Target Thermo-Mechanical Modeling and Analysis

1. Target Thermo-Mechanical Modeling and Analysis Presented by A.R. Raffray Other Contributors: B. Christensen, J. Pulsifer, M. S. Tillack, X. Wang UCSD D. Goodin, R. Petzoldt General Atomics HAPL Program Meeting University of Wisconsin, Madison September 24-25, 2003 HAPL Program Meeting, UW, Madison

2. 1 m CH +500 Å Au CH Foam + DT 1.95 mm DT Fuel 1.69 mm DT Vapor 0.3 mg/cc 1.50 mm CH foam  = 20 mg/cc Target Survival During Injection:What is the problem and what are the possible solutions? • Target heat source: energy exchange from chamber protective gas and radiation from chamber wall - Gas pressure up to ~50 mtorr at 1000-4000 K (qcond’’= 4 -12 W/cm2 for Xe) - Chamber wall temperature ~ 1000-1250 K (qrad’’~ 0.3 -0.7 W/cm2) - q’’ to reach DT-TP for current target ~ 0.68 W/cm2 • Need ways to increase thermal robustness of target: 1. Design modification to create more thermally robust target (e.g. add an outer insulating foam layer) 2. Possibility of injecting target at lower base temperature - Andy Schmitt's target calculations show no degradation in gain with no gas in the target center with target temperature down to 11.9 K ( 1-D runs) - Jim Hoffer and John Sheliak’s experimental results indicate that decreasing the initial DT temperature could still result in a smooth layer 3. Explore possibility of relaxing phase change constraint - Solution must accommodate target physics requirements HAPL Program Meeting, UW, Madison

3. Plastic Shell Vapor Gap DT Vapor Core Rigid DT Solid Simplified Target Cross Section • Foam analysis with new model - temperature-dependent properties over a wide operating temperature range (previous calculations assumed constant properties at higher T’s > 50-100K) - perform parametric analysis for different values of foam thickness and density, and target initial temperature - effect of surface temperature dependent heat flux Focus of this presentation • Phase change analysis with new model - effect of initial vapor gap present at DT/plastic outer coat interface (imperfect bond, He-3 bubbles trapped in foam structure…) - importance of plastic shell deformation - vapor region behavior as a function of heat flux for cases with and without foam Target survival workshop presentation Progress on Target Survival Analysis and Possible Design Solution • Develop integrated 1-D thermo-mechanical target model - phase change (solid/liquid/vapor) - effect of solid outer coat deflection on vapor region behavior - capability to include outer insulating foam region - fine spatial and temporal resolution - model has been tested and validated against analytical and numerical solutions - model + results to be published in journal paper • Update property data - polystyrene thermal properties over wide temperature range (important for cases with outer insulating foam region) HAPL Program Meeting, UW, Madison

4. Solid Polystyrene Thermal Properties Vary Markedly with Temperature • Density = 1100 kg/m3 • Density and thermal conductivity are adjusted according to foam porosity • Updated property data and references can be found at: http://aries.ucsd.edu/pulsifer/PROPS/ • Rapid rise of Cp with temperature helps foam insulating layer accommodate higher heat fluxes HAPL Program Meeting, UW, Madison

5. Decreasing the Initial Target Temperature Helps but is Not Sufficient by Itself Effect of Initial Target Temperature on the Time to Reach the Triple Point (19.79 K) for a Target without Insulation • For a 0.015 s time of flight (target injected at 400 m/s in a 6 m chamber), the max. allowable q’’ is increased from 0.68 to ~2 W/cm2 when Tinit is reduced from 18K to 14K - This certainly helps but needs to be supplemented by another measure to reach the ~10 W/cm2 desired objective - Target design modification (e.g. insulating layer) - Allowing some level of phase change HAPL Program Meeting, UW, Madison

6. High-Z coat Insulating foam x DT + foam 0.289 mm Dense plastic overcoats (not to scale) DT solid 0.19 mm 80-130mm Constant Foam Density 10mm Foam Linearly Increasing Density 10mm Foam Linearly Decreasing Density 2mm Inner Plastic Shell DT gas 5mm Outer Plastic Shell 1.5 mm Fully Dense Polystyrene Outer Plastic Shell 5%, 10%, or 25% Dense Polystyrene Inner Plastic Shell DT Foam Insulator Inner Surface of Shell Outer Surface Target Configuration with Outer Insulating Foam Layer Graded change in foam density assumed in the analysis HAPL Program Meeting, UW, Madison

7. Combined Effect of Insulating Foam and Lower Initial Target Temperature on the Time to Reach the DT Triple Point • • Example case: 100mm, 10% dense foam layer • - Major improvement: Allow. q’’ up to ~ 18 W/cm2 for Tinit=14 K • (corresponding to Xe at ~75 mtorr/4000K) • Maximum foam temperature can be quite high but below polystyrene glass transition temperature of 370 K (and of melting point) HAPL Program Meeting, UW, Madison

8. Example Results of Effect of Foam Insulator Density and Thickness on the Time to Reach the DT Triple Point • From previous ANSYS estimates based on constant properties at high T’s and coarser mesh, q’’ to reach T.P. = 15.5 W/cm2 for a 152mm, 10% dense foam layer and ~15.5 K initial target temp. • New results show even higher heat flux accommodation for similar case (150mm, 10% dense, 16 K initial temp.) : max. q’’>>20 W/cm2 • Max. foam temp. < 370°C • Very encouraging results; would open up the chamber gas density window substantially(~100mtorr Xe) and/or even allow to some degree for accommodation of energy transfer from residual plasma - Can it be done? - Fabrication, integrity and physics considerations - To be discussed during target survival workshop Tinit = 16 K Tinit = 16 K HAPL Program Meeting, UW, Madison

9. Heat Flux Into the Target as a Function of Time for Several Xe Gas Temperatures and for Target Surface Temperature History for a Case with 100 microns, 10% Dense Insulating Foam Region • As the target temperature surface increases, the energy transfer from the chamber gas decreases • This helps somewhat but the effect is relatively small as illustrated above for 100mm, 10% dense foam layer configuration HAPL Program Meeting, UW, Madison

10. Simplified Target Cross Section Local Vapor Region ro • Phase change allowance can help accommodate additional heat fluxes - pre-existing vapor bubbles could close if bubble size is below a critical value and heat flux above a critical value - limit on q’’ is then homogeneous nucleation - ~5 W/cm2 for previous target configuration - Possibility of going to even high heat fluxes with insulating foam layer tv,o DT Vapor Core Plastic Shell Rigid DT Solid Conclusions • Insulating foam enhances tremendously target thermal robustness - 100 mm, 10% dense foam, Tinit=16 K --->q’’=18W/cm2 - 150 mm, 10% dense foam, Tinit=16 K --->q’’>>20W/cm2 - allows for protective gas density 50-100 mtorr, which substantially open the armor survival window - could even accommodate some residual plasma - performance can be demonstrated and is predictable - fabrication and integrity of foam must be confirmed - are effects on target physics acceptable? More details presented at Target Survival Workshop HAPL Program Meeting, UW, Madison