1. A. R. Raffray, B. R. Christensen and M. S. Tillack Can a Direct-Drive Target Survive Injection into an IFE Chamber? Japan-US Workshop on IFE Target Fabrication, Injection and Tracking Osaka, Japan 18-19 October 2004 Mechanical and Aerospace Engineering Department and the Center for Energy Research

2. Degradation of targets in the chamber must not exceed requirements for successful implosion Spherical symmetry Surface smoothness Density uniformity T DT (<19.79 K?) Better definition is needed Physics requirements: IFE Chamber (R~6 m) Protective gas (Xe, He) at ~4000 K heating up target Chamber wall ~ 1000–1500 K, causing q’’ rad on target Target Injection (~400 m/s) Target Implosion Point

3. We have characterized target heat loads and the resulting thermomechanical behavior in order to help define the operating parameter windows Energy transfer from impinging atoms of background gas  Enthalpy transfer (including condensation) or convective loading  Recombination of ions (much uncertainty remains regarding plasma conditions during injection) Radiation from chamber wall  Dependent on reflectivity of target surface and wall temperature  Estimated as 0.2 – 1.2 W/cm 2 for  = 0.96 and T wall = 1000 – 1500 K Heat loads: 1.Convective loading using DSMC 2.Integrated thermomechanical model developed at UCSD, including phase change behavior of DT Analyses performed:

4. 1.Computation of energy transfer from background gas using DS2V

5. The DSMC method has been used to study targets in a low density (3x10 19 – 3x10 21 m –3 ) protective gas where Kn is moderately high (0.4–40) Assumptions Axially symmetric flow Stationary target Xe stream  velocity = 400 m/s  T = 4000 K  density=3.22x10 21 m -3 Target surface fixed at T = 18 K Sticking coefficient 0<  Accommodation coefficient 0<  No target rotation Temperature field around a direct drive target Flow  = 0  = 0

6. If the stream density is high, the number flux at the target surface increases when the sticking coefficient (  ) decreases n = 3.22x10 21 m -3 Instead of screening incoming particles, stagnated particles add to the net particle flux Kinetic theory and DS2V show good agreement decreasing 

7. Conversely, if the stream density is high, the heat flux at the target surface decreases when the sticking coefficient decreases The strong dependence of heat flux on position suggests that the time-averaged peak heat flux could be reduced significantly by rotating the target. n = 3.22x10 21 m -3 The heat flux decreases when  = 0 due to the shielding influence of low temperature reflected particles interacting with the incoming stream For the low density cases there is less interaction between reflected and incoming particles. decreasing 

8. The sticking coefficient (  ) and accommodation coefficient (  ) both have a large impact on the maximum heat flux at the leading edge Region of no screening Parameters : –400 m/s injection into –Xe @ 3.22x10 21 m -3 –4000 K –max. heat flux = 27 W/cm 2 (with  = 1 and  =1) Experimental determination of the sticking coefficient and accommodation coefficient is needed

9. 2.Integrated thermomechanical modeling of targets during injection

10. A 1-D integrated thermomechanical model was created to compute the coupled thermal (heat conduction, phase change) and mechanical (thermal expansion, deflection) response of a direct drive target The maximum allowable heat flux was analyzed for several target configurations where failure is based on the triple point limit The potential of exceeding the triple point (allowing phase change ) was explored In the following, we discuss:  a description of the model  validation of the model  the effect of initial target temperature  the effect of thermal insulation  the effect of injection velocity  the effect of allowing a melt layer to form  the effect of allowing a vapor layer to form Background

11. The 1D transient energy equation is solved in spherical coordinates Discretized and solved using forward time central space (FTCS) finite difference method Temperature-dependent material properties Apparent c p model to account for latent heat of fusion (at melting point) Interface Boundary Condition

12. Outer polymer shell deflection Membrane theory for shell of radius r pol and thickness t pol : Inner solid DT deflection Thick spherical shell with outer and inner radii, r a and r b : Deflection of polymer shell and DT nonlinearly affects the pressure and vapor layer thickness

13. The model was validated using an exact solution for a solid sphere Initial temperature T=T m (the melting point) Surface suddenly raised to T s =25 K at t=0 The solution converged to the exact solution as the mesh size was decreased. The melt layer thickness is correctly modeled. Slight error exists in the temperature profile.

14. DT triple point temperature is assumed as limit. Take the required “target survival time” to be 16.3 ms. Decreasing the initial temperature from 16 K to 14 K does not have as large of an effect as a decrease from 18 K to 16 K. Reducing the initial temperature of a basic target increases the maximum allowable heat flux

15. An insulating foam on the target could allow very high heat fluxes Failure is assumed at the DT triple point temperature Required “target survival time” assumed = 16.3 ms. Initial target temperature = 16 K. A 150  m, 25% dense insulator would increase the allowable heat flux above 12 W/cm 2, nearly an order of magnitude increase over the basic target. DT gas 1.5 mm DT solid 0.19 mm DT + foam x Dense plastic overcoats (not to scale) 0.289 mm Insulating foam High-Z coat

16. For a basic target, using the TP limit, there is an optimum injection velocity when  = 1  = 1  = 0 DS2V is used to predict heat flux, and the integrated thermomechanical model is used to predict the response This optimum occurs due to a competition between increasing heat flux vs. lower thermal penetration

17. For an insulated target, higher injection velocity significantly increases the maximum allowable gas density 100 mm, 10% dense insulator,  (sticking coefficient) = 1

18. If only melting occurs, the allowable heat flux is increased by ~ 3–8 times over the cases where the DT triple point temperature is used as the failure criterion Possible failure criteria: –Homogeneous nucleation of vapor bubbles in the DT liquid (0.8T c ). –Ultimate strength of the DT solid or polymer shell is exceeded. –Melt layer thickness exceeds a critical value (unknown). For targets with initial temperatures of 14 K, 16 K, and 18 K, 0.8T c was reached before the ultimate strength of the polymer was exceeded. The maximum allowable heat fluxes were found to be (@ 16.3 ms): –5.0 W/cm 2 (T init = 18 K) –5.5 W/cm 2 (T init = 16 K) –5.7 W/cm 2 (T init = 14 K) T init = 16 K

19. However, the amount of superheat (with melting only) indicates a potential for nucleating & growing bubbles For a basic target with initial temperatures of 16 K, the super heat is > 2-3 K for input heat fluxes > 2.5 W/cm 2. For a initial temperature of 14 K, the superheat is negative when the heat flux is 1.0 W/cm 2 (see figure to the right). 5.5 W/cm 2 2.5 W/cm 2 1.0 W/cm 2 T init = 14 K Due to the presence of dissolved He-3 gas, and small surface defects (nucleation sites), vapor formation is expected to occur before 0.8T c. For bubble nucleation and growth to occur (at nucleation sites), the liquid must be superheated by 2-3 K, where the superheat is defined as:

20. If a vapor layer is present, the allowable heat flux is increased by ~ 1.5–3 times over the cases where the DT triple point temperature is used as the failure criterion Possible failure criteria: –Ultimate strength of the DT solid or polymer shell is exceeded. –Vapor layer thickness exceeds a critical value (unknown). For targets with initial temperatures of 14 K, 16 K, and 18 K, The polymer ultimate strength was reached before the DT ultimate strength. The maximum allowable heat fluxes were found to be (@ 16.3 ms): –2.2 W/cm 2 (T init = 18 K) –2.5 W/cm 2 (T init = 16 K) –2.9 W/cm 2 (T init = 14 K)

21. For some initial temperatures and heat fluxes, the vapor layer closes, suggesting that bubbles can be minimized or eliminated in some circumstances For a target with an initial temperature of 18 K the vapor layer thickness increases rapidly for heat fluxes > 2.5 W/cm 2. For a target with an initial temperature of 14 K the vapor layer thickness goes to zero when the heat flux  1.0 W/cm 2. This vapor layer closure occurs because the DT expands (due to thermal expansion and melting) faster that the polymer shell expands (due to thermal expansion and the vapor pressure load). T init = 18 K T init = 14 K

22. Future model development activities are guided by the desire to plan and analyze experiments The coupled thermal and mechanical response of a direct drive target has helped us understand the behavior of the target and limiting factors on target survival However, the simple 1D vapor model does not account for real-world heterogeneities Future numerical model improvements will include a prediction of the nucleation and growth (homogeneous or heterogeneous from He 3 ) of individual vapor bubbles in the DT liquid We are evaluating the feasibility of a 2D model of the energy equation