## 2 Primary Energy Measurement with a Calorimeter  
The technical realization of modern ionization calorimeters can be variable, but the idea remains invariable: the primary particle enters into a dense substance (absorber), in which numerous nuclear and electromagnetic interactions take place. It gives rise to a cascade of secondary particles. To measure the characteristics of the cascade, the dense substance is sandwiched with special detectors. By measurement of signals from these detectors, the cascade curve is formed. By their design, calorimeters are divided into homogeneous and heterogeneous. Heterogeneous calorimeters consist of layers of a substance with a high density (lead, tungsten), where particles lose their energy during passage, alternating with layers of detectors (silicon), where the energy released by the particles of the cascade is measured. Homogeneous calorimeters use substances (bismuth germanate crystal, lead tungsten, etc.) which are simultaneously both an absorber and a detector. The geometric dimensions of heterogeneous calorimeters are usually significantly lower than those of homogeneous ones. In addition, they have better spatial resolution as they are segmented in both the longitudinal and lateral directions. A significant drawback of heterogeneous calorimeters is the transient effect due to the significant difference in the densities of the absorber and detector. Cascade curves develop differently in different materials. Consequently, the behavior of the cascade curve is violated when the cascade transitions from one material to another. In this regard, fluctuations in the development of the cascade from layer to layer can be observed. The strongest fluctuations from layer to layer are at the beginning of the development of the cascade. This makes the analysis very difficult [20]. Several methods have been developed to measure the primary energy of cosmic rays using different types of calorimeters. The PAMELA calorimeter is a heterogeneous calorimeter. It consists of 22(x, y) silicon detector planes alternating with tungsten absorber planes. The calorimeter thickness is 16.3 radiation lengths. In the PAMELA experiment, the primary energy is estimated from the maximum of the cascade curve describing the longitudinal profile of the shower developed in the calorimeter. If the shower maximum is located outside the calorimeter, then the energy released in the last layer of the calorimeter is used to estimate the energy. This technique provides an energy resolution for protons of \(\sim\)40% [14]. The NUCLEON calorimeter thickness is 15.3 radiation lengths (the silicon microstrip detectors interleaved with thin tungsten layers). The proposed technique for primary CR energy measurement is based on the generalized Castagnoli kinematical method (KLEM method) developed for emulsion. In this method, the primary energy is reconstructed by registering the spatial density of the secondary particles. Secondary particles are generated by the first hadronic inelastic interaction in a carbon target. Additional particles are then produced in a thin tungsten converter by electro-magnetic and hadronic interactions. This method provides an energy resolution of \(\sim\)70% [16]. CALET is a homogeneous calorimeter made of lead tungstate (PbWO\({}_{4}\)) bars arranged in 12 layers. The total thickness of the device is equivalent to 30 radiation lengths. The primary particle energy is calculated from the total energy release in the calorimeter. The energy released in the calorimeter is scaled linearly with the energy of the incident particle. The obtained energy resolution is close to 30% [17]. ATIC is a homogeneous calorimeter consisting of 10 layers of 40 bismuth germanium scintillation crystals (BGO). The total thickness is approximately 22 radiation lengths. For protons, most of the released energy is not recorded by the calorimeter detectors. In this regard, the selection of events was carried out according to predetermined conditions, such as the interaction near the upper boundary of the calorimeter.