Multi-material simulation of laser-produced plasmas by Smoothed Particle Hydrodynamics A. Sunahara France /5-11. Institute for Laser Technology, Japan Institute of Laser Engineering, Osaka Univ.

Co-workers S. Misaki K. Kageyama Dr. K. Tanaka Dr. T. Johzaki

Introduction and Motivations Simulation for Laser produced plasmas Droplet Long scale expansion Connection to DSMC* simulations Simulation for inertial confinement fusion Smoothed Particle Hydrodynamics (SPH) may be suitable for the above calculations. (multi-materials) (large deformation) (large dynamic range in space) (particle to particle) * Direct Simulation Monte-Carlo

ICF examples CH DT CH Au Multi-materials are used for the ICF target.

0.3 mm optical back light image EUVimage Tin droplet Diameter mm (36microns) 1.06 micron wavelength Laser Tin droplet is irradiated by the laser for EUV emission, where large deformation occurs. Simulation of droplet

YAG Laser (Wavelength:355 nm,Pulse:6 ns, Frequency;10 Hz) Plumes intersect each other in 90. The point of intersection of two ablation plumes Tungsten target Tungsten plumes Carbon plumes Carbon target Laboratory Experiments on Aerosol Formation by Colliding Ablation Plumes, LEAF-CAP has been proposed for reactor wall study. 5cm 1.5cm 0.5cm YAG Laser (line focused) Solid target (Carbon, Tungsten etc) Target Close-up View 0

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

SPH was developed by Lucy 1977, Gingold and Monagahan 1977 for astrophysics problems. Smoothed Particle Hydrodynamics (SPH) 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. SPH is fully Lagrangian particle method, which has advantage for the problem having a large dynamic range in space.

2h Radius of influence W(r-r’,h) r h area = 1 r r’r’ x= r h Kernel function is differentiable, non-negative and symmetric. Integration over x=r/h is 1. approximation

Governing equation Continuity equation Velocity equation Internal energy equation Change of the position EOS

Kernel Artificial viscosity Smoothing length piecewise quintic

Laser ray Electron density Velocity equation of the laser ray Change of the position Electron density gradient : critical density Deposition of laser power

dr t1t1 t2t2 t3t3 Laser ray smoothing radius of the ray h ray P(x=r) Smoothing length h ray = factor * wavelength of the laser = constant with time estimation of, r ray n+1 = r ray n + v ray * Δtv ray n+1 = v ray n + a ray * Δt Δt=Δr/c 4th order Runge-Kutta Procedures estimation of for each ray, each position factor is set to be 5 X4

2D Plane foil (ideal gas γ=1.67) ρ=1000kg/m 3 =1g/cm 3 100μm X10μm t 1.06μm wavelength laser I L = W/cm 2 Flat top 50μm 100μm Laser Δt= sec

2D Plane Density (kg/m 3 ) (m)

2D axis-symmetry axis symmetry mirror particles copy ~ 2 max(h i ) V // mirror = V // i V mirror = -V i X // mirror = X // i X mirror = -X i ρ mirror = ρ i m mirror = m i h mirror = h i e mirror = e i mirror particles summation of deposited energy P dep = P dep + P mirror dep original particles axis symmetry Laser 1 2 return

foil (ideal gas γ=1.67) ρ=1000kg/m 3 =1g/cm 3 100μm X10μm t 1.06μm wavelength laser I L = W/cm 2 Flat top 50μm 100μm Laser Δt= sec 2D axis-symmetry Half (upper) side is only calculated.

2D axis-symmetry Density (kg/m 3 ) (m)

2D Plane 2D axis-symmetry (m) axis symmetry

2D axis-symmetry (cylinder) foil (ideal gas γ=1.67) ρ=1000kg/m 3 =1g/cm 3 60μm Φ droplet 1.06μm wavelength laser I L = W/cm 2 Flat top 60μm Φ Δt= sec

2D axis-symmetry (cylinder) Density (kg/m 3 ) (m)

DSMC Direct Simulation Monte-Carlo was developed by Bird. ν = n σ v neutral-neutral collision Coulomb collision (ion-ion) ν = v3v3 4 π n ((Ze) 2 /m) 2 lnΛ if they collide Cell (*) 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, (1977) **

Group1 Group2 drift velocity : 10 6 cm/s X Y 0.75cm 0.39cm v Z X 3D image particle : Carbon, Tungsten (neutral, cluster, ion(+1,+3)) density : /cm 3, /cm 3 initial temperature : 1eV drift velocity : 10 6 cm/s number of particle : 35×10 4 calculating area : 3cm,3cm,3cm cell : 10 6 Simulation condition of direct simulation monte-carlo (DSMC) estimated from experimental observations

炭素の中性粒子 Carbon neutral-neutral interaction n=10 13 cm -3 neutral-neutral (m) Collisionless (m) *)

一価の炭素イオン三価の炭素イオン Carbon ion-ion interaction n=10 13 cm -3 ion(+1)-ion(+1) Collisional ion(+3)-ion(+3) Collisional (m)

Tungsten neutral-neutral interaction n=10 13 cm -3 炭素の中性粒子 neutral-neutral Collisionless (m)

Tungsten ion-ion interaction n=10 13 cm -3 一価の炭素イオン三価の炭素イオン ion(+1)-ion(+1) Collisionless ion(+3)-ion(+3) Collisionless (m)

10 13 cm cm -3 neutral X ion(+1) XX ion(+3) X Tungsten cm cm -3 neutral X ion(+1) ion(+3) Carbon Summary of simulations collisional X collisionless 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.