.2
when dealing with Cherenkov based electromagnetic calorimeters. Other effects
include:
– longitudinal and transverse shower containment
– efficiency of light collection
– photoelectron statistics
– electron carrier attachment (impurities)
– space charge effects, . . .
These effects will be considered when dealing with examples where they are
particularly relevant. The closer a detector approaches the intrinsic resolution—
like for Ge crystals—the more important are the above limitations. In practice,
large calorimeter systems for high energy showers based on homogeneous semiconductor crystals are unaffordable. Scintillating crystals and pure noble liquids
are the best compromise between performance and cost, but do suffer from other
limitations, as illustrated in examples given below.
6.2.4 Sampling Calorimeters and Sampling Fluctuations
In the simplest geometry, a sampling calorimeter consists of plates of dense, passive
material alternating with layers of sensitive material.
For electromagnetic showers, passive materials with low critical energy (thus
high Z) are used, thus maximizing the number of electrons and positrons in a shower
to be sampled by the active layers. In practice, lead is most frequently used. Uranium
has also been used to optimize the response towards hadrons (Sect. 6.2.7), and
tungsten has been used in cases where compactness is a premium.
The thickness t of the passive layers (in units of X 0 ) determines the sampling
frequency, i.e. the number of times a high energy electron or photon shower is
‘sampled’. Intuitively, the thinner the passive layer (i.e. the higher the sampling
frequency), the better the resolution should be. The thickness u of the active layer
is usually characterized by the sampling fraction f S which is the ratio of dE/dx of a