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Multi-material simulation of laser-produced plasmas by Smoothed Particle Hydrodynamics A. Sunahara Institute for Laser Technology, Japan Institute of Laser Engineering, Osaka Univ. [email protected], France 2011 9/5-11. Co-workers • S. Misaki • K. Kageyama • Dr. T. Johzaki • Dr. K. Tanaka Introduction and Motivations Simulation for inertial confinement fusion (multi-materials) Simulation for Laser produced plasmas Droplet (large deformation) Long scale expansion (large dynamic range in space) Connection to DSMC* simulations (particle to particle) *Direct Simulation Monte-Carlo Smoothed Particle Hydrodynamics (SPH) may be suitable for the above calculations. ICF examples Multi-materials are used for the ICF target. Au CH CH DT 0.3 mm Tin droplet Diameter 0.036 mm (36microns) 1.06 micron wavelength optical back light image EUVimage 0.3 mm Laser Simulation of droplet Tin droplet is irradiated by the laser for EUV emission, where large deformation occurs. Laboratory Experiments on Aerosol Formation by Colliding Ablation Plumes, LEAF-CAP has been proposed for reactor wall study. 0 Plumes intersect each other in 90. YAG Laser (Wavelength:355 nm,Pulse:6 ns, Frequency;10 Hz) The point of intersection of two ablation plumes Tungsten plumes Carbon plumes Target Close-up View 0.5cm 1.5cm YAG Laser (line focused) 5cm Tungsten target Solid target (Carbon, Tungsten etc) Carbon target In order to model intersecting laser-produced plumes, we have conducted two types of simulations. • Radiation hydrodynamic simulation for generation of the plume and its dynamics • Direct simulation Monte Carlo (DSMC) for simulating the intersecting two plumes Outline • Introduction and motivations • Smoothed Particle Hydrodynamics • Laser ray-trace • Direct Simulation Monte Carlo • Summary and conclusions • Future prospectives Smoothed Particle Hydrodynamics (SPH) SPH was developed by Lucy 1977, Gingold and Monagahan 1977 for astrophysics problems. SPH is fully Lagrangian particle method, which has advantage for the problem having a large dynamic range in space. SPH is based on the δ-function theory. W is the finite size smoothing kernel with radius h. Hydro equation can be written by summation of each contribution. Radius of influence x= r’ r h 2h r Kernel function is differentiable, non-negative and symmetric. Integration over x=r/h is 1. W(r-r’,h) area = 1 approximation x= r h Governing equation Continuity equation Velocity equation Change of the position Internal energy equation EOS Kernel piecewise quintic Smoothing length Artificial viscosity Laser ray Electron density Electron density gradient Velocity equation of the laser ray : critical density Change of the position Deposition of laser power t2 t3 t1 Laser ray dr smoothing radius of the ray hray P(x=r) Smoothing length hray = factor * wavelength of the laser = constant with time Procedures factor is set to be 5 for each ray, each position estimation of , rrayn+1 = rrayn + vray * Δt vrayn+1 = vrayn + aray * Δt estimation of 4th order Runge-Kutta X4 Δt=Δr/c 2D Plane 100μm foil (ideal gas γ=1.67) ρ=1000kg/m3=1g/cm3 100μm X10μmt 50μm Laser 1.06μm wavelength laser IL = 1012 W/cm2 Flat top Δt=10-12sec 2D Plane Density (kg/m3) 2D axis-symmetry 1 V// mirror = V// i V mirror = -V i ρ mirror = ρ i m mirror = m i X// mirror = X// i e mirror = e i X h mirror = h i mirror = -X i axis symmetry copy 2 mirror particles ~ 2 max(hi) original particles Laser axis symmetry return mirror particles summation of deposited energy Pdep = Pdep + Pmirror dep 2D axis-symmetry 1.06μm wavelength laser IL = 1012 W/cm2 Flat top 100μm 50μm Laser Half (upper) side is only calculated. foil (ideal gas γ=1.67) ρ=1000kg/m3=1g/cm3 100μm X10μmt Δt=10-12sec 2D axis-symmetry Density (kg/m3) 2D Plane 2D axis-symmetry axis symmetry 0 -0.0002 -0.0004 0.0005 2D axis-symmetry (cylinder) 1.06μm wavelength laser IL = 1012 W/cm2 Flat top 60μmΦ foil (ideal gas γ=1.67) ρ=1000kg/m3=1g/cm3 60μmΦ droplet Δt=10-12sec 2D axis-symmetry (cylinder) Density (kg/m3) DSMC * Direct Simulation Monte-Carlo was developed by Bird. if they collide neutral-neutral collision ν=n•σ•v Coulomb collision (ion-ion) ν= Cell 4π n 2 2 ((Ze) /m) lnΛ v3 (*) G. A. Bird, “Molecular gas dynamics and the direct simulation of gas flows”, Clarendon Press, (1994) (**) T. Takizuka and H. Abe, Journal of Computational Phys. 25, 205-219(1977) ** Simulation condition of direct simulation monte-carlo (DSMC) Y Group2 3D image Z Group1 0.39cm X 0.75cm drift velocity : 106cm/s X particle : Carbon, Tungsten (neutral, cluster, ion(+1,+3)) density : 1013/cm3, 1015/cm3 estimated from experimental observations initial temperature : 1eV drift velocity : 106cm/s number of particle : 35×104 calculating area : 3cm,3cm,3cm cell : 106 Carbon neutral-neutral interaction (m) 炭素の中性粒子 neutral-neutral Collisionless (m) *) n=1013cm-3 Carbon ion-ion interaction (m) n=1013cm-3 (m) ion(+1)-ion(+1) 一価の炭素イオン Collisional (m) ion(+3)-ion(+3) 三価の炭素イオン Collisional (m) Tungsten neutral-neutral interaction (m) 炭素の中性粒子 neutral-neutral Collisionless n=1013cm-3 Tungsten ion-ion interaction (m) n=1013cm-3 (m) ion(+1)-ion(+1) 一価の炭素イオン Collisionless (m) ion(+3)-ion(+3) 三価の炭素イオン Collisionless (m) Summary of simulations collisional X collisionless Carbon Tungsten 1013cm-3 1015cm-3 neutral X ion(+1) ion(+1) X ion(+3) ion(+3) X neutral X 1013cm-3 1015cm-3 X Simulated results successfully reproduced the experiments. Summary and conclusions We have developed the simulation codes for the laser ablated plasma by SPH and DSMC. We tested laser energy deposition with ray-tracing. We demonstrated simulation for CH plate and droplet. We showed DSMC simulation for C and W. Future prospectives Detailed comparison with other scheme, and solution. Installation of Electron conduction and radiative transfer Combination of SPH and DSMC.