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

2. Protective gas (Xe, He) at ~4000 K heating up target
Degradation of targets in the chamber must not exceed requirements for successful implosion
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
Physics requirements:
Spherical symmetry
Surface smoothness
Density uniformity
TDT (<19.79 K?)
Better definition is needed

3. We have characterized target heat loads and the resulting thermomechanical behavior in order to help define the operating parameter windows
Heat loads:
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/cm2 for e = 0.96 and Twall = 1000 – 1500 K
Analyses performed:
Convective loading using DSMC
Integrated thermomechanical model developed at UCSD, including phase change behavior of DT

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 (3x1019 – 3x1021 m–3) protective gas where Kn is moderately high (0.4–40)
Temperature field around a direct drive target
Assumptions
Axially symmetric flow
Stationary target
Xe stream
velocity = 400 m/s
T = 4000 K
density=3.22x1021 m-3
Target surface fixed at T = 18 K
Sticking coefficient 0<s<1
Accommodation coefficient 0<a<1
No target rotation
Flow
s = 0
a = 0

6. If the stream density is high, the number flux at the target surface increases when the sticking coefficient (s) decreases
n = 3.22x1021 m-3
decreasing s
Instead of screening incoming particles, stagnated particles add to the net particle flux
Kinetic theory and DS2V show good agreement

7. Conversely, if the stream density is high, the heat flux at the target surface decreases when the sticking coefficient decreases
n = 3.22x1021 m-3
The heat flux decreases when s = 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 s
The strong dependence of heat flux on position suggests that the time-averaged peak heat flux could be reduced significantly by rotating the target.

8. The sticking coefficient (s) and accommodation coefficient (a) both have a large impact on the maximum heat flux at the leading edge
Region of no screening
Parameters:
400 m/s injection into
3.22x1021 m-3
4000 K
max. heat flux = 27 W/cm2 (with a = 1 and s =1)
Experimental determination of the sticking coefficient and accommodation coefficient is needed

9. 2. Integrated thermomechanical modeling of targets during injection

10. Background
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

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 cp model to account for latent heat of fusion (at melting point)
Interface Boundary Condition

12. Deflection of polymer shell and DT nonlinearly affects the pressure and vapor layer thickness
Outer polymer shell deflection
Membrane theory for shell of radius rpol and thickness tpol:
Inner solid DT deflection
Thick spherical shell with outer and inner radii, ra and rb :

13. The model was validated using an exact solution for a solid sphere
Initial temperature T=Tm (the melting point)
Surface suddenly raised to Ts=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. Reducing the initial temperature of a basic target increases the maximum allowable heat flux
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.

15. An insulating foam on the target could allow very high heat fluxes
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
Failure is assumed at the DT triple point temperature
Required “target survival time” assumed = 16.3 ms.
Initial target temperature = 16 K.
A 150 mm, 25% dense insulator would increase the allowable heat flux above 12 W/cm2, nearly an order of magnitude increase over the basic target.

16. For a basic target, using the TP limit, there is an optimum injection velocity when s = 1
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. 100 mm, 10% dense insulator, s (sticking coefficient) = 1
For an insulated target, higher injection velocity significantly increases the maximum allowable gas density
100 mm, 10% dense insulator, s (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 (0.8Tc).
Ultimate strength of the DT solid or polymer shell is exceeded.
Melt layer thickness exceeds a critical value (unknown).
Tinit = 16 K
For targets with initial temperatures of 14 K, 16 K, and 18 K, 0.8Tc 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/cm2 (Tinit = 18 K)
5.5 W/cm2 (Tinit = 16 K)
5.7 W/cm2 (Tinit = 14 K)

19. However, the amount of superheat (with melting only) indicates a potential for nucleating & growing bubbles
Due to the presence of dissolved He-3 gas, and small surface defects (nucleation sites), vapor formation is expected to occur before 0.8Tc.
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:
Tinit = 14 K
5.5 W/cm2
2.5 W/cm2
1.0 W/cm2
For a basic target with initial temperatures of 16 K, the super heat is > 2-3 K for input heat fluxes > 2.5 W/cm2.
For a initial temperature of 14 K, the superheat is negative when the heat flux is 1.0 W/cm2 (see figure to the right).

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/cm2 (Tinit = 18 K)
2.5 W/cm2 (Tinit = 16 K)
2.9 W/cm2 (Tinit = 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
Tinit = 18 K
For a target with an initial temperature of 18 K the vapor layer thickness increases rapidly for heat fluxes > 2.5 W/cm2.
For a target with an initial temperature of 14 K the vapor layer thickness goes to zero when the heat flux  1.0 W/cm2.
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).
Tinit = 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 He3) of individual vapor bubbles in the DT liquid
We are evaluating the feasibility of a 2D model of the energy equation