C. K. Li 25th Fusion Energy Conference St Petersburg, Russia 13 -18 - PowerPoint PPT Presentation

v shock Rebound Shock: 𝛂𝑼 i D Gradients cause 𝛂𝑸 i 3He 𝛂𝝔 differential mass flux      d d ln P e            Mass flux i D k k k ln T i ,   D p E T 3 He dx dx k T   B 𝛽 = 𝜍 𝐸 𝜍 𝑢𝑝𝑢 ~𝑔 𝐸 Classical Baro- Electro- Thermo- diffusion diffusion diffusion diffusion C. K. Li 25th Fusion Energy Conference St Petersburg, Russia 13 -18 Oct. 2014

Summary Measurements of 4 nuclear fusion products provide important information about the effects of ion diffusion on the separation of fusion fuel species ► Ratios of T 3 Hed to D 3 Hep reaction yields, and DDp to DTn reaction yields quantitatively illustrate the fusion yield anomaly in directly driven, exploding – pusher ICF implosions. ► In contrast to the case of acceleration driven isothermal atmosphere during compression burn, shock driven ion diffusions cause specie separation at shock flash. ► Barodiffusion and electrodiffusion are likely the dominant effects. ► More detailed future work will focus on quantitative study of each individual effect. This is an ongoing experiment project

Collaborators J. Frenje P. Amendt R. Betti M. Gatu Johnson C. Bellei D. Meyerhofer D. Casey H. Rinderknecht J. Soures S. Wilks M. Rosenberg F. Séguin H. Sio A. Zylstra R. Petrasso

Ablation is used to generate the extreme pressures required to compress a capsule to ignition conditions 1. Lasers or x-rays irradiate and heat the outer surface of the capsule DT ice Ablator 2. Ablation of the outer surface material accelerates the inner part of the capsule inwards DT gas DT gas 3. As capsule compresses, temperature and density increase 4. Nuclear production period (~100ps) Neutron Alpha Hot-spot ignition requires a core temperature >10 keV and a fuel-areal density exceeding ~300 mg/cm 2 4

Mainline ICF simulations are made with average-ion hydrodynamic codes 𝜖𝜍 𝜖𝑢 + 𝛂 𝜍𝐰 = 0 Single-fluid 𝜖𝑤 𝜍 𝜍 𝜖𝑢 + 𝐰 ∙ 𝛂 v v = 𝛂𝐊 × 𝐂 - 𝛂𝑄 + 𝑛 F model 𝑛 𝜖𝐊 1 1 𝑓𝑜 𝛂𝑄 𝑓 −  𝐊 𝜖𝑢 = E E + v × 𝐂 - 𝑓𝑜 𝐊 × 𝐂 + 𝑜𝑓 2 𝜍 = 𝑜 𝑗 𝑛 𝑗 + 𝑜 𝑓 𝑛 𝑓 𝜍 = 𝑜𝑗𝑛𝑗 + 𝑜𝑓𝑛𝑓 𝜍 = 𝑜𝑗𝑛𝑗 + 𝑜𝑓𝑛𝑓 P = P 𝑗 + P e P = P 𝑗 + P e P = P 𝑗 + P e 1 1 1 Averaged v = v = v = 𝜍 𝑜 𝑗 𝑛 𝑗 𝐰 𝑗 + 𝑜𝑓𝑛 𝑓 𝐰 𝑓 𝜍 𝑜 𝑗 𝑛 𝑗 𝐰 𝑗 + 𝑜𝑓𝑛𝑓𝐰 𝑓 𝜍 𝑜 𝑗 𝑛 𝑗 𝐰 𝑗 + 𝑜𝑓𝑛𝑓𝐰 𝑓 quantities over J J = 𝑓𝑜 𝐰 𝑗 − 𝐰 𝑓 J J = 𝑓𝑜 𝐰 𝑗 − 𝐰 𝑓 J J = 𝑓𝑜 𝐰 𝑗 − 𝐰 𝑓 all species 5

Fuel-shell interface Compression burn Radius Shock burn Time 500-800 ps 6

7 C. Bellei et al, Phys. Plasmas 20, 012701 (2013)

The observed ICF fusion yield anomaly has been related to the imbalance of fuel species densities in the burn region For the hydrodynamic equivalent mixtures, the scaled yields are  2 ( 3 f ) ~  D Y Y n n 2 f D  2 ~ ( 3 f )  D Y Y  p p f ( 1 f ) D D The effects of ion diffusion have been proposed to cause separation of fuel species, leading to this imbalance J R. Rygg et al., Phys. Plasmas (2008) P. A. Amendt et al ., Phys. Rev. Lett. 109 225001 (2010)

Observation of self-generated radial electric fields in an imploded capsule has been made LILAC simulations by J. Delettrez t = 0.8 ns 1.6 ns 1.9 ns 2.1ns 10 15  P e Data 10 10 10 5 E P e n e 0 (V/m) -10 5 Simulation -10 10 t = 1.9 ns -10 15  P e P e n e 0.8 ns 1.2 ns 1.4 ns C. K. Li et al ., PRL 100 225001 (2008)

Recent work by Amendt et al delineates the effects of ion diffusion in plasmas of imploded capsule Classical Barotropic Electro Thermal diffusion diffusion diffusion diffusion   d ln P eE d ln T         Mass diffusivity flux i D k ln P k k k    1 p E T   dx k T dx B            m Z T ZT   Classical diffusion coefficient k  :              1 2 e e k 1 1 1 f , Z , Z , m / m , T / T    1 2 1 2 e     m T T   2     1 Z   1 Z       1 2 1   m m    Barodiffusion coefficient k p :      1 2 k p 1 Z Z         2 1 Z 1 Z   Z 1 Z       1 1 1 2 1   m m 1 2       Z Z      Electrodiffusion coefficient k E :             1 2 k E 1 m m 1   1 2    m m  1 2    k Z Thermaldiffusion coefficient k T :       k k k 1                       p E   Z m / m 1 Z 1 Z 1 1 Z m / m  1 1 2 2 1 2 1 2 k    T Zm k 1     1 P. A. Amendt et al ., PRL. 109 225001 (2010)           m 1 Z 1 m / m 2 1 2 PRL, accepted (2012)

NIF hot-spot ignition simulation OMEGA exploding pusher simulation Rev 5 implosion 1000 SiO 2 [2.3 μ m] from A. Zylstra (HYADES) from H. Robey CH [60 μ m] D 3 He 800 DT ice ρ gas = 0.3 Radius (µm) DT vapor Radius (µm) mg/cm 3 ρ gas = 0.4 600 mg/cm 3 400 M shock ~ 10-50 M shock ~ 10-50 200 λ ii ~ 100 μ m λ ii ~ 100 μ m 0 16 18 20 22 Time (ns) Shock phase characterized by high temperature, moderate density, large λ ii , kinetic effects 11

Key measurements: - DD and D 3 He yields - Burn-averaged T i - DD and D 3 He burn histories - DD and D 3 He burn profiles Implosion - Fuel ρ R (ion density) - X-ray self-emission images (R) Compact proton spectrometers - Scattered light 12

The first spectra of 4 nuclear reactions are simultaneously measured from a single capsule implosion that filled with DT 3 He gas 2.5 m m SiO 2 15 atm 5.E+10 DT 3 He T- 3 He d Shot 14972 (X50) D-T alpha Yield / MeV D- 3 He p (X0.002) D-D p 0.E+00 0 3 6 9 12 15 18 Energy (MeV)

The Y T3HeD /Y DHep and Y DDn /Y DT yield ratios are deviated from the predictions, qualitatively indicating the fuel stratification 0.03 T 3 HeD/D 3 Hep 0.02 0.01 DDp/DT 0 0 5 10 15 20

While DD yields relative to the DT yield are lower than expected, TT reaction yields are higher than expected (assuming a constant density ratio f t /f d) x10 -3 x10 -3 8 6 6.E-03 8.E-03 data 5 5.E-03 6 6.E-03 4 YDDp/YDT 4.E-03 Y TT /Y DT Y DD /Y DT YTT /YDT LILAC LILAC 3 4 3.E-03 simulation 4.E-03 simulation 2 2.E-03 Expected 2 2.E-03 1 1.E-03 data 0 0 -1.E-17 0.E+00 0 5 10 15 0 5 10 15 Temperature [keV] Temperature [keV] D. T. Casey et al, Phys. Rev. Lett. 108, 075002 (2012).

16 Hong Sio et al ., to be submitted (2014)

DD-p or D 3 He-p image Exploding pusher 3-MeV DD-p & Penumbra 15-MeV D 3 He-p proton tracks / cm 2 Average Radial Burn Profiles Tracks/cm 2 Reactions (µm -3 ) Reactions (µm -3 ) 3x10 4 3x10 4 0.4 mg/cm 3 3E+4 3E+4 2.3 mg/cm 3 (Kinetic-like) (Hydro-like) 2E+4 2E+4 2x10 4 2x10 4 D 3 He D 3 He 1E+4 1E+4 DD DD 1x10 4 1x10 4 0E+0 0E+0 0 0 0 50 100 150 0 50 100 150 Radius (µm) Radius (µm) 17 Séguin et al ., RSI (2004), PoP (2006)

0.4 mg/cm 3 (kinetic regime) Simulated brightness profiles Measured brightness profiles 2x10 6 2.E+06 Proton fluence [1/Area] D 3 He w/ Diffusion (Yieldx100) Particles / μ m 2 Hydro D 3 He-p only 1x10 6 1.E+06 DD 0 0.E+00 100 0 0 50 100 Radius [ m m] Radius (µm) These results further demonstrate that ion diffusion is substantial in the long- λ ii implosio Simulations by P. Amendt, LLNL 18

Summary Measurements of 4 nuclear fusion products provide important information about the effects of ion diffusion on the separation of fusion fuel species ► Ratios of T 3 Hed to D 3 Hep reaction yields, and DDp to DTn reaction yields quantitatively illustrate the fusion yield anomaly in directly driven, exploding – pusher ICF implosions. ► In contrast to the case of acceleration driven isothermal atmosphere during compression burn, shock driven ion diffusions cause specie separation at shock flash. ► Barodiffusion and electrodiffusion are likely the dominant effects. ► More detailed future work will focus on quantitative study of each individual effect. This is an ongoing experiment project