Will the current in the wire attract each other

[ENDLESSYOU]

I wonder whether the current in a single wire will attract each other?
Eventually shrink to a line?

 

[mfb]

In which way?
If you consider a current in a cable with finite cross-section and no net charge, electron density might be a big higher in the interior due to magnetic fields. I think I calculated that once, and the result was very small for realistic current flows. A higher electron density adds repulsion, which cancels the magnetic forces soon.