Survivable Target Strategy and Analysis

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 HAPL meeting, G.Tech.

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

4. Low Temp. Target • Initial Temp. = 16 K • Allowable q’’ = 1.5 W/cm2 • Xe Pres. ~ 2 mtorr Experiment Numerical Model • Basic Target • Initial Temp. = 18 K • Allowable q’’ = 0.7 W/cm2 • Xe Temp. ~4000 K • Xe Pres. ~ 0 (@300K) DT/foam Mechanical Properties Exper. • Basic Target with Phase Change • Initial Temp. = 18 K • Allowable q’’ = 6.5 W/cm2 • Melt Depth = 34 m • Xe Pres. ~ 20 mtorr LLE (UR) Schafer, GA Chamber Effort UCSD, GA Legend: NRL • Low Temp. Target with Phase Change • Initial Temp. = 16 K • Allowable q’’ = 6.5 W/cm2 • Melt Depth = 30 m • Xe Pres. ~ 23 mtorr LANL Base Target Strategy Is Low Temperature Acceptable for DT Layering? Outer Coat/DT Phase Change/DT Solid Interaction, Vapor Growth, Impact on Target Symmetry Vapor Bubble/Phase Change Exper.? Will Liquid Layer/Vapor Bubbles Meet Physics Requirements? Physics Simulation Which target design(s) fit within background gas requirements? Timeline(?) Downselect in mid-Phase II HAPL meeting, G.Tech.

5. Low Temp. Insulated Target • Initial Temp. = 16 K • Allowable q’’ > 18 W/cm2 • Xe Pres. ~ 70 mtorr • Insulated Target with Phase Change • Initial Temp. = 18 K • Allowable q’’ = 20 W/cm2 • Melt Depth = 2.5 m • Xe Pres. ~80 mtorr LLE (UR) Schafer, GA Chamber Effort UCSD, GA Legend: NRL • Low Temp. Insulated Target with Phase Change • Initial Temp. = 16 K • Allowable q’’ = 20 W/cm2 • Melt Depth = 0 m • Xe Pres. ~80 mtorr • Insulated Target Standard Design • 150 m of Insulation • 10 % Dense Insulation • Initial Temp. = 18 K • Allow. q’’ = 12 W/cm2 • Xe Temp. ~4000 K • Xe Pres.~50mtorr (@300 K) LANL Insulated Target Strategy Which target design(s) fit within background gas requirements? Timeline(?) Downselect in mid-Phase II Is Low Temperature Acceptable for Layering? Experiment Manufacturing Process and Cost Study? Does Foam Insulator Meet Manufacturing and Physics Requirements? Physics Simulation Does Liquid Layer/Vapor Bubbles Meet Physics Requirements? Numerical Model Outer Coat/DT Phase Change/DT Solid Interaction, Vapor Growth, Impact on Target Symmetry Vapor Bubble/Phase Change Exper.? DT/foam Mechanical Properties Exper. HAPL meeting, G.Tech.

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

8. Condensation (Sticking) Coefficient of High Temperature Gas on Cryogenic Target(Very Little Data Found, Applicable to our Prototypical Conditions) CO2 Beam on Cu Target • Condensation coefficient is a function of several parameters, including: - Ttarget, Tgas, flux, angle of incidence... • Condensation coefficient decreases rapidly with Ttarget 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 (CO2) = 194.6 K - BP (CO2) = 217.5 K• For an insulated target the surface temperature will increase rapidly; thus the condensation coefficient will decrease rapidly 4 x 1016 s-1cm-2 Condensation Coefficient 2 x 1014 s-1cm-2 4 x 1015 s-1cm-2 Target Temperature (K) 1400 K Ar Beam on Cu Target Condensation Coefficient 300 K HAPL meeting, G.Tech. Target Temperature (K)

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 ~ 15-20 % Maximum Reduction for High Density Case, 100 mTorr Xe Minor Effect for Low Density Case, 1 mTorr Xe Xenon Gas @ 4000 K, vT = 400 m/s Surface Temperature = 18 K (Constant) Complete Accommodation 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 (H2, CH4, CO, CO2) 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 HAPL meeting, G.Tech.

11. 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 3He Modeling the Behavior of a Vapor Bubble Simplified Target Cross Section ro Plastic Shell Preexisting Vapor Bubble tv DT Vapor Core Rigid DT Solid HAPL meeting, G.Tech.

12. Uniform Internal Pressure, P t r t ro P R 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* - Where A is a numerical coefficient =f (ro , R, t, m) - 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, 6th Edition, p. 546 HAPL meeting, G.Tech.

13. ro R Comparison of the Calculated Deflection of the Plastic Shell by Membrane and Bending Theory for a Pressure of 104 Pa for Several Vapor Bubble Sizes , ro • Bubble size for which bending theory approaches membrane theory is independent of pressure, ~ 37 mm in this case • Would need much smaller bubble size in target to avoid large “membrane-like” deflections HAPL meeting, G.Tech.

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