1. HAPL Modeling  Ion and Heat Transport Qiyang Hu, Nasr Ghoniem, Shahram Sharafat, Mike Anderson Mechanical & Aerospace Engineering University of California, Los Angeles May 15 th, 2006

2. Outline  HEROs: Helium Diffusion Model revisited Results updated Future schedule  Analytical approach: temperature profile Green ’ s function formulation Results comparison Plans for next step

3.  HEROs: Helium Diffusion  Analytical approach: temperature profile

4. serious Previous HEROs code has serious numerical instability problem: In most cases: Time to be simulated < 100 sec Running Time> 6 hours Time step > 2000 steps Temperature range< 2000 K

5. HEROs model is completely revisited  Still, spatial & kinetic:  Simplify the equation Ignore some cluster effects: (e.g. vacancy clusters, interstitial clusters etc.) 18 variables/equations  13 Ignore bubble coalescence  Start from spatial-independent case

6. HEROs numerical scheme: … variable bin sizeW front W back Implantation profile Temperature profile Within a bin, each C (i) is in an average sense

7. We want to use our new HEROs code to model different conditions. Helium ImplantationDamage We re-simulated UWM ’ s “ steady ” implantation case constant temperature

8. Experiments ( Cipiti & Kulcinski, 2004 ) show: 1  m 1160 °C 2.6x10 16 He/cm 2 -s 2.5 min. 990 °C 8.8x10 15 He/cm 2 -s 7.5 min. 1  m 730 °C 2.2x10 15 He/cm 2 -s 30 min. 40 KeV He On W 510 18 ion/cm 2 Temperature Pore Size Pore Density

9. stable New HEROs code is stable and gives the correct information about pore sizes:

10. So does the pore density …

11. HEROs also gives the spatial distribution information (average sense): 40 KeV; Temperature=1160 o C; Bin Number=20; Total width=10m

12. Helium retention: Most of He are in grain boundary

13. largely Capabilities of new HEROs code are largely improved HEROs Total time to be simulated Running time Required time steps Temperature range Previous <100 sec >6 hrs>2000 steps<2000 K Current>10 6 sec<5 mins< 100 steps<3500 K

14. Planning on HEROs:  Implement “ pulsed ” cases: UWM UNC IFE  Add bubble coalescence  Exceed the 0-order (average) description Include 1 st -order size distribution

15.  HEROs: Helium Diffusion  Analytical approach: temperature profile

16. We are doing 1-D heat diffusion:  Well-known equation:  Adiabatic boundary condition:  If material properties are constant:

17. Numerical approximations:  Discrete time steps:  Volumetric heating  Surface heat

18. Good agreement is achieved: (Blanchard 2005)

19. Planning:  Real cases of heating: Volumetric heating IFE condition  Couple temperature into HEROs Same “ kinetic-equation ” structure 13 variables/equation  14

20. Thanks!