Dual Nuclear Shock Burn:

Transcription

1 Dual Nuclear Shock Burn: Experiment, Simulation, and the Guderley Model J.R. Rygg, J.A. Frenje, C.K. Li, F.H. Séguin, and R.D. Petrasso MIT PSFC J.A. Delettrez, V.Yu Glebov, D.D. Meyerhofer, and T.C. Sangster UR LLE FSC Summer School - Berkeley, CA Aug 11, 5

2 Summary Experimental measurements of dual nuclear burn histories during ICF implosions gives yields and timing of shock burn Hydrodynamic codes (such as LILAC) often have trouble matching experimental shock data Guderley s analysis of a self-similar collapsing shock can be used to directly model the dual burn histories The Guderley analysis matches 3 experimental observables with one parameter Guderley analysis models later times best, when the shock front has decoupled from its generating boundary J. Ryan Rygg FSC HEDP summer school Aug 11, 5

3 ICF implosion timeline µm CH 45 µm Initial Target Shock Burn Compression Burn D + 3 He gas (18 atm) Power (TW) 1 Laser Pulse (E = 3 kj) D 3 He burn rate (shot 9835) t (ns) nuclear burn rate (s -1 )

4 Dual burn histories are measured using two distinct nuclear reactions D + 3 He 4 He (3.6) + p (14.7 MeV) D + D 3 He (.8) + n (.45 MeV) 1-15 Thermal Reactivity Time History (OMEGA Shot 9835) 1 <σv> (cm 3 /s) DD-n D 3 He 1 18 D 3 He burn rate (s -1 ) shock compression DD-n burn rate (s -1 ) Ti (kev) Time (ns)

5 Hydrodynamic codes (such as LILAC) have trouble matching experimental shock data Motivation for this work: Shock yield Shot 9835 DD-n D 3 He shock peak D 3 He burn history time (ps) shock duration Experiment.8e8 3.43e LILAC (f =.6).e9 6.15e Ratio (yields) 16% 186% Difference (times) Exp. Error ± 5% ± 15% ±5 ±15 The burn at shock collapse: has been demonstrated to be unaffected by turbulent mix depends only weakly on low-mode drive nonuniformities

6 Guderley collapsing shock Shock front shocked gas re-shocked gas unshocked gas An imploding strong shock converges on the center and rebounds, reshocking previously shocked material

7 Self-similar representation of fluid flow: Self-similar flow Where: α is the self-similarity exponent, uniquely determined by choice of γ. the physical scale is determined by choice of r, t, ρ. shocks discontinuities must lie on curves of constant ξ. A self-similar flow is invariant to a change in scale. In other words, if one changes the "distance" scale by some amount, then the flow variables still have the same "shape", provided they are scaled by a suitable amount Basic advantage of self-similar analysis: problem depends on one coordinate instead of two ) ( ), ( ) ( ), ( ) ( ), ( / / ), ( ξ ρ ξ ρ ρ ξ ξ α Z t r t r P G t r U t r t r u t t r r t r = = = = pressure: flow velocity: density: coordinate:

8 Self-similar solution, γ = 5/3 (α.688) Flow state along particle streamline: 3 Density 1.5 shock (ξ = ξ s ) ρ / ρ 1 r / r 1.5 reshock T m u shock reshock Temp. particle streamline t / t P ρ u Pressure u =.688 r /t = shock speed at {r, t } t / t

9 Flow state before and after shock collapse 3 t / t = -1 3 t / t = +1 ρ / ρ 1 ρ / ρ T m u. T m u P 1 P ρ u.5 ρ u r / r r / r

10 Dual burn history results of Guderley model.e+18 Imploding shock with ξ s = 35 t = 1 ns r = ξ s [µm] ρ = 18 atm D 3 He gas 1.E+18 (s -1 ) 5.E+17 DD-n burn D 3 He burn Integrated nuclear burn until reshock reaches particle that started at 3µm. (After which compression burn starts) Y DDn =.4e8 Y D3He = 3.86e7 <T i > DDn = 4.5 kev <T i > D3He = 14. kev.e t (ns)

11 Instrument response smoothing Imploding shock with ξ s = 35.E+18 DD-n: 4 ps gaussian smoothing 1.E+18 (s -1 ) DD-n burn D 3 He: 5 ps gaussian smoothing 5.E+17 D 3 He burn Broadened D 3 He burn duration: FWHM D3He = 86 ps.e t (ns)

12 Yield and burn duration vs. shock strength 1.E+11 Yield vs ξ s 5 Burn duration vs ξ s (after 5 ps broadening) Y D3He FWHM D3He 1.E+1 Y DDn 1.E+9 Yield 1.E+8 15 FWHM (ps) 1 1.E E ξ s ξ s

13 Three experimental observables are matched with one shock strength 1.E+11 Yield vs ξ s 5 Burn duration vs ξ s (after 5 ps broadening) Y D3He FWHM D3He 1.E+1 Lilac (9835) Y DDn 1.E+9 Yield 1.E+8 Exp. (9835) 15 FWHM (ps) 1 Lilac (9835) 1.E+7 5 Exp. (9835) 1.E ξ s ξ s

14 The model does well during the burn phase, but the shock does not extrapolate well to early times r (µm) Original Shell Shock (ξ s = 35) D 3 He burn, ξ s =35 D 3 He burn (exp) t (ns)

15 Future work Improvement on the Guderley model should be possible by including additional physics: Thermal conduction Kinetic effects Two coalescing shocks Two species plasma (ion and electron) Evaluation of these additional physics effects can be done by direct comparison to experimental data from a wide range of implosions by varying implosion parameters, including: Target shell thickness Target fill pressure Target fuel composition Driver laser energy

16 References and Related work 1. V.G. Guderley, Starke kugelige und zylindrische Verdichtungsstöße in der Nähe des kugelmittelpunktes bzw. der Zylinderachse, Luftfahrtforschung 19, pp 3-31 (194).. R.B. Lazarus, Self-similar solutions for converging shocks and collapsing cavities, SIAM J. Numer. Anal. 18: (1981). 3. Zeldovich and Raizer, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, pp , Dover Publications, New York, (). 4. Atzeni and Meyer-ter-Vehn, The Physics of Inertial Fusion, pp 17-19, Oxford University Press, New York, (4). 5. E.B. Goldman, Numerical Modeling of Laser Produced Plasmas: The Dynamics and Neutron Production in Dense Spherically Symmetric Plasmas, Plas. Phys. 15, pp (1973). 6. P. Reinicke and J. Meyer-ter-Vehn, The point explosion with heat conduction, Phys. Fluids A 3 No 7, pp (1991). 7. A. Kemp, J. Meyer-ter-Vehn, and S. Atzeni, Stagnation Pressure of Imploding Shells and Ignition Energy Scaling of Inertial Confinement Fusion Targets, Phys. Rev. Lett. 86 No 15, pp (1).