## 3 Results
### Dielectric Loss Tangent
\[\text{Re}\;[\hat{\varepsilon}(\omega;\text{T})]=\varepsilon_{\infty}\frac{1- \Gamma_{\text{LM}}^{(\omega)}(\text{T})}{\left(1-\Gamma_{\text{LM}}^{(\omega) }(\text{T})\right)^{2}+\left(\Gamma_{\text{LM}}^{(\omega)}(\text{T})\right)^{ 2}},\text{Im}\;[\hat{\varepsilon}(\omega;\text{T})]=\varepsilon_{\infty} \frac{\Gamma_{\text{LM}}^{(\omega)}(\text{T})}{\left(1-\Gamma_{\text{LM}}^{( \omega)}(\text{T})\right)^{2}+\left(\left(1-\Gamma_{\text{LM}}^{(\omega)}( \text{T})\right)^{2}+\left(\Gamma_{\text{LM}}^{(\omega)}(\text{T})\right)^{2} \right)^{2}} \tag{156}\]  
After some transformation of number series (154), a format convenient for analytical studies is acquired. \[ \begin{split}&[\hat{\varepsilon}^{(\omega)}]_{\text{M}}^{/} \approx\varepsilon_{\infty}\Big{(}(\pi\omega T_{M})^{2}\sqrt{1+\omega^{2}T_{M }^{2}}(\text{cos}\;(2\Delta_{1})+\text{ch}(2\Delta_{1}))\times\frac{T_{D}}{T_ {M}}+\\ +& 4(\Delta_{1}\text{sin}\;(2\Delta_{1})+\Delta_{2} \text{sh}(2\Delta_{2}))+4\omega T_{\text{M}}(\Delta_{2}\text{sin}\;(2\Delta_{ 1})-\Delta_{1}\text{sh}(2\Delta_{2}))\times\\ \times&\Big{(}(\pi\omega T_{M})^{2}\sqrt{1+\omega^{2}T _{M}^{2}}(\text{cos}\;(2\Delta_{1})+\text{ch}\;(2\Delta_{2}))\times\frac{T_{D} }{T_{M}}+8\omega T_{M}\times\\ \times&(\Delta_{2}\text{sin}\;(2\Delta_{1})-\Delta_{ 1}\text{sh}(2\Delta_{2}))+4(\text{ch}\;(2\;\Delta_{2})-\text{cos}\;(2\Delta_{ 1})))^{-1}\Big{)},\end{split}  \tag{157}\]  
\[ \begin{split}&[\hat{\varepsilon}^{(\omega)}]_{\text{M}}^{/} \approx\varepsilon_{\infty}((\pi\omega T_{M})^{2}\sqrt{1+\omega^{2}T_{M}^{2}}( \text{cos}\;(2\Delta_{1})+\text{ch}(2\Delta_{2}))\times\frac{T_{D}}{T_{M}}+ \\ +& 4(\Delta_{2}\text{sin}\;(2\Delta_{1})+\Delta_{1} \text{sh}(2\Delta_{2}))-4\omega T_{\text{M}}(\Delta_{1}\text{sin}\;(2\Delta_{ 1})+\Delta_{2}\text{sh}(2\Delta_{2}))\times\\ \times&\Big{(}\Big{(}\pi\omega T_{M})^{2}\sqrt{1+ \omega^{2}T_{M}^{2}}(\text{cos}\;(2\Delta_{1})+\text{ch}(2\Delta_{2}))\times \frac{T_{D}}{T_{M}}+8\omega T_{M}\times\\ \times&(\Delta_{2}\text{sin}\;(2\Delta_{1})-\Delta_{ 1}\text{sh}\;(2\Delta_{2}))+4(\text{ch}\;(2\Delta_{2})-\text{cos}\;(2\Delta_{ 1})))^{-1}\Big{)}.\end{split}  \tag{158}\]  
Here, \(\Delta_{1,2}=\frac{\pi}{\sqrt{2}}\sqrt{\frac{T_{D}}{T_{M}}}\Big{[}\sqrt{1+ \omega^{2}T_{M}^{2}}\mp 1\Big{]}\). The tangent of the dielectric loss angle at the fundamental frequency of the field is as follows:  
\[ \begin{split}&\Big{[}\text{tg}\delta^{(\omega)}\Big{(}\frac{T_{D}}{T _{M}};\omega T_{M}\Big{)}\Big{]}_{\text{M}}=\frac{\big{[}\hat{\varepsilon}^{( \omega)}\Big{(}\frac{T_{D}}{T_{M}};\omega T_{M}\Big{)}\big{]}_{M}^{/}}{\big{[} \hat{\varepsilon}^{(\omega)}\Big{(}\frac{T_{D}}{T_{M}};\omega T_{M}\Big{)} \big{]}_{M}^{/}}=\\ &=\Big{\{}\Big{(}\pi\omega T_{M})^{2}\sqrt{1+\omega^{2}T_{M}^{2}}( \text{cos}\;(2\Delta_{1})+\text{ch}(2\Delta_{1}))\;+4(\Delta_{2}\text{sin}\;(2 \Delta_{1})-\Delta_{1}\text{sh}(2\Delta_{2}))-\\ -& 4\omega T_{\text{M}}(\Delta_{1}\text{sin}\;(2\Delta_{1})+ \Delta_{2}\text{sh}(2\Delta_{2}))\Big{\}}\times\Big{\{}\Big{(}\pi\omega T_{M})^{2 }\sqrt{1+\omega^{2}T_{M}^{2}}(\text{cos}\;(2\Delta_{1})+\text{ch}(2\Delta_{1})) +\\ +& 4(\Delta_{1}\text{sin}\;(2\Delta_{1})+\Delta_{2} \text{sh}(2\Delta_{2}))+4\omega T_{\text{M}}(\Delta_{2}\text{sin}\;(2\Delta_{1})- \Delta_{1}\text{sh}(2\Delta_{2}))\}^{-1}.\end{split}  \tag{159}\]  
Figures 1 and 2 in Appendix B show the dependency graphs  
\[\Big{[}\text{tg}\delta^{(\omega)}\Big{(}\frac{T_{D}}{T_{M}};\omega T_{M}\Big{)} \Big{]}_{\text{M}},\;\Big{[}\hat{\varepsilon}^{(\omega)}\Big{(}\frac{T_{D}}{T_{M}}; \omega T_{M}\Big{)}\Big{]}_{\text{M}}^{/}\]  
for various values of the parameter \(\alpha_{1}=\frac{T_{D}}{T_{M}}\), which is calculated according to Formulas (157)-(159) using a computer program. Comparative Analysis of the Mechanisms of Maxwell and Diffusion Relaxation with Respect to Volumetric Charge  
For the practical application of Formulas (157)-(159), it is convenient to express them in terms of static permittivity \(\varepsilon_{s}\) and permeability at high frequencies \(\varepsilon_{\infty}\).