1. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 1 Thin liquid Pb wall protection for IFE chambers D. A. Haynes, Jr. and R. R. Peterson Fusion Technology Institute

2. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 2 Summary/Outline We present results from vaporization and preliminary condensation calculations. BUCKY simulations are presented for the ~400MJ closely coupled HIB target and the laser direct-drive NRL target (160MJ) in a thin liquid wall (1mm Pb) chamber. For chambers with radii of 4.5m and 6.5m, and a starting chamber pressure of 1mTorr, these preliminary results indicate that the chambers recover before the next shot, assuming a 5Hz rep. rate. Brief review of relevant processes and examples of BUCKY simulation of them. Vaporization results Preliminary condensation results Future work

3. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 3 Wetted-Wall Chamber Physics Critical Issues Involve Target Output, and First Wall Response Target Output Simulations (BUCKY, etc) Target Disassembly Energy Partition Target Output Simulations (BUCKY, etc) Target Disassembly Energy Partition Liquid Dynamics Simulations (BUCKY) X-ray Deposition Vaporization Self-Shielding Shocks in Liquid Liquid Dynamics Simulations (BUCKY) X-ray Deposition Vaporization Self-Shielding Shocks in Liquid Chamber Recovery Simulations (1-D: BUCKY, 2, 3-D TSUNAMI, ?) Re-condensation, Substrate Survival Chamber Recovery Simulations (1-D: BUCKY, 2, 3-D TSUNAMI, ?) Re-condensation, Substrate Survival X-rays, Ion Debris, Neutrons Vapor Mass Impulse Rep-Rate Target Design Wall Design Low T, Hi  Opacity Liquid Properties Beam Transport Criteria Vapor Opacity

4. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 4 We have obtained or generated relevant Pb properties Thermal properties linked by ARIES web site http://www.efunda.com/materials/eleme nts/element_info.cfm?Element_ID=Pb T melt = 601K T vap = 2022K Q vap = 866.31 J/g Heat capacity = 141.9 J/kg-K (@600K) Thermal conductivity = 31.4 W/m-K (@600K) Cold attenuation coefficients from Biggs and Lighthill EOS and Opacity for Pb calculated using FTI’s UTAOPA

5. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 5 BUCKY divides the mesh into two types of zones, vapor zones which participate in the hydrodynamic motion, and condensate zones which do not move. As vaporization/condensation occurs, zones are dynamically reclassified. Vapor Condensate 1 Initial condition (pre-shot) 2 After prompt x-rays from target strike the condensate, superheated vapor zones are created at high temperatures and densities 3 As the newly vaporized zones move out into the chamber, radiating and absorbing target ions 4 The heat and radiation from the newly created vapor zones further vaporizes the condensate 5 As the vapor cools, zones re-condense, Leaving the hydridynamic mesh and re-joining the condensate

6. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 6 Of the two targets considered here, the HIB target is considerably more threatening

7. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 7 Target x-ray deposition, initial vaporization, and shock Target x-rays are rapidly deposited in the protecting liquid. Vapor rapidly moves off of surface t ~ 1-10 ns Impulse launches shocks that might damage substrate and/or splash liquid. 4.5m radius, HIB target in 1mm Pb thin liquid wall protected chamber, T cool =600C: The prompt x-rays heat the 1mTorr Pb gas to high temperatures and high ionization stages (~100eV at center of chamber). Of the 119MJ of target x-rays, 9MJ are deposited volumetrically in the liquid, and approximately 110MJ vaporize and ionize the first 4.6 microns (11.6kg) of Pb (vapor is heated to 10s of eV). Peak shock loading (over-pressure) of 1.5e4 J/cm 3 occurs during this time.

8. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 8 Comparison of target x-ray spectra and Pb attenuation lengths 95% of the HIB target’s x-ray energy is emitted at energies where the attenuation length is less than 1 micron.

9. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 9 Snapshot: 4.5m radius chamber, HIB target, 10ns Chamber gas (including blow-off from wall) conditions vary by many orders of magnitude 10ns after the target goes off.

10. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 10 Target ions are mostly stopped in the vapor, with only the most energetic particles reaching the liquid. Debris Ions are stopped in vapor and the energy is re-radiated, some of it going to the liquid causing more vaporization. t ~ 1-10  s 4.5m radius, HIB target in 1mm Pb thin liquid wall protected chamber, T cool =600C: Of the 22MJ of energy in target ions, only 5.3 MJ are deposited in the wall, penetrating 0.646mm into the liquid. The remaining 16.7MJ of target ion energy is deposited in the chamber gas and the vaporized liquid. As the energy is re-radiated, the total vaporized mass increases to 20.94kg. By 10  s, the target chamber gas and vapor have cooled to 1.4eV and less than 0.2eV, respectively.

11. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 11 For the 4.5m radius chamber with a thin Pb liquid wall, and the HIB target at around 100  s, shock fronts from target blast and interact, and blind continuation of 1-d simulation results deserves skepticism. Plan of attack: “Homogenize” chamber, converting bulk kinetic energy into thermal energy. Start condensation run from these conditions. Geometry dependent uncertainty: how long does it take to homogenize, and will there be any x-ray pulse produced by stagnation on axis?

12. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 12 Preliminary modeling of the condensation phase (no effects from non- condensable target ions trapped in gas or vapor, lack of self-consistency between starting vapor pressure (1mTorr) and final vapor pressure) Condensation occurs as vapor atoms transit the Knudsen layer, which becomes filled with non- condensable gas. t ~ 1-100 ms Vapor atoms migrate towards Knudsen layer at thermal velocity

13. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 13 Re-establishment of conditions suitable for target injection t ~ 100-500 ms Vapor density and temperature are suitable for beam transport and target injection Protecting liquid is re-established. We need to decide on the parameters space in which we want to identify operating windows, and what constitutes an acceptable design: Target Output Driver/Transport Method Radius Liquid Wall temperature

14. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 14 To obtain consistent chamber (pre-shot and post-condensation), the simplest “knob” is the temperature at the back of the thin liquid. In BUCKY, the vaporization and condensation rates are calculated using the kinetic theory model described by Labuntsov and Kryukov (Int. J. Heat Mass Transfer 22, 989 (1979). Vaporization rate is proportional to the saturation vapor pressure, which depends strongly on T vap,0 /T condensate. Condensation rate depends on vapor pressure of condensable material in the chamber.

15. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 15 Summary of these preliminary results 1mm thick Pb liquid wall, starting Pb vapor density 1mTorr, all ions are stopped within chamber or within liquid HIB target 4.5m chamber radius Amount of material vaporized: 21.4kg Maximum over-pressure: 1.4861E+04 (J/cm 3 ) Time (post-homogenization) to reach vapor equilibrium: 0.15s (600C T cool, 0.2mTorr) 6.5m chamber radius Amount of material vaporized: 38.5kg Maximum over-pressure: 8.7121E+03 (J/cm 3 ) Time (post-homogenization) to reach vapor equilibrium: 0.2s (600C T cool, 0.2mTorr), 0.15s (685C T cool, 1.4mTorr) NRL160 target 4.5m chamber radius Amount of material vaporized: 9.2kg Maximum over-pressure: 1.7767E+03 (J/cm 3 )

16. DAH, RRP, UW - FTI ARIES-IFE, January 2002, 16 Conclusions/Summary We present results from vaporization and preliminary condensation BUCKY simulations are presented for the ~400MJ closely coupled HIB target and the laser direct-drive NRL target (160MJ) in a thin liquid wall (1mm Pb) chamber. For chambers with radii of 4.5m and 6.5m, and a starting chamber pressure of 1mTorr, these preliminary results indicate that the chambers recover before the next shot, assuming a 5Hz rep. rate. 1mm of liquid Pb protects permanent target chamber structures from x-ray and ion loads with a 1mTorr initial chamber gas pressure. We will investigate the effects of higher pressures before the next ARIES meeting Chamber conditions are re-established by 0.2s after homogenization. How long does that homogenization take? The transit time for the shock waves from the target and the flash vaporization is on the order of a few tenths of a millisecond. Are 5 of these periods enough? Are 1000 needed? Experiment or higher dimensional simulations may be required if the latter is more likely than the former. A self-consistent chamber pressure pre- and post-shot can be attempted to be achieved by varying T cool. These results are preliminary. I’d like to benchmark the condensation part of the code with experiment, or at least with CONRAD, and also take into account the effects any non-condensable target material left in the chamber, and the thermal properties of the equilibrium liquid composition.