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Multiphase code development for simulation of PHELIX experiments

M.E. Povarnitsyn, N.E. Andreev, O.F. Kostenko, K.V. Khischenko and P.R. Levashov

Joint Institute for High Temperatures RAS, Moscow, Russiapovar@ihed.ras.ru

EMMI WorkshopGSI, Darmstadt, Germany

22 November, 2008

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• Motivation• PHELIX setup parameters and targets• Model and problems of realization

— Multiscale and multistage tasks

— Adaptive mesh refinement

— Summary of our model• Preliminary results• Conclusions and future plans• Discussion

Outline

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Setup parameters & tasks

= 1.053 mkm, ~ 500 fs 10 ns,E ~ 200 500 J, F ~ 1015 1018 W/cm2

PHELIX

Hybrid: metals, dielectrics

Foils & clusters

Actual questions:• warm dense matter• increase absorption efficiency• high temperature and ionization• radiation loss

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Time & space scales for PHELIX setup

time, fs

pulse duration

el-ion exchange

ionization rate

103

100

106

laser frequency

laser wavelength

space, nm

plasma cloud

cluster size

skin layer

103

100

106

foil thickness

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Limitations of modeling

QMC ~ 100 particles

MD ~ 1 mkm3 (~105 processors, Blue Gene etc.)

Hydrodynamics – real size systems, but…

…kinetic models

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Multiscale problem

1 mkm

1000 mkm

100

0 m

km

Time steps ~ 105

Uniform mesh2D ~ 106 108 cells3D ~ 109 1012 cells

AMR2D ~ 105 107 cells3D ~ 107 1010 cells

Expecting AMR profit2D ~ 10 times

3D ~ 100 times

PHELIX

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Adaptive mesh refinement

Refinement is appliedin zones of interest (interfaces, high gradientsof parameters) while the restof domain is resolvedon a coarse mesh

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Advance in time (3 levels of AMR)

Δt

Δt /2

Δt/2

Δt /4

Δt /4

Δt /4

Δt /4

lev0 lev1 lev2

t

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Multi-material Godunov’s framework with AMR

Pb powder on Al at 5 km/s Grid: 4x106 cells,104 Pb particles (0.1 mm)12 proc, 10 hours

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Multiscale problem

Time steps ~ 105

Uniform mesh2D ~ 106 108 cells3D ~ 109 1012 cells

AMR2D ~ 105 107 cells3D ~ 107 1010 cells

Expected AMR profit2D ~ 10 times

3D ~ 100 times

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Two-temperature multi-materialEulerian hydrodynamics

Basic equations Mixture model

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Interface reconstruction algorithm

(a) (b)

(c) (d)

(e)

D. Youngs (1987)

D. Littlefield (1999)

Specific corner and specific orientation choice makes only five possible intersections of the cell

Symmetric difference approximationor some norm minimization is usedto determine unit normal vector

j+1

j

j-1

i-1 i i+1

U*t

U*

3D2D

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Two-temperature semi-empirical EOS

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

l+g

(s)

(g)

(s+l)

(l)

Te

mp

era

ture

, kK

Al

s

lg

s+g

s+l

CP

bnunstable

sp

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Ablation of metal targets by fs pulses

M. E. Povarnitsyn et al. // PRB 75, 235414 (2007).M. E. Povarnitsyn et al. // Appl. Surf. Sci. 253, 6343 (2007)M. E. Povarnitsyn et al. // Appl. Surf. Sci. (in press, 2008)

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Extra effects in hot plasma

)(3

ieeei

Bei TTn

m

mkQ

20 |/|}Im{ LLL EEkIQ

hoteBF

mete r

mTk

,

/,min

0

2

23

62/1

3

16

3

2e

eBrad Zn

mc

e

m

TkQ

eqieie Z

ZnnkS 1

12/12/3

3 1exp

eee

Hi T

I

T

I

T

I

I

IAk

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1. Multi-material hydrodynamics (several substances + phase transitions)

2. Two-temperature model (Te Ti)

3. Two-temperature equations of state (Khishchenko)

4. Wide-range models of el-ion collisions, conductivity, heat conductivity (, , )

5. Model of laser energy absorption (electromagnetic field)

6. Model of ionization & recombination (metals, dielectrics)

7. Model of radiation loss (bremsstrahlung + spectral radiation)

8. Parallel realization with AMR

Model & code features

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1. Multi-material hydrodynamics (several substances + phase transitions)

2. Two-temperature model (Te Ti)

3. Two-temperature equations of state (Khishchenko)

4. Wide-range models of el-ion collisions, conductivity, heat conductivity (, , )

5. Model of laser energy absorption (electromagnetic field)

6. Model of ionization & recombination (metals, dielectrics)

7. Model of radiation loss (bremsstrahlung + spectral radiation)

8. Parallel realization with AMR

Model & code features

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Interaction with Al foil

0 3 9 12

t, ns

I, a.u.

6

single-proc

problem domain

single-proc

I0 = 5x1011 W/cm2, =1.054 mkm, thickness = 2 mkm, Gauss r0 = 6 mkm

Single-processor mode, uniform mesh

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Interaction with Al foil

I0 = 5x1011 W/cm2, =1.053 mkm, thickness = 2 mkm, Gauss r0 = 6 mkm

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Interaction with Cu clusters (ne/ncr)

#14

[g/cc] 2.8

Te [ev] 620

Ti [ev] 75

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.2

0.4

0.6

0.8

1.0

I [a

.u.]

time [ps]

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

4000 50 100 150 200 250 300 350 400

y, n

m

x, nm

1.0E-3

0.010

0.10

1.0

10

= 1.053 mkm

I0 = 1017 W/cm2

= 500 fs

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Interaction with Cu clusters (ne/ncr)

#14 #6

[g/cc] 2.8 1

Te [ev] 620 970

Ti [ev] 75 60

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.2

0.4

0.6

0.8

1.0

I [a

.u.]

time [ps]

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

4000 50 100 150 200 250 300 350 400

y, n

m

x, nm

1.0E-3

0.010

0.10

1.0

10

= 1.053 mkm

I0 = 1017 W/cm2

= 500 fs

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Conclusions and Outlook

• Simulation results are sensitive to the models used: absorption, thermal conductivity, electron-ion collisions, EOS, etc…

• Interaction with cluster targets can produce warm dense matter with exceptional parameters

• Adaptive mesh refinement can give an essential profit in runtime and work memory used

• For 2D and 3D simulation of PHELIX experiments we develop hydro-electro code with AMR and in parallel

• Multidimensional calculations with AMR and in parallel are in sight

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Discussion