Two- and three-dimensional modeling of the different phases of wire-array z-pinch evolution J.P. CHITTENDEN, S.V. LEBEDEV, S.N. BLAND, J. RUIZ-CAMACHO, F.N. BEG, and M.G. HAINES Blackett Laboratory, Imperial College, London SW7 2BZ, UK ~Received 22 May 2000; Accepted 22 February 2001! Abstract A series of specialized multidimensional resistive magnetohydrodynamic ~ MHD! models have been developed to tackle the different phases of evolution of wire array z-pinch implosions. Two-dimensional ~ r–z ! “cold-start” or “wire initiation” simulations of single wires indicate the persistence of a two-component structure with a cold, dense core embedded within a much hotter, low density, m 5 0 unstable corona. Cold-start simulations with similar conditions to wires in an array show a general trend in the plasma structure from discrete wires with large m 5 0 perturbation amplitudes to partially merged wires with smaller perturbation amplitudes as the number of wires is increased. Two-dimensional ~ r–u! simulations then show how the persistence of dense wire cores results in the injection of material between the wires into the interior of the array, generating radial plasma streams which form a precursor plasma upon reaching the axis. Higher-resolution 2-D ~ r–u! simulations show similar behavior for large number wire arrays in use at Sandia National Laboratories. This model is also used to predict which modes of implosion are in operation in nested wire array experiments. Separate r–u plane simulations of the flux of plasma imploding towards the axis from the outer array and the bombardment of the inner array by this flux are presented. Finally, 2-D ~ r–z ! simulations of the Rayleigh– Taylor instability during the final implosion phase are used to illustrate the effect upon the power and duration of the radiation output pulse. The results of low-resolution 3-D resistive MHD simulations are also presented. The need for much higher resolution 3-D simulations of certain aspects of wire array evolution is highlighted. 1. INTRODUCTION AND BACKGROUND Despite the recent spectacular increases in X-ray power obtained from wire array z pinches ~Sanford et al., 1996; Deeney et al., 1998!, achieving high yield fusion in a z-pinch- driven hohlraum will require still further substantial in- creases in both X-ray power and yield ~ Hammer et al., 1999!. Being able to design optimal load configurations which maximize the power output would significantly re- duce the cost of future generators designed for high-yield experiments. However, the factors that limit the X-ray power in present generation experiments are still not well under- stood. The two main limiting factors are thought to be the slow rate of wire ablation, which leads to injection of mass into the interior of the array prior to implosion and the development of the Rayleigh–Taylor instability. Computa- tional modeling of these phenomena can be extremely com- plex due to the intrinsically three-dimensional ~3-D! nature of the problem. While 3-D resistive MHD codes are now becoming available, simulations of the entire experiment with adequate spatial resolution remains unfeasible. In this paper, we present an alternative approach, which is to model different phases of the evolution using different specialized two-dimensional ~2-D! and 3-D models and attempt to link them together to form a composite model of the whole ex- periment. This has the added advantage that this series of simpler problems can be more readily compared to experi- ments for the all important code verification. We continue Section 1 by describing the different stages of wire array z-pinch evolution and describing low-resolution 3-D modeling of the implosion. In Section 2 we describe 2-D “cold-start” or “wire initiation” calculations of single wires, showing how the passage of current begins the plasma formation process but also excites the m 5 0 instability in each wire. The results of this section are then used in Sec- tion 3 to initialize 2-D simulations in the r–u plane which show how the mass injected between the wires determines the radial profile for the implosion. This model is also used, in Section 4, to explore the different modes of collision between nested wire arrays. In Section 5, the results of the two models described in Sections 2 and 3 are then used to Address correspondence and reprint requests to: J.P. Chittenden, Black- ett Laboratory, Imperial College, London SW7 2BZ, United Kingdom. E-mail: j.chittenden@ic.ac.uk Laser and Particle Beams ~2001!, 19, 323–343. Printed in the USA. Copyright © 2001 Cambridge University Press 0263-0346001 $12.50 323