Recombination-Enhanced Surface Expansion of Clusters in Intense Soft X-Ray Laser Pulses

We studied the nanoplasma formation and explosion dynamics of single large xenon clusters in ultrashort, intense x-ray free-electron laser pulses via ion spectroscopy. The simultaneous measurement of single-shot diffraction images enabled a single-cluster analysis that is free from any averaging over the cluster size and laser intensity distributions. The measured charge state-resolved ion energy spectra show narrow distributions with peak positions that scale linearly with final ion charge state. These two distinct signatures are attributed to highly efficient recombination that eventually leads to the dominant formation of neutral atoms in the cluster. The measured mean ion energies exceed the value expected without recombination by more than an order of magnitude, indicating that the energy release resulting from electron-ion recombination constitutes a previously unnoticed nanoplasma heating process. This conclusion is supported by results from semiclassical molecular dynamics simulations.

Figure 1

Ion time-of-flight spectra of single large clusters [radii of $180(\pm 30)\mathrm{nm}$, $250(\pm 40)\mathrm{nm}$, $400(\pm 50)\mathrm{nm}$, and $600(\pm 50)\mathrm{nm}$] sorted by cluster size and laser intensity, derived by comparison with Mie simulations; see text. The spectra are sorted from bottom to top by increasing image brightness; corresponding colors reflect similar estimated FEL intensities. Offsets are applied for better visibility. Please note that the 400 nm ion spectra constitute a representative selection out of 94 spectra, while in the other size regimes only 5–10 events were collected. The FEL intensity values experienced by the clusters, as indicated in the figure, have to be considered as orientation only, as the intensity assignment may be compromised by detector nonlinearities [42] and intensity-dependent ultrafast electronic changes in the cluster [44].

Figure 2

(a) Most intense time-of-flight spectrum of $R=400\mathrm{nm}$ clusters. The light peak and ion charge states up to $q=5$ are indicated. Flight-times of atomic ions are given for comparison. The ${\mathrm{Xe}}^{1+}$-back-peak can be observed at $5.5\mu \mathrm{s}$ (“back-peaks” have been excluded for analysis; see Supplemental Material [51]). (b) Kinetic energy distribution of each charge state for the same ion spectrum as a function of $E_{\mathrm{kin}}$ per charge state, corrected for the spectrometer transmission. (c) Evolution of the charge state-resolved kinetic energies for $R=400\mathrm{nm}$ clusters irradiated with different FEL intensities. Note that the spectra show narrow energy distributions and essentially no slow ions for $q>1$. Any signal of slow ions would have been enhanced by the spectrometer transmission.

Figure 3

Average kinetic energy $\overline{E}$ per average charge state $\overline{Q}$ measured for $R=400\mathrm{nm}$ clusters. Each point has been calculated from one spectrum in Fig. 2, as indicated by the color coding. Energy conservation demands that an upper limit for the average ion energy for pure hydrodynamic expansion, neglecting recombination, is given by $\overline{E}=(3/2)k_B{T}_e\overline{Q}$ [47]. The dashed line represents the expected curve for an average electron energy of 32 eV. The slope of the measured curve corresponds to an effective electron temperature of 700 eV.

Figure 4

Semiclassical molecular dynamics simulation of ${\mathrm{Xe}}_{24739}$ under a 12 fs XUV laser pulse ($h\nu =90\mathrm{eV}$, $I=5\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$). (a) Ion spectra including recombination (see inset) after 4 ps propagation. Spectra for $q<5$ are omitted as recombination in later stages will still change their distributions substantially. Note that the spectra reflect the energy per charge state. (b), (c) Time-dependent evolution of electron numbers and thermal energy of free, delocalized, and localized (recombined) electrons.