1. February 5-6, 2004 HAPL meeting, G.Tech. 1 Survivable Target Strategy and Analysis Presented by A.R. Raffray Other Contributors: B. Christensen, M. S. Tillack UCSD D. Goodin, R. Petzoldt General Atomics HAPL Meeting Georgia Institute of Technology Atlanta, GA February 5-6, 2004

2. HAPL meeting, G.Tech. 2 Outline Survivable Target Strategy Accommodation and Sticking Coefficients Phase Change Summary

3. February 5-6, 2004 HAPL meeting, G.Tech. 3 Overall Strategy to Develop a Survivable Target Uncertainty in chamber gas requirements and resulting heat flux on target -Min. gas density set by chamber wall protection - Max. gas density set by target placement and tracking accuracy -Uncertainty in accommodation and sticking coefficients for high temp. chamber gas on cryogenic target Prudent to consider dual target approach and address key issues -Basic target -Thermally robust target with insulated foam coating -Increase target heat flux accommodation through low temp. target and possible allowance of phase change Once sufficient information available down-select “best”target design Integrated “team” approach

4. February 5-6, 2004 HAPL meeting, G.Tech. 4 Basic Target Strategy Basic Target Initial Temp. = 18 K Allowable q’’ = 0.7 W/cm 2 Xe Temp. ~4000 K Xe Pres. ~ 0 (@300K) Low Temp. Target Initial Temp. = 16 K Allowable q’’ = 1.5 W/cm 2 Xe Pres. ~ 2 mtorr Basic Target with Phase Change Initial Temp. = 18 K Allowable q’’ = 6.5 W/cm 2 Melt Depth = 34  m Xe Pres. ~ 20 mtorr Low Temp. Target with Phase Change Initial Temp. = 16 K Allowable q’’ = 6.5 W/cm 2 Melt Depth = 30  m Xe Pres. ~ 23 mtorr Numerical Model Outer Coat/DT Phase Change/DT Solid Interaction, Vapor Growth, Impact on Target Symmetry Is Low Temperature Acceptable for DT Layering? Experiment Physics Simulation Will Liquid Layer/Vapor Bubbles Meet Physics Requirements? DT/foam Mechanical Properties Exper. Vapor Bubble/Phase Change Exper.? Which target design(s) fit within background gas requirements? Timeline(?) Downselect in mid-Phase II LANL NRL UCSD, GA LLE (UR) Chamber Effort Schafer, GA Legend:

5. February 5-6, 2004 HAPL meeting, G.Tech. 5 Insulated Target Strategy Insulated Target Standard Design 150  m of Insulation 10 % Dense Insulation Initial Temp. = 18 K Allow. q’’ = 12 W/cm 2 Xe Temp. ~4000 K Xe Pres.~50mtorr (@300 K) Low Temp. Insulated Target Initial Temp. = 16 K Allowable q’’ > 18 W/cm 2 Xe Pres. ~ 70 mtorr Insulated Target with Phase Change Initial Temp. = 18 K Allowable q’’ = 20 W/cm 2 Melt Depth = 2.5  m Xe Pres. ~80 mtorr Low Temp. Insulated Target with Phase Change Initial Temp. = 16 K Allowable q’’ = 20 W/cm 2 Melt Depth = 0  m Xe Pres. ~80 mtorr Is Low Temperature Acceptable for Layering? Does Foam Insulator Meet Manufacturing and Physics Requirements? Manufacturing Process and Cost Study? Physics Simulation Does Liquid Layer/Vapor Bubbles Meet Physics Requirements? Experiment DT/foam Mechanical Properties Exper. Numerical Model Outer Coat/DT Phase Change/DT Solid Interaction, Vapor Growth, Impact on Target Symmetry Vapor Bubble/Phase Change Exper.? Which target design(s) fit within background gas requirements? Timeline(?) Downselect in mid-Phase II LANL NRL UCSD, GA LLE (UR) Chamber Effort Schafer, GA Legend:

6. February 5-6, 2004 HAPL meeting, G.Tech. 6 Chamber Gas Density and Target Heat Flux Background Gas Density Target Placement &Tracking, and Repeatability Armor+System Analysis Resulting heat flux on target based on gas & target surface conditions SPARTAN/ DSMC Model & expt. for sticking & accomm. coeff. Minimum Gas Density Maximum Gas Density Which target design(s) fit within background gas requirements? Sufficient Chamber Wall Protection? LANL NRL UCSD, GA LLE (UR) Chamber Effort Schafer, GA Legend: Downselect in mid-Phase II

7. February 5-6, 2004 HAPL meeting, G.Tech. 7 Several Factors Influence the Heat Flux on the Target from the Chamber Gas The condensation or ‘sticking’ coefficient The accommodation coefficient (≈ “fraction of energy transfer”) Target shielding by cryogenic particles leaving the surface of the target Evaporation/sublimation of condensed background gas due to radiation heat transfer Incoming High Temperature Background Gas (T ~ 4000 K) Condensed Material Outgoing Cryogenic Gas Radiation From Chamber Walls IFE TARGET

8. February 5-6, 2004 HAPL meeting, G.Tech. 8 Condensation (Sticking) Coefficient of High Temperature Gas on Cryogenic Target (Very Little Data Found, Applicable to our Prototypical Conditions) 2 x 10 14 s -1 cm -2 4 x 10 15 s -1 cm -2 4 x 10 16 s -1 cm -2 CO 2 Beam on Cu Target Ar Beam on Cu Target 1400 K 300 K Condensation coefficient is a function of several parameters, including: -T target, T gas, flux, angle of incidence...Condensation coefficient decreases rapidly with increasing T target past a certain point (Brown, et al., 1969) -No obvious mechanisms causing the threshold (i.e melting or boiling point of gas species) -MP (Ar) = 83.8 K -BP (Ar) = 87.3 -MP (CO 2 ) = 194.6 K -BP (CO 2 ) = 217.5 KFor an insulated target the surface temperature will increase rapidly; thus the condensation coefficient will decrease rapidly Condensation Coefficient Target Temperature (K)

9. February 5-6, 2004 HAPL meeting, G.Tech. 9 DSMC Results of Heat Flux for No Sticking and Complete Accommodation Results shown in Frost (1975) indicates accommodation close to unity for 1400K Ar over a wide range of Cu target temperature and surface conditions (77-280 K)Effect of shielding from no sticking for accommodation of unity show a slight reduction in heat flux due to shielding effect Xenon Gas @ 4000 K, v T = 400 m/s Surface Temperature = 18 K (Constant) Complete Accommodation ~ 15-20 % Maximum Reduction for High Density Case, 100 mTorr Xe Minor Effect for Low Density Case, 1 mTorr Xe

10. February 5-6, 2004 HAPL meeting, G.Tech. 10 A Significant Reduction in Accommodation Coefficient Would be Very Beneficial as the Heat Flux on the Target Would Vary Accordingly Recent results from CERN indicate a possibility of much lower sticking coefficients for various gases (H 2, CH 4, CO, CO 2 ) on cryogenic (5-300K) targets (and perhaps accommodation coefficient?) Experiments with prototypical materials and conditions would help better understand and estimate the actual accommodation and sticking coefficients In the mean time, for current analysis it seems prudent to assume unity for both coefficients until data become available

11. February 5-6, 2004 HAPL meeting, G.Tech. 11 Modeling the Behavior of a Vapor Bubble Assumptions 1-D heat transfer DT liquid remains static The cryogenic polymer shell behaves according to the theory of elasticity Solid portion of DT is rigid Pre-existing bubble due to defect at plastic/DT interface or presence of 3 He Plastic Shell Preexisting Vapor Bubble Rigid DT Solid Simplified Target Cross Section DT Vapor Core tvtv roro

12. February 5-6, 2004 HAPL meeting, G.Tech. 12 Deflection of the Plastic Shell due to DT Vapor Pressure Two Possible Cases: Membrane theory (valid for r/t > 10) for a sphere with a uniform internal pressure From bending theory, max. deflection under the center of the load* Uniform Internal Pressure, P r t -Where A is a numerical coefficient =f (r o, R, t,  ) -This equation is valid for any edge support positioned 3 degrees or more from the center of the load *Roark’s Formulas for Stress & Strain, 6 th Edition, p. 546 t roro R P

13. February 5-6, 2004 HAPL meeting, G.Tech. 13 Comparison of the Calculated Deflection of the Plastic Shell by Membrane and Bending Theory for a Pressure of 10 4 Pa for Several Vapor Bubble Sizes, r o roro R Bubble size for which bending theory approaches membrane theory is independent of pressure, ~ 37  m in this case Would need much smaller bubble size in target to avoid large “membrane-like” deflections

14. February 5-6, 2004 HAPL meeting, G.Tech. 14 Pre-existing Vapor Bubbles Could Close if Initial Bubble is Below a Critical Size and the Heat Flux Above a Critical Value Plastic Shell Local Vapor Bubble Rigid DT Solid t v,o roro Encouraging results for self-healing Need verification with 2-D model + experimental data Physics requirements (bubble has close but are solid+liquid layers ok?) t = 0.015 s T init = 18 K +

15. February 5-6, 2004 HAPL meeting, G.Tech. 15 Summary A dual-target strategy is proposed: basic target + thermally robust target Converge on final target design once sufficient information is obtained on: -Target fabrication and behavior -Heat loads on target (chamber gas density, sticking + accommodation coefficients) -Physics requirements Small pre-existing vapor bubbles (defects) could be eliminated by solid to liquid phase change (self-healing) -Depends on heat flux and size of bubble -Based on 1-D model and assumptions such as rigid solid DT -Need experimental data and 2-D model to better understand -Is this acceptable based on target physics requirements?