Also called a Zeta pinch, a Z-pinch occurs when the electric current in plasma generates a magnetic field that compresses the plasma. The Z-pinch term refers to the z-axis direction of the electric current on a 3-D graph.
High-intensity electric current going through plasma is spiral in form. Called Birkeland currents, the spirals occur in pairs and compress matter between them, whether ionized or not. That's the Z-pinch.
A Z-pinch is a result of the Lorentz force, F=qE+qv x B, in which a current-carrying conductor in a magnetic field B experiences the force F. For example, two parallel wires carrying current in the same direction attract each other. Replace the cables by a plasma, which is basically many current-carrying wires, and the plasma particles will attract each other by the Lorentz force. Nice and straightforward. The result is a plasma contraction, hence the term 'pinch.'
The Z-pinch seems to explain why matter in the Universe forms stringy filaments.