This paper is devoted to the development of generalized (for a wide range of fields (100 kV/m–1000 MV/m) and temperatures (0–1500 K) in the radio frequency range (1 kHz–500 MHz)) methods for the theoretical investigation of the physical mechanism of nonlinear kinetic phenomena during the establishment of the relaxation polarization, due to the diffusion motion of the main charge carriers in dielectrics with ionic–molecular chemical bonds (hydrogen-bonded crystals (HBC), including layered silicates, crystalline hydrates and corundum–zirconium ceramics (CZC), etc.) in an electric field. The influence of the nonlinearities equations of the initial phenomenological model of dielectric relaxation (in HBC-proton relaxation) on the mechanism for the formation of volume–charge polarization in solid dielectrics is analyzed. The solutions for the nonlinear kinetic Fokker–Planck equation, together with the Poisson equation, for the model of blocked electrodes are built in an infinite approximation (including all orders k of smallness without dimensional parameters) of perturbation theory for an arbitrary order r of the frequency harmonic of an alternating external polarizing field. It has been established that the polarization nonlinearities in ion-molecular dielectrics, already detected at the fundamental frequency, are interpreted in the mathematical model (for the first time in this work) as interactions of the relaxation modes of the volume charge density calculated on different orders of spatial Fourier harmonics. At the fundamental frequency of the field, an analytical generalized expression is written for complex dielectric permittivity (CDP), which is expressed analytically in terms of special relaxation parameters, which are quite complex real functions in the fields of frequency and temperature. The theoretical CDP and the dielectric loss tangent spectra studied depend on the nature of the relaxation processes in the selected temperature range (Maxwell and diffusion relaxation; thermally activated and tunneling relaxation), which is relevant from the point of view of choosing exact calculation formulas when analyzing the optimal operating modes of functional elements (based on dielectrics and their composites) for circuits of instrumentation, radio engineering and power equipment in real industrial production.

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Methods quasiclassical kinetic theory investigate the phenomena of nonlinear ion-relaxation polarization in solid dielectrics with a compound structure of the crystal lattice. As a particular case, the mechanism of nonlinear proton-relaxation polarization in hydrogen-bonded crystals (HBC), classified according the electrophysical properties as proton semiconductors and dielectrics (PSD) is theoretically studied. Generalized kinetic equation and spectra of complex permittivity (CP), which allow to describe the nonlinear properties of dielectric losses in HBC in range of ultra-low temperatures (1- 10 K) and low fields (100 kV/m - 1000 kV/m), and in range of ultra-high temperatures (550-1500 K) and strong fields (10 MV/m - 1000 MV/m). The scientific and practical significance of received results consists in development of the theoretical basis of algorithm for computer prediction of materials properties and parameters that are functional elements of technological schemes of industrial installations and systems.

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