Multiphoton Multielectron Ionization of Rare Gas Atoms under FEL Radiation (An attempt at interpreting existing experimental data from FLASH)

Transcription

1 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

2 PREAMPLE High Intensity Non-linear Processes 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 appro- ximatuion.

3 When is the radiation strong? A relevant measure of intensity Ponderomotive Energy: U p I/ ω 2 U p / ω I / ω 3 U(p) ) also represents the shift of highly excited states

4 Ionization Rates under LOPT PonderomotiveEnergy: U p 2 I/ ω ω Single-photon Ionization Rate: W σ I N-photon Ionization Rate: W N σ N I N 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?

5 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 N process is N, if neither the initial nor the daughter species are depleted significantly.

6 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.

7 Ionization Rates, Ponderomotive Energy and MP Cross Sections Single-photon Ionization: W σ I N-photon Ionization: W N σ N I N Ponderomotive Energy: U I / ω p 2

8 Multiphoton Ionization A general formal expression for the (generalized) cross section for K-photon K ionization. Can something like this be calculated?

9 Calculated 6-photon 6 ionization (generalized) cross section of hydrogen

10 4-photon ionization cross section of helium

11 Multiple Ionization of Xenon by UV Radiation of ps duration and intensity up to 10^16 W/cm^2, around

12 Scaling of cross sections Λ κ =(σ κ ) (1/κ) Multiple excitation and ionization of atoms by strong lasers P. Lambropoulos and X. Tang JOSA B, Vol. 4, Issue 5, pp (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.

13 ENTER THE FEL Photon energies from XUV to hard X-raysX 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 (?) 2 nd and/or 3 rd harmonic of intensity a few percent (?) of the fundamental.

14 Scaling of Ponderomotive Energy with Photon Energy

15 BEYOND WEAK FIELD SINGLE PHOTON PROCESSES Pump-probe 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..

16 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.

17 Experiments and Atomic Species 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 *

18 Xenon under 12.7 ev Radiation Rate (kinetic) Equations for ionic species during the pulse

19 Spatial Averaging of Interaction Volume

20 Xenon under 12.7 ev Radiation Effect of Intensity Fluctuations (dot-dashed lines) E f

21 Cross sections and saturation intensities

22 Xenon under 12.7 ev radiation Single atom (dashed line), space averaged (solid) Data Wabnitz et al. PRL 94, (2005) Theory Makris and PL, PRA 77, (2008), Also Santra and Greene, PRA 70, (04)

23 Comparison with data

24 Pathways Neon under 38.4 and 42.8 ev

25 Neon under 38.4 and 42.8 ev Rate equations (including 2 nd harmonic)

26 Neon under 38.4 and 42.8 Radiation Sorokin et al PRA 75, (R) (2007) Theory Makris and PL, PRA 77, (2008) Ne 3+ Ne 2+ Ne + Ne

27 Neon under 38.4 and 42.8 ev Radiation

28 Neon under 38.4 and 42.8 ev Comparison to experiment

29

30 Xenon at 93 ev Main Pathways

31 Kinetic Equations for Xe at 93 ev

32 Xenon under 93 ev radiation Data: Sorokin et al. PRL 99, (2007) Theory: Makris, Mihelic and PL (preprint available upon request)

33 So, what is the story? 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.

34 λ (nm) ћω (ev) U p (ev) I (U p ћω ) W/cm