Thermal Control Techniques for Improved DT Layering of Indirect Drive IFE Targets

1. Thermal Control Techniques for Improved DT Layering of Indirect Drive IFE Targets John E. Pulsifer and Mark S. Tillack University of California, San Diego Dan T. Goodin and Ron W. Petzoldt General Atomics

2. Statement of Work • IFE Target Layering: Indirect Drive • Layering with capsule already assembled in the hohlraum is advantageous • Eliminates necessity of “layering spheres” • Eliminates rapid assembly of hohlraum after layering • Requires highly uniform DT surface temperature (~100mK) for up to several hours • Need a tightly controlled temperature profile on hohlraum • Determine required temperature profile and suggest method(s) for implementation • Heater array on staging tubes • Tailor target material properties in our favor

3. Target Design • Close-coupled, distributed radiator heavy ion target • Materials: A: AuGd <1% denseB: AuGd 100% denseC: Fe 0.2% denseD: (CD2)AuE: AuGd <1% denseF: Al <3% denseG: AuGd <2% denseH: CD2I: Al 2% denseJ: AuGd 4% denseK, L: DTM: BeBr or PolystyreneN: (CD2)Au From Nuclear Fusion, Vol. 39, No. 11D.A. Callahan-Miller and M. Tabak (LLNL)

4. Axisymmetric ANSYS Model of Target FliBe AuGd He (used to model all low-density materials) DT BeBr or Polystyrene

5. We explored the effectiveness of various thermal control techniques for BeBr and polystyrene shells. • Begin with benchmark of previous work by Nathan Siegel (constant T at hohlraum surface and BeBr shell) • Repeat benchmark problem using polystyrene in place of BeBr • Analyzed effect of “B” layer conductivity • Determine the hohlraum surface temperature profile necessary for a given DT heat generation • Apply hohlraum surface temperature profile and check uniformity of DT surface temperature • Add low density material properties and experiment with anisotropy in interior regions

6. Benchmark with BeBr shell agreed with prior work. • BeBr shell around capsule acts as an “integrating sphere” • Constant surface temperature of 19.2 K on right boundary • Agrees with prior work (3 mK variation at DT surface)

7. Polystyrene shell does not smooth DT surface temperature. • Constant surface temperature of 19.2 K results in 10 mK variation at DT surface

8. Temperature profile at hohlraum surface does not matter when the AuGd layer “B” is present. • To affect the variation of temperature at the DT surface, we must eliminate conduction along the “B” layer • Thermal conductivity of the “B” layer in the y-direction is modeled with helium properties

9. Determining the correct Temperature profile to Apply • Attach a block of material that is 10% of the conductivity of FliBe to the target model • Temperature at DT surface is fixed at 18 K • Heat Flux applied at the right boundary is calculated based on 48,700 W/m3 volumetric heat generation in DT layer • Solution gives temperature distribution to apply to the target model • Nodal temperatures at the FliBe surface are recorded • The FliBe surface nodal temperatures are applied to the target model

10. Results of Applying Temperature Profile to hohlraum surface • Variation at DT surface is 500 mK over p/2 radians (800 mK over p radians) • Automatic mesh is not symmetric about the x-axis and will need refinement Applied Nodal Temperatures

11. Material tailoring could relax the requirements on the varying surface temperature. Ideally, a sphere of highly conductive material concentric with the capsule (like the BeBr shell) will smooth the DT surface temperature variation. • Anisotropic properties (such as in insulating foils) may be used to approximate a sphere through regions I, J, F, G, E, D, and A. • With a perfect sphere, the DT surface temp is not as sensitive to temperature at the hohlraum surface (constant T at hohlraum would be acceptable)

12. Observations • Benchmark using BeBr shell agreed well with prior work. • Target model using polystyrene in place of BeBr does not provide a smooth DT surface temperature distribution. • AuGd layer “B” must be modified in order to minimize conduction along the length of the target and allow hohlraum outer surface to “communicate” with the capsule. • Application of a calculated temperature profile at hohlraum surface reduces the temperature variation from 10mK to ~500mK. • Tailoring of materials inside the hohlraum may relax outer surface temperature profile requirements.

13. Future Work • Test sensitivity of the DT surface temperature to changes in the applied temperature profile • Model coupling of energy from an outside source to the surface of the hohlraum Model of energy coupling to the hohlraum while in a transport tube • Experiment with anisotropic material properties inside the hohlraum • Modify the target’s internal geometry to control heat flow