Sheath-current retrapping in the Z mitls

An important issue in designing a higher-power version of the Z machine at Sandia national laboratories is electron current loss in the vacuum section, which consists of four radial transmission lines and a convolute (current-adder). There is evidence from experiments on Z that 1-2 MA of current out of about 20 MA is lost in the vacuum section before reaching the wire-array load Spielman, RB et al., (1997). Calculations using the LSP and QUICKSILVER Quintenz, JP et al., (1994) particle-in-cell codes have shown much less current loss. The current loss in the calculations is due to sheath-current loss in the region of the convolute, and is associated with the magnetic nulls which are intrinsic to the current splitting in the convolute. Detailed 2-D calculations for the radial MITLs show that, in the region between the insulator stack and a radius of about 20 cm (over which the radial-line vacuum impedance increases slowly from 2 /spl Omega/, to 3 /spl Omega/), excess electron sheath current is mostly retrapped to the cathode electrode. The electron sheath current is given approximately by Mendel\´s force-balance expression Mendel, CW et al., (1983) applied locally, and as a result, the sheath current decreases as Z/sub v//sup -2/, where Z/sub v/ is the vacuum impedance. Between a radius of 20 cm and the convolute, where the radial-line vacuum impedance increases more sharply (to 6 /spl Omega/ at 10 cm) there is significant "launching" of sheath current. The sheath behavior in this region is qualitatively similar to that predicted using a "constant flow impedance" model, but in the simulations the sheath is unstable and breaks up into vortices.