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Measuring fundamental properties of dense plasmas on X-ray Free-Electron Lasers
1
Sam VinkoWorkshop on Modern Methods in Plasma Spectroscopy
Trieste, 23 March 2015 [email protected]
Collaborators
2
U Oxford: Orlando Ciricosta, David Rackstraw, Thomas Preston, Justin Wark
SLAC: Bob Nagler, Hae Ja Lee, Phillip Heimann
U Berkeley: Richard Lee
GIST: Byoung-ick Cho
LBNL: Kyle Engelhorn, Roger Falcone
IAEA: Hyun-Kyung Chung
Czech IOP: Jaromir Chalupsky, Tomas Burian, Vera Hajkova, Libor Juha
European XFEL: Ulf Zastrau
… and others – see all authors of Nature Communications 6, 6397 (2015), Nature 482, 59 (2012).
Outline
‣ X-ray Free Electron Lasers & High Energy Density Matter (HDM and WDM)
‣ Isochoric heating to HDM conditions on LCLS
‣ Spectroscopic plasma studies of HDM‣ Ionization Potential Depression‣ Electron Collisional Ionization Rates
‣ Future directions & conclusions
What is a Free Electron Laser (FEL)?
4
Courtesy of PSI
LCLS – Linac Coherent Light Source
5
SLAC Linac (3km)
LCLS injector
Near and Far Experimental Halls
World’s first X-ray Free-Electron Laser ‣ tunable photon energy range: <500 eV – 12 keV (fundamental);‣ pulse repetition rate 120 Hz;‣ ~1-3 mJ average pulse energy;‣ bandwidth 0.3%‣ variable pulse length: <10 fs - 300 fs‣ focusing to achieve X-ray intensities >1018 Wcm-2
4th generation FEL light sources
‣ Peak brightness 9 orders of magnitude higher than 3rd generation synchrotrons
‣ short X-ray pulses ( 1–100 fs);
‣ lots of photons per pulse (≥1012);
‣ fully tunable wavelength
‣ Hard X-ray FELs:‣ LCLS at SLAC, USA : 0.12-2.5 nm, 2009
‣ SCSS at SPring-8, Japan : 0.1 - 3.6nm, 2011
‣ European X-FEL at DESY, Germany: 0.1 - 6nm, 2016
‣ Swiss-FEL at PSI : 0.1 - 7nm, 2016
6
0.01 0.1 1 10 100Energy (keV)
1x1016
1x1018
1x1020
1x1022
1x1024
1x1026
1x1028
1x1030
1x1032
1x1034
Pea
k B
right
ness
(ph
oton
s/s/
mm²/
mr²
/0.1
% b
andw
idth
)
2016
2009
20172011
European XFELLCLS
SwissFELSACLA
FLASH
FERMI
2005
2011
XFELSpontaneous
LCLSSpontaneous
LaboratoryX-ray laser
High HarmonicGeneration
Syn
chro
tro
n Li
ght
So
urce
Cap
abili
ty
ESRF/APSUndulator
DiamondUndulator
APSWigglers
ALSUndulator
ALS200 fs source
NSLS
High energy-density systems: Warm and Hot Dense Matter
7
Hydrogen Phase Diagram Aluminium Phase Diagram
classical plasma
dense plasma
high densitymatter
Γ = 1
Γ = 10
Γ = 100
Density ( g/cm3)
103
104
101
102
102 104100
10-4 10-2 1
WDM
Tem
per
atu
re (
eV)
Tem
pera
ture
(eV)
Tem
pera
ture
(eV)
Density (g/cm3) Density (g/cm3)
R.W. Lee et al., J. Opt. Soc. America B 20, 770 (2003).
Γ =VCoulomb
EKinetic
Outline
‣ X-ray Free Electron Lasers & High Energy Density Matter (HDM and WDM)
‣ Isochoric heating to HDM conditions on LCLS
‣ Spectroscopic plasma studies of HDM‣ Ionization Potential Depression‣ Electron Collisional Ionization Rates
‣ Future directions & conclusions
8
The experiment at the Linac Coherent Light SourceX-ray Free-Electron Laser
X-ray spectrometer: K-alpha emission Al around 1200-1900 eV
LCLS pulse
Photon energy: 1300–2000 eVPulse length < 80 fs Pulse Energy ~1 mJBandwidth ~ 0.4%
Diode
Braggcrystal
9
1 micron thick Al, Mg, Si sample
Vinko et al., Nature 482, 59 (2012)Cho et al., PRL 109, 245003 (2012)Ciricosta et al., PRL 109, 065002 (2012)
CCD
Peak Intensity ~1017 W cm-2
K-edge
L-edge
ωp
σff
(μm
-1)
Ephot
ωp
σff
EEphot
K-edggge
LCLS
K: 1s2
L: 2s2 2p6
Photo-ionization
Neutral Al
Electronic structure of Aluminium
Core-hole lifetime ~1fs
K-edge
L-edge
ωp
σff
(μm
-1)
Ephot
ωp
σff
EEphot
K-edggge
LCLSNeutral Al
K: 1s1
L: 2s2 2p6
K-alpha emission
Electronic structure of Aluminium
Core-hole lifetime ~1fs
Kα photon
Electronic structure of Aluminium
Photo-excitation (of 6+)
Ionized Al:
K: 1s2
L: 2s2 2p3
K: 1s1
L: 2s2 2p3
K-alpha emission line VIIfrom different charge states
Kα photon
~96% of all recombination is Auger, not radiative!This keeps the energy in the system and it heats up.
X-ray isochoric heating: plasma evolution
13
0 1 2 3 4 5 6 7 8 9 10 11 12 13Charge state
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Frac
tiona
l yie
ld in
tegr
ated
ove
r pu
lse
1580 eV1630 eV1680 eV1730 eV1780 eV1830 eV
0 20 40 60 80 100 120 140 160Time (fs)
1x1023
2x1023
3x1023
4x1023
5x1023
6x1023
Den
sity
(ele
ctro
ns c
m-3
)
0 20 40 60 80 100 120 140 160Time (fs)
0
50
100
150
200
Tem
pera
ture
(eV
)
X-ray pulse
Vinko et al., Nature 482, 59 (2012)[email protected]
K-shell spectroscopy of Hot Dense Aluminium
14
IV V VI VII VIII IX XIX V VI VII VIII IX X
Emitted photon energy (eV)
En
erg
y o
f x−
ray F
EL
excita
tio
n (
eV
)
1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680
1475
1500
1525
1550
1575
1600
1625
1650
1675
1700
1725
1750
1775
1800
1825
Resonant transitio
ns
Cold K-edge
Single K-shell hole Double K-shell hole
Vinko et al., Nature 482, 59 (2012)
K-shell spectroscopy of Hot Dense Aluminium
15
VIIIV
K shell
L shell
Continuum
L shell
K shell
FEL
pho
ton
ener
gy
0
Continuum
We observe very clean absorption [email protected]
Outline
‣ X-ray Free Electron Lasers & High Energy Density Matter (HDM and WDM)
‣ Isochoric heating to HDM conditions on LCLS
‣ Spectroscopic plasma studies of HDM‣ Ionization Potential Depression‣ Electron Collisional Ionization Rates
‣ Future directions & conclusions
16
Continuum lowering in dense plasmas
17
Figure taken from Umstadter, Physics 5, 88 (2012)
Isolated atom
In dense systems at some radius outer orbitals may overlap – these can no longer be considered bound to a specific ion
ionised.
This means the energy required to ionise a bound state is reduced as the density increases:
Ionization Potential Depression (IPD)
‣ Analytical models used when fast calculations required (atomic kinetics, hydrodynamic codes, etc.):‣ Ion sphere (compute total energy of free electron in Wiegner-Seitz ion sphere, originates from
condensed matter theory):
‣ Debye-Hückel (calculate electrostatic energy of electron/ion + Debye cloud, works in weak-coupling):
‣ Stewart & Pyatt model (bridges between the two above):
‣ Ecker & Kröll model (different Z scaling, matches LCLS data)
Some simple Ionization Potential Depression models
ΔIIS =3
2
ze2
4πε0rSP
ΔIEK = Cze2
4πε0rEK
ΔISP =kBT
2(z∗ + 1)
{(3(z∗ + 1)ze2
4πε0λDkBT+ 1
)2/3
− 1
}ΔIDH =
ze2
4πε0λD
18
4π
3r3SP = n−1
i
4π
3r3EK =
1
ne + ni
Preston et al., HEDP 9, 258 (2013)
1500 1550 1600 1650 1700 1750 1800Photon energy (eV)
1x104
1x105
1x106
1x107
Em
issi
on (p
hot/
eV/s
tera
d)
IVVVIVII
Resonant emission peaks
Ionization thresholds
Experimental IPD = Atomic edge - Measured edge
Experimental measurement of IPD on LCLS
Emitted photon energy (eV)
Energ
y o
f x−
ray F
EL e
xcitation (
eV
)
1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680
1475
1500
1525
1550
1575
1600
1625
1650
1675
1700
1725
1750
1775
1800
1825
IV V VI VI VI IX XIX V VI VI VI IX X
Resonant transitio
ns
19
Ciricosta et al., PRL 109, 065002 (2012)[email protected]
K-shell spectroscopy of Hot Dense Aluminium
20
VIIIV
K shell
L shell
Continuum
L shell
K shell
FEL
pho
ton
ener
gy
0
Continuum
We observe very clean absorption thresholds
Modelling the data via collisional-radiative super-configuration code SCFLY
‣ Proven to work in modelling intense X-ray interaction with atoms in the collision-less regime
‣ All atomic configurations up to n=3 included
‣ Self-consistent temperature calculated via X-ray deposition within duration of pulse (with instant thermalization)
‣ Spectral synthesis via a super-configuration transition array model
‣ Included opacity via escape factor formalism, IPD via a choice of IS, SP and EK models
21 [email protected] 22
Ciricosta et al., PRL 109, 065002 (2012)
1580 eV
1600 eV
1630 eV
1650 eV
1720 eV
1830 eV
LCLS pump energy:
Continuum lowering results on LCLS
Experimental measurement of IPD on LCLS
O.Ciricosta et al., PRL 109, 065002 (2012)
1450 1500 1550 1600 1650 1700 1750 1800Energy from K-shell (eV)
IV
V
VI
VII
VIIIL M
50 100 150IPD (eV)
EK
SPexp
continuumatomic edgeSP edgeEK edge
range ofexperimental edge
Single core holes Double core holes
Note: M-shell always in continuum according to EK model.
~50 eV!
23 [email protected] 24
Proven impossible (so far) to reproduce set of experimental spectra using the SP IPD model.
1.Possibly explained by pumping bound states below continuum? No states are expected at the threshold energies observed; any such states would still have to show a sharp edge and be broadened to ~50-100 eV to yield the spectra.
2.Possibly explained via spectator M-shell electrons? No model predicts rebinding below line 8. Emission from higher charge states with spectators is inconsistent with spectral lineouts.
Emitted photon energy (eV)
En
erg
y o
f x−
ray F
EL
excita
tio
n (
eV
)
1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680
1475
1500
1525
1550
1575
1600
1625
1650
1675
1700
1725
1750
1775
1800
1825
IV V VI VII VIII IX XIX V VI VII VIII IX X
Resonant transitio
ns
SP edges
Experimental measurement of IPD on LCLS
EK model “works” because ionization thresholds match EK K-edges.
These IPD measurements have spurred further modelling
25
3 4 5 6 7Charge state
0
50
100
150
200Io
niza
tion
Pot
entia
l Dep
ress
ion
(eV
) Exp.; Ciricosta et al., PRL109, 065002 (2012)Stewart & Pyatt, ApJ 144, 1203 (1966)Ecker & Kroll, Phys Fluids 6, 62 (1963)Son et al., PRX 4, 031004 (2014)Crowley, HEDP 13, 84 (2014)
Aluminium
Continuum lowering via Density Functional Theory
‣ There is a fundamental problem with the way we think of continuum lowering‣ cannot explain the experimental observations: EK works only in some cases, SP only in others
‣ we seem to be missing some physics
‣ Treatment of shells near continuum (M-shell) in analytical models is very poor‣ models need a sharp cutoff to what is physically a continuous process
‣ states within a shell not always treated individually
‣ Lets try a different approach that we know works for ground-state metals:‣ Calculate IPD independent of a specific analytical model
‣ Want the results to be consistent with relevant atomic physics and thermodynamics
‣ Applicable to the plasma conditions reached on LCLS
‣ Possibly extend beyond the average atom picture
26
7+
7+
Continuum lowering via DFT - add electrons
27
6+
6+
6+
4+ 5+
Box should be charge neutral (here I need 41 electrons)
Find the free-electron density via finite temperature DFT
Excited state PAW potentials
‣ Core-excited (rather than ionised) = global charge neutrality of the system
‣ PAW formalism is key‣ allows for frozen-core, all-electron potentials
‣ can calculate all core wave functions for excited atomic configurations to whatever accuracy required
‣ can freeze holes in core states – allows for a fully 3D multi-centred approach of charge states which are integers (no average atom approximation for ionization)
‣ charge state independent of temperature/density: can model equilibrium (pick the right temperature for the mean chosen ionization) or non-equilibrium systems (in terms of the ionization), includes some fluctuations (ensemble of integer charge states is simulated directly),
‣ can reconstruct the “real” valence density everywhere, including on ionic cores, where overlap with core wave functions becomes relevant
28
Identical to above, but with additional 1 K-shell hole in ionof interest
Calculate the IPD from first principles - Roadmap
29
Generate pool of excited-configuration PAW potentials with frozen inner shell core-hole states
Input: ion structure (crystal), charge state distribution and temperature
FT-DFT calculation: minimize energy under constraint of potentials
K-edge via free-energy difference
IPD!
Vinko, Ciricosta & Wark, Nature Comm 5, 3533 (2014)
What do we calculate?
30
Dens
ity o
f Sta
tes
Energy
Valence
2p states
2s states1s states
Populations selected in creation of the potentialCalculated in the single atom limit (radial DFT, Hartree-Fock-Dirac, etc.)
Core
Determined from 3D DFT calculation: the lowest energy configuration possible given our choice of the core (still formally ground-state)
Populations determined by chosen temperature via the Fermi-Dirac distribution
3s states
Continuum
Al continuum structure at different charge state
31
7+
X+X+
X+
Atomic-like 3s state
Calculation box:
Calculation for cold system @ 1eV
-20 -15 -10 -5 0 5 10Energy (eV)
0
5
10
15
20
25
30
35
40
Den
sity
of S
tate
s (s
tate
s/eV
/cel
l)
Total DOSpDOS of 7+ central ion
X = 3+
4+
5+
6+
7+
8+
9+
11+
10+
Vinko, Ciricosta & Wark, Nature Comm 5, 3533 (2014)
-20 -10 0 10Energy (eV)
0
5
10
15
20
25
Den
sity
of S
tate
s (s
tate
s/eV
/cel
l)
Al continuum structure at different temperatures
32
7+
6+6+
6+
Calculation box:
Atomic-like 3s state
(Electron density 3.75 x1023 cm-3)
100 eV
75 eV
50 eV
25 eV
10 eV
1 eV
Vinko, Ciricosta & Wark, Nature Comm 5, 3533 (2014)
K-shell spectroscopy of Hot Dense Aluminium: 3+
33
IV
L shell
Continuum
K shell
FEL
pho
ton
ener
gy
0
1800
1700
1600
1500
DFT
K-shell spectroscopy of Hot Dense Aluminium: 6+
34
VII
FEL
pho
ton
ener
gy
0
1800
1700
1600
1500
DFT
K shell
L shell
Continuum
3 4 5 6 7 8 9Charge state
0
50
100
150
200
250
Ioni
zatio
n P
oten
tial D
epre
ssio
n (e
V)
ExperimentSP (a.a.)EK (a.a.)DFT (a.a., Gamma point)DFT (a.a., p-like)S-K Son et al., PRX 4, 031004 (2014)B Crowley, HEDP (2014)
35
Comparison of calculations with experiment: Aluminium
0
50
100
150
200
250
DFT method reproduces experimental IPDs
36
Electron interactions with ions and other electrons remains strong in the conditions generated on LCLS. At solid density, continuum states are formed due to the interaction of M-shell states which form the conduction band (tight-binding picture).
Vinko, Ciricosta & Wark, Nature Comm 5, 3533 (2014)
0 0.5 1 1.5 2 2.50
2
4
6
8
10
Atomic core density 7+Atomic valence density 7+Average valence densityDFT 1 eVDFT 10 eVDFT 25 eVDFT 50 eVDFT 75 eVDFT 100 eV
r (a0)
Ele
ctro
n de
nsity
4π
r2 ρ(r)
(a0-1
)
1s2 2s2 2p2
Aluminium
Atomic bound-bound transitions can be a good approximation for bound-free edge
K: 1s2
L: 2s2 2p6
M: 3s2 3p1
Isolated Al Atom Al Atom in metal
Atomic Continuum
Continuum in dense system
37
Higher statesConduction bandIPD
K-M bound bound transitions
model the K-edge
Outline
‣ X-ray Free Electron Lasers & High Energy Density Matter (HDM and WDM)
‣ Isochoric heating to HDM conditions on LCLS
‣ Spectroscopic plasma studies of HDM‣ Ionization Potential Depression‣ Electron Collisional Ionization Rates
‣ Future directions & conclusions
38
IV V VI VII VIIILine
K-edge region
Emission only due to collisions from lower charge state(s)
Experimental measurement of collisional ionization rates on LCLS
1500 1550 1600 1650 1700 1750 1800Photon energy (eV)
1x104
1x105
1x106
1x107
Em
issi
on (p
hot/
eV/s
tera
d)
IVVVIVII
IV V VI VII VIIILine
Clear steps in emission are observed below the K-edge of a given charge state!
Experimental measurement of collisional ionization rates on LCLS
Vinko et al., Nature Communications 6, 6397 (2015)
Process that produces Kα emission
41
K2Lμ
K1Lμ
K2Lμ-1K2Lμ-2
K-shellPhotoionization
Auge
r
LCLS Pulse
Radi
ativ
e Kα photon
L-shell collisionalionization K2Lμ-1
K-edge is too high for photoionization:no emission!
Process that produces Kα emission
42
K2Lμ
K1Lμ
K2Lμ-1K2Lμ-2
K-shellPhotoionization
Auge
r
LCLS Pulse
Radi
ativ
e Kα photon
K1Lμ-1
K2Lμ-2K2Lμ-3
Auge
r
Radi
ativ
e Kα photon
L-shell collisionalionization
Collisions occur within Auger lifetime of K-shell
43
1590 eV 1630 eV
102
103
104
105
106
Intensity (a.u.)
IV V VI VII VIIIInte
nsity
(a.
u.)
IV V VI VII VIII
ExperimentSimulation
a b
IVV VVV VVVIIIVV VVVV
Above-edge Below-edge Above-edge Below-edge
KβKβ
Collisions Collisions
Vinko et al., Nature Communications 6, 6397 (2015)[email protected]
We can model the effect of stronger/weaker collisions
44
1550 1575 1600 1625 1650 1675 1700Photon Energy (eV)
0.01
0.1
1
10
Em
issi
on In
tens
ity (
a.u.
)
ExperimentSim 0.2xCRSim 1.0xCRSim 3.0xCRSim 5.0xCR
V
VI
VII
VIII
IV
Rates are underestimated by a factor between 3 and 5!Vinko et al., Nature Communications 6, 6397 (2015)
The system becomes thermal very quickly
45
De la Varga et al., HEDP 9 (2013) 542
For Ne, 10^22 atoms/cm3 – Al density is 6x higher!
Temperatures also ~10x lower
0 20 40 60 80 100 120 140 160
Time (fs)
1x1010
1x1011
1x1012
1x1013
1x1014
1x1015
1x1016
Ioni
zatio
n ra
te (
Hz) Thermal
Photons
Auger
0
0.5
13+
4+5+ 6+ 7+ 8+
Fractional yield ofground state ions
-40-60-80 -20 0 20 40 60 80
Calculation for Auger relaxation in the time-dependent atomic kinetics in SCFLY(O. Ciricosta, Oxford)
Plasma conditions are well-defined
‣ Spectra are space and time averaged, but most of the emission comes from well-defined plasma conditions
46
1x1015 1x1016 1x1017
Intensity (W cm-2)
0
10
20
30
40
50
Ele
ctro
n te
mp
erat
ure
(eV
)
1x1023
2x1023
3x1023
4x1023
5x1023
Ele
ctro
n d
ensi
ty (
cm-3
)
1x1015 1x1016 1x1017
Intensity (W cm-2)
0
10
20
30
40
50
Ele
ctro
n te
mp
erat
ure
(eV
)
1x1023
2x1023
3x1023
4x1023
5x1023
Ele
ctro
n d
ensi
ty (
cm-3
)
FEL Intensity (Wcm-2)FEL Intensity (Wcm-2)
Ele
ctro
n de
nsity
(cm
-3)
Ele
ctro
n de
nsity
(cm
-3)
Line VI1590 eV
Line VII1630 eV
a b
Contribution to emission from various regions in the sample irradiated at different intensities.
Vinko et al., Nature Communications 6, 6397 (2015)
Conclusions
‣ LCLS can create well-defined plasmas at solid densities and at temperatures in the 100-200 eV range. X-ray-driven emission spectroscopy can be used to study the electronic structure of dense plasmas.
‣ We have measured threshold K-shell ionization energies in Mg, Al, Si, and compounds, resolved by core charge state (K and L shell populations). Results show the ionization energies in dense systems are lower than predicted by the most commonly used IPD models in similar conditions (Stewart & Pyatt, Ion sphere).
‣ Calculations based on DFT + excited potentials reproduce experimental absorption thresholds very well.
‣ We have measured electron collisional ionization rates in a solid-density plasma at temperatures ~30 eV. The experimental collisional rates are higher than predicted by standard models (W. Lotz, Burgess & Chidichimo) by a factor of 3-5.
47
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