FIGURE 2.

Relationships $\eta =\eta (\mathrm{\Psi })$ (left diagram) and $\overline{\varphi }(\mathrm{\Psi })$ (right diagram) according to Equation 13. Curves of the same color refer to $z=2$ (red), $z=4$ (blue), and $z=6$ (green) and are calculated for $\omega =1/2$ (solid colored lines), $\omega =1$ (broken lines), and $\omega =1.5$ (dotted lines). For $\omega =0$ , Equation 13 predicts $\eta =-\tanh (\mathrm{\Psi })$ irrespective of $z$ (the black curve on the left diagram). All curves colored red $(z=2)$ follow the explicit expressions in Equation 15. The thick transparent lines in the left diagram represent third-order approximations of $\eta (\mathrm{\Psi })$ , as specified in Equations 29, 30. They will be utilized in Sections 3.1, 3.2 to calculate the differential capacitance for the linearized model and beyond that using a perturbation approach.