Kink and displacement instabilities in imploding wire arrays

Abstract

Cylindrical arrays of parallel wires can be imploded by the magnetic forces generated by currents through the wires to form hot, dense Z-pinch plasmas. Analytic growth rates of displacements and deformations of wires in imploding wire arrays are calculated. Arrays of six or more wires are reasonably stable against asymmetric displacements. The growth rate of the kink instability on a single wire of linear mass density μ, radius a, and carrying current I peaks at λmax = 0.7I/μ1/2ca at a kink wavelength of about 4a. The most unstable kink modes of n-wire arrays are the symmetric (l = 0) radial modes and antisymmetric (l = n/2) tangential modes. The effect of a center wire is to tend to destabilize radial kink modes and stabilize tangential modes. In the experimental parameter range of the largest current generators, the number of kink growth times before collision is insensitive to values of maximum current and current pulse width. In general, the kink instability will grow nonlinearly if the initial array radius is more than a few plasma wire radii. In the limit of long wavelengths, the kink instability is shown to be equivalent to the displacement instability.