October 27-28, 2004 HAPL meeting, PPPL 1 Target Survival During Injection Presented by A.R. Raffray Other Contributors: K. Boehm, B. Christensen, M. S. Tillack UCSD D. Goodin General Atomics HAPL Meeting PPPL Princeton, NJ October 27-28, 2004

HAPL meeting, PPPL 2 Outline Reminder: Why is target survival important? Our modeling activities: -Detailed characterization of heat flux on target -Modeling of target thermo-mechanical behavior What we have learned from recent studies: -Characterization of limiting heat flux based on TP -Effect on target survival of: -Lower initial temperature -Thermally robust design (insulating layer) -Injection velocity -Allowing for phase change Simplifying assumption in model: -Continuous vapor region instead of individual bubble formation Scoping study of 3 He effect on bubble formation Future effort

October 27-28, 2004 HAPL meeting, PPPL 3 Why Is Target Survival Important? Spherical symmetry Surface smoothness Density uniformity T DT (<19.79 K?) Better definition is needed Physics requirements: 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 Degradation of Targets in the Chamber Must Not Exceed Requirements for Successful Implosion

October 27-28, 2004 HAPL meeting, PPPL 4 We Have Characterized Target Heat Loads for Thermo- Mechanical Analysis of the Target 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/cm 2 for  = 0.96 and T wall = 1000 – 1500 K Convective loading analysis using DSMC Temperature field around a direct drive target (from DS2V) Flow  = 0  = 0 Example Results*: The heat flux decreases when sticking coefficient,  = 0 due to the shielding influence of low temperature reflected particles interacting with the incoming stream. *More details in: B. Christensen, R. Raffray, M. Tillack, “Thermal Loading of a Direct Drive Target in rarefied Gas,” presented at the 16th ANS TOFE, Sept. 2004, to appear in Fusion Science & Technology. n = 3.22x10 21 m -3 decreasing  (rad)

October 27-28, 2004 HAPL meeting, PPPL 5 We Have Developed a 1-D Thermo-Mechanical Model of the Target, Including Phase Change, to Help Understand and Assess Target Behavior During Injection* *More details in: B. Christensen, R. Raffray, M. Tillack, “Modeling DT Vaporization and Melting in a Direct Drive Target,” presented at the 16th ANS TOFE, Sept. 2004, to appear in Fusion Science & Technology. The model solves the coupled thermal (heat conduction, phase change) and mechanical (thermal expansion, deflection of shell and solid DT) response of a direct drive target during injection. -1D transient energy equation in spherical coordinates discretized and solved using forward time central space (FTCS) finite difference method -Temperature-dependent material properties -Apparent c p model to account for latent heat of fusion (at melting point) -Interface boundary conditions: Outer polymer shell deflection based on membrane theory for shell of radius r pol and thickness t pol : Inner solid DT deflection based on thick spherical shell with outer and inner radii, r a and r b :

October 27-28, 2004 HAPL meeting, PPPL 6 DT gas 1.5 mm DT solid 0.19 mm DT + foam x Dense plastic overcoats (not to scale) mm Insulating foam High-Z coat We Have Determined the Heat Load Limits for the Base Target and Looked at Ways to Accommodate Higher Loads* Target with Insulating Layer as Back-Up Option -Impact on physics and fabrication being assessed *More details in: B. Christensen, R. Raffray, M. Tillack, “Modeling DT Vaporization and Melting in a Direct Drive Target,” presented at the 16th ANS TOFE, Sept. 2004, to appear in Fusion Science & Technology. The maximum allowable heat flux was analyzed for several target configurations where failure is based on the triple point limit to ascertain the effect of: -Initial target temperature - Thermal insulation (e.g with 10% dense foam) - Injection velocity -Allowing for phase change (ms)

October 27-28, 2004 HAPL meeting, PPPL 7 Is There an Optimum Injection Velocity Based on Target Survival? Two competing factors: -Higher velocity results in a higher atomic number flux on target, and thus, a higher heat flux on the target but over a shorter time (shorter flight time).  = 1  =  m, 10% dense insulator,  = 1 - The max. allow. Xe gas density (4000 K) to reach the TP increases with injection velocity for a sticking coefficient,  =0 and shows a peak for  =1 -It increases significantly with injection velocity for insulated target even for  =1 as the effect of the shorter time for thermal diffusion across the insulation outweighs the corresponding higher heat flux

October 27-28, 2004 HAPL meeting, PPPL 8 The Potential of Exceeding the Triple point (Allowing Phase Change) Was Explored If only melting is assumed (no vapor gap), 3 possible failure criteria are identified: -Assumed threshold of spontaneous homogeneous nucleation of vapor bubbles in the DT liquid (~0.8T c ). -Ultimate strength of thick inner DT solid (~0.3 MPa) or of thin outer polymer shell (~30 MPa) is exceeded. -Melt layer thickness exceeds a critical value (unknown, based on physics requirements). T init = 16 K 0.8 T c is limiting criterion in this case -Allowable heat flux is increased by ~ 3–8 times over the cases where the DT triple point temperature is used as the failure criterion. -But is this criterion acceptable? DT liquid CH DT solid DT vapor q o ’’

October 27-28, 2004 HAPL meeting, PPPL 9 The Presence of a Vapor Layer Generally Results in Higher Pressure on the Outer Shell Possible failure criteria: -Ultimate strength of the DT solid or polymer shell is exceeded. For cases considered, the polymer ultimate strength was reached before the DT ultimate strength -Vapor layer thickness exceeds a critical value (unknown, based on physics requirements). DT liquid CH DT solid DT vapor q o ’’ DT vapor 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 For some combinations of T init and q o ’’, the vapor layer closes, suggesting that bubbles can be minimized or eliminated in some circumstancesThis is due to DT expanding faster than the polymer shell T init = 14 K

October 27-28, 2004 HAPL meeting, PPPL 10 The Integrated Thermo-Mechanical Model Has Helped Us Understand the Target Behavior and the Factors Affecting Its Survival During Injection. However, There is a Major Simplification in the Model So Far: 1-D Vapor Region Instead of Bubble Formation Unlikely to have continuous vapor region at DT/shell interface Conditions (superheat, critical radius) might not induce spontaneous homogeneous nucleation. However: -Even a limited number of bubble formation might be unacceptable. -Presence of 3 He would promote nucleation. -Presence of defects at interface or within site might also promote nucleation (heterogeneous nucleation). 3 He would be formed prior to injection and might be in such quantity that 3 He bubble formation might not only occur in the liquid during injection but also in the solid prior to injection. Recent results from LANL DT heating experiments show the huge potential for bubble formation. This is the one area where we really need better understanding and which will be the focus of our near-term effort to help analyze the LANL experimental results as well as to apply them to the target situation.

October 27-28, 2004 HAPL meeting, PPPL 11 Scoping Study of Potential Impact of 3 He on Bubble Formation The presence of 3 He decreases the critical radius, r crit, for bubble formation in liquid DT (and, thus, enhances nucleation). r crit is plotted as a function of the molar fraction of 3 He normalized to the maximum solubility limit. Based on available solubility data (data for low P not found), x/x s is shown for concentrations of 3 He corresponding to 2 hrs, 8 hrs and 24 hrs after layering, respectively. r crit decreases with increasing 3He concentration, the effect being more marked for higher pressures. 1 hr 1 day 3 He formation due to radioactive decay of T as a function of time. ~4.8x10 24 atoms of 3 He/m 3 after a day.

October 27-28, 2004 HAPL meeting, PPPL 12 Can 3 He Bubble Formation Occur in Solid DT? It depends on the existence of defect at interface or in the foam and on the bubble surface energy requirements However, 3 He atoms need time to diffuse and coalesce to form bubble Let us assume a critical radius of 0.5  m. The corresponding number of 3 He is ~ 4x10 7 atoms. The volume (and characteristic dimension) of DT containing this number of 3 He atoms is shown as a function of time following layering. The corresponding diffusion coefficient required for the 3 He atoms to diffuse and coalesce is shown below. We have not found data for diffusivity of 3 He in DT, but based on H self-diffusion, 3 He could start coalescing very soon after layering (<1 hour).

October 27-28, 2004 HAPL meeting, PPPL 13 Summary Our 1-D integrated thermo-mechanical model has helped us understand the target behavior and the factors affecting its survival during injection. However, a major simplification in the phase-change model is the assumption of a continuous vapor region instead of individual bubble formation. Scoping studies show that 3 He formation between layering and injection could substantially lower the critical radius for nucleation in the DT liquid and even provide the possibility of bubble formation in the solid if small defects are present (to be further studied). The implosion physics requirements on density non-uniformity seem quite demanding but have not yet been clearly defined. It is not clear what size and number density (if any) of bubbles would be acceptable. DT heating experiments at LANL have also shown formation of bubbles. Our next-step effort is to develop a bubble formation and behavior model (homogeneous + heterogeneous nucleation) which can then be coupled to the 1-D thermo-mechanical model to help in better understanding this important issue and to help in analyzing & guiding the experimental work incoordination with our LANL colleagues.