1. April 22, 2002/ARR 1 1. Concluding Sacrificial Liquid Film Activities 2. Starting Thick Liquid Wall Activities A. R. Raffray, J. Pulsifer, M. Zaghloul University of California, San Diego ARIES-IFE Meeting University of Wisconsin April 22-23, 2002

2. April 22, 2002/ARR 2 Outline Thin liquid film -Condensation -Aerosol source term -Documentation Thick liquid wall -Key Issues -How to address them within ARIES

3. April 22, 2002/ARR 3 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 j cond j evap TfTf PgTgPgTg

4. April 22, 2002/ARR 4 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)

5. April 22, 2002/ARR 5 Pb Vapor Diffusion Rate and Characteristic Time as a Function of Xe Gas Pressure for Different Pb Vapor Pressure Values At higher Xe pressure, Pb diffusion rate in Xe limits the effective condensation rate and decreases rapidly with increasing concentration of Xe (non-condensable gas) For the example considered the Xe pressure threshold for diffusion control is ~ 1.5 Pa for a Pb vapor pressure of 100 Pa and ~ 0.1 Pa for a Pb vapor pressure of 2 Pa Chamber size = 5 m Pb film temperature = 1000 K Pb vapor temperature = 2000 K

6. April 22, 2002/ARR 6 Processes Leading to Aerosol Formation following High Energy Deposition Over Short Time Scale Energy Deposition & Transient Heat Transport Induced Thermal- Spikes Mechanical Response Phase Transitions Stresses and Strains and Hydrodynamic Motion Fractures and Spall Surface Vaporization Heterogeneous Nucleation Homogeneous Nucleation (Phase Explosion) Material Removal Processes Expansion, Cooling and Condensation Surface Vaporization Phase Explosion Liquid/Vapor Mixture Spall Fractures Liquid Film X-Rays Fast Ions Slow Ions Impulse yy xx zz

7. April 22, 2002/ARR 7 Vaporization from Free Surface Occurs continuously at liquid surface Governed by the Hertz-Knudsen equation for flux of atoms  e = vaporization coefficient,  c = condensation coefficient, m = mass of evaporating atom, k = Boltzmann’s constant, Liquid-vapor phase boundary recedes with velocity: For constant heating rate, , and expression for saturation pressure as a function of temperature the following equation can be integrated to estimate fractional mass evaporated over the temperature rise. The results are shown for Pb. Photon-like heating rate Ion-like heating rate P s = saturation pressure P v = pressure of vapor T f = film temperature T v = vapor temperature Free surface vaporization is very high for heating rate corresponding to ion energy deposition For much higher heating rate (photon-like) free surface vaporization does not have the time to occur and its effect is much reduced

8. April 22, 2002/ARR 8 Vaporization into Heterogeneous Nuclei Occurs at or somewhat above boiling temperature, T 0 For heterogeneous nucleation, the vapor phase appears at perturbations in the liquid (impurities etc.) From Matynyuk, the mass vaporized into heterogeneous nuclei per unit time is given by: The equation can be integrated over temperature for a given heating rate, , and following some simplifying assumptions (Fucke and Seydel). The results are shown for Pb.  v = density of vapor in the nucleus,  H v = enthalpy of vaporization per unit mass,  0 = density of saturated vapor at normal boiling temperature (T 0 ) P 0 is the external static pressure Vaporization into Heterogeneous nuclei is dependent on the number of nuclei per unit mass but is very low for heating rate corresponding to ion energy deposition and even lower for photon-like energy deposition Photon-like heating rate Ion-like heating rate

9. April 22, 2002/ARR 9 Phase Explosion (Explosive Boiling) (I) Rapid Rapid boiling involving homogeneous nucleation both at and beneath the surface. High heating rate  P vapor does not build up as fast and thus falls below P sat @ T surface  superheating to a metastable liquid state  limit of superheating is the limit of thermodynamic phase stability, the spinode (defined by  P/  v) T = 0) A given metastable state can be achieved in two ways: a) by raising the temperature from the boiling point while keeping the pressure lower than the corresponding saturation values (e.g. high heating rate) b) by reducing the pressure from the saturated value while keeping the corresponding temperatures lower than the saturated values (e.g. rarefaction wave) A metastable liquid has an excess free energy, so it decomposes explosively into liquid and vapor phases. -As T/T tc increases past 0.9, Becker-Döhring theory of nucleation indicate an an avalanche-like and explosive growth of nucleation rate (by 20-30 orders of magnitude)

10. April 22, 2002/ARR 10 E sens = Energy density required for the material to reach the saturation temperature E t = Total evaporation energy (= E sens + E Evaporation ) E = Energy density required heat the material to 0.9 T tc E ( 0.9 T tc )= Energy density required heat the material to 0.9 T tc Phase Explosion (Explosive Boiling) (II) Volumetric Model with Phase Explosion from Photon Energy Deposition Liquid and vapor mixture evolved by phase explosion shown by shaded area (~0.5  m for Pb with quality >~0.8; ~2.9  m for Li) Could be higher depending on behavior of 2-phase region behind Very challenging to predict aerosol size and number from this

11. April 22, 2002/ARR 11 Upper Bound Estimate of Combination of Number of Droplets and Droplet Size as a Function of Evaporated Film Thickness Suggest to do aerosol calculations for two case assuming a drop radius based on pressure and surface tension equilibrium: 1. Assume all liquid in 2-phase region in aerosol form 2. Assume all liquid in explosive ablation layer in aerosol form Sensitivity analysis on droplet size

12. April 22, 2002/ARR 12 Proposed Outline of Thin Liquid Film Paper (I) (First draft to be written over next 3-4 months and to be published in FE&D) DRAFT 1. Introduction (R. Raffray) (~ 0.5 page) 2. Example configuration (~ 0.5-1 page) (L. Waganer) 3. Driver requirements (~ 2 pages) -Heavy Ion beam (C. Olson, S. Yu) (~ 1 page) -Laser (M. Tillack, J. Sethian) (~ 1 page) 4. Target requirements (D. Goodin, R. Petzold) (~ 2 pages) -Indirect drive -Direct drive 5. Film analysis (S. Abdel Khalik, M. Yoda) (~ 2-3 pages) -Flowing film -Continuous injection from the back ( e.g. through porous media) 6. Energy deposition (D. Haynes) (1-2 pages) -Based on Pb vapor pressure and any additional chamber gas -Other liquids (FLiBe?)

13. April 22, 2002/ARR 13 Proposed Outline of Thin Liquid Film Paper (II) (First draft to be written over next 3-4 months and to be published in FE&D) 7. Chamber clearing (thermal and mass transfer analysis) -Condensation scoping analysis (R. Raffray) (1 page) -Source term for aerosol formation (A. Hassanein, D. Haynes) (2 pages) -Aerosol analysis (P. Sharpe) (1 page) 8.Design window (Raffray, others)(1 page) -Aerosol size and concentrations -Incorporate estimate based on conditions and driver and target requirements 9.Radiological issues (L.El-Guebaly) (0.5 page) -Choice of liquids -Effect on overall waste disposal issues 10.Safety issues (D. Petti, L. El-Guebaly) (0.5 page) 11. Key remaining issues (R. Raffray, all) (0.5 page) 12.Conclusions (R. Raffray, all) (0.5 page) Total = ~ 17 journal pages

14. April 22, 2002/ARR 14 Beam ports and solid shielding structure (same both sides) Stationary grid of cylindrical jets Porosity in liquid blanket Venting path for target and ablation debris Oscillating liquid jets Heavy ion target Schematic of a potential thick-liquid pocket, showing major pocket features. Some Thoughts on Assessing the Thick Liquid Wall Option (I) Major issues tend to be design dependent; e.g. for HYLIFE Hydraulics Jet formation to assure coverage while providing pocket for target explosion and channels for driver firing and target injection, and chamber clearing This is is being addressed by an ongoing modeling and experimental fluid dynamics program -ARIES would not be able to provide much more in this areawithin the time frame and scope of the study Chamber clearing Return chamber environment to a condition which allows successful target and driver propagation -Many issues similar to thin liquid wall option, including aerosol formation and condensation -Fluid dependent (analysis should be done for FLiBe and other fluids?)

15. April 22, 2002/ARR 15 Some Thoughts on Assessing the Thick Liquid Wall Option (II) Interface and integration issues Areas where ARIES could best provide some insight, trade-offs and design windows Demand on nozzle -Mechanical design of nozzle (moving parts) -Reliability for such demanding performance -Effect of malfunction -irradiation effect -out of phase oscillation -nozzle choking because of impurity in fluid -fluid chemistry control requirements -presence of debris and holhraum materials Choice of fluid and structural materials -Shielding performance (what is the goal, class C???) -Lifetime of structural materials -Power cycle. Can it be optimized? -Poor thermal conductivity of FLiBE -ok for volumetric heat deposition -poor heat transfer leads to large HX or  T between primary and secondary fluids -Pressure drop and pumping power

16. April 22, 2002/ARR 16 Some Thoughts on Assessing the Thick Liquid Wall Option (III) Interface and integration issues Adequate shielding for last focus magnet -Further analysis? Specific target and driver requirements for thick liquid wall option -Vapor pressure of FLiBe (opening of pocket would create a pressure increase due to suction effect) -Aerosol formation (droplets) -Possible condensation of FLiBe in lines (effect on heavy ion beam) Gaps required for driver and target -Possibility of bare wall seeing photons and ions in direct line of sight -effect of off-centered micro-explosion -consequences -would you a thin liquid film be needed? Safety issues -e.g. possible accident scenarios