HAPL Modeling Ion and Heat Transport Qiyang Hu, Nasr Ghoniem, Shahram Sharafat, Mike Ander son Mechanical & Aerospace Engineering University of California, Los Angeles May 15 th , 2006
HAPL Modeling Ion and Heat
Transport
Qiyang Hu, Nasr Ghoniem, Shahram Sharafat, Mike AndersonMechanical & Aerospace EngineeringUniversity of California, Los Angeles
May 15th, 2006
Outline HEROs: Helium Diffusion
Model revisited Results updated Future schedule
Analytical approach: temperature profile Green’s function formulation Results comparison Plans for next step
HEROs: Helium Diffusion
Analytical approach: temperature profile
Previous HEROs code has seriousserious numerical instability problem:
In most cases:
Time to be simulated < 100 sec Running Time > 6 hours Time step > 2000 steps Temperature range < 2000 K
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
Generation Reaction , Diffusion Drift
ii j i iC C C C C
t
HEROs numerical scheme:
…
variable bin sizeW front W back
Implantation profileTemperature profile Within a bin, each C(i) isin an average sense
We want to use our new HEROs code to model different conditions.
Helium Implantation Damage
We re-simulated UWM’s “steady” implantation caseconstant temperature constant temperature
Experiments (Cipiti & Kulcinski, 2004) show:
1 m1 m
1160 °C2.6x1016 He/cm2-s2.5 min.
990 °C8.8x1015 He/cm2-s7.5 min.
1 m
730 °C2.2x1015 He/cm2-s30 min.40 KeV He
On W51018 ion/cm2
Temperature
Pore Size
Pore Density
New HEROs code is stablestable and gives the correct information about pore sizes:
So does the pore density …
HEROs also gives the spatial distribution information (average sense):
40 KeV; Temperature=1160 oC; Bin Number=20; Total width=10m
Irradiation Time (sec)
HeliumAm
ount(appm)
10-6 10-4 10-2 100 102 104 10610-6
10-4
10-2
100
102
104
106
UWM Steady (Polycrystal)
Total ImplantedHe Retention
In GB
In Bubble
In Clusters
Helium retention:
Most of He are in grain boundary
Capabilities of new HEROs code are largely 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 >106 sec <5 mins < 100 steps <3500 K
Planning on HEROs: Implement “pulsed” cases:
UWM UNC IFE
Add bubble coalescence
Exceed the 0-order (average) description Include 1st-order size distribution
HEROs: Helium Diffusion
Analytical approach: temperature profile
We are doing 1-D heat diffusion: Well-known equation:
Adiabatic boundary condition:
If material properties are constant:
,T TT c T k T Q x tt x x
0
0x
Tx
, amT t T
2 24 4
0 0
1,2
tx x t t x x t t
amQT x t T dt dx e ec t t
, , ,G x x t t
Numerical approximations: Discrete time steps:
Volumetric heating Surface heat
1
1
0 0
,, , , ,
ntn
am n n
Q x tT x t T dt dx G x x t t
T c T
0.7
depl xFQ e
t
Good agreement is achieved:
(Blanchard 2005)
Planning: Real cases of heating:
Volumetric heating IFE condition
Couple temperature into HEROs Same “kinetic-equation” structure 13 variables/equation 14
Thanks!