FUEL ASSEMBLY: Theory and Experiments C. Zhou, R. Betti, V. Smalyuk, J. Delettrez, C. Li, W. Theobald, C. Stoeckl, D. Meyerhofer, C. Sangster FSC

The hydro-efficiency, areal density and implosion velocity are required to calculate the energy gain = fraction burned FSC

1D simulations with E L = 25 – 750kJ, V I = e7cm/s  =0.7-3 The hydrodynamic efficiency depends mainly on the implosion velocity V I FSC

The areal density is weakly dependent on velocity. It increases for lower adiabats and greater energies FSC

The density is independent of energy. It increases with the velocity and decreases with the adiabat FSC

 R is independent of the implosion velocity  increases with V I  R and  increase for lower  ’s FSC

Low adiabats lead to high  and  R with low velocities, large masses and high gains Choose the lowest possible adiabat. Limitation to the minimum adiabat comes from laser pulse length and pulse contrast ratio.  =0.7 seems a reasonable value Choose your stagnation density. If your goal is an average density of 300g/cc, then choose  max =600g/cc Find the implosion velocity from the density equation FSC

For a fixed ignition-energy requirement on the PW laser, fixed minimum adiabat and fixed peak density, the gain (without PW) depends only on the driver energy  = fraction of  R available for burn G E L (kJ)  = 1  = 0.5 FSC

The in-flight aspect ratio of such slow targets is small For V i = and  if =0.7 FSC

The capsule is designed by assigning the laser intensity, power and the implosion velocity  Set I  W/cm 2  Since E L ~1/2 E NIF  P w ~ ½ P NIF ~200TW  Find capsule outer radius from power and intensity R out =1.26mm  Find final mass from kinetic energy  Assuming a 20% mass ablated leads to an initial mass  Mass and outer radius yield the inner radius of R inn =670  m FSC

This pulse is within NIF capabilities.

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Energy Rh/sRh/s Est. Gain 25kJ DT ice DT gas 298μm 90μm CH 2μm2μm DT ice CH(DT) 6 40μm A 25kJ driver can assemble fuel for Fast Ignition using low-adiabat implosions of thick shells with a pulse compatible with the OMEGA laser system DT gas Imp. Vel.Max. Den.Max cm/s 700 g/cc 0.8 g/cm  m foam target driven on  = 1 FSC

390μm 40μm CH D2D2  1.3 V I  2e7 Plastic shell implosions have been used to reproduce fast ignition fuel assembly FSC

X-ray images show a fairly uniform core Courtesy of V. Smalyuk FSC

Time(ns) E+21 Frame001  13Jan2006  TheoryExp N-Yield1.7e111.9e9 _n* Bang time  R(g/cm 2 ) Neutron rate The experimental yields were much lower than predicted. One shot provided sufficient protons for  R measurements * Courtesy of C. Li (MIT) FSC

gt 2 =80microns H mixing =  gt 2  (1/2)gt Time(ns) DD-CH interface Free-fall line The highly convergent hot spot can be quenched by short wavelength mixing FSC

TheoryExp N-Yield1.6e101.9e9 _n Bang time  R with D 2 fill  R with D 8 CH fill N-rate with DD fill N-rate with D 8 CH fill 1-D simulations of a pre-mixed fill yield predicted performances closer to experiments FSC

 A method to assemble fuel with densities and areal density required for high gain fast ignition has been developed FSC  A set of spherical implosion experiments have been carried out  Additional experiments are planned for ’06. The FSC effort in fuel assembly is making advances in both theory and experiments