## 2 Materials and Methods (Theoretical Bases and Methods)
In Equations (9) and (10), in addition to [1; 2; 7], elements, \(\frac{1}{2}\exp(\mathfrak{n}(t))\times\left(1\pm\exp(-2\xi(t))\right)\) indicates the influence of external indignation in the form of correction parameters \(\xi(t)=\left|\frac{\Delta\mathrm{U}(t)}{\mathrm{k_{B}T}}\right|\), \(\mathfrak{n}(t)=\Lambda\left|\frac{\Delta\mathrm{U}(t)}{\mathrm{U}_{0}}\right|\) on non-stationary kinetic coefficients \(\Omega^{(\omega)}(t)\), \(\Xi^{(\omega)}(t)\). Earlier, such amendments were not taken into account. Their consideration in these functions will make it possible to more strictly assess the influence of the external electric field on the solutions of the kinetic equation and, accordingly, polarization. The study of dielectric relaxation in layered dielectrics uses the solution of the kinetic equation [6]:  
\[\frac{\mathrm{d}\Delta n^{(\omega)}(t)}{\mathrm{dt}}+2\Omega^{(\omega)}(t) \Delta n^{(\omega)}(t)=\frac{1}{3}n_{0}\Xi^{(\omega)}(t) \tag{11}\]  
In (11), \(\Delta n^{(\omega)}(t)=\Delta n^{(\omega)}(t)-n_{0}\) is a concentration of relaxers (protons) in excess of the balanced concentration \(n_{0}\). No initial polarization was used: \(\Delta n^{(\omega)}(0)=0\). Kinetic Equation (11) was built and studied in [6; 8]. Moreover, Ref. [2] solved an even more physically stringent kinetic equation regarding proton (for HBC) and ion (for a wide class of dielectrics) relaxation based on a multi-pit crystal potential model. Here, we limit ourselves to a simpler kinetic equation for a dual-symmetric potential pit model, with the aim that the format of this model will qualitatively fit the Bucci-Rive thermally stimulated depolarization (TSCD) current calculation scheme described below. The disadvantage of the kinetic equation solutions we chose is that this model does not consider the heterogeneity of the electric field in the dielectric, unlike other works [1; 2]. However, since we did not conduct studies on the electro-tertiary effect and the effects associated with homocharge relaxation in this manuscript, the physical severity of the final re-results is not at all reduced when choosing a more simplified kinetic Equation (11). In addition, in this work, in continuation of that of [6], we will strengthen the influence of external perturbation parameters \(\xi(t)=\left|\frac{\Delta\mathrm{U}(t)}{\mathrm{k_{B}T}}\right|\), \(\mathfrak{n}(t)=\Lambda\left|\frac{\Delta\mathrm{U}(t)}{\mathrm{U}_{0}}\right|\) on the final solutions to Equation (11). To this end, solutions of Equation (11) must be written using perturbation theory methods, allowing for their decomposition into infinite power series by degrees of perturbation parameters \(\xi(t)\) in the form:  
\[\Delta n^{(\omega)}(t)=\sum_{s=1}^{\infty}\xi_{0}^{s}\Delta\Big{(}\Delta n^{ (\omega)}(t)\Big{)}^{(s)},\]  
According to the relation \(\frac{\mathfrak{n}(t)}{\xi(t)}=\frac{\mathrm{T}}{\Gamma_{\alpha}}\), the auxiliary identities hold. \[\left(\xi(t)\right)^{l}(\mathfrak{n}(t))^{\mathrm{P}}=\left(\xi(t)\right)^{l+ \mathrm{P}}\times\left(\frac{\mathrm{T}}{\Gamma_{\alpha}}\right)^{\mathrm{P}},\ \left(\xi(t)\right)^{l}(\mathfrak{n}(t))^{\mathrm{P}}=\left(\mathfrak{n}(t) \right)^{\mathrm{P}+l}\times\left(\frac{\mathrm{T}_{\alpha}}{\mathrm{T}} \right)^{l}.\]  
Elements of series \(\left(\Omega^{(\omega)}(t)\right)^{(s)}\), \(\left(\Xi^{(\omega)}(t)\right)^{(\mathrm{P})}\) follow from Equations (9) and (10). This method is effective in the construction of solutions to Equation (11) for the processes of dielectric losses when the electric field is variable and the parameters \(\xi(t)\), \(\mathfrak{n}(t)\) are considered only as functions of time. This work examines the process of thermally stimulated depolarization; therefore, there is no strict need to apply perturbation theory methods and the work can be limited to other, more mathematically simple methods, which are set out below. However, it should be noted that the methods of perturbation theory are the solutions of Equation (11).