How to Maximize the Radius of a Wire-Array$Z$-Pinch for the 100-ns to 1-$muhboxs$Implosion Time Scales

The Centre d'Etudes de Gramat is now studying long implosion time (about 1 mus) plasma radiation sources. Z-pinches are routinely used by other laboratories in the 100-ns regime with the well-known experimental result, in which an about 2-cm initial radius should not be exceeded to preserve the quality of the implosion for a single array. In a many hundreds of nanoseconds implosion time scale, the question is raised if a bigger radius could be shot. This paper discusses a theoretical approach, which shows that a 7-cm radius is acceptable in the 1-mus regime. It is based on an analysis of magneto-Rayleigh-Taylor instabilities of the accelerating sheath in the r-z plane. It will be demonstrated that all the spatial features of the implosion are determined by the magnetic skin depth, and so essentially depend on the square root of the implosion time. Experiments were carried out with SPHINX generator at the 4-MA level with 800-ns implosion time and confirmed these results