When two wires parallel to each other has the same current running in the same direction, there is a force attracting th

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When two wires parallel to each other has the same current
running in the same direction, there is a force attracting the two
wires together that is responsible for the pinch effect in
electric arcs and other plasmas. The force exists whether the
currents are in wires or not. It is only apparent if the
overall charge density is zero; otherwise, the Coulomb repulsion
overwhelms the magnetic attraction.
In the situation described above, how is it possible for the
current to have an overall charge density of zero?