1. Great feeling
Walking Ifen
without
machines
Sunday
Jan 26, 2007

2. VUV photon absorption in warm dense matter
J. Meyer-ter-Vehn and A. Tronnier
Max-Planck-Institute for Quantum Optics, Garching, Germany
V. Krainov (MIFT, Moscow)
Al (solid density)

3. DESY VUV-FEL (FLASH) parameters 2006
1.5 *1012 photons
l= 32.3 nm (38 eV) fs
focus: 20 – 35 mm
presently
implies
Pulse energy: ≈10 µJ
Pulse power: 250 MW
Intensity: ≤ 1014 W/cm2
heats metals up to ≈ few eV
38 eV photons
Al foil
Major problem for DESY
peak intensity experiments
is presently to reduce the
focal spot.
Now campaign for 2 mm focus!

4. VUV-photon interaction model:
Collisional absorption and photo-ionisation
Dispersion relation
Light intensity
I ~ |E |2 ~ exp(-kx)
Dielectric function for quasi-free electrons (Drude model)
collision frequency ne << w

5. What we used so far at MPQ
Eidmann et al., PRE62, 1202 (2000)
Al refl.
Laser absorption (l = 0.8 mm)
in Al versus
intensity (temperature)
Expt: Price et al.,
PRL 75, 252 (1995)

6. Photon absorption by inverse Bremsstrahlungx Z w
Start from spontaneous Bremsstrahlung emission rate
Use differential cross-section (Sommerfeld, atomic units):
Do not forget about stimulated emission :
stimulated
emission
Photon number per quantum state

7. Absorption by Inverse BremsstrahlungZ x w
Photon absorption rate
Ratio of absorption and emission rate only depends on final state densities:
Total absorption rate:
stim. emission
absorption

8. Parameter plane of radiative Coulomb scattering
(I) Fast electrons (Born approx.)
Spitzer
result
Slow electrons (p3/Zw>1)
V.Krainov, JETP 92, 960 (2001)
fast
slow
electrons
high low frequency
(I)
(II)
(III) 1
(III) Slow electrons (p 3/Zw<1)
V. Krainov, J.Phys.B33, 1585 (2000)

9. Fermi average <1/p> including Pauli blocking
Integration over Fermi sphere ( , , ):
Collision frequency (slow electrons):

10. Collision frequency (interpolated model)
Fermi correction
Al (solid density)
hn =1 eV
hn =10 eV
hn =100 eV
(> wp)
log neff 1
0.1 10
100
1000
Te (eV)

11. Maximum Temperature (Te) and Transmisson vs Intensity
100 fs pulse of
38 eV photons
50 nm Al foil
550 eV
FLASH 2006
FLASH 2006

12. Heating and expansion of 50 nm Al foil at 1015 W/cm2
38 eV photons
Al foil
Density
Electron temperature

13. VUV transmission data as function of photon energy
in cold Al compared with present model
L edge
plasma
frequency
present
model for
T=300 K
Keenan et al. (2002)
Rus exp. 2006
DESY
exp. 2006
exp.
Berkeley
tables
Al (T=300 K)
100 nm
XUV

14. DC limit w -> 0 of compares surprisingly well with data
obtained from measured electric and thermal conductivities
Temperature (K) Ag
Exp
Temperature (K) Au
Exp

15. Conclusions For VUV interaction with warm dense matter, the
the Drude-Fermi description appears to be adequate,
when combined with radiative Coulomb scattering
appropriate for`slow electrons´, as derived by Krainov.
A simple analytical expression is derived for the
collision frequency, covering the full temperature
range from solids to plasma and photons ranging
from optical to X-rays.
It is in reasonable agreement with existing data.

16. First Transmission Experiment
Measured by Sokolowski-Tinten, Tschentscher Krzywinski, Juha, Sobierajski et al
Deduced absorption length in cold AL: L=130 nm

17. Light propagation in plasma
EL=E0 exp{ikr-iwt}
plane wave
wp2 = 4pe2n/m
plasma frequency
(k2 - w2/c2) EL = (4piw/c2) j
Maxwell equation
w2 = wp2 /(1+ine/w) + k2 c2
dispersion relation
j = -enu
-iw u = -(e/m) EL - neu
electron current
du/dt
collisions wp w k
light
propagates
reflection

18. Te (eV) hn (eV) log neff log neff hn =10 eV hn =1 eV hn =100 eV 0.1 1
1000
Te (eV) 10
1000
100 1
hn (eV)
log neff
300 K
Te = 10 eV
Te = 1 keV

19. Inverse bremsstrahlung rate for slow electrons (Krainov,J. Phys
Inverse bremsstrahlung rate for slow electrons (Krainov,J.Phys.B33,1585(2000))
1.32

20. Absorption by Inverse Bremsstrahlung
Photon absorption rate Z x w x Z w
Photon emission rate (spontaneous)
Total photon emission rate
stimulated
emission
Photon number per quantum state

21. Rates are related by detailed balance
total absorption
absorption
stim. emission
Total photon emission rate
stimulated
emission
Photon number per quantum state

22. Photon absorption by inverse Bremsstrahlung
Spontaneous photon emission rate:
Bremsstrahlung cross-section:
Detailed balance
(Einstein relations)
Stimulated emission rate:
Photon absorption rate:
(radiation energy density)

23. XFEL Heating with 3 keV photons
Specific energy deposited:
e(J/g) = k(cm2/g) I(W/cm2) t(s)
1 keV
5 Gbar
t = 100 fs
I = W/cm2
3.1 keV photons
= 103 cm2/g
gold opacity
e = J/g

24. Transmission vs. photon energy
Berkeley X-ray data :
Transmission vs. photon energy
20 nm Cu
20 nm Ag
20 nm Au

25. Collosional absorption
wave vector (from dispersion relation)
light intensity
I ~ |E |2 ~ exp(-kx)
absorption coefficient (ne<< w )

26. Unique feature: Explore absolute peak of photo-absorption in solid-density matter
ionisation
Laser
Electrons nc 10
100
1000 1
hn (eV)
as a function of
photon energy
photo-absorption 10
100
1000 1
T (eV)
plasma
solid
TTFermi
as a function of
temperature

27. Foils as Ultra-Fast Switches18
10 W/cm 2
hn = 30 eV
50 nm Al foil
1.0
0.0
0.5
transmission
absorption
reflection
6 fs 10 20
time (fs)