Unstructured grids 3D simulations of imploding cylindrical laser targets GIFIFP ETSIAUPM Rafael...

Unstructured grids

3D simulations of imploding cylindrical laser targets

GIFIFP ETSIA UPM

Rafael RamisUniversidad Politécnica de Madrid

7th Direct Drive and Fast Ignition Workshop, May 3-6, 2009, Prague, Czech Republic

Hydro code MULTI3D

●Developed from MULTI1D (1986) and MULTI2D (1992)●Modular structure●Hydrodynamics (2007)●Beam deposition (2008)●Heat transport (2009) + applications●AEL hydrodynamics (?)●Radiation (?)●Nuclear Reactions (?)

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R. Ramis, J. Meyer-ter-Vehn, and J. Ramírez, Comp. Phys. Comm. (2009)doi: 10.1016/j.cpc.2008.12.033

R. Ramis, R. Schmaltz, and J. Meyer-ter-Vehn, Comp. Phys. Comm. 49 (1988) 475


MULTI3D uses a non-structured grid composed of tetrahedrical cells.The core of the code are the conectivity tables are used to define the computational domain

Table of conectivities cell-to-node

Table of coordinates

Unstructured gridsGIFIFP UPM / ETSIA


Table of conectivities cell-to-node

Table of coordinates

Unstructured grids

Nodes

Cell

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MULTI3D uses a non-structured grid composed of tetrahedrical cells.The core of the code are the conectivity tables are used to define the computational domain


Lagrangian hydrodynamics

The lagrangian algorithm uses a staggered grid. Velocities are defined at nodes while pressures, densities

and internal energies are defined at cells. Mass, energy and momentum (linear and angular) are preserved.

External source

From tables from SESAME library or generated by MPQEOS

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Ray tracing

Energy beams (laser or ions) are decomposed into a large number of “beamlets”. Each “beamlet” carries

ni particles with energy e

i. Output values n

i and e

i of at cell exit are computed from input values,

distance x, and cell thermodynamical values k, Z

k, A

k and T

k

Refraction currently not implemented

Ion beam

laser

Ray tracing requires the numbering of interfaces between cells, and the creation of cell-to-interface andcell-to-cell conectivity tables.

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Ion stopping power modelGIFIFP UPM / ETSIA


Laser absporption model

(The condition log >2 is forced)

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Application to Proton Fast Ignition

hydro+beam packages have been validated by running benchmark problems (currently in progress) and by comparison with other hydro codes (DUED).

M Temporal, R Ramis, J J Honrubia and S Atzeni, Plasma Phys. Control. Fusion 51 (2009) 035010 (10pp)

A precompressed DT sphere (r=60m and =500 g/cm3) is ignited by a composite proton pulse (T

p= 4 Mev, d=500 m, and 1 MeV<e

p<40 MeV)

Pulse #1 : 1 kJ (total) Pulse #2 : 7 kJ (delay=30 ps)

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Application to Proton Fast IgnitionGIFIFP UPM / ETSIA

Temperature

Density

Density at Z=52 m

Time = 0

The effect of a finite number of beams to achieve high compression has been assesed by MULTI3D simulations (only the first pulse has been considered)



Temperature

DensityTime = 6 ps



Density at Z=52 m


Temperature

DensityTime = 10 ps



Density at Z=52 m


Temperature

DensityTime = 16 ps



Density at Z=52 m


Temperature

DensityTime = 20 ps



Density at Z=52 m


Temperature

DensityTime = 28 ps



Density at Z=52 m


Temperature

DensityTime = 33 ps



Density at Z=52 m


Temperature

DensityTime = 36 ps



Density at Z=52 m


M Temporal, R Ramis, J J Honrubia and S Atzeni, Plasma Phys. Control. Fusion 51 (2009) 035010 (10pp)

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● Ignition calculations have been done by using the 2D code DUED that includes all neccesary physics (hydro + heat + radiation + burning + alpha heating).

● Axial symmetry is assumed● Ignition occurs as a result of the

synergetic action of the shocks

generated by proton energy

deposition

Density and temperature contours from DUED


The agreement between both codes (MULTI3D and DUED) is

“perfect” for N=∞ and thermal conductivity in DUED is switched out.

Colors (MULTI)Lines (DUED)

Density contours

Compressed mass

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Heat transfer

The heat tranfer algorithm uses a node defined temperatures and energies. Thermal flux is assumed

uniform inside each cell and discontinuous at interfaces. The integral of these discontinuities is

distributed in equal parts between adjacent nodes.

The algorithm is described in:

R. Ramis, J. Meyer-ter-Vehn, and J. Ramírez, Comp. Phys. Comm. (2009), doi: 10.1016/j.cpc.2008.12.033

The coupling with hydrodynamic algoritm (where energies are defined at cells) require interpolation of internal energies at cells to compute conductivities and pressures, and distribution of deposition terms (hydro work and beams) to nodes.

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Linear heat transfer

Initial condition: random temperature

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Time = 0

Isolated body with constant conductivity and heat capacity


Linear heat transferGIFIFP UPM / ETSIA

Time = 1




Time = 2




Time = 3




Time = 4




Time = 5




Time = 6




Time = 7




Time = 8




Time = 9




Time = 10




Time = ∞




For small wavenumbers:

You see here the mode n=1(modes with n>1 damp fasterand mode n=0 is not visible)

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To obtain mode n=2 one has to remove mode n=1 from the initial condition and integrate again until t >>1.

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n=1




n=1 n=2

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To obtain mode n=3 one has to remove modes n=1 and n=2, and so on ...

n=1 n=2 n=3

n=4 n=5 n=6

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Time integration by SSI method

Explicit: unstable for large t

The algorithm is described in:

R. Ramis, J. Meyer-ter-Vehn, and J. Ramírez, Comp. Phys. Comm. (2009), doi: 10.1016/j.cpc.2008.12.033

Implicit: stable, requires to solve a system of equations

MIxed: energy error

SSI: energy error coupled in the next time step

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Non-linear heat transfer

Test case: evolution of a 3D non-linear thermal wave (non dimensional units)

Isolated walls

T=1 forced here

T=0 initially

~ T5/2

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Non-linear heat transfer

Test case: evolution of a 3D non-linear thermal wave (non dimensional units)

~ T5/2

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Isolated walls

T=1 forced here

HiPER experiment at Vulcan

Short pulse (~500J, 10ps) fired into imploded column of CH plasma

Fluorescent emission from Cu tracer layers / Cu particles in foam monitored by spectroscopy and imaging

Pre-heater beam conditions diagnosed by Ti k-alpha radiography and absorption spectroscopy (foam doped with Cl)

Implosion pulse ~ 80J per beam, 1ns

Sept/Dec 2008 - Hot electron transport in cylinder Experiment

PI's M. Koenig and D. Bataniwith

LULI, RAL, CELIA, U-Milan, U-Oxford, LLNL, UPM, U-Pisa

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4 x 70 J 1 ns 0.35 m

Supergaussian cross sectionwith between 70 and 140 m

200 m diameter200 m lenghtpolymide foam(100 mg/cm3 )

30 m polymide shell

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CHIC calculations

Equal beam energy

Final conditions ~ 5 g/cc and ~50 to 100eV in 20 to 40m diameter column (dependent upon initial foam density)

20 % lack

Longitudinal 2D simulations

Cross section 2D simulations

Perfect slide

HiPER experiment at VulcanGIFIFP UPM / ETSIA



nodes = 15585cells = 80556beamlets = 1152

CPU = 5 hourssteps = 19509



x

y z

Temperature (0 to 15 MK) Foam geometry + laser deposition zone

MULTI 3D simulations of cylindrical implosion phaseMULTI 3D simulations of cylindrical implosion phase

GIFIFP UPM / ETSIA


x

y z





Now, consistent longitudinal an cross profiles can be obtained from 3D simulations(Figures for =140 m)


Grid asymmetriesGIFIFP UPM / ETSIA


Cubic elements (quadrangles)

preserve RZ symmetry

Numerical asymmtries are inherent to discretization using tetrahedrical elements (triangles)

“crests”

“grooves”



Alternating two modes of triangle division preserves XY symmetry, but peaks appear



In 2D geometry one can use two grids simulaneously, and syncronize node quantitiesafter each time step.

As in other lagrangian schemes, four pressures are defined inside a given quadrangle

+ =



In 2D geometry each hexahedron can be divided in five tetrahedra in two different ways:

Ten pressures are defined inside a given hexahedron



Each hexahedron divided in 6 tetrahedra Each hexahedron divided in 5+5 tetrahedra

The grid assymetries disappears with this method

OLD ALGORITHM NEW ALGORITHM

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Implosion symmetry

Beam radius:=80 m

Cylinder radius: r=130 m

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Implosion symmetry

Beam radius:=100 m


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Implosion symmetry

Beam radius:=120 m


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Implosion symmetry

Beam radius:=140 m


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Implosion symmetry

Beam radius:=180 m


Implosion symmetryGIFIFP UPM / ETSIA


Large focus produce improve symmetry but reduce implosion intensity

These results are in agreement with 2D studies with MULTI2D and CHIC: R. Ramis, J. Ramírez, and G. Schurtz, Laser and Particle Beams (2008), 26, 113-126

Density from 2 to 14 g/cc and temperature from 30 to 140 eV (for s=140 m)

SummaryGIFIFP UPM / ETSIA

● MULTI3D is now available for laser-matter interaction studies● There is a qualitative agreement with 2D simulations on

imploding cylindrical targets.● Quantitative comparisons have to be carried out.● This requires the use of hexahedrical cells.● Lagrangian limitations (cell distorsion and multivaluated regions)

are similar as the one in 2D● Simulations sugest to use eliptical focal spots

Thanks for your attention!



Implosion shape depends on laser beam diameter. Only when >r a cylindrical column is obtained

This results is in agreement with 2D studies with MULTI2D and CHIC:R. Ramis, J. Ramírez, and G. Schurtz, Laser and Particle Beams (2008), 26, 113-126



Density (Kg/m3) Temperature (K) Pressure (Pa)

Density from 2 to 14 g/ccTemperature from 30 to 140 eV

Final conditions for =140 m

NUMERICAL DEFECTS ARE VISIBLE IN THIS PLOTS: PEAKS AND LOST OF X-Y SYMMETRY


Unstructured grids 3D simulations of imploding cylindrical laser targets GIFIFP ETSIAUPM Rafael...

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