1. November 2002 15th TOFE, Washington, D.C. 1 Thermal Behavior and Operating Requirements of IFE Direct-Drive Targets A.R. Raffray 1, R. Petzoldt 2, J. Pulsifer 3, M. S. Tillack 1, and X. Wang 3 1 Mechanical and Aerospace Engineering Department and Center for Energy Research, University of California, San Diego, EBU-II, Room 460, La Jolla, CA 92093-0417 2 Inertial Fusion Technology Division, MS 13-501, General Atomics, La Jolla, CA 92186- 5608 3 Center for Energy Research, University of California, San Diego, EBU-II, Room 460, La Jolla, CA 92093-0417 Presented at the 15th Topical Meeting on the Technology of Fusion Energy Washington, D.C. November 2002

2. 15th TOFE, Washington, D.C. 2 Abstract During injection, inertial fusion energy (IFE) direct drive targets are subject to heating from energy exchange with the background gas and radiation from the wall. This heat deposition could lead to deuterium-tritium (DT) phase change and target deformation violating the target physics symmetry requirements. This paper assesses the thermal behavior of the target under such conditions and explores possible ways of extending the target lifetime through design modification(s) and/or through a better understanding of the effect of energy deposition and phase change on the target density symmetry.

3. November 2002 15th TOFE, Washington, D.C. 3 Typical Direct Drive Target Configuration Spherical shell ~4 mm in diameterComposed mainly of solid DT at 18KInjected in IFE chamber at velocities up to about 400 m/s For maximum energy yield from the fusion micro- explosion: -Temperature of DT layer must be held at ~18.5 K -High degree of spherical symmetry and surface smoothness must be maintained

4. November 2002 15th TOFE, Washington, D.C. 4 Injected Target Heating through Energy Exchange from Background Gas Background gas (e.g. xenon or helium) might be needed for chamber wall protection Energy transfer from impinging atoms of background gas on target -Enthalpy transfer -Condensation (latent heat transfer) in the case of gas with boiling point and melting point above target temperature (18K) (e.g. for Xe) -Possible recombination of ions at the surface if plasma conditions remain in the chamber -Much uncertainty remains regarding plasma conditions during injection -For simplicity, plasma effects are not included in the calculations presented here -Results will be revisited as new information on plasma remnants in the chamber becomes available.

5. November 2002 15th TOFE, Washington, D.C. 5 Condensation from Xe as Background Gas No data found for condensation coefficient,  c, for Xe at ~1,000's K condensing on an 18 K surface.  c = 0.99-0.6 for 2,500K Ar beam condensing on a 15 K Cu/Ar with incident angle of 0 o -60 o. It seems prudent to assume  c values of ~1 to estimate Xe condensation heat fluxes.

6. November 2002 15th TOFE, Washington, D.C. 6 Condensation from He as Background Gas Heat flux on the target from He are comparable to those from Xe case even in the absence of condensation. -Latent heats have only a small effect on the overall energy transfer which is governed by change in gas enthalpy - Molecular flux of He target is higher than that of Xe for same P and T Use of He has the advantage that the He atoms after transferring their energy to the 18 K target will likely be reflected back thereby shielding the target from subsequent He atom collisions.

7. November 2002 15th TOFE, Washington, D.C. 7 Radiation Heat Transfer from Chamber Wall Simple estimate given by: Where: T w is the wall temperature (assumed as a black body)  S-B is Stefan-Bolzmann constant, and  the target surface reflectivity. Highly reflective target surface is required to minimize total absorbed heat flux. For very thin (275–375 Å) gold coating, a reflectivity of about 96% is anticipated. Effort underway to estimate more accurately the radiated energy absorption and reflection based on a multi- layer wave model. As an illustration, q rad ’’ ranges from 2300 W/m 2 for T w =1000K to 11,000 W/m 2 for T w =1500 K.

8. November 2002 15th TOFE, Washington, D.C. 8 Initial Target Thermal Analysis Transient thermal analysis using ANSYS -Target is not tumbling -2-D heat flux distribution from DSMC results -Temperature dependent DT properties including latent heat of fusion at triple point to model phase change Max. temp. limit to prevent unacceptable target deformation not well known -Previous assumption was to maintain DT below its triple point (19.79 K) Heat flux to reach triple point only ~ 6000 W/m 2 for a 6-m radius chamber ~ q cond ’’ from 1000K/7.6 mtorr or 4000 K/2.5 Xe; or q rad ’’ from T w =1275K Major constraint on background gas density that might be required for wall protection.

9. November 2002 15th TOFE, Washington, D.C. 9 Add Outer Insulating Foam Layer to Enhance Target Thermal Robustness Simple assumption: adjust thickness of DT+foam layer accordingly to maintain same overall dimension DT gas 1.5 mm DT solid 0.19 mm DT + foam x ~  m’s Dense plastic coat (not to scale) (0.289-x) mm Insulating foam Au or Pd Properties of cryogenic foam based on those of polystyrene -Density and thermal conductivity adjusted according to foam region porosity -Thermal conductivity further scaled by 2/3 to account for possible optimization of porous micro-structure to minimize the conductivity. -As conservative measure, higher thermal conductivity values found in the literature used, ranging from 0.088 W/m-K at 19 K to 0.13 W/m-K at 40 K -Heat capacity values used range from 100 J/kg-K at 20 K to 225 J/kg-K at 40 K

10. November 2002 15th TOFE, Washington, D.C. 10 DT Interface Temperature History for q’’=2.2 W/cm 2 and for Different Thicknesses(  m)of 25% Dense Outer Foam Region Transient analyses performed using ANSYS -q’’ = 2.2 W/cm 2 -e.g. corresponding to condensation from 10 mTorr/4000 K Xe -Outer foam region density = 25% ~130  m (32  m of equivalent solid polystyrene) would be sufficient to prevent DT from reaching the triple point after 0.015 s (corresponding to a target velocity of 400 m/s in a chamber of radius 5 m). As comparison, DT would reach the triple point after about 0.0022 s in the absence of the outer foam layer.

11. November 2002 15th TOFE, Washington, D.C. 11 Summary of Thermal Analysis Results on Effectiveness of Insulating Outer Foam Layer To increase target thermal robustness: -maximize both thickness and porosity of outer foam layer while -accommodating target physics and structural integrity requirements. Increasing plastic coating thickness from ~1  m to 10  m provides only marginal improvement.

12. November 2002 15th TOFE, Washington, D.C. 12 Another Means to Extend Target Lifetime is by Relaxing DT Thermal Limit and Allow Some Phase Change What is the effect on target density symmetry relative to target physics requirements? The target is covered by a ~1  m solid plastic coating -Vapor might form at DT-foam/plastic coating interface resulting in density variation - Nature of bond between DT-foam and plastic coating key factorPerfect bond---> vapor formation through homogeneous nucleation. -However, under target conditions, homogeneous nucleation is virtually zero at T 34 K. Imperfect bond -Heterogeneous nucleation could be a problem for nucleation sites of the order of 1  m. Finite gap -Surface evaporation -This worse-case scenario was further assessed.

13. November 2002 15th TOFE, Washington, D.C. 13 Thermo-mechanical Model for Rigid DT q’’ Plastic coating DT gas DT + foam Melt layer Evaporated layer  V/V due to phase-change equivalent to P on plastic sphere  V=total volumetric change of target V s =Equivalent solid volume of phase change region V l and V v =liquid and vapor volumes of phase change region  V th =volumetric thermal expansion of plastic coating Both liquid and vapor densities of DT are lower than the DT solid density

14. November 2002 15th TOFE, Washington, D.C. 14 Simple Model Development The initial solid volume, V s, that has undergone phase change is given by: Assume that a mass fraction x l of the phase change region,  p-c, is liquid and (1-x l ) is vapor: Substitution in  V/V eqn. leads to a quadratic equation for P: The volumetric expansion of the plastic coating is given by:

15. November 2002 15th TOFE, Washington, D.C. 15 Thermo-Mechanical Analysis Procedure The phase change thickness and DT interface temperature were first estimated as a function of incident heat flux from a series of 2-D ANSYS runs and used as input for the thermo-mechanical model. The model solves for the pressure of the DT liquid and vapor for a given vapor region thickness. Iterate to obtain vapor/liquid interface temperature and pressure consistent with saturation conditions from the phase diagram. solid liquid vapor Triple point Critical point

16. November 2002 15th TOFE, Washington, D.C. 16 DT Evaporated Region Thickness as a Function of Maximum Heat Flux for Different Plastic Coating Thicknesses Is 1% density variation acceptable based on target physics requirements? -For the 289  m foam+DT region--> ~3  m vapor region -e.g. for 8  m plastic coating maximum allowable q’’~4.2 W/cm 2 A thicker plastic coating is preferred to minimize vapor region thickness

17. November 2002 15th TOFE, Washington, D.C. 17 Hoop Stress as a Function of Maximum Heat Flux for Different Plastic Coating Thicknesses A maximum q’’ of ~5-5.5 W/cm 2 for a plastic region thickness of 8  m is allowable based on the ultimate tensile strength of polystyrene

18. November 2002 15th TOFE, Washington, D.C. 18 DT Vapor and Maximum Interface Temperatures as a Function of Maximum Heat Flux Homogeneous nucleation increases dramatically as T--> 34 K, corresponding to q’’ > 6 W/cm 2

19. November 2002 15th TOFE, Washington, D.C. 19 Equivalent q’’ required to evaporate vapor region is small for vapor region thicknesses ~ 1-10  m (<< heat flux on target) Equivalent Heat Flux as a Function of DT Evaporated Thickness

20. November 2002 15th TOFE, Washington, D.C. 20 DT Evaporated Thickness as a Function of Maximum Heat Flux for Different Plastic Coating Thicknesses for a Case with a 72-  m 25% Dense Insulating Outer Foam Layer Based on the 1% density variation (~3  m vapor region ), the maximum allowable q’’ is now ~8.6 W/cm 2 for a 8  m plastic coating (compared to 4.2 W/cm 2 for case without insulating foam layer)

21. November 2002 15th TOFE, Washington, D.C. 21 Hoop Stress as a Function of Maximum Heat Flux for Different Plastic Coating Thicknesses with a 72-  m 25% Dense Insulating Outer Foam Layer A maximum q’’ of ~9.5 W/cm 2 for a plastic region thickness of 8  m is allowable based on the ultimate tensile strength of polystyrene

22. November 2002 15th TOFE, Washington, D.C. 22 DT Vapor and Maximum Interface Temperatures as a Function of Maximum Heat Flux for a Case with a 72-  m 25% Dense Insulating Outer Foam Layer

23. November 2002 15th TOFE, Washington, D.C. 23 Conclusions (I) The potential benefit on target lifetime of adding an insulating foam layer and/or of better understanding vapor formation processes have been examined. For a typical target configuration the maximum q’’ for DT to reach its triple point is only about 0.6 W/cm 2 for a 6-m radius chamber. –This would place an important constraint on background gas density that might be required for wall protection. Adding a 130-  m 25% dense outer foam layer would increase the allowable q’’for DT to reach its triple point to 2.2 W/cm 2 and a 152  m 10% dense insulating foam layer would increse q’’ up to 7.5 W/cm 2. For increased target thermal robustness, it is preferable to have the maximum thickness and porosity outer foam layer which can still accommodate the target physics and structural integrity requirements.

24. November 2002 15th TOFE, Washington, D.C. 24 Conclusions (II) Allowing for vapor formation would relax the target thermal constraint A simple thermo-mechanical model was developed to help in better understanding the DT phase change process. -A thicker plastic coating was found preferable to reduce the vapor region thickness. -A ~1% change in region density corresponds to ~ 3  m of vapor region at the DT-foam/plastic coating interface. -If this were acceptable, the maximum allowable q’’ is ~4 W/cm 2 for the original target design and ~ 9 W/cm 2 for a target design with 72-  m thick, 25%-dense outer insulating foam layer and an 8-  m thick plastic coating. -In both cases, the corresponding hoop stresses in the plastic coating are less than the anticipated ultimate tensile strength.

25. November 2002 15th TOFE, Washington, D.C. 25 Conclusions (III) The results from the simple thermo-mechanical model have helped to highlight the benefits of relaxing the DT vapor formation constraint and of including design modifications such as an insulating outer layer. -However, this model has limitations and a better understanding of the phase change processes would be obtained from a fully integrated model including the interactions of all key processes. -For example, the assumption of surface evaporation is conservative and infers the presence of a minute gap at the DT-foam and plastic coating interface -For a good-quality interface bond, DT boiling is more likely to occur through nucleation which should be included in the model. This also indicates the need for an experimental effort to better characterize the quality and behavior of this bond ideally by using or possibly by simulating the actual materials. In addition, guidance is needed from the target physics perspective to understand better the constraints and limitations imposed on such actions.