}^{2}}\left[
\Phi _{m,\omega }\frac{\partial \Phi _{m,-\omega }^{\ast }}{\partial x}-\Phi
_{m,-\omega }^{\ast }\frac{\partial \Phi _{m,\omega }}{\partial x}\right] ,
\label{current}$$calculated at the SI and FS interfaces and in the electrodes.

In the further analysis carried out below we limit ourselves to the consideration of the most relevant case of low-transparent tunnel barrier at SI interface$$\gamma _{BI}\gg 1.  \label{LargeGammaBI}$$In this approximation, the junction resistance $R_{N}$ is fully determined by the barrier resistance $R_{BI}$. Furthermore the current flowing through the electrodes can lead to the suppression of superconductivity only in the vicinity of sF and FS interfaces. That means, up to terms of the order of $\gamma _{BI}^{-1}$ we can neglect the effects of suppression of superconductivity in the region $x\leq -d_{s}~$ and write the solution in the form $$\Phi _{S}(x)=\Delta _{S}(x)=\Delta _{0}.  \label{Sol_Left}$$Here without any lost of generality we put $\chi (-\infty )=\chi
(-d_{s}-0)=0 $ (see Fig. \[design\]c).

Substitution of (\[Sol\_Left\]) into boundary conditions (\[BCIF\]) gives$$\gamma _{BI}\xi _{S}G_{s}\frac{d}{dx}\Phi _{s}=-\frac{\Omega }{\sqrt{\Omega
^{2}+\Delta _{0}^{2}}}\left( \Delta _{0} -\Phi _{s}\right) .  \label{BCIFmod}$$Further simplifications are possible in a several limiting cases.

The high temperature limit $T\approx T_{C}$\[SecHighTC\]
========================================================

In a vicinity of critical temperature the Usadel equations in the F layer can be linearized. Writing down their solution 