Identification of Auger electron heating and inverse Auger effect in experiments irradiating solids with XUV Free Electron

Laser radiation at intensities larger than 1016 W/cm2

Frank B. Rosmej*a,b, Frédérick Petitdemangea, E. Galtierc

aSorbonne Universités, Pierre et Marie Curie UPMC, UMR 7605, LULI, case 128, 4 place Jussieu, 75252 Paris Cedex 05, France

bEcole Polytechnique, Laboratoire pour l’Utilisation des Lasers Intenses, Atomic Physics in Dense Plasmas - PAPD, 91228 Palaiseau, France

c SLAC-LCLS, Matter in Extreme Conditions, 2575 Sand Hill Road, Menlo Park 94025, CA, USA

ABSTRACT

We present simulations that allow studying Auger heating and the subsequent evolution of the radiation emission of near solid density matter. Particular emphasize is paid to the multi-charge state inverse Auger-effect in dense plasmas which is proposed to explain the target emission when the conduction band at solid density becomes more atomic like as energy is transferred from the electrons to the ions. Simulations are discussed along with the first available experimental data.

Keywords: VUV-Free Electron Laser, dense strongly coupled plasmas, Auger effect, dielectronic satellites, spectroscopy, diagnostics, Auger electron heating, simulations of the spectral distribution

1. INTRODUCTION In the past few years, the development of light sources of the 4th generation, namely XUV/X-ray Free Electron Lasers provides to the scientific community outstanding tools to investigate matter under extreme conditions never obtained in laboratories so far. The use of this new generation Free Electron Lasers (XUV-FEL and X-FEL) is a possible way forward to study of dense strongly coupled plasmas DSCP and warm dense matter WDM1,2,3,4. Such matter is difficult to handle theoretically, with electrostatic and thermal energies being of equivalent importance, rather than one being a perturbation of the other as in solid state physics or classical plasma physics. Moreover, in this regime experimental data is not easy to obtain and one of the key issues is the ability to create uniform well-defined samples of matter near solid density but with temperatures of ~ 1-100 eV. Free electron XUV- and X-ray lasers allow volumetric heating because the plasma frequency of the solid is smaller than the laser frequency. The radiation penetrates therefore deep into the solid and the analysis of the data does not suffer from critical surface effects. Moreover, in regimes where thermal energies are too low to create short wavelength radiation that can exit a high-density sample without reabsorption, the emission from photo-ionized core states, allows to get information on high energy density matter at low temperatures. As theory is at its infancy, the analysis of matter via the self-emission of the target is of central importance. We have therefore studied a solid-to-plasma transition via the self emission by irradiating Al foils with the FLASH XUV free electron laser: photon energy of 92 eV, pulse duration of 20 fs, micro-focusing and intensities larger than 1016 W/cm2. Intense XUV self-emission has been observed showing spectral features that are consistent with emission from regions of very high density, but that go beyond single inner-shell photo-ionization of solid. Auger heating of the electrons in the conduction band that occurs immediately after the absorption of the XUV laser energy by the crystal has been identified as the dominant heating mechanism via characteristic features of intra-shell transitions1. In the following paper, we develop atomic physics models to analyze the spectral distribution with respect to temperature and density variations to characterize matter irradiated by intense radiation fields. *frank.rosmej @upmc.fr; phone +33-(0)1.44.27.43.01; fax +33-(0)1.44.27.43.01

X-Ray Lasers and Coherent X-Ray Sources: Development and Applications IX, edited by James Dunn, Annie Klisnick, Proc. of SPIE Vol. 8140, 81400R · © 2011 SPIE

CCC code: 0277-786X/11/$18 · doi: 10.1117/12.892094

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2. EXPERIMENT 2.1 Experimental setup

The experiment1 was carried out using the FLASH XUV-Free Electron Laser Facility at DESY in Germany, the experimental scheme is depicted in Fig. 1. Solid Al-foils were irradiated with intense pulses of λ = 13.5 nm radiation operating at 5 Hz. The pulse length was τ ~15 fs and the beam was focused down to about 1 μm diameter with a multilayer parabolic optic (multilayer Mo-Si) with a focal length of 269 mm to achieve intensities up to 1017

Wcm-2. A 3 mm aperture in the beam limited its size and the pulse energies varied between 5 and 10 μJ on target.

Figure 1. Scheme of the experimental setup

The best focus was established by analysis of PMMA (Polymethylmethacrylate) ablation using a range of target positions relative to the focus optic and a range of pulse energies. This analysis established that the best focus was ~1 μm FWHM. The reflectivity of the optic was measured after the experiment: 48%. The spectrometer employed a 1200 lines/mm Hitachi grating with variable line spacing to create a flat spectral focal plane on a CCD camera positioned on a vacuum flange, providing a spectral coverage from ~ 10-30 nm. An Al edge filter was used to establish that the spectral resolution achieved was ~ 0.1 nm thus providing an effective spectral resolution of about λ/δλ ~150 in the relevant spectral range. The target samples were composed of 10 μm thick Al foils that were continuously moved transverse to the FEL beam across the focus to expose a fresh surface each shot.

Figure 2. Experimental spectrum (solid black curve) and simulation (solid blue curve) of Ne-like 3-2 transitions in

aluminum. The red arrows indicate missing transitions when employing a simulation of the Al IV emission only.

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2.2 Identification of line emission

Fig. 2 shows an experimental spectrum obtained by integrating 2000 shots at irradiation intensities of about 1016 W/cm2. The dominant spectral feature (Fig. 2) is identified as ionic Al IV lines: 1s22s22p6-1s22s22p5 (2P°)3s 1P and 3P at 16.1 nm and 16.2 nm. The transitions at shorter wavelengths are related to transitions 1s22s22p6-1s22s22p5 3d 1P, 3P and 3D at 13.0 nm, 13.1 nm and 13.2 nm respectively. As can be seen from Fig. 2 simulations that are based only on ionic Al IV line emission do not permit to explain the data (red arrows). It is known that transitions located at the red wing of resonance line transitions might be due to screened transitions, so called satellite transitions. The observed transitions on the red wavelength wing of the Al IV resonance line transitions originate from XUV-transitions into the L-shell of heated Al while spectator electrons are present in the M-shell4:

I. K2L7M3 → K2L8M2 + hνAl II II. K2L7M2 → K2L8M1 + hνAl III

Taking into account Al IV emission (Fig. 2) as well as Al II and Al III emission of K1L7M2 and K2L7M3 configurations, the experimental data are well described1, see Fig. 3.

Figure 3. Fit (solid green curve) of the experimental spectrum (solid black curve) taking into account screened

transitions from K2L7M2 (solid blue curve) and K2L7M3 (solid red curve) configurations.

We note that the simulations shown in Fig. 3 include the ionic Al IV lines (Fig. 2) as well as the screened transitions according I. and II. The good overall agreement indicates the importance of multiple excited autoionizing states for the data analysis.

3. AUGER ELECTRON HEATING AND SPECTRAL EMISSION 3.1 Photoionization, Auger electron emission and Auger electron heating

A temperature Te, which is much higher than melt, enables one to construct a qualitative model of electron heating. After photoionization of the LII and LIII shells an excess energy of ~19 eV will be distributed amongst the 4 conduction band electrons. Assuming rapid thermalization on sub fs-scale and accounting for the 12 eV Fermi energy for Al, a kTe of ~8 eV is obtained (note that a laser intensity greater than about 1016 W/cm2 allows photoionization of almost every atom in the crystal structure). This Te represents an excited transient state that will start relax after ~40 fs by either radiative decay or by autoionization. As the branching ratio favors autoionization by 99.8 % the energy of the decaying electron is shared with the three remaining conduction band electrons.

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Simulations show (see Fig. 3) that the energy difference, e.g. between the configuration K2L8M2 and K2L7M3 is about 70 eV which is equivalent to the kinetic energy of the Auger electrons. Assuming that all the Al atoms in the intense FEL beam are photoionized this excess 70 eV will rapidly thermalize with the 8 eV electrons resulting in an expected electron temperature of Te of ~22 eV. This electron temperature is in reasonable agreement1 with the temperature obtained from the simulations of the screened transitions I. and II. shown in Fig. 2. After Auger electron heating, phonon coupling takes place and the crystalline structure starts to disassemble. 3.2 Inverse Auger effect and emission from multiple excited states

By the principle of detailed balance, the inverse Auger effect (dielectronic capture) must exist. If the electron temperature is of the order of the dielectronic capture energy Ekj, the inverse Auger effect is very effective as the exponential factor is small:

Inverse Auger rate ∝ Γjk

exp(−Ekj /kTe )(kTe )3 / 2 (1)

Equation (1) shows that the inverse Auger rate is proportional to the Auger rate Γkj itself, therefore the response to photoionization and to dielectronic capture is quite different. In the case of photoionization, radiation emission is strongly suppressed, because the Auger rates are much larger (for aluminum) than the spontaneous radiative decay rates. However, in a regime where the inverse Auger effect is pronounced, the non-favorable branching factor

Branching factor K ji ∝A ji

A jll

∑ + Γjkk

∑ (2)

almost cancels for the effective photon intensity, see Table 1:

Intensity ∝ Aji

Γ jk + Ajll

∑k

∑Γ jk

exp −Ekj / kTe( )kTe( )3/2 ≈ Aji

exp −Ekj / kTe( )kTe( )3/2 (3)

This is a further indication that the observed radiation emission (see Fig. 2) is located at times, when the crystalline structure starts to disassemble and the emission becomes more atomic like (for densities lower than about 2 g/cm3 for Al). Due to the large Autoionizing rates, the time scale of the radiation emission is of the order of the characteristic time scale of the autoionizing rate (fs) itself5, indicating that the screened transitions are emitted immediately after Auger electron heating has become effective. The analysis of the spectral distribution of the screened transitions I. and II. can therefore provide the electron temperature and density of the near solid density plasma. We therefore analyze in the next paragraph the underlying theory and investigate the temperature and density sensitivity of the spectral emission originating from multiple excited hole states.

Table 1: Effect of autoionization rate on branching factor for dielectronic capture

Level i Level j Aji (s-1) Kji Level k Γjk (s-1) Kji×Γjk (s-1) 1s2 2s2 2p6 3s1 1s2 2s2 2p5 3p2 6.2×109 3.7×10-4 1s2 2s2 2p6 1.7×1013 6.3×109 1s2 2s2 2p6 3s1 1s2 2s2 2p5 3p2 1.5×109 2.8×10-5 1s2 2s2 2p6 5.2×1013 1.5×109 1s2 2s2 2p6 3s1 1s2 2s1 2p6 3p1 3d1 6.4×107 1.8×10-7 1s2 2s2 2p5 3p1 1.1×1014 2.0×107 1s2 2s2 2p5 3s1 3d1 1s2 2s1 2p6 3s2 1.6×108 9.4×10-8 1s2 2s2 2p5 3s1 1.5×1015 1.4×108 1s2 2s2 2p6 3s1 1s2 2s1 2p6 3p1 3d1 6.4×107 1.8×10-7 1s2 2s2 2p5 3s1 5.1×1010 9.2×103 1s2 2s2 2p5 3s1 3d1 1s2 2s1 2p6 3s2 1.6×108 9.4×10-8 1s2 2s2 2p5 3p1 2.4×1011 2.3×104 1s2 2s2 2p5 3p1 3d1 1s2 2s1 2p6 3p1 3d1 1.8×109 4.6×10-6 1s2 2s2 2p5 3s1 2.3×1011 1.1×106

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4. SIMULATIONS OF THE SPECTRAL EMISSION DRIVEN BY INVERSE AUGER EFFECT

4.1 Population kinetics of multiple excited states and spectral distribution

LSJ-split simulations (including intermediate coupling and configuration interaction) of the emission of multiple excited states are very complex and request a large set of atomic data for the population matrix. These data (energy levels, radiative decay rates, electronic collisional excitation rates, autoionization rates, etc) have been obtained from FAC6 to feed a LSJ-split multi-level atomic population kinetics code7. In the present analysis we focus on the emission originating from the configuration K2L7M2.

Figure 4. configurations and atomics processes taken into account

Figure 4 shows the energy level diagram of single and multiple excited states of Al IV and Al III. It can be seen clearly that multiple excited states are connected to Al III states K2L8M1 by collisions, and to Al IV states (ground and excited states) by autoionization and dielectronic capture. The generalized population matrix Wij allows calculating the population of each state, including the multiple excited states because all collisions and radiative decays between the all levels (ground and excited) are taken into account7:

dni

dt= −ni × Wij

j∑ + nk × Wki

k∑ (4)

It is important to emphasize that this generalized approach allows exact treatment of excited states coupling of autoionization/dielectronic capture8 which is very important in dense plasmas. Wij is the generalized population matrix:

Wij = Aij + ne × Cij + Γij + ne × DCij + ne × Iij + ne2 × Tij + ... (5)

A more detailed description of the simulation code developed is given in [7].

4.2 Investigation of temperature variations on the spectral distribution

The dielectronic capture rate is a function of the electron temperature Te. We present below two graphs for 2 different densities where we calculate the emission for 3 different temperatures (Fig 5), kTe=10 eV, 20 eV and 30 eV. In order to facilitate the following discussion multiple excited states are only populated by inverse Auger effect (means collisional excitation from the ground state is artificially switched off).

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Figure 5. Effect of electronic temperature on the spectral distribution for two electronic densities if multiple excited states are only

populated by dielectronic capture The simulations of the spectral emission (Fig. 5) shows 3 emission groups of lines. The ones near 14 nm and 17 nm correspond to transitions 1s2 2s2 2p6 3s1 - 1s2 2s2 2p5 3l 3l’ and the one near 26 nm corresponds to transitions between multiple excited states 1s2 2s1 2p6 3l 3l’ - 1s2 2s2 2p5 3l 3l’ (intra-shell transitions). In each case, when temperature increases, we see that levels with higher energy (see Fig. 4) are more and more populated: for Te=10 eV, the emission shows a maximum at 17.5 nm, and for Te=20 eV, the maximum is located near 14 nm. Moreover, the intensity of the transitions between multiple excited (intra-shell transition near 26 nm) increase too. This is due to the exponental factor in equation (1) which rises with increasing kTe. In the next paragraph, we discuss the spectral evolution with density.

4.3 Investigation of density variations on the spectral distribution

Figure 5 shows that with increasing density, the spectral distribution shows characteristic changes: emission from highly excited levels (Fig. 4) become increasingly important. Below we present simulations for different electron densities and kTe=25 eV (which corresponds to the temperature deduced from the analysis of the experimental data1). Fig. 6 shows the spectral emission taking into account two excitation channels: electron impact excitation and dielectronic capture (fig 6). It shows that the emission tends to be Boltzmann for densities larger than about ne=1020 cm-3.

Figure 6. Spectral distribution of multiple excited states for Te=25 eV and densities ne varying from 1018 cm-3 to 1022 cm-3 when

inverse Auger effect and electron impact excitation are taken into account

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Usually, this happens when collisions are more important than radiative decay and autoionization:

ne × C >> A + Γ (6)

As shown by figure 7 where dielectronic capture is artificially turned off, the collisions are not enough efficient to drive the spectral distribution toward a Boltzmann one. This can be qualitatively understood considering averaged rates:

A ≈109 s−1

Γ ≈1014 s−1

C ≈10−8 cm3 ⋅ s−1

⎧

⎨ ⎪

⎩ ⎪

⇒ ne >>A + Γ

C ≈1022cm−3 (7)

The high-density threshold (to obtain a Boltzmann distribution) according (7), however, is inconsistent with the simulation where all atomic processes are active.

Figure 7. Spectral distribution for Te=25 eV and different electron densities ne when dielectronic capture is artificially turned off

These results lead us to the conclusion that the inverse Auger channel (dielectronic capture) is a mechanism to achieve a Boltzmann distribution under less stringent conditions, Fig. 8. The mechanism to drive the spectral distribution towards a Boltzmann one due to inverse Auger effect can be analytically explained as follows. The detailed balance in steady state leads to

ne × nj × Cjij∈G .S∑ + ne × nj ' × C j 'i

j '∈satellite∑ + ne × nl × Ali

l '>i∑ + ne × nk × DCki

k∑ =

ni × Ail 'l '<i∑ + ni × Γ ik '

k '∑ + ni × ne × Cij ''

j ''∑

(8)

Using average rates, we find:

ne × nk × DCki ≈ ni × Γik (9)

which connects the multiple excited state i with the resonant level k via the Saha-Boltzmann relation. As a consequence, if the levels k (ground state and singly excited states), have a Boltzmann population, then the multiple excited states have a Boltzmann distribution too. To complete these scheme, we see that the average rates linking ground state and singly excited states of Al IV are A=109 s-1 and C=10-8 cm3s-1, so the density needed to achieve a Boltzmann distribution according to equation (8, 9) is ne>1019 cm-3 which is consistent with simulations (e.g., Fig. 8). As demonstrated by Fig. 4, almost all levels of the configuration 1s22s12p63l3l’ are connected via the inverse Auger effect from excited states 1s22s22p53l’. Moreover, even similar configurations are coupled via excited states, Table 2 (a) and (b).

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Figure 8. Spectral distribution for Te=25 eV and different electron densities ne taking into account dielectronic capture from the ground state and singly excited states of Al III. Population of multiple excited states by electron impact excitation is artificially

switched off

Table 2 (a) : Excited states coupling of inverse Auger effect for equivalent configurations 1s22s22p53l3l’ – 1s22s22p53l

Transition

1s22s22p53l3l’ – 1s22s22p53l Γjk (s-1)

Γjkk

∑ (s-1)

k ∈ 1s22s22p53l k ∈ 1s22s12p63l k ∈ 1s22s22p53l

+1s22s12p63l

k ∈ 1s22s22p6

+1s22s22p53l

+1s22s12p63l [2p+3(j=3/2) 3d-1(j=3/2) 3d+1(j=5/2)]J=11/2

- [2p+3(j=3/2) 3s+1(j=1/2)]J=2 2.05×1014 3.25×1014 0 3.25×1014 3.25×1014

[2p+1(j=1/2) 3d-2(j=2)]J=5/2

- [2p+3(j=3/2) 3s+1(j=1/2)]J=2 1.10×1014 1.79×1014 0 1.79×1014 1.93×1014

[2p+3(j=3/2) 3d-1(j=3/2) 3d+1(j=5/2)]J=9/2

- [2p+3(j=3/2) 3s+1(j=1/2)]J=2 1.46×1014 3.23×1014 0 3.23×1014 3.24×1014

[2p-1(j=1/2) 3d-1(j=3/2) 3d+1(j=5/2)]J=7/2

- [2p-1(j=1/2) 3s+1(j=1/2)]J=1 1.24×1014 3.11×1014 0 3.11×1014 3.14×1014

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Table 2 (b) : Excited states coupling of inverse Auger effect for equivalent configurations 1s22s12p63l3l’ – 1s22s12p63l

Transition

1s22s12p63l3l’ – 1s22s12p63l Γjk (s-1)

Γjkk

∑ (s-1)

k ∈ 1s22s22p53l k ∈ 1s22s12p63l k ∈ 1s22s22p53l

+1s22s12p63l

k ∈ 1s22s22p6

+1s22s22p53l

+1s22s12p63l [2s+1(j=1/2) 3d+2(j=2)]J=5/2

- [2s+1(j=1/2) 3s+1(j=1/2)]J=1 3.99×1013 4.89×1014 5.81×1013 5.48×1014 5.48×1014

[2s+1(j=1/2) 3d-1(j=3/2) 3d+1(j=5/2)]J=9/2

- [2s+1(j=1/2) 3s+1(j=1/2)]J=1 2.40×1014 4.62×1014 3.13×1014 7.75×1014 7.76×1014

[2s+1(j=1/2) 3d-1(j=3/2) 3d+1(j=5/2)]J=7/2

- [2s+1(j=1/2) 3s+1(j=1/2)]J=1 2.40×1014 4.62×1014 3.13×1014 7.75×1014 7.76×1014

[2s+1(j=1/2) 3d+2(j=0)]J=1/2

- [2s+1(j=1/2) 3s+1(j=1/2)]J=1 7.02×1013 4.81×1014 1.13×1014 5.94×1014 5.94×1014

5. CONCLUSION The high-resolution spectroscopic analysis of line emission from multiple excited states (hole states) provides insight in the understanding of the interaction of intense fs VUV-Free Electron Laser radiation with matter. It has been demonstrated that the inverse Auger effect allows characterizing the temporal evolution of irradiated matter even from time integrated spectral emission. This is a great step forward in the analysis, as fs-streak cameras will not be available in nearest future for the Free Electron Laser community. Atomic population kinetics of autoionizing hole sates has been developed to investigate temperature and density sensitivities from the spectral distribution. Employing a detailed LSJ-split atomic level structure it has been demonstrated, that increasing temperature raises considerably intra-shell emission and that excited states coupling effects play an important role in the formation of the spectral distribution of hole states. The developed simulations present benchmark simulations to understand complex radiative properties of high-density matter driven by intense VUV/X-ray Free Electron Laser radiation.

6. ACKNOWLEDGEMENT Financial support from the project “EMERGENCE-2010” of the University Pierre and Marie Curie, Paris is greatly acknowledged.

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