1. RRP:3/9/01Aries IFE 1 Parametric Results for Gas-Filled Chamber Dynamics Analysis Aries Workshop March 8-9, 2001 Livermore, CA Robert R. Peterson and Donald A. Haynes Fusion Technology Institute University of Wisconsin-Madison

2. RRP:3/9/01Aries IFE 2 First Wall Erosion and Target Heating During Injection are Competing Concerns in Direct-Drive Laser Fusion Dry-Wall Target Chambers

3. RRP:3/9/01Aries IFE 3 Check results for knock-on ions with finer time resolution for deposition. (cf. Raffray) deposited ion density/flux in useful form Wall load (total and differentiated as to source) as a function of time more snap shots of wall temperature as a function of depth W  +SiC armor Scale up NRL target yield to SOMBRERO levels , for density-radius parameter space scan: warning: partitioning may not remain the same, can this be checked HI target: Threat spectrum still needed Au coated chamber for NRL Au-coated target, W coating for W coated NRL target Consider molecular buffer gases Re-visit 0 Torr case for NRL target (in particular, ion deposition depths) non-Au coated NRL target: need threat spectra Begin work on wetted wall? Chamber Dynamics Action Items: From December 2000       

4. RRP:3/9/01Aries IFE 4 Chamber Physics Critical Issues Involve Target Output, Gas Behavior and First Wall Response Design, Fabrication, Output Simulations, (Output Experiments) Design, Fabrication, Output Simulations, (Output Experiments) Gas Opacities, Radiation Transport, Rad-Hydro Simulations Gas Opacities, Radiation Transport, Rad-Hydro Simulations Wall Properties, Neutron Damage, Near-Vapor Behavior, Thermal Stresses Wall Properties, Neutron Damage, Near-Vapor Behavior, Thermal Stresses X-rays, Ion Debris, Neutrons Thermal Radiation, Shock Target OutputGas BehaviorWall Response UW uses the BUCKY 1-D Radiation-Hydrodynamics Code to Simulate Target, Gas Behavior and Wall Response.

5. RRP:3/9/01Aries IFE 5 1-D Lagrangian MHD (spherical, cylindrical or slab). BUCKY, a Flexible 1-D Lagrangian Radiation-Hydrodynamics Code; Useful in Predicting Target Output and Target Chamber Dynamics Thermal conduction with diffusion. Applied electrical current with magnetic field and pressure calculation. Equilibrium electrical conductivities Radiation transport with multi-group flux-limited diffusion, method of short characteristics, and variable Eddington. Non-LTE CRE line transport. Opacities and equations of state from EOSOPA or SESAME.

6. RRP:3/9/01Aries IFE 6 BUCKY, a Flexible 1-D Lagrangian Radiation-Hydrodynamics Code; Useful in Predicting Target Output and Target Chamber Dynamics Thermonuclear burn (DT,DD,DHe 3 ) with in-flight reactions. Fusion product transport; time-dependent charged particle tracking, neutron energy deposition. Applied energy sources: time and energy dependent ions, electrons, x-rays and lasers (normal incidence only). Moderate energy density physics: melting, vaporization, and thermal conduction in solids and liquids. Benchmarking: x-ray burn-through and shock experiments on Nova and Omega, x-ray vaporization, RHEPP melting and vaporization, PBFA-II K  emission, … Platforms: UNIX, PC, MAC

7. RRP:3/9/01Aries IFE 7 Radiation Transport and Hydrodynamics are Crucial to IFE Fill-Gas Calculations: Validated for BUCKY and EOSOPC EOSOPC represents an improvement over IONMIX for LTE plasmas: Atomic Physics: multi-electron wavefunctions (UTA) Degeneracy lowering: Hummer-Mihalas formalism is implemented Additional effects in EOS: (partial degeneracy, modified Debye-Hückel interaction) Results from EOSOPC have been benchmarked against burnthrough experiments, and compared with other major opacity codes, such as STA. X-Ray Burnthrough of Au Nova Experiments vs. BUCKY simulations assuming 150 TW/cm^2 Laser Burnthrough time (ns) Slab Thickness (mm) 1 2 3 0.5 1.0 1.5 2.0 430-570 eV SXI 210-240 eV SXI 208-236 eV BUCKY 451-537 eV BUCKY

8. RRP:3/9/01Aries IFE 8 Direct-Drive Targets Under Consideration Have Different Output DT Vapor DT Fuel Foam + DT 1  CH + 300 Å Au 0.265g/cc 0.25 g/cc 1.50 mm 1.69 mm 1.95 mm DT Vapor DT Fuel Foam + DT 1  CH 0.265g/cc 0.25 g/cc 1.22 mm 1.44 mm 1.62 mm Direct-drive Laser Targets CH SOMBRERO (1990)NRL (1999) Laser Energy: 1.3 MJ Laser Type: KrF Gain: 127 Yield: 165 MJ Laser Energy: 1.6 MJ Laser Type: KrF Gain: 108 Yield: 173 MJ Laser Energy: 4 MJ Laser Type: KrF Gain: 100 Yield: 400 MJ Debris Ions 94 keV D - 5.81 MJ 141 keV T - 8.72 MJ 138 keV H - 9.24 MJ 188 keV He - 4.49 MJ 1600 keV C - 55.24 MJ Total -83.24 MJ per shot Standard Direct-Drive Radiation Tailored-Wetted Foam Wetted Foam DT Vapor DT Fuel 3.0 mm 2.7 mm 2.5 mm Spectra: Calculated with BUCKY Calculated by NRL Calculated with Lasnex Spectra: Not Yet Calculated The energy partition and spectra for SOMBRERO were supplied by DOE and need to be calculated.

9. RRP:3/9/01Aries IFE 9 Implosion, Burn and Explosion of NRL Radiation Smoothed Direct-Drive Laser Fusion Target 22% of DT ice is burned; NRL and LLNL get about 32 %, though peak  R (LLNL) and bang time (NRL) do agree. This calculation yielded 115 MJ; another, 200 MJ Very little DT in wetted foam is burned. Other yields would be achieved with further tuning. Target expands at a few time 10 8 cm/s and radiates.

10. RRP:3/9/01Aries IFE 10 We Have Isolated the Differences Between the UW and NRL Target Implosion and Burn Calculations: Laser Deposition Subtle differences in implosion geometry at ignition. UW BUCKY calculation from UW designed laser pulse gives green curve and 115 MJ. NRL calculation from NRL designed laser pulse give red curve and 160 MJ. UW BUCKY calculation starting from red curve give 158 MJ. Therefore the burn in the two calculations agrees and it is subtle differences in the implosion caused by differences in the laser deposition that leads to the differences in yield. UW and NRL are working on importing NRL laser deposition model into BUCKY. BUCKY NRL =>BUCKY

11. RRP:3/9/01Aries IFE 11 Ion Spectrum for NRL Radiation Pre-Heated Target Depends on Yield Wetted Foam Plastic Au DT Ice DT Gas SOMBRERO Wetted Foam Plastic Au DT Ice DT Gas SOMBRERO The particle energy of each species in each zone is then calculated as mv 2 /2 on the final time step of the BUCKY run. This time is late enough that the ion energies are unchanging. The numbers of ions of each species in each zone are plotted against ion energy. The spectra from direct fusion product D, T, H, He 3, and He 4 are calculated by BUCKY but they don’t make it out of the target. Knock-ons not included. The ion spectra is more energetic for 200 MJ yield Ion Spectrum for 115 MJ Yield NRL Target Ion Spectrum for 200 MJ Yield NRL Target

12. RRP:3/9/01Aries IFE 12 Ions from Hydro Expansion (18% of Yield)Knock-on Ions (12% of Yield) John Perkins (LLNL) has Performed Target Output Calculations Perkins’ calculations of ion spectra from NRL radiation pre-heated target have been used to analyze dry-wall gas-protected chambers. E ion = m ion u 2 /2 n + ion => n ´ + ion ´

13. RRP:3/9/01Aries IFE 13 Open collimator LOS 1/2 8” from Z Pin Hole Camera 10 degrees tilt to center. 9” from center of camera hole plate to blast shield. L I D CR39 film measures ion energy through damage track lengths. Z-pinch x-ray source Ion Spectrum Experiments on Z are in Progress to Validate Target Output Calculations SHOT # 603 06/26/00 16:13 Damage by ions Z X-rays CR39 detector Ablator Material Concept Ion track analysis and supporting BUCKY simulations are in progress.

14. RRP:3/9/01Aries IFE 14 BUCKY-Produced X-ray Spectra from Targets Are Used; They are Changed by High Z Components and Yield X-ray spectra are converted to sums of 3 black-body spectra. Time-dependant spectra are in Gaussian pulses with 1 ns half- widths and are used in chamber simulations. Time-integrated fluences are shown for 115 MJ and 200 MJ NRL and 400 MJ SOMBRERO. The presence of Au in the NRL targets adds emission in spectral region above a few keV. At higher yield the Au is more important. NRL 116 MJ NRL 200 MJ SOMBRERO 400 MJ

15. RRP:3/9/01Aries IFE 15 LLNL-Produced X-ray Spectra from Targets Show How Direct and Indirect-Drive Differ

16. RRP:3/9/01Aries IFE 16 The threat spectrum can be thought of as arising from three contributions: fast x-rays, unstopped ions, and re-radiated x-rays Some debris ions are deposited in chamber gas, which re-radiates the energy in the form of soft x-rays The x-rays directly released by the target are, for Xe at the pressures contemplated for the DD target, almost all absorbed by the wall. Some debris ions are absorbed directly in the wall. The wall (or armor) reacts to these insults in a manner largely determined by it’s thermal conductivity and stopping power.

17. RRP:3/9/01Aries IFE 17 For example, the first wall does not vaporize for the SOMBRERO target in a 6.5m radius chamber filled with 0.1 torr Xe and a wall equilibrium temperature of 1450C. The separation in time of the insults from the prompt x-ray, the ions, and the re-radiated x-rays is crucial to the survival of the wall. The Xe serves to absorb the vast majority of the ion energy and almost half of the prompt x-rays and slowly re- radiates the absorbed energy at a rate determined by the Plank emission opacity of the Xe. Neutrons Neutron deposition begins after 1 st peak but continues into 2 nd. Enhanced neutron sputtering?

18. RRP:3/9/01Aries IFE 18 For the current calculations, IONMIX has been used to generate Non-LTE Xe opacity tables Xe gas at or below 0.5 Torr in Density is not in LTE. The Xe opacity can differ substantially between LTE (EOSOPC) and Non-LTE (IONMIX). IONMIX opacities are used in this study. Non LTE (IONMIX) ionization is substantially below the LTE (Saha) ionization.

19. RRP:3/9/01Aries IFE 19 A scan of Xe density holding the first wall equilibrium temperature fixed at 1450C was performed to examine the onset of vaporization. For the SOMBRERO target in a 6.5m graphite chamber, the prompt x-rays are the major threat. Even at 0.05 Torr Xe, 78MJ of the 83MJ of ion energy is absorbed by the gas, slowly re- radiated to contribute to the second peak in temperature. The sublimation threshold occurs when the prompt x-rays loading is above 1.88 J/cm 2 for x-rays with the SOMBRERO spectrum, for this equilibrium wall temperature.

20. RRP:3/9/01Aries IFE 20 The SOMBRERO and NRL targets differ significantly in yield, partitioning, and spectra. These differences lead to very different target chamber dynamics. Even if the NRL spectra are scaled up by the ratio of the total yields (400/165), it poses considerably less threat to the target chamber. It has fewer of the dangerous, prompt x-rays and a different ion spectrum. For instance, the first wall survives at conditions where the SOMBRERO target vaporizes 6.7g of wall material per shot. (This assumes that the energy is increased by increasing the flux, and not the shape, of the spectra..)

21. RRP:3/9/01Aries IFE 21 Wall temperature as a function of depth at the times of the first and second peaks of surface temperature, and at the local minimum between. 0.05 Torr Xe, T_equil. = 1450C, Radius = 6.5m, Graphite Wall Note the differences in temperature scales!

22. RRP:3/9/01Aries IFE 22 Detail: Carbon and deuterium deposition and X-ray spectra for SOMBRERO and Scaled NRL Targets in 6.5m Radius C Chamber The spectra differ primarily due to the Au and knock-ons in the NRL spectrum and the 55MJ of 1.6MeV C ions in the SOMBRERO spectrum. The NRL knock-ons heat the 1st mm of the wall volumetrically. Xe density is 50 mtorr and wall temperature is 1450 ° C.

23. RRP:3/9/01Aries IFE 23 A C-C Target Chamber Can Survive, with Proper Gas Protection and Wall Temperature A series of BUCKY calculations have been performed of the response of a 6.5 m radius graphite wall to the explosions of SOMBRERO and NRL targets. Time-of-flight dispersion of debris ions is important, especially for low gas density. The gas density and equilibrium wall temperature have been varied to find the highest wall temperature that avoids vaporization at a given gas density. Vaporization is defined as more than one mono- layer of mass loss from the surface per shot. The use of Xe gas to absorb and re-emit target energy increases the allowable wall temperature substantially. 160 MJ 400 MJ W NRL 400 MJ

24. RRP:3/9/01Aries IFE 24 Region Excluded due to Radiation Damage Accumulation When Considering Target Heating and Graphite Neutron Damage, Wall Temperature and Gas Density Constraints are More Restrictive 160 MJ 400 MJ Chamber radius of 6.5 m Tumbling target

25. RRP:3/9/01Aries IFE 25 Tungsten armor has been considered. There are at least two major differences between it and graphite: melting, and x-ray stopping length

26. RRP:3/9/01Aries IFE 26 The decreased stopping length of W requires a lower equilibrium wall temperature for operation with no Xe than does Graphite, if vaporization is to be avoided. For the NRL target and no Xe, the W wall starts to vaporize for T equil of 1450C, to be compared with the 1570C for the C-C wall

27. RRP:3/9/01Aries IFE 27 The shorter x-ray deposition depths of Tungsten lead to both a higher peak surface temperature and a sharper temperature gradient. N.B.-Note Different Scales

28. RRP:3/9/01Aries IFE 28 Though the x-rays are the dominant threat, we note that the ion energy is deposited closer to the surface in a W wall than in a C wall. NRL target No Xe T_equil. = 1450C 6.5 meter radius

29. RRP:3/9/01Aries IFE 29 Done knock-on ions with finer time resolution for deposition. Deposited ion density/flux in useful form ? Have shown wall load as a function of time. Have shown more snap shots of wall temperature as a function of depth. Have studied W armor but not SiC armor. Scaled up NRL target yield to SOMBRERO levels, for density-radius parameter space scan: warning: partitioning may not remain the same. HI target have threat spectrum but haven’t done calculations yet. Have not considered Au coated chamber for NRL Au-coated target, W coating for W coated NRL target Have not considered molecular buffer gases. Have found that Vacuum chamber works for NRL target at reduced wall temperature. Need threat spectra for non-Au coated NRL target Begin work on wetted wall? Chamber Dynamics Action Items: Status March 2001

30. RRP:3/9/01Aries IFE 30 Status of Aries Dry-Wall Chamber Dynamics: Baseline C-C Composite Work is Complete Maximum wall operating temperatures have been found for C-C composite chambers at various Xe fill-gas densities. Three targets were considered; 165 MJ NRL target, 400 MJ SOMBRERO target, and scaled 400 MJ NRL target. Kr fill-gases were found to be less effective in protecting the first wall, requiring 10% more gas than Xe. Tungsten walls were found to have no advantage over C-C composites. Consistency between chamber survival, target injection and optimum neutron damage condition is difficult to achieve.