1. January 1, 2002/ARR 1 1. “Overlap” Design Regions for IFE Dry Wall 2. Scoping Analysis of Condensation for Wetted Wall A. R. Raffray, D. Blair, J. Pulsifer, M. S. Tillack, X. Wang University of California, San Diego ARIES-IFE Meeting UCSD January 10-11, 2002

2. January 1, 2002/ARR 2 Overlap Design Regions for IFE Dry Wall Simple self consistent calculationDriver/target parameters Chamber geometry and chamber wall design Power to chamber wall Coolant outlet temperature Cycle efficiency Thermal-hydraulic parameters Maximum temperature of chamber wall -Chamber wall power assumed to be spread over the complete period between successive shots (optimistic assumption) Run a few example cases with the goal of maintaining SiC f /SiC T max at the wall < 1000°C -Results will show acceptable combination of parameters (design window)

3. January 1, 2002/ARR 3 Simple Estimate of Maximum W and SiC f /SiC Temperature Under IFE Energy Deposition for 2 Direct-Drive and 2 Indirect- Drive Driver/Target Cases Chamber Wall Coolant Inlet Energy Front Assume Channel L =  R 4-mm SiC f /SiC Wall Chamber Wall Coolant Outlet 5-mm Cooling Channel Max. SiC f /SiC Temp. 1-mm W Armor Direct Drive LY: Driver Energy = 1.2 MJ Gain = 128 Yield = 153.6 MJ Driver Efficiency = 0.07 Indirect Drive 1: Driver Energy = 3.3 MJ Gain = 139 Yield = 458.7 MJ Driver Efficiency = 0.25 Direct Drive HY: Driver Energy = 2.9 MJ Gain = 138 Yield = 400 MJ Driver Efficiency = 0.07 Indirect Drive 2: Driver Energy = 6 MJ Gain = 63 Yield = 378 MJ Driver Efficiency = 0.47 Maximum temperature estimate based on heat deposition averaged over time between shots

4. January 1, 2002/ARR 4 Combination of Parameters to Maintain T max,SiC/SiC < 1000°C for Direct Drive Target Adjust R and Rep. Rate Direct Drive LY: Driver Energy = 1.2 MJ Gain = 128 Yield = 153.6 MJ Driver Efficiency = 0.07 Example trade-off - What is preferable? a small size chamber with low rep rate and electric power or the opposite (not clear) a small size chamber with lower cycle efficiency and electric power or the opposite Direct Drive HY: Driver Energy = 2.9 MJ Gain = 138 Yield = 400 MJ Driver Efficiency = 0.07 Adjust T cool,out (and, hence,  c ) and R Fusion power = 2121 MW Fusion power = 2181 MW

5. January 1, 2002/ARR 5 Combination of Parameters to Maintain T max,SiC/SiC < 1000°C for Indirect Drive Target Adjust R and Rep. Rate Adjust T cool,out (and, hence,  c ) and R Indirect Drive 2: Driver Energy = 6 MJ Gain = 63 Yield = 378 MJ Driver Efficiency = 0.47 Indirect Drive 1: Driver Energy = 3.3 MJ Gain = 139 Yield = 458.7 MJ Driver Efficiency = 0.25 Example trade-off - What is preferable? a small size chamber with low rep rate and electric power or the opposite (not clear) a small size chamber with lower cycle efficiency and electric power or the opposite

6. January 1, 2002/ARR 6 Example Strawman Parameters (as of Jan 10, 2002)

7. January 1, 2002/ARR 7 Example Strawman Parameters (as of Jan 10, 2002)

8. January 1, 2002/ARR 8 Example Strawman Parameters (as of Jan 10, 2002)

9. January 1, 2002/ARR 9 Major Issues for Wetted Wall Chambers Wall protection -several processes involved -photon/ion penetration depth for energy deposition -evaporation -armor film re-establishment -recondensation -fresh injection -supply method (method, location) -coverage -hot spots, film flow instability, geometry effects Chamber clearing -target, driver and pumping requirements -vapor pressure and temperature -aerosol concentration and size -condensation trap in pumping line Drop condensation Film condensation

10. January 1, 2002/ARR 10 Condensation Scoping Analysis Initial analysis used RECON - example results previously shown -several processes involved -difficult to fully understand individual effects and influences Seems wise to first focus on the fundamentals of condensation for better understanding and then plan accordingly for an integrated analysis -film condensation equation based on kinetic theory -droplet condensation equations based on droplet/environment equilibrium and nucleation theory Assess effect on condensation rate and characteristic time to clear chamber of various parameters, including: -chamber vapor conditions -film temperature -velocity of vapor -presence of non-condensable gas

11. January 1, 2002/ARR 11 Fundamental Film Condensation Equation Based on Kinetic Theory j net = net condensation flux (kg/m 2 -s) M = molecular weight (kg/kmol) R = Universal gas constant (J/kml-K)  = correction factor for vapor velocity towards film  c  e  condensation and evaporation coefficients P g, T g = vapor pressure (Pa) and temperature (K) P f, T f = saturation pressure (Pa) and temperature (K) of film Example Scoping Calculations Assume: Indirect-Drive Target Evaporated thickness and vapor temperature rise from photon and debris ion energy -E photons =115 MJ -E debris = 18 MJ -E fast ions = 8 MJ Liquid Pb as film material Chamber radius = 5 m j cond j evap TfTf PgTgPgTg

12. January 1, 2002/ARR 12 Condensation Flux and Characteristic Time to Clear Chamber as a Function of Pb Vapor and Film Conditions - Characteristic time to clear chamber, t char, based on condensation rates and Pb inventory for given conditions -For higher P vap (>10 Pa for assumed conditions), t char is independent of P vap -For lower P vap as condensation slows down, t char increases substantially

13. January 1, 2002/ARR 13 Vaporized Thickness is Dependent on Energy Deposition Depth Based on condensation: -A short penetration depth resulting in less vaporized mass but at higher temperature seems preferable - Softness of spectrum will determine penetration depth and vaporized thickness - What is preferable less vapor at high temperature or more vapor at lower temperature?

14. January 1, 2002/ARR 14 Vapor Motion Toward Chamber Enhances Condensation Rate, as Shown by Example Case Pb velocity toward the chamber wall increases the condensation rate by up to about a factor of ~3.6 at sonic velocity-like levels

15. January 1, 2002/ARR 15 Vapor Condensation Rate can be Affected by Presence of Non-Condensable Gas When pressure of vapor is of the same order as that of non- condensable gas, overall pressure equilibrium results in local vapor and gas gradients and condensation becomes diffusion-limited P P v,o P g,o P g,i T v,o T v,i  P v,i j cond = condensation flux (kg/m 2 -s) K v,g = binary mass transfer coefficient for diffusion of vapor and gas over diffusion length (m/s)  v = vapor density (kg/m 3 ) P g,lm = log mean pressure of non-condensable gas (Pa) P v,o, P v,i = vapor pressure in chamber and at interface (Pa)

16. January 1, 2002/ARR 16 Vapor Condensation Rate and Characteristic Time as a Function of Xe Gas Pressure for Different Pb Vapor Pressure Values Pb condensation rate decreases with increasing concentration of non- condensable gas However, in the range of anticipated vapor and gas pressures, the effect seems negligible Chamber size = 5 m Film temperature = 1000 K  Approximate range of interest

17. January 1, 2002/ARR 17 Vapor Condensation Rate and Characteristic Time as a Function of Pb Film Temperature Pb condensation rate increases substantially within a short film temperature range at about the local BP. Can this be used as a mean of in- situ recoating very thin film or dry spots? Condensation flux  f,a  f,b ww Coolant Pb SiC/SiC T film,def. T film If T film,def. < T film can deficient film formation be adequately corrected by preferential condensation?

18. January 1, 2002/ARR 18 Can Film Thickness Non-Uniformity be Remedied by Condensation? Consider 3 Example Scenarios. -j cond is about the same in regular region and film deficient region. No preferential correction possible. If anything, T film,def. > T film in the initial cool down phase, reversing to T film,def. < T film much later (when j cond is much smaller) as heat capacity and diffusion interplay. 2. Uniform film formation but following energy deposition and evaporation, part of the Pb film locally detaches (due to some instability). In this case, T film > T film,def. -Best scenario. Preferential condensation will occur but how much correction can be achieved is not clear. 3. Film formation leaves dry local region. Following energy deposition and evaporation, local SiC f /SiC temperature > Pb film temperature (T film <T film,def. ) 1.Uneven film formation leaves local region with much smaller thickness. Following energy deposition and evaporation, T film is at the local BP everywhere (T film = T film,def. ) -Worse scenario. Solution must come from Pb injection from the inside rather than from condensation. Porous medium would help as maximum temperature of bare surface would always be ~ T film. Preferential condensation is scenario limited and cannot be relied upon to ensure film deficiency correction

19. January 1, 2002/ARR 19 Aerosol Formation Based on Chamber Conditions Critical radius (at equilibrium) as a function of surface tension, vapor temperature, and saturation ratio

20. January 1, 2002/ARR 20 Droplet Nucleation Estimate Based on Classical Homogeneous Nucleation Theory Effective saturation ratio threshold depending on vapor temperature What saturation ratio can be achieved in IFE case?

21. January 1, 2002/ARR 21 Droplet Growth Based on Kinetic Theory for Small Droplets For low Pb vapor pressure (~100 Pa) droplet growth does not seem to be a problem For higher Pb vapor pressure (~10 4 Pa), droplet growth could be a problem for low vapor temperature (< ~ 2000K) and high saturation ratio. However, this is an unlikely combination. Assuming heat removal through conduction

22. January 1, 2002/ARR 22 Upper Bound Estimate of Combination of Number of Droplets and Droplet Size as a Function of Evaporated Film Thickness What are the limits based on target and driver requirements?

23. January 1, 2002/ARR 23 Several Observations Emerged from the Condensation Scoping Study Above a certain “threshold” the condensation characteristic time to clear chamber does not change appreciably with vapor pressure and is much lower than the IFE time between shots Normal vapor velocity at the interface enhances condensation rate but by no more than about half an order of magnitude The presence of non-condensable gas can slow down condensation but effect important at P g higher than anticipated for IFE Based on condensation, it seems somewhat better to have a shorter penetration depth (softer spectrum) resulting in less vapor at a higher temperature Correction on film thickness unevenness by preferential condensation can happen for a given scenario producing the required local film  T. However, it cannot be relied upon and other means of correction are required to account for all possible scenarios. Aerosol formation could be a problem although it is not clear that IFE conditions would result in droplet growth (at least based on conduction) What next? To shed more light on the evolution of chamber conditions between shots, it would be very useful to run an integrated model including film and drop condensation but also fluid dynamics and heat transfer with the right physics

24. January 1, 2002/ARR 24 A Laser Material Ejecta Model is Being Developed as Part of UCSD’s Effort on Laser/Material Interaction (D. Blair/M. Tillack) Model includes: -Laser energy depostion -Ejecta (evaporation) -Hydrodynamics -Drop condensation -Aerosol formation -Film condensation Striking similarity with IFE armor case with only a few differences -Different time scale (ns-ms modeling compared with up to 0.1 s for IFE) -Different dimension (mm’s vs m’s for IFE) -Laser energy deposition vs photon + ion energy deposition for IFE -Geometry and boundary conditions

25. January 1, 2002/ARR 25 Observations from Condensation Scoping Study Normal vapor velocity at the interface enhances condensation rate but by no more than about half an order of magnitude The presence of non-condensable gas can slow down condensation but effect important at P g higher than anticipated for IFE

26. January 1, 2002/ARR 26 Example Run Based on IFE-like Conditions (8  s run) (Model needs to be further modified for detailed IFE analysis)

27. January 1, 2002/ARR 27 Future Work Run IFE cases with modified laser ejecta code to better understand chamber conditions prior to each shot. E.g. -Residual aerosol characteristics -Vapor density, temperature and pressure -Effect of background gas -Effect of chamber size -Effect of penetration depth Input on driver and target requirements Possibility of self-healing of film thickness deficiency

28. January 1, 2002/ARR 28 Extra Slides

29. January 1, 2002/ARR 29 Parametric Studies for Dry Wall with Direct Drive Target (LY) Under Constraint: T max,SiC/SiC < 1000°C Direct Drive LY: Driver Energy = 1.2 MJ Gain = 128 Yield = 153.6 MJ Driver Efficiency = 0.07

30. January 1, 2002/ARR 30 Parametric Studies for Dry Wall with Direct Drive Target (HY) Under Constraint: T max,SiC/SiC < 1000°C Direct Drive HY: Driver Energy = 2.9 MJ Gain = 138 Yield = 400 MJ Driver Efficiency = 0.07

31. January 1, 2002/ARR 31 Parametric Studies for Dry Wall with Indirect Drive Target 1 Under Constraint: T max,SiC/SiC < 1000°C Indirect Drive 1: Driver Energy = 3.3 MJ Gain = 139 Yield = 458.7 MJ Driver Efficiency = 0.25

32. January 1, 2002/ARR 32 Parametric Studies for Dry Wall with Indirect Drive Target 2 Under Constraint: T max,SiC/SiC < 1000°C Indirect Drive 2: Driver Energy = 6 MJ Gain = 63 Yield = 378 MJ Driver Efficiency = 0.47