Asymmetry in fast Z-pinches with thin liners

We use a well-known, two-dimensional solution to Laplace´s equation for the vector potential between two perfectly conducting, individually axisymmetric but mutually eccentric, current carrying cylinders to model the geometry and time evolution of an asymmetric Z-pinch. Cylinder eccentricity correlates with an azimuthal variation in the axial current, the magnetic field, and the force on the liner. The asymmetric force sums to a net force tending to restore the inner cylinder to concentricity. Complete pinch compression and concentricity are achieved simultaneously when the initial radius of the inner cylinder R_i(0) is about 2/3 the radius of the outer return current cylinder R_o or, equivalently, when the initial liner inductance per unit length is about 0.82·nH/cm. Compressing the liner onto a finite-sized cylindrical target boosts this critical ratio only up to R_i(0)/R_o≈3/4. Recent and planned liner compression experiments are evaluated according to these criteria.