## 1 Introduction  
In the last twenty years in the industry, hydrogen-bonded crystals (HBC)-based materials (and their composites) have been widely used in insulating and cable technology, capacitor technology (electrically controlled nonlinear capacitors), physicochemical technologies (solid state electrolytes), laser technology (regulators of laser radiation parameters and electric shutters), radio electronics, radio engineering (elements of radiation generators and microwave control systems), etc. [1; 2]. The materials of the class of HBC, from the point of view of mineralogy, belong to the class of layered crystals. They are divided into crystalline hydrates and layered silicates, which differ in the presence of a hydrogen sublattice in their structure and the possibility of hydrogen ions (protons) moving along hydrogen links. The displacement of protons in HBC along hydrogen bonds can be carried out both due to thermal activation (classical transitions) and tunneling (quantum transitions). Therefore, the imposition of an electric field on the crystal (directed along the crystal axis) leads to the diffusion motion of protons in the direction of field lines (proton conductivity). Thus, according to electrophysical properties, HBC are classified as proton semiconductors and dielectrics (PSCD) [1; 2; 3; 4]. According to the results of experiments, in HBC, in a wide range of polarizing field strengths (100 kV/m-100 MV/m) and temperatures (50-550 K), volume -charge polarization is established. It possesses a relaxation nature and significantly depends on the parameters of the crystal structure, of the external electrical field (amplitude and frequency of EMF) and the selected temperature range. Polarization phenomena at low temperatures (50-100 K) appear as quantum polarization due to the tunneling motion of protons inside and between ions of the anion sublattice; at high temperatures (450-550 K), they appear as a nonlinear space charge polarization due to the mixed type of proton motion (both due to thermal activation and tunneling) [1]. The analytical study of the nonlinear relaxation polarization is an applied scientific direction relevant for electrophysics and electrical engineering. It allows, in a wide range of polarizing field intensities (100 kV/m-1000 MV/m) and temperatures (0-1500 K), the identification of the patterns of behavior of the current spectra of thermally stimulated polarization and dielectric losses in the dielectrics class of PSCD, in dielectrics and a wider range of crystals with a type of conductivity similar to HBC in terms of physical mechanism. This type of crystal has ionic-molecular chemical bonds, characterized by high (and in some cases very high) ionic conductivity (perovskites, clay minerals, corundum-zirconium ceramics (CZC) [5], etc.). It should be noted that some materials of this class belong to high-temperature superconductors. For example, high-temperature superconducting ceramics (HTSC-ceramics) and ceramics created on the basis of oxide high-temperature superconductors. In microwave components, thin films of HTSC ceramics on single-crystal substrates are used. In zirconium oxide crystals stabilized by ion implantation, the formation of nanoclusters is observed, and conductivity maxima are found due to the resonant tunneling of electrons through dielectric potential barriers with transparency depending on the cluster size, electron energy and voltage on the structure [6]. The area of abnormally high nonlinearities is of special interest. It manifests in PSCD in the range of ultra-low (helium) temperatures (1-10 K) in the region of weak fields (100 kV/m-1000 kV/m) and the range of ultra-high temperatures (550-1500 K) in the region of strong fields (10-1000 MV/m) ([1], p. 43; [2], p. 74). Conditions of this type can be defined as extreme for the operation of the heterogeneous functional elements of process circuits of electrical (instrumentation, computer, etc.)