Multiphoton Multielectron
Ionization of Rare Gas Atoms
under FEL Radiation
(An attempt at interpreting existing
experimental data from FLASH)
Hamburg Oct. 8 – 10, 2008
P. Lambropoulos
in collaboration with
M.G. Makris and A. Mihelic
PREAMPLE
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High Intensity Æ Non-linear Processes Æ
Multiphoton and (depending on conditions)
Multiple Ionization.
What is known as Strong Field, Nonperturbative
phenomena (such as ATI and HOHG) are of
relevance, only under long wavelength (infrared)
and rely on the Single Active Electron approximatuion.
When is the radiation strong?
„
A relevant measure of intensity
„
Ponderomotive Energy:
U p ≈ I /ω
U
„
p
2
/ω ≈ I /ω 3
U(p) also represents the shift of highly excited states
Ionization Rates under LOPT
U p ≈ I /ω2 ω
„
PonderomotiveEnergy:
„
Single-photon Ionization Rate:
W ≈ σ I
„
N-photon Ionization Rate:
WN ≈ σ N I
„
Under these conditions a log-log plot of ion
signal versus intensity should be a straight
line of slope N. If not, something is wrong ?
N
A bit of prehistory
From about the early 1970’s
through the late 1980’s.
Subnanosecond to a few picosecond pulse
durations.
„
Important point: The slope in an N-photon
process is N, if neither the initial nor the
daughter species are depleted significantly.
An example of data on high order multiphoton ionization of the rare
gases, in the early days of the Nd-glass laser, is shown below.
The slopes of the log-log plot of the ionization signal did follow up to a point
the order of the process expected in perturbation theory, but it was the
beginning of discussions and arguments as to when perturbation theory ceases
to be valid.
Ionization Rates, Ponderomotive
Energy and MP Cross Sections
„
Single-photon Ionization:
W ≈ σ I
„
N-photon Ionization:
WN ≈ σ N I
N
≈ I /ω
2
„
Ponderomotive Energy:
U
p
Multiphoton Ionization
„
A general formal expression for the (generalized)
cross section for K-photon ionization.
Can something like this be calculated ?
Calculated 6-photon ionization (generalized) cross
section of hydrogen
4-photon ionization cross section of helium
Multiple Ionization of Xenon by UV Radiation of ps
duration and intensity up to 10^16 W/cm^2, around
1983-84
Scaling of cross sections
Λκ=(σκ)(1/κ)
Multiple excitation and ionization of atoms by strong lasers
P. Lambropoulos and X. Tang
JOSA B, Vol. 4, Issue 5, pp. 821-832 (1987);also Madsen
and PL, PRA 59, 4574 (1999).
Although, in principle, multiphoton ionization cross sections can be calculated, to
some degree of approximation, this is not necessary, as far as general features of the
processes are concerned. For such purposes, an approach based on scaling has been
developed. Details can be found in the above reference.
ENTER THE FEL
„
„
„
„
„
Photon energies from XUV to hard X-rays
Relatively High Intensity, but U(p) << ω
Pulse durations a few fs, but many cycles of the
field
Intensity fluctuations: For chaotic light, the
cross section is effectively multiplied by N!
Inevitable (?) 2nd and/or 3rd harmonic of
intensity a few percent (?) of the fundamental.
Scaling of Ponderomotive Energy with
Photon Energy
BEYOND WEAK FIELD SINGLE
PHOTON PROCESSES
„
„
„
„
„
„
„
Pump-probe and Stark splitting of resonances.
Two or few-photon multiple ionization.
Strongly-driven Auger resonance.
Double Auger excitation.
Stimulated hole filling.
Probing of relaxation following Auger or double
excitation (ionization).
And more…………..
Available Data from FLASH
„ Let us then look at one class of
these processes (few- to
multiphoton ionization) for the
shorter wavelengths, with data
available so far; specifically for the
atoms of Neon and Xenon.
Experiments and Atomic Species
„
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„
„
„
„
Helium under ~ 13 eV radiation
Xenon under 12.7 eV radiation *
Neon under 38.4 eV and 42.8 eV radiation *
Xenon under 93 eV radiation *
Helium under 42 to 45 eV radiation (Two-photon
Double Ionization)
In the following slides, we discuss the three cases above
marked by *
Xenon under 12.7 eV Radiation
Rate (kinetic) Equations for ionic
species during the pulse
Spatial Averaging of Interaction Volume
Xenon under 12.7 eV Radiation
Effect of Intensity Fluctuations (dot-dashed lines)
E
f
Cross sections and saturation intensities
Xenon under 12.7 eV radiation
Single atom (dashed line), space averaged (solid)
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Data – Wabnitz et al. PRL 94, 023001 (2005)
Theory – Makris and PL, PRA 77, 023415 (2008),
Also – Santra and Greene, PRA 70, 053401 (04)
Comparison with data
Neon under 38.4 and 42.8 eV
„
Pathways
Neon under 38.4 and 42.8 eV
„
Rate equations (including 2nd harmonic)
Neon under 38.4 and 42.8 Radiation
Sorokin et al PRA 75, 051402(R) (2007)
Theory – Makris and PL, PRA 77, 023401 (2008)
Ne3+
Ne2+
Ne+
Ne
Neon under 38.4 and 42.8 eV Radiation
Neon under 38.4 and 42.8 eV
„
Comparison to experiment
Xenon at 93 eV – Main Pathways
Kinetic Equations for Xe at 93 eV
Xenon under 93 eV radiation
„
Data: Sorokin et al. PRL 99, 213002 (2007)
Theory: Makris, Mihelic and PL (preprint available upon request)
So, what is the story?
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Some general experimental features are reproduced by
theory, within the framework of kinetic equations.
The experimental data for Xenon under 93 eV radiation
are compatible with multiphoton perturbation theory,
with no evidence for non-perturbative behaviour.
Still, some difficult to understand qualitative
discrepancies, such as certain slopes, persist.
Further insight and understanding will require much
more detailed experimental data, beyond the slopes of
inonization signals.
λ (nm)
ћω (eV)
Up (eV)
I (Up≈ ћω ) W/cm2
1242
1
1.27
7.8 1012
621
2
0.31
6.3 1013
310.5
4
7.9 10-2
5.0 1014
155.2
8
1.9 10-2
4.0 1015
77.6
16
4.9 10-3
3.2 1016
38.8
32
1.2 10-3
2.6 1017
19.4
64
3.1 10-4
2.1 1018
9.7
128
7.7 10-5
1.6 1019
4.9
256
1. 10-5
1.3 1020
2.4
512
4.8 10-6
1.1 1021
1.2
1024
1.2 10-6
8.4 10 21