2D R-Z Simulations for SPHINX Experiments - Numerical Study of Axial Inhomogeneities in the Ablation Process of Wire Arrays

Summary form only given. On shot #543 the SPHINX machine based on microsecond LTD technology was used to implode a nested tungsten wire array with 140-74 mm outer-inner diameters, 144-90 (outer-inner) 4 mum W wires and 5 cm height. The maximum current was 4.2 MA and the implosion time (time of maximum of first X-ray peak) was 783 ns. An axial inhomogeneity of the implosion occurs in this shot and impacts the radiation output. Shot #543 was interesting because visible 2D images clearly show the formation of a precursor pinch growing from the anode to the cathode, creating a big upper bubble. This effect is seen on many shots even with aluminum wires but is less impressive that the one observed on shot #543. In this presentation we try to explain this phenomenon by a continuous variation of wire ablation velocity from the anode to the cathode (Vabl=Vabl(z)) using the model" that links the mass rate and the inverse of Vabl(z). As a consequence, if Vabl(anode) is higher, the precursor pinch will appear first near the anode and then will grow from bottom to top and if Vabl(cathode) is lower, the wire ablation will end sooner so the implosion will start sooner as well. Numerical simulations of this shot presented here was done with Marple2D (Fortran version), a 2D(r,z) MHD code developed by IMM (Moscow). These MHD simulations allow us to quantify possible variations of Vabl(z) in order to fit experimental results. 2D simulations are shown, a relation between Vabl and the physical velocity of the plasma front is given and the implementation in this code of the mass injection law is explained. The link between Er(z) (radial electric field) and Vabl(z) and the issue of simulating in the proper way the interaction between the precursor plasma and the inner array are also discussed.