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Hydrodynamic and Symmetry Safety Factors of Hiper’s targets 35 th European Physical Society Conference on Plasma Physics Hersonissos, Crete, 9-13 june, 2008 L. Hallo, M. Olazabal-Loume, V. Drean, X. Ribeyre, G. Schurtz J.-L. Feugeas, J. Breil, Ph. Nicolai, P.-H. Maire

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HIPER specifications : 300 kJ on target – 6 kJ / beam – 50 3 At 3 : 50 beams x 15 kJ per beam at the output of the amplifier section x 50 % : conversion at 3 (70% at 2 ) 2 x 80 % : transmission 300 kJ 70 kJ 10 ps PW 300 kJ 50 beams 5 ns, 2 -3 2 1/e a m=1 m=2 m=3 m=4 Numb. laser beams and focusing section are « Free » parameters Optimisation is required

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CECLAD illumination code, J.-L. Feugeas et al, HiPer Workshop, Lisboa A 48 beams configuration is a good candidate The 48 beams configuration gives sensible : - intensity on the cone : max of intensity 26 % - intensity in the cone : max of intensity 2 % Other configurations lead to higher intensity on/in the cone.

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Legendre analysis of an “optimized” 48 beams configuration (CECLAD) Low l-modes non-uniformity appear l=12, 8 and 10 –modes are dominant Full spectrum illumination The 48 beams yield : 1) rms 0.15 % 2) energy ratio : 94% Consequences of hydrodynamic instabilities on energy gain ?

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Presentation of three possible targets within Fast Ignition HIPER framework

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All DT target with laser energy totally absorbed at n c (Atzeni’s like design) 211 µm 833 µm DT ice DT gas One sector simulation Ray tracing with focal spot shape ncnc One ray absorbed totally at critical density Same performances Adiabat (α)≈ 1.0 IFAR max ≈ 35 Imploded mass (M imp )≈ 0.28 mg Implosion velocity (V imp )≈ 2.9x10 7 cm/s Peak density (ρ peak )≈ 740 g/cm 3 Peak areal density (ρR peak ) ≈ 1.5 g/cm 2 Totally absorbed design is independant of the ablator and simplify the model validation. * Ref : Atzeni et al. POP (2007, 2008) HiPER baseline target *

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Two types of target design Adiabat (α)≈ 1.0 IFAR max ≈ 15 Imploded mass (M imp ) ≈ 0.32 mg Implosion velocity (V imp ) ≈ 2.1x10 7 cm/s Peak density (ρ peak ) ≈ 500 g/cm 3 Peak areal density (ρR peak ) ≈ 1.57 g/cm 2 Adiabat (α)≈ 1.0 IFAR max ≈ 15 Imploded mass (M imp ) ≈ 0.34 mg Implosion velocity (V imp ) ≈ 2.5x10 7 cm/s Peak density (ρ peak ) ≈ 550 g/cm 3 Peak areal density (ρR peak ) ≈ 1.50 g/cm µm 492 µm DT ice DT gas * Ref : Betti et al. POP (2006) All DT Betti’s like design * 200 kJ laser : absorbed 120 kJ 170 kJ laser : absorbed 145 kJ CHDT 6 (foam) ablator target Atzeni’s like design 70 µm 830 µm DT gas DT ice DTgas CHDT µm

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Reduced model for ablative Rayleigh- Taylor instability (isobaric) x , T e g laser aa TaTa P

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Ablation zone defined by Ablation zone defined by dimensionless parameters - optimisation procedure to determine Va, g, L 0, Fr and ’’’’’ ’ Pressure and density profiles extracted from CHIC simulations Πa = Va / √ (Pa / a) L0L0 x FA xcxc Growth rate (Betti et al Phys. Plasma (5) ) Growth rate (Betti et al Phys. Plasma (5) ) Kull (Phys. Fluids B,1989)

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2D multi- and monomode hydrodynamic simulations (CHIC)

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11 11 ns 10.4 ns 10.6 ns 10.8 ns Mode 12 analysis with the code CHIC (i) 11 ns 2a R≈10 m, R ≈ 150 m → l R/R ≈7.5 Feedthrough negligeable

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Mode 12 analysis with the code CHIC (ii) - Perturbation growth remains linear - Small energy mode redistribution after free fly phase

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Mode analysis CHIC v.s. reduced model (iii) - Reduced model is in agreement with 2D CHIC simulations - Mode 12 will dominate in spectrum analysis

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Initial perturbation: laser imprint Laser imprinting model (Goncharov et al. Phys. Plasma 2000) - Good initial guess for Ablative Rayleigh-Taylor model - Depends only on 1D flow (L 0,, V c, V bo …)

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Self-consistent perturbation growth - Dominant mode l=12, I/I 0 =5x10 -3, ~ a 0 =5x10 -6 (12/l) 1-1/2 - ART Kull-Betti (Reduced model) a/a 0 =18 - Convergence effect (Bell-Plesset) a 1 /a 0 =R foc /R ff =7.2 Model final amplitude 6.5 microns 11 ns (Richtmyer-Meshkov phase is neglected in the present work) 2 a=12 m CHIC

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Mode12, perturbations influence on density Consequence: Self-consistent model post-treatment is in agreement with CHIC’s maximum perturbed density

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Consequence on gain target (Atzeni’s design) Hypothesis: - 1D target design enables combustion - Burn fraction is expressed by f= R/( R+7) Application on Atzeni’s design -1D f 1D =0.176, Gain prop. to f -Optimised 48 beams target f op = Si hd =f op /f 1D =0.83 The 48 optimised beams (rms 0.15 %, energy ratio 94%) has 83 % of the 1D energy gain

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Betti and Atzeni (CHDT6) designs Design from Betti (massive target) V c =3.5x10 5 cm, L 0 =2x10 -5 cm, =2.3 a 1 =6.8 m (14 m), max =420 g/cm 3 R max =1.1g/cm 2, Si hd =f op /f 1D =0.13/0.183=0.71 Design from Atzeni (with CHDT6) V c =4.37x10 5 cm, L 0 =2.08x10 -5 cm, =2.33 a 1 =6.6 m (13 m), max =430 g/cm 3 R max =1.1g/cm 2, Si hd =f op /f 1D =0.13/0.18=0.72

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Energy - Power diagram Betti design, SiHD=0.71 Atzeni design, SiHD=0.83 Atzeni CHDT6 design, SiHD=0.72

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20 Conclusions and perspectives Introduction point : Multi-mode illumination perturbations from a 48 beams configuration (CECLAD) Presentation of 3 « possible » targets within Fast Ignition HIPER framework (1D simulation and gain estimates) 2D multi and monomode hydrodynamic simulations (Atzeni design) Reduced model for ablative Rayleigh-Taylor instability (2D cross-checking) Safety factor and classification of 3 « possible » targets

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