Stanislav said:
Closely to Tc the pair density tends to zero, so the velocity of remaining pairs should strongly increase (in order to keep the current stable). Thermal energy kT is quanized and cannot strongly accelerate each remaining pair. Or we must do a new assumption that each remaining pair can absorb a serie of heat quanta, and allways into a certain direction only. A magic again
The pairs are in a condensate and the whole condensate has to be accelerated. The acceleration of the condensate is due to the electric field generated by the decaying normal current. You made me look up some basics isn "Michael Tihnkham, Introduction to Superconductivity", namely section 2.5 on non-static solutions and Gortner's two fluid model. There, it is clearly stated that non- zero electric fields are possible in superconductors.
I tried to work out as an example the case of a superconducting medium filling the half space x<0. The other half space is filled with a magnetic field ##B(x\ge0)=B_z=\mathrm{const}##. On the left, B has still only a z component but its value will be a function of x and t.
Likewise, on the left, we have an electric field ##E_y## and normal and superconducting currents ##j_\mathrm{n}## and ##j_\mathrm{s}## and respective densities
##n_\mathrm{n}## and ##n_\mathrm{s}## the latter being constant for t>0. (##n_\mathrm{n}## is the additional normal conductive density due to the temperature change).
At t=0 the temperature is assumed to jump so that the densities change, but the total current is continuous ##j(t_-)=j(t_+)##.
The currents fulfill the equations ##\dot{j}_\mathrm{s}=\frac{n_\mathrm{s}e^2}{m}E## and ##\dot{j}_\mathrm{n}=\frac{n_\mathrm{n}e^2}{m}E+j_\mathrm{n}/\tau##. Here, e and m are the charges and masses of the charge carriers (i.e. cooper pairs, whether broken or not), and ##\tau## is the mean intercollision time.
Considering the Fourier components ##\omega## and ##k=k_x##, I get
## (\omega^2-k^2)E=\left(\frac{n_\mathrm{s}e^2}{m}+\frac{i\omega}{i\omega+1/\tau}\frac{n_\mathrm{n}e^2}{m}\right)E##.
Similar equations hold for B, and the currents.
Considering values of ##\omega## much smaller than the absolute value of ##k##, the square of ##\omega## may be dropped. Furthermore we distinguish between ##\omega < 1/\tau## and ##\omega >1/\tau## and get
## -k^2-\frac{n_\mathrm{s}e^2}{m}+\frac{n_\mathrm{n}e^2}{m}=0## for ##\omega > 1/\tau## and
## -k^2-\frac{n_\mathrm{s}e^2}{m}=0## for ##\omega < 1/\tau##
The high frequency components interfere destructively for ##t >> \tau##.
The low frequency contributions initially have to interfere destructively due to the boundary conditions. Their superposition becomes non-zero for ##t>\tau## but finally they will also die out.
Note that k is purely imaginary, describing the screening of the fields.
Upon heating, the screening length increases within time ##\tau## to the new larger value, before the electric fields finally die out.
