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!