full-scale modeling of fast ignitiona new tool for efﬁcient · 0 = 350 fs (1d); 200 fs (2d) ๏ l...

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A new tool for efficient full-scale modeling of fast ignition

F. Fiúza1

M. Marti1, R. A. Fonseca1,2, L. O. Silva1

J. Tonge3, J. May3, W. B. Mori3

1GoLP/Instituto de Plasmas e Fusão NuclearInstituto Superior Técnico (IST)Lisbon, Portugalhttp://golp.ist.utl.pt2DCTI, ISCTE - Lisbon University Institute3University of California Los Angeles

F. Fiuza | Lisbon, November 12 | IPFN workshop 2010

http://cfp.ist.utl.pt/golp

http://cfp.ist.utl.pt/golp

Outline

Introduction/Motivation

New hybrid-PIC algorithm for inhomogeneous plasmas

Full-scale modeling of fast ignition

Conclusions and perspectives


Towards inertial fusion energy

HiPER: a high-gain approachIgnition at NIF by 2011

Fast ignition

compression ignition+

http://www.hiper-laser.org/

Indirect drive

https://lasers.llnl.gov/


http://www.hiper-laser.org

http://www.hiper-laser.org

https://lasers.llnl.gov

https://lasers.llnl.gov

Fast ignition modeling is demanding due to different scales involved

‣ Ignition scale lasers are now coming online: predictive capability is required

‣ Several important questions need to be addressed:

• What are the dominant laser absorption mechanisms?

• How does laser absorption/e-

spectrum changes during 15 ps?

• What is the beam divergence?

• What are the stopping mechanisms?

• How important is the modeling of spherical isolated targets?

Full-scale modeling is crucialVery different scales involved


Hybrid modeling

Current approach to model ignition is not complete/self-consistent

Full - PIC

Ignition laser hot e-

ne < 102 nc

Hybrid

ne ~ 105 nc

ne ~ 103 nc

Full-PIC modeling

Kinetic modeling of laser-plasma interaction and electron acceleration

Hybrid modeling of electron transport and energy deposition

Improved algorithms are required


New hybrid algorithm*

Ignition laser

Full-PIC code

• Full Maxwell’s equations

• Kinetic species

• n0 < 1023 cm-3

• pt < O(1)

• xp/c < O(1)

• ct/x < 1

Hybrid-PIC code

• Maxwell’s equations + Ohm’s law (inertialess)

• Kinetic species

• n0 > 1023 cm-3

• eit < O(1)

• ct/x < 1

If resistivity (Ohm’s law)

matches collisional model

transition is natural

and self-consistent

ne < 102 nc

ne ~ 105 nc

* B. Cohen, A. Kemp, and L. Divol, J. Comp. Phys. 229, 4591 (2010)


New Features in v2.0

· High-order splines· Binary Collision Module

· Tunnel (ADK) and Impact Ionization

· Dynamic Load Balancing

· PML absorbing BC· Parallel I/O

osiris framework

· Massivelly Parallel, Fully Relativistic Particle-in-Cell (PIC) Code

· Visualization and Data Analysis Infrastructure

· Developed by the osiris.consortium⇒ UCLA + IST

Ricardo Fonseca: [email protected] Tsung: [email protected]

http://cfp.ist.utl.pt/golp/epp/ http://exodus.physics.ucla.edu/

OSIRIS 2.0


mailto:[email protected]




http://cfp.ist.utl.pt/golp/epp

http://cfp.ist.utl.pt/golp/epp

http://exodus.physics.ucla.edu/

http://exodus.physics.ucla.edu/

Algorithm description and implementation: current deposition

Hybrid-PIC algorithm*

Δt

dudt

=qmE + 1

γ cu × B

⎛

⎝⎜⎞

⎠⎟

∂E∂t

= c∇ × B − 4π j

∂B∂t

= −c∇ × E

Integration of equations of motion, moving particles

Weighting

Integration of Field Equations on the grid

Fi → ui → xi

Jj →( E , B )j

( E , B )j → Fi

Weighting

(x,u)i → Jfast

(x,u)i → Ji

Weighting

(x,u)i → Jf

(x,u)i → Ji

∂E∂t

= c�∇×B− 4π(Jf + Ji + Je) → Je

= 0

calculate Je from Ampère’s law (possibility to drop displacement current)

0 = E +∇pe

ene− η(Je + Ji)−

Je ×Benec

+�

d

dt

�

coll,f−e

Pe,f

ene

separate fast (f) and cold (e) electrons (v> vth)

deposit currents

* B. Cohen, A. Kemp, L. Divol, J. Comp. Phys. 229, 4591 (2010) F. Fiuza | Lisbon, November 12 | IPFN workshop 2010

* B. Cohen, A. Kemp, L. Divol, J. Comp. Phys. 229, 4591 (2010)

Algorithm description and implementation: field solver

Hybrid-PIC algorithm

Δt

dudt

=qmE + 1

γ cu × B

⎛

⎝⎜⎞

⎠⎟

∂E∂t

= c∇ × B − 4π j

∂B∂t

= −c∇ × E

Integration of equations of motion, moving particles

Weighting


Fi → ui → xi

Jj →( E , B )j

( E , B )j → Fi

Weighting(x,u)i → Jfast

(x,u)i → Ji

→ Je


0 = E +∇pe


Je ×Benec

+�

d

dt

�

coll,f−e

Pe,f

ene

Jj →( E , B )j

0 = E +∇pe


Je ×Benec

+�

d

dt

�

coll,f−e

Pe,f

ene

advance E using inertialess plasma e- eq. of motion (Ohm’s law)

∂E∂t

= c∇ × B − 4π j

∂B∂t

= −c∇ × E

advance B using Faraday’s law

whereη = meνei/nee

2

νei =∗∗ 0.51× 4√

2πe4Z2i ni/(3

�(me)Te3/2)

** S.I. Braginskii, Rev. Plasm. Phys. 1, 205 (1965)

(possibility of spatially/temporally smooth all quantities)

pe =�

(v − ve)(v − ve)fe d3v

ne =�

fed3v

ve =�

vfed3v

Te = pe/ne


x1 [ m]100806040200

Den

sity

[1023

cm

-3]

5.0

4.0

3.0

2.0

1.0

0.0

Numerical Parameters

๏ 400 cells/μm (full-PIC)๏ 42 cells/μm (hybrid-PIC)๏ hybrid/full-PIC transition = 100 nc

๏ Part. per cell = 200 (1D) - 9 (2D)๏ cubic interpolation

OSIRIS simulation setup: laser-solid interactions

๏ λ0 = 1μm๏ I0 = 5x1019

๏ W0 = 5 μm๏ τ0 = 350 fs (1D); 200 fs (2D)

๏ L = 30 x 5 μm2

๏ ne0 = 1000 nc (1D) - 500 nc (2D)๏ mi/me = 1836

Physical Parameters

Laser

Plasma

0

5

x 2 [µ

m]

PIC

Monte Carlo Coulomb collisions modeled in all simulations

Laser

Solid target

hybrid PIC


# io

ns [a

rb. u

nits

]

104

102

100

10-2

p1 [me c]0.20.10.0-0.1

New algorithm allows for smooth hybrid-PIC transition and accurate results

full-PIC

hybrid-PIC

1D simulations @ 0.85 ps

Den

sity

[1024

cm

-3]

1.0

0.8

0.6

0.4

0.2

0100

full-PIChybrid-PIC

22.5 MeV

90X FASTER


OSIRIS

Very large speed-ups can be achieved while maintaining the accuracy

300X FASTER

2D simulations @ 0.5 ps

h-OSIRIS



๏ 42 cells/μm๏ hybrid/full-PIC transition = 100 nc

๏ Particles per cell = 1000๏ # time steps = 2.5x105

๏ cubic interpolation

OSIRIS simulation setup: HiPER modeling*

๏ λ0 = 1μm

๏ I0 = 5x1019 - 2x1020 Wcm-2

๏ τ0 = 20 ps

๏ L = 800 μm

๏ ne0 = 1 nc - 1.5x105 nc

๏ mi/me = 3672

Physical Parameters

Laser

Plasma

* HiPER profile from J. R. Davies and X. Ribeyre

hybrid PICPIC

Ignition laser DTtarget


Higher intensities required in order to obtain ignition

17% total

8% @ core

electronsions

6

3

0

Ti [

keV

]

~1.3 keV

core

T i [k

eV]

6

5

4

3

2

1

0

[cm

-3]

700

600

500

400

300

200

100

0x1 [ m]

450400350300

21% total

10.5% @ core

electronsions

[cm

-3]

700

600

500

400

300

200

100

0x1 [ m]

450400350300

T i [k

eV]

10

8

6

4

2

0

10

5

0

Ti [

keV

]

~4 keV

core

I = 5x1019 Wcm-2 I = 2x1020 Wcm-2

Hea

t flu

x / L

aser

flux

[%]

60

50

40

30

20

10

0x1 [ m]

6004002000

# e

-

E [MeV]0 5 10

# el

ectro

ns [a

rb. u

nits

]

102

101

100

10-1

10-2

10-3

10-42015105

1.5x pond. scaling

0.3x pond. scaling

Hea

t flu

x / L

aser

flux

[%]

60

50

40

30

20

10

0x1 [ m]

6004002000

# el

ectro

ns [a

rb. u

nits

]

102

101

100

10-1

10-2

10-3

10-42015105

# e

-

E [MeV]0 5 10

pond. scaling

0.25x pond. scaling



๏ 42 cells/μm๏ hybrid/full-PIC transition = 100 nc

๏ Particles per cell = 64๏ # time steps = 105

๏ cubic interpolation

OSIRIS simulation setup: isolated target*

๏ λ0 = 1μm๏ I0 = 5x1019 - 2x1020 Wcm-2

๏ W0 = 4 μm๏ τ0 = 5 ps

๏ L = 150 x 120 μm2

๏ ne0 = 10 nc - 2x105 nc

๏ mi/me = 3672

Physical Parameters

Laser

Plasma

* HiPER profile from J. R. Davies and X. Ribeyre

Ignition laser DTtarget

15010050 0 0

50

100

x1 [µm]

x 2 [µ

m]

hybrid

PIC


50

100

50 100

50

100

50 100

Reduced divergence in spherical isolated targets

~20º

50

100

50 100

B 3 [M

G]

10

0

-10

pond. scaling

0.5x pond. scaling

@ 0.6 ps


x 2 [

m]

100

50

x1 [ m]100 500

B3 [M

G]

100

50

0

-50

-100

50

100

50 100

~33º - 50º

Modeling of realistic targets is crucial

B 3 [M

G]

10

0

-10

1.1x pond. scaling

0.5x pond. scaling

x 2 [

m]

100

50

0x1 [ m]

100 500

n e /

n c

105

104

103

102

101

100

@ 0.6 ps


Towards full-scale modeling of fast ignition

2D full-scale 3D scaled down 3D full-scale

6-12 6-12 6-1220-30 7-10 20-30

15 15 15

102-2x105 102-2x105 102-2x105

300x300 100x100x100 300x300x300

2x1011 4x1013 1x1015

1x106 7x106 2x108

a0

Laser

Target

Simulation time [CPU hours*]

Spot [μm]

Duration [ps]

Density [nc]

Size [μm2(3)]

PIC

Hybrid-PICF. Fiuza | Lisbon, November 12 | IPFN workshop 2010

OSIRIS is highly optimized for modeling at very large scales

OSIRIS strong scaling up to ~300k CPUs

✴ Spatial domain decomposition✴ Local field solver✴ Minimal communication✴ Dynamic Load Balancing

New hardware features

SIMD units

tailored code already in production

GPUs

CUDA development (test PIC code)1

10

100

104

105

Sp

eed

up

CPUs

81% efficiency 294,912 CPUs

Ideal

JUGENEGermany

4,096


Conclusions and perspectives

New algorithm allows for full-scale modeling of fast ignition

Physics behind transport and stopping can be understood in a self-consistent way

e- cooler than pond. scaling allow for high efficiency at core with ultrahigh laser intensities

Modeling of spherical isolated targets crucial to infer ignition conditions

New approach can have significant impact in modeling and guiding of future experiments

Next steps

Modeling full-scale FI with isolated targets

Compare cone guided FI with channeling

Model shock ignition scenario

Full-scale 3D modeling of ion acceleration in laser-solid interactions


full-scale modeling of fast ignitiona new tool for efﬁcient · 0 = 350 fs (1d); 200 fs (2d) ๏ l...

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