1 of 38

1

Laser driven shocks (laser matter interaction, hydrodynamics, fusion, etc…)

Bakandreas Stavros

Ph.D. candidate

stavros.bakandreas@polytechnique.edu

2 of 38

2

Outline

Shock generation via lasers
Inertial Confinement Fusion basic concepts
FLASH HD code
How to come to France

3 of 38

3

Outline

Shock generation via lasers
Inertial Confinement Fusion basic concepts
FLASH HD code
How to come to France

4 of 38

4

How to generate a shock using laser

A shock can be created by different techniques:

Pusher

Sample

Laser

5 of 38

5

Laser and shock relation

• The target is heated locally by the laser and compressed.

• From the laser to the shock wave:

Laser absorption: the electrons start to oscillate in the presence of the laser field which, by collision, heats the matter.

• Ionization and expansion of the target: A few picoseconds

later, the target surface is ionized and start to expand toward the laser.

ρ

6 of 38

6

Laser and shock relation

Propagation into the plasma: The laser propagates till the electron density reaches the critical density value.

Absorption of the laser energy

I_l<10¹⁵ W/cm² : the absorption is mainly collisional and localized near the critical density.

The electrons, set in motion by the laser field, undergo elastic collisions with the ions. The oscillation energy is converted into thermal energy and an increase in electronic temperature

The collisional absorption is not efficient at high intensities

n_e

n_c

Absorption (%)

Intensity (W/cm²)

corona

conduction zone

7 of 38

7

Laser and shock relation

Propagation into the plasma: The laser propagates till the electron density reaches the critical density value.

Absorption of the laser energy

I_l<10¹⁵ W/cm² : the absorption is mainly collisional and localized near the critical density.
I_l>10¹⁵ W/cm²: The electric field of the electronic plasma waves accelerate fast electrons (keV, MeV) which do not contribute to the ablation process.

The electrons, set in motion by the laser field, undergo elastic collisions with the ions. The oscillation energy is converted into thermal energy and an increase in electronic temperature

The collisional absorption is not efficient at high intensities

n_e

n_c

Absorption (%)

Intensity (W/cm²)

corona

conduction zone

1ω

2ω

3ω

4ω

e^-

8 of 38

8

Laser and shock relation

n_e

corona

conduction zone

n_e

corona

conduction zone

X-rays

n_c

9 of 38

9

Laser and shock relation

Ablation: The ablation front separate the hot matter, which expands into vacuum, from the matter pushed towards the target (rocket effect *)

Shock wave: A shock is produced from the rapid and localized heating of the target

P. Mora, Phys. Fluids 25, 1051 (1982)

* Tsiolkovsky rocket equation

m

10 of 38

10

Outline

Shock generation via lasers
Inertial Confinement Fusion basic concepts
FLASH HD code
How to come to France

11 of 38

Why Fusion ?

11

Conversion to electricity

η=40%

Laser efficacity

η=10%

LASER

grid

Target production

Target injector

Gain

G=200

1429 MW

571 MW

500 MW

71 MW

7.1 MW

857 MW (heat)

64 MW

714 kJ 10 Hz

Energy flux

Heat to extract

Flux of matter

820 000 target / day ⁽¹⁾

material

(D,T)

Reaction

residues

10 Hz

12 of 38

Why Fusion ?

12

13 of 38

13

Inertial Confinement Fusion (ICF)

p-p chain (26.7 MeV)

DT chain (17.6 MeV)

Neutron (14.1 MeV)

Helium (3.5 MeV)

Tritium

Deuterium

4

2

Lawson criterion

14 of 38

14

Inertial Confinement Fusion (ICF)

Density

Temperature

Confinement time

10⁴x solid

1 keV

10⁵ years

solid / 10⁸

10 keV

seconds

10³x solid

10 keV

10’s ps

15 of 38

15

Direct Drive Schematic

Incident radiation

Low density corona

Cold dense fuel shell

Gas fill

Ablation driven implosion

Material ablated from

capsule surface

Hotspot

CH

DT solid

DT gas

High convergence

2 mm

Fusion fuel is encased in a sphere of

high density carbon (synthetic diamond)

the size of a pepper corn

100 μm

16 of 38

16

Instabilities

Laser Plasma instabilities

Stimulated Raman Scattering (SRS)
Stimulated Brillouain Scattering (SBS)
Two Plasmon Decay (TPD)
Cross-Beam Energy Transfer (CBET)

Hydrodynamic instabilities

Rayleigh Taylor (RT)

Richtmyer-Meshkov (RM)

Forbes, Walters, & Turner (2024) Water Waves, 6(1).

Prime, M. (2018). Proc. Conf. Extreme Loading, 13–16.

First design proposed by Sacks et al.

Increase laser energy coupling
Mitigate hydro instabilities
Smoothing of laser/X-ray drive non-uniformities
Shock timing and pressure shaping

DT gas

Solid DT

Wetted foam

Underdense foam

17 of 38

17

Porous materials

Chemical synthesis of foam from liquid gels: K. Nagai et al. Phys. Plasmas 2018: multi-stage fabrication process, random fractal structure, pore size 1-2 µm, materials: carbon, hydrogen, oxygen, wire thickness 100s nm

Carbon nanotube & graphene target fabrication technology: P. Wang et al. HPLSE 2019: catalyst chemical vapor deposition on a substrate, pore size < 1 µm, 95% of carbon, folded foil structure, sheet thickness 10s nm

Additive manufacturing of foams: J. Fischer & M. Wegener, Laser Photon. 2013: a novel technique of 3D printing 2P LL: better control of foam properties and higher rigidity, pore size 10-50 µm, wire thickness ~few microns

Octet truss
Voronoi cells
Gyroid cells
Octet with density gradient

1 mm

Foam target design

18 of 38

18

Porous materials

Shock propagation on stochastic and 3d printed structures
Equation of state (EOS)
How the energy of the system is affected by the presence of foam
Homogenization timescales
What if we wet them ?

Οpen Research Questions…

Conduct Experiments

Develop diagnostics

(VISAR, SOP)

Simulations

(FLASH, Hydra…)

19 of 38

19

Experimental Campaign

Pulse energy: 15J

Pulse duration: 5ns

Spot diameter: 260μm

Target

12.6 cm

55.0 cm

XFEL

Electron energy: 7keV

Pulse duration: 8 - 10fs

Compression wave

Plasma wave

LiF Holder

LiF Crystal

Kameshima detector

Aluminium

Sample

20 of 38

20

Outline

Shock generation via lasers
Intertial confinment fusion basic concepts
FLASH HD code
How to come to France

21 of 38

21

A few words for FLASH Code…

22 of 38

> 5000 users worldwide https://flash.rochester.edu >1,300 papers published
FLASH (Fryxell+ ApJS 2000) is a publicly available, HPC, AMR, finite-volume, radiation hydro and MHD code with extended physics capabilities (Tzeferacos+ HEDP 2015), developed by the Flash Center for Computational Science. The development is supported primarily by the U.S. DOE NNSA, LANL, LLNL, and LLE.
FLASH is professionally managed software in continuous development for > 20 years: coding standards; version control; daily automated regression testing; documentation; user support; integration of code contributions from external users.

22

A few words for FLASH Code…

Laser

23 of 38

FLASH Capabilities

23

A portable, scalable, application code, composed of units and modules
Modules are set up and assembled to run different physics problems
Written in Fortran, C, Python, >1.2 million lines, 75% code, 25% comments Infrastructure: Configuration, Mesh Management, Parallel I/O, Monitoring, Verification