Calorimeter

  A composite detector using total absorption of particles to measure the energy and position of incident particles or jets. In the process of absorption showers are generated by cascades of interactions, hence the occasionally used name shower counter for a calorimeter. In the course of showering, eventually, most of the incident particle energy will be converted into ``heat'', which explains the name calorimeter (calor = Latin for heat) for this kind of detector; of course, no temperature is measured in practical detectors, but characteristic interactions with matter (e.g. atomic excitation, ionization) are used to generate a detectable effect, via particle charges. Calorimetry is also the only practicable way to measure neutral particles among the secondaries produced in a high-energy collision.

Calorimeters are usually composed of different parts, custom-built for optimal performance on different incident particles. Each calorimeter is made of multiple individual cells, over whose volume the absorbed energy is integrated; cells are aligned to form towers typically along the direction of the incident particle. The analysis of cells and towers allows one to measure lateral and longitudinal shower profiles, hence their arrangement is optimized for this purpose, and usually changes orientation in different angular regions. Typically, incident electromagnetic particles, viz. electrons and gammas, are fully absorbed in the electromagnetic calorimeter , which is made of the first (for the particles) layers of a composite calorimeter; its construction takes advantage of the comparatively short and concentrated electromagnetic shower shape to measure energy and position with optimal precision for these particles (which include 's, decaying electromagnetically). Electromagnetic showers have a shape that fluctuates within comparatively narrow limits; its overall size scales with the radiation length.

Incident hadrons, on the other hand, may start their showering in the electromagnetic calorimeter, but will nearly always be absorbed fully only in later layers, i.e. in the hadronic calorimeter , built precisely for their containment. Hadronic showers have a widely fluctuating shape; their average extent does not scale with the calorimeter's interaction length, but is partly determined by the radiation length.

Discrimination, often at the trigger level, between electromagnetic and hadronic showers is a major criterion for a calorimeter; it is, therefore, important to contain electromagnetic showers over a short distance, without initiating too many hadronic showers. The critical quantity to maximize is the ratio , which is approximately proportional to Z^1.3 (see [Fabjan91]); hence the use of high-Z materials like lead, tungsten, or uranium for electromagnetic calorimeters.

Calorimeters can also provide signatures for particles that are not absorbed: muons and neutrinos. Muons do not shower in matter, but their charge leaves an ionization signal, which can be identified in a calorimeter if the particle is sufficiently isolated (and the dynamic range of electronics permits), and then can be associated to a track detected in tracking devices inside the calorimeter, or/and in specific muon chambers (after passing the calorimeter). Neutrinos, on the other hand, leave no signal in a calorimeter, but their existence can sometimes be inferred from energy conservation: in a hermetically closed calorimeter, at least a single sufficiently energetic neutrino, or an unbalanced group of neutrinos, can be ``observed'' by forming a vector sum of all measured momenta, taking the observed energy in each calorimeter cell along the direction from the interaction point to the cell. The precision of such measurements, usually limited to the transverse direction, requires minimal leakage of energy in all directions, hence a major challenge for designing a practical calorimeter.

The shower development is a statistical process (see Electromagnetic Shower, Hadronic Shower). This explains why the relative accuracy of energy measurements in calorimeters improves with increasing energy, according to the empirical formula

where E = energy of incident particle, = standard deviation of energy measurement, and a and are constants depending on the detector type, e.g. the thickness and characteristics of active and passive layers. The overall constant includes the systematic errors of the individual modules. Other, similar formulae, with different energy-dependent terms are in use; for more details, Energy Resolution in Calorimeters, Compensating Calorimeter.

From the construction point of view, one can distinguish between:

• a) Homogeneous Shower Counters . In homogeneous calorimeters the functions of passive particle absorption and active signal generation and readout are combined in a single material. Such materials are almost exclusively used for electromagnetic calorimeters, e.g. crystals ( Crystal Calorimeter), composite materials (like lead glass, viz. PbO and SiO₂) or, usually for low energy, liquid noble gases (see [Walraff91], [Fabjan95a]).
• b) Heterogeneous Shower Counters (= Sampling Calorimeters). In sampling calorimeters the functions of particle absorption and active signal readout are separated. This allows optimal choice of absorber materials and a certain freedom in signal treatment. Heterogeneous calorimeters are mostly built as sandwich counters, sheets of heavy-material absorber (e.g. lead, iron, uranium) alternating with layers of active material (e.g. liquid or solid scintillators, or proportional counters). Only the fraction of the shower energy absorbed in the active material is measured. Hadron calorimeters, needing considerable depth and width to create and absorb the shower, are necessarily of the sampling calorimeter type.
  

  In practical constructions the ratio of energy loss in the passive and active material is rather large, typically of the order of 10. Although performance does not strongly depend on the orientation of active and passive material, their relative thickness must not vary too much, to ensure an energy resolution independent of direction and position of showers. Only a few percent of the energy lost in the active layers is converted into detectable signal. For a discussion, [Fabjan91].

Calorimetry is the art of compromising between conflicting requirements; the principal requirements are usually formulated in terms of resolution in energy, spatial coordinates, and time, in triggering capabilities, in radiation hardness of the materials used, and in electronics parameters like dynamic range, and signal extraction (for high-frequency colliders). In nearly all cases, cost is the most critical limiting parameter. Depending on the physics goals, the energy range that has to be considered, the accelerator characteristics, etc., some goals will be favoured over others. The span of possible solutions for calorimeters is much wider than for tracking devices, and quite ingenious solutions have been found by imaginative experimental teams over the last 15 years, since calorimeters became key components of particle detectors.

For further reading, e.g. [Fabjan91], [Wigmans91a], [Cushman92], [Gratta94], [Gordon95], [Colas95], [Weber95], and references given there.