Energy Transport Dynamics in Warm Dense Copper using femtosecond time-resolved XANES spectroscopy - ESRF
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Energy Transport Dynamics in Warm Dense Copper
using femtosecond time-resolved XANES
spectroscopy
Ludovic LECHERBOURG
3rd workshop on Studies of Dynamically Compressed Matter with X-rays 2021 January 14-15
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Collaborators
Ludovic Lecherbourg Fabien Dorchies Kim Ta Phuoc
Patrick Renaudin Julien Gautier
Vanina Recoules CELIA, Talence, France
LOA, Palaiseau, France
CEA, DAM, DIF, Arpajon, France
Noémie Jourdain
Adrïan Grolleau
Thesis CEA/CELIA
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Warm Dense Matter regime (1/2)
Warm Dense Matter (WDM) is involved in different fields of physics
Astrophysics Inertial Confinement Fusion Laser processing
Planetary science (cores, First moments of the Precision laser ablation
mantle, etc...) laser-holrhaum interaction (Au)
Laser engraving for
Stars (brown dwarves structure, Compression of the ablator (CH) nano-electronics components
neutron stars surface) Compression of the fuel (D2 )
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Warm Dense Matter regime (2/2)
Between plasma physics and solid state physics
Warm : . 10 eV and Dense : ∼ ρ0
OCP DOS
104
TFermi η∝ ∼1 10 5 0 5 10 15 20 25
10102 4 10 2 100 102 104
Kinetic energy
Energy - EFermi [eV]
Density [g. cm ]
3
Complex theoretical description of this regime
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Phase transition from solid to WDM
Laser produced Warm Dense Matter : solid → plasma transition regime
Step 1 : Cold solid Step 2 : HETL WDM Step 3 : ETL WDM
Te = Ti = 300 K Ti < Tfusion Ti ≈ Te & 1 eV
Te ∼ few eV
t =0s t . 1 − 10 ps t & 10 ps
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Ultrafast energy transport in laser-heated thin metal layers (1/3)
Chen et al. measured in 2012 surface reflectivity changes of gold after
laser heating (400 nm, 45 fs FWHM) using chirped optical probe (800
nm).
They highligthed a threshold in the relative reflectivity changes, de-
pending on the absorbed flux.
Results suggest two different regimes for the energy transport.
Figures are from Chen et al., Phys. Rev. Letters 108, 165001 (2012).
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Ultrafast energy transport in laser-heated thin metal layers (2/3)
Electrons are excited within the laser skin-depth
#1 Energy is transported by ballistics electrons in the sample over their
mean free path (MFP).
They thermalise through electrons-electrons collisions and heat the
sample in few tens of fs.
⇒ homogeneous heating if sample thickness . δλ + MFP
#2 Electrons heat up more and thermalize much faster, in few fs after
heating, therefor within the laser skin-depth
Mueller et al., Phys. Rev. B 87, 3 (2013)
Fourment et al., Phys. Rev. B 89, 161110 (2014)
Energy reservoir on the front side heats the whole sample by thermal
conduction
⇒ inhomogeneous heating lead by thermal conduction
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Ultrafast energy transport in laser-heated thin metal layers (3/3)
Performing XANES spectroscopy using a betatron source
Direct measurement of Te
XANES → In-depth probing ⇒ Follow in detail the dynamics of Te
Betatron femtosecond time resolution
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Methodology : Hydrodynamic Simulations (1/4) Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 7 / 21
Two-Temperatures Model (TTM)
Local coupled differential equations describing both elec-
trons and ions temperatures dynamics : Te
2.0 Ti
dTe
Temperature [eV]
Ce = −Gei (Te − Ti ) + ∇(κe ∇Te )+S(t)
dt 1.5
dT
Ci i = Gei (Te − Ti ) + ∇(κi ∇Ti )
dt 1.0
0.5
The physics lies in the coefficients :
Ce , Ci heat capacities 0.0
Gei coupling parameter 0 1 2 3 4 5 6
Time [ps]
κe , κi conductions
Illustrative 1D Hydrodynamics TTM simulations
using E STHER code.
Ce , Gei and κe can be computed from various models, in
particular from ab-initio QMD simulations.
Lin et al., Phys. Rev. B 77 (2008)
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 8 / 21Methodology : Ab-initio QMD Simulations (2/4) Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 8 / 21
XANES is a diagnostic of both electronic and ionic structures
XANES = X-ray Absorption Near-Edge Spectroscopy
Probes the (unoccupied) electron DOS from a core level
Sensitive to the spatial organization of neighboring ions
⇒ Very proven technique since the 70’s and 80’s, in condensed and diluted media, but needs to be
revisited in the extreme conditions of WDM
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 9 / 21Ab-initio QMD simulations with A BINIT
Generation of a thermodynamic
configuration Calculation of photoabsorption cross section
∼50 h on 500 CPU ∼10 h on 500 CPU
|hφf ,k |∇|φ2p,k i|2
norbitales
1 − f (f ,k ) δ(2p − f − hν)
X
2
σk (hν) = 4π hν
Fermi-Dirac Transition matrix KS
i=1
occupations elements eigenvalues
Density Fonctional Theory
1.0 QMD
Local Density Approximation exp.
exchange and correlation 0.8
Absorption [a. u.]
Projected Augmented Wave 0.6
scheme
0.4
108 atoms
3x3x3 grid 0.2
0.0920 930 940 950 960 970
Energy [eV]
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 10 / 21QMD : a tool to extract Te (1/2)
Te = 300 K Te = 0.5 eV Te = 0.75 eV Te = 1.0 eV
1 1 1 1
s-band
s-band
s-band
s-band
0 0 0 0
d-band
d-band
d-band
d-band
1 1 1 1
0 10 0 10 20 30 0 10 0 10 20 30 0 10 0 10 20 30 0 10 0 10 20 30
E - µ (eV) E - µ (eV) E - µ [eV] E - µ (eV)
1.0 1.0 1.0 1.0
Absorption [a. u.]
Absorption [a. u.]
Absorption [a. u.]
Absorption [a. u.]
0.8 0.8 0.8 0.8
0.6 0.6 0.6 0.6
0.4 0.4 0.4 0.4
0.2 0.2 0.2 0.2
0.0920 930 940 950 960 970 0.0920 930 940 950 960 970 0.0920 930 940 950 960 970 0.0920 930 940 950 960 970
Energy [eV] Energy [eV] Energy [eV] Energy [eV]
When Te increases, available levels appear in the d-band, which increases the absorption before the Fermi level.
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 11 / 21QMD : a tool to extract Te (2/2)
1.0 9 g/cm³, Ti = 300 K
Pre-edge integral [/eV]
6 9 g/cm³, Ti = Te
Absorption [a. u.]
0.8 8 g/cm³, Ti = Te
0.6 4 6 g/cm³, Ti = Te
0.4 300 K
0.50 eV 2
0.2 0.75 eV
1.00 eV
0.0920 930 940 950 960 970 0
0.0 0.5 1.0 1.5 2.0
Energy [eV] Temperature [eV]
The electronic temperature Te can be measured with the integral of the pre-edge.
A function to attribute a Te to our experimental data have been deduced.
N. Jourdain et al., Phys. Rev. B 101, 125127 (2020)
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Samples design
Two heating regimes investigated
Working regime 30 nm : quasi homogeneous energy deposition
Based on Chen et al. work 100 nm : inhomogeneous energy deposition
Copper deposition
Realized by evaporation
Substrat : 1 µm of PET "Mylar"
Laser skin depth @ 800 nm ∼ 13 nm
1 eV electrons ballistic range ∼ 70 nm
Nguyen-Truong, J. Phys. : Condens. Matter 29 (2017)
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 13 / 21Experimental setup - LOA facility, "Salle jaune"
Pump beam (on sample) Betatron drive beam Betatron X-ray beam
φ = [380 ± 10] µm - top-hat ∼ 50 TW Low divergence ∼ 10 mrad
Incidence⊥ = [2.2 ± 0.2]◦ On gas jet ∼ 3 × 1019 W /cm2 φ ≈ 150 µm on sample
Pulse duration FWHM = 30 fs Gas jet : 99%He / 1%N, ∼ 20 Normal incidence on sample
[1.1 ± 0.3] × 1014 W /cm2 bars . 6.5 × 104 ph / eV / shot
@ ∼ 930 eV
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 14 / 21Experimental setup - X-ray characteristics Betatron pulse duration estimated from PIC simulations Betatron emission spectrum for 1019 W /cm2 800 nm laser. Mahieu et al., Nature Comm. 9(1), 2018 Figure from Corde et al., Rev. Mod. Phys. 85 :1-48, 2013 Temporal resolution is then limited by pump-probe angle of 2.2◦ and X-ray spot size of ∼ 150 µm leading to ∼ 20 f s resolution. Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 15 / 21
Acquisition routine
Accumulation required : betatron spectrum stability
over ∼ 100 shots/series.
Hot spots filtration (3-axis filtering).
A hole is created by the pump beam at each shot : the
sample is automatically moved to a clean area bet-
ween two shots (0.3 Hz). Shot to shot stability over 100 images
200
100 images filtered stack 1.5 Cold spectrum
Hot spectrum
Absorption (norm. unit.)
Routine to minimize errors during XANES spectra ex- 150
1.25
traction : ROI
1
Pixels
100 0.75
one reference serie ”R” without sample ;
0.5
one cold serie ”C” at ambiant temperature ; 50
0.25
0
one hot serie ”H” with the pump beam. 0
0 100 200 300 400 920 925 930 935 940 945
Pixels Energy (eV)
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 16 / 21Results 1/2 : Experimental overview
Differents delays probed to infer the dynamics of Pre-edge integral is transformed into electrons temperature
Te (∼ 25 min / delay). using the model from ab initio simulations.
Pre-edge absorption increases as sample is Almost no energy is lost in the substrate for 30 nm samples
heated. during the heating, as Te rises 3 times higher than for the 100
Uncertainties : photons counting statistics (colo- nm samples ⇒ energy deposition < 30 nm.
red areas). 10
100 nm Experimental 30 nm Experimental
1.5 Cold spectrum
8
0.13 ps
0.47 ps
1.25
1.13 ps
Absorption (norm. unit.)
Temperature (eV)
6
1
0.75 4
0.5
2
0.25
0
0
0 1 2 3 4 5 6
920 925 930 935 940 945 Time (ps)
Energy (eV)
Data presented has required ∼ 10’000 shots, acquired during 3 days plus 3
weeks for preparation.
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Results 2/2 : Comparison with TTM simulations
4
Experimental data show a slow increase to ∼ 1.5 eV in ∼ 1 ps
Experimental
TTM: ballistic regime
TTM Simulations (E STHER code) : TTM: thermal regime
3
absorbed flux based on energy and absorption coefficient
measurements
Temperature (eV)
uncertainties on absorbed energy is represented by colored
areas 2
Ballistic regime : instantaneous heating, then electron-ions colli-
sions ⇒ do not reproduce T e dynamics during the first ps 1
Thermal regime : slower heating, Te rises to 1.5 eV in 0.7 fs
, Experimental data unveals the conduction phase inside the
sample, below the first picosecond 0
/ Errorbars are still too high to differenciate conduction models
−0.5 0 0.5 1 1.5 2 2.5
Long time Te for [100 nm] simulation is consistant with experimen- Time (ps)
tal data, in agreement with previous work
Jourdain et al. Phys. Rev. B 97, 075148 (2018)
Commissariat à l’énergie atomique et aux énergies alternatives DyCoMax | Ludovic Lecherbourg | 2021-01-14 & 15 19 / 21Summary
Copper (30 nm and 100 nm) samples were heated using femtosecond laser at ∼ 1 × 1014 W /cm2 .
Almost no energy is lost in the substrate for 30 nm samples during the heating, as Te rises 3 times higher than
for the 100 nm samples ⇒ energy deposition < 30 nm.
Electrons temperature dynamics is inferred using femtosecond TR-XANES, which highlight 3 thermodynamics
steps :
1. electronic temperature rise quickly in the skin depth during laser pulse ;
2. the energy reservoir created heat the whole sample by conduction for ∼ 1 ps ;
3. electrons heat the lattice by electron-ion collisions.
Grolleau et al. in preparation
Improve the signal to noise ratio (better hot electrons filtration, higher betatron source flux) ⇒ possibility to
differienciate conduction models ?
Other materials (study on molybdenum is on-going)
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Job offer at CEA, DAM, DIF : Plasma Experiments Conductor
Fields Location
Nuclear physics, plasma physics, atomic physics, molecu- 26 Rue de la Piquetterie, 91680 Bruyères-le-Châtel,
lar physics. France (30 km south-west from Paris).
Description - Missions Requirements
Design, conduction and analysis of plasma experi- PhD in Physics, good knowledge in plasma physics,
ments on Laser MégaJoule (LMJ) and partners faci- programming and signal processing.
lities. Good french and english speaking.
Collaboration with plasma diagnostics development
service and analysis programs developpers.
Availability
Collaboration with simulations codes developpers.
September, 2021
International collaborations.
Contact
berenice.loupias@cea.fr
stephanie.brygoo@cea.fr
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