## 1 Introduction
and power (insulation coatings of current removal elements of electric generators and transformers of thermal power plants) plants and systems ([3], p. 7). The practical use and scientific practical significance of the non-linear elements based on PSCD are detailed more in ([1], pp. 41-42) and pertain to space technologies, nanotechnologies and high-voltage technology [3; 4]. In [1], a detailed analysis of the influence of voltage source parameters (amplitude and frequency of EMF), dielectric temperature and thickness on the properties of the complex dielectric permittivity (CDP) spectra \(\hat{\epsilon}^{(\omega)}(\mathbb{T})\) for PSCD was performed; effects ofthe interaction of relaxation modes at the main field frequency \(\omega\)[3] were detected. It can be the basis for the development of experimental methods for amplifying signals in the radio frequency range (microwave generators). Since control measuring and power equipment during operations, in most cases, is tuned to the fundamental frequency of the alternating field \(\omega\), further theoretical studies of the behavior of the parameters of relaxation processes (probability rates of transitions of relaxers, relaxation times, kinetic coefficients, etc.) and the polarization itself, depending on temperature, field strength and dielectric structure parameters, on the fundamental frequency harmonic \(\mathrm{P}^{(\omega)}(t)\) are possible. It is important to construct algorithms for calculating higher-order polarization harmonics (starting from the third \(\mathrm{P}^{(3\omega)}(t)\)) based on recurrent analytical expressions, which also allow the calculation of the components of the complex permittivity in an arbitrary approximation with respect to the polarizing field. Mathematical and Physical Model of the Nonlinear Relaxation Polarization. Setting of the Research Objective  
In [3], nonlinear solutions of the semi-classical kinetic equation in complex with the Poisson equation for the model of blocking electrodes were obtained with accuracy to the cubic term (by a small parameter \(\gamma\)[3], pp. 13-14). By the method of mathematical induction in the infinite approximation of the perturbation theory at the main frequency \(\omega\), the frequency harmonic of polarization \(\mathrm{P}^{(\omega)}(t)\) ([3], p. 16) was calculated and the nonlinear frequency-temperature spectra of the CDP were constructed and studied in detail ([1], pp. 43-49). At the same time, the polarization harmonics \(\mathrm{P}^{(3\omega)}(t)\) following \(\mathrm{P}^{(\omega)}(t)\) and multiplied by the frequency \(3\omega\) according to the methodology [1; 3] can no longer be calculated. The purpose of this paper, in the continuation of [1; 3; 2], is to develop generalized (for any approximation of the perturbation theory) methods for the analytical study of the influence of the nonlinearities of the kinetic equations of the original phenomenological model ([3], p. 13) on the mechanism for the formation of the volume-charge distribution in the dielectrics type of hydrogen-bonded crystals (HBC). The results of these studies can be used in the mathematical description and modeling of the ionic conductivity and relaxation polarization processes in crystals with ionic-molecular chemical bonds, a special case of which are hydrogen-bonded crystals (characterized by proton conductivity). This paper is devoted to the development of generalized (for a wide range of field and temperature parameters) analytical methods for solving the nonlinear kinetic Fokker-Planck equation, together with the Poisson equation, in an infinite approximation (including all orders of smallness from k = 0 to k = \(\infty\) without dimensional parameter \(\gamma<1\)) of perturbation theory for an arbitrary order of the frequency harmonic of an alternating polarizing field \(\mathrm{P}^{(\tau\omega)}(t)\).