C O 2 exploding clusters dynamics probed by XUV fluorescence
M. Negro, H. Ruf, B. Fabre, F. Dorchies, M. Devetta, D. Staedter, C. Vozzi, Y. Mairesse, S. Stagira
aa r X i v : . [ phy s i c s . a t m - c l u s ] F e b CO exploding clusters dynamics probed by XUVfluorescence M. Negro , H. Ruf , B. Fabre , F. Dorchies , M. Devetta , D.Staedter , C. Vozzi , Y. Mairesse , S. Stagira CNR-IFN, I-20133 Milan, Italy CELIA, Universit´e de Bordeaux, CEA, CNRS, F-33405 Talence, France Universit´e de Toulouse, UPS, F-31062 Toulouse, France Politecnico di Milano - Physics Department, I-20133 Milan, ItalyE-mail: [email protected]
Abstract.
Clusters excited by intense laser pulses are a unique source of warm densematter, that has been the subject of intensive experimental studies. The majorityof those investigations concerns atomic clusters, whereas the evolution of molecularclusters excited by intense laser pulses is less explored. In this work we trace thedynamics of CO clusters triggered by a few-cycle 1.45- µ m driving pulse through thedetection of XUV fluorescence induced by a delayed 800-nm ignition pulse. Strikingdifferences among fluorescence dynamics from different ionic species are observed. O exploding clusters dynamics probed by XUV fluorescence
1. Introduction
The nonlinear interaction of laser pulses with clusters has been the subject of intensetheoretical and experimental research in the last two decades [1]. Particular attentionhas been devoted to the complex cluster dynamics occurring during and after theinteraction with a high-energy ultrashort laser pulse; time-resolved experiments havebeen performed in single and double-pulse configurations, looking to electron and ionspectra [2, 3, 4], to the efficiency in laser absorption and scattering [5, 6] as well as tothe emission in the XUV [7, 8, 9, 10] and X ray [11, 12, 13] spectral regions.Most of these time-resolved studies have been performed with Ti:Sapphire lasersoperating at 800 nm, which were the only sources of intense and ultrashort laser pulses inoperation up to a decade ago. However impressive advances in laser science are quicklydriving the investigation of laser-clusters interaction towards new frontiers. On the onehand, studies concerning clusters exposed to intense XUV an X ray pulses are nowadaysmade possible by the availability of Free Electron Lasers [14, 15, 16, 17] and laser-drivenHigh Order Harmonic sources [18, 19]. On the other hand, the recent development ofintense and ultrafast laser sources based on optical parametric amplifiers [20] has openedthe way to the study of strong-field laser-matter interaction in the mid-IR spectral region[21]. In spite of the large number of experimental investigations, the mentioned studiesmostly concentrate on atomic clusters made of noble gases, whereas the evolution ofmolecular clusters excited by intense laser pulses is much less explored [2, 16].In this work we present an experimental investigation of CO cluster dynamics drivenby a few-cycle 1.45- µ m laser pulse and probed by a delayed 800-nm pulse; the dynamicswas traced by recording XUV fluorescence lines emitted by different ionic species asa function of the pump-probe delay and of the average cluster size. Fluorescenceis a powerful probe of the cluster environment, since it is sensitive to the electrontemperature as well as to collisional excitation and ionization mechanisms at work. Its Ti:Sapphire
800 nm, 60 fs10 Hz, 15 mJ BS gas cell
DM DSglass plate
OPA
XUVspectrometer Even-Lavie valve FM Figure 1.
Experimental setup. BS: beam splitter; HWP: half-wave plate; OPA:optical parametric amplifier; DS: delay stage; DM: dichroic mirror; FM: focusingmirror. O exploding clusters dynamics probed by XUV fluorescence p (bar) T ( ◦ C) N (molecules)12 80 320012 31.4 610030 150 820030 80 1700030 33.7 31000 Table 1.
Experimental conditions explored in this work; p : CO valve backingpressure; T : valve temperature; the corresponding average cluster sizes N werecalculated according to [22]. potential can be fully accomplished by time-resolved techniques, as in a pump-probemeasurement, providing access to dynamical processes occurring in the cluster. Themain findings of our investigation are that: (i) at a larger cluster size corresponds aslower growing and decay dynamics of XUV ionic emission lines; (ii) the fluorescencedecay dynamics is well fitted by a linear decay law; (iii) lower ionization stages emitearlier than higher ones along the pump-probe delay scan. The latter finding pointsto intriguing opportunities for probing phenomena occurring inside clusters excited byintense laser pulses.By a simple elaboration of the experimental outcomes we also evaluate the initialelectron temperature of the CO clusters ionized by the driver pulse; we show that, inspite of the relatively high peak intensity of the driver, the interaction of a CO clusterwith a mid-IR pulse leads to the generation of a cold nanoplasma, with a temperatureinversely proportional to the square of the number of molecules inside the cluster. Thisresult shows that intense mid-IR pulses, which are usually considered as ideal driversfor accelerating electrons to very high ponderomotive energies [21], can be effectivelyexploited as ultrafast drivers of nanoscale warm matter with solid-state density andelectron temperatures in the range of a few to a few tens of electronvolts.
2. Experimental setup
The experimental setup is shown in Figure 1. A Ti:Sapphire amplified laser systemprovides 60-fs pulses at 10 Hz repetition rate centered at 800 nm with an energy of 15mJ. A large portion of the beam (about 90% in energy) pumps an Optical ParametricAmplifier (OPA) which provides tunable, intense and ultrashort pulses in the mid-IR[20]. The OPA can operate between 1.3 and 1.8 µ m, generating pulses with a temporalduration between 18 and 25 fs, according to the working wavelength, and mJ-levelenergy. In the present work, the OPA was tuned at 1.45 µ m and produced a 1.3 mJpump pulse with 20 fs duration (hereafter called driver ).The remaining portion of the Ti:Sapphire beam (about 10% in energy) is used forgenerating the probe pulse (hereafter called heater ). This beam undergoes opticalfilamentation in an argon-filled cell (not shown in the figure); the filamentation processO exploding clusters dynamics probed by XUV fluorescence Figure 2.
Pump-probe scan in CO clusters as a function of the delay between driverand heater and of the fluorescence wavelength; the average number of molecules percluster was N = 6100. The driver and heater polarizations were perpendicular. ensures a good spatial profile of the beam at the output of the cell. Furthermore, thelarge spectral broadening induced by filamentation is exploited for temporal stretchingof the pulse up to 100 fs by propagation through a glass plate. Afterwards, the heaterbeam propagates through a half-wave plate for controlling the polarization state.The driver and the heater are recombined with a dicroic beam splitter and propagatethrough an iris which is used for tuning the on-target energy. A translation stage isused for changing the temporal delay between the pulses; in the following, positivedelays correspond to a heater pulse coming after the driver one. The beam is thensent in the vacuum interaction chamber where a spherical mirror (curvature radius R = −
300 mm) focuses it into the target. The on-target pulse energies were 0.45 mJ(driver) and 0.3 mJ (heater); the estimated peak intensities were about 2 × W / cm and 4 × W / cm respectively. In this work the target was a jet of clusters obtainedby supersonic expansion of noble or molecular gases [22] through an Even-Lavie valve[23] with a trumpet shaped nozzle of 250 µ m diameter synchronized to the laser sourceand operating with an opening time of 25 µ s. The average size of the clusters could bechanged by tuning the gas backing pressure and the valve temperature; the experimentalcondition we explored are summarized in Table 1.The XUV fluorescence emitted by the excited CO clusters was detected by a flat-fieldXUV spectrometer in grazing incidence geometry [24] as a function of the delay betweenthe two laser pulses; the spectrometer was calibrated in wavelength on the basis of somestrong fluorescence lines emitted by Krypton clusters compared against the NIST AtomicO exploding clusters dynamics probed by XUV fluorescence
15 20 25 30 35 40 4502000400060008000 O V I . - . O III . O III . - . O III . - . O III . - . C I V . - . O V I . O V . - . O V . - . O I V . - . O V . - . O I V . - . O V I . - . O V . C III . O V . - . C I V . - . O III . O III . O III . - . O I V . - . O I V . - . O I V . - . CO , 30 bar, 33.7 (cid:176)C I n t en s i t y ( a r b . un . ) Wavelength (nm)parallel conf. = 1.4 ps O I V . - . Figure 3.
Emission spectrum in CO clusters with average size N = 31000 at adriver-heater delay τ = 1 . Spectra Database [25]. The spectrometer was aligned on the direction of the laser beam,thus allowing the detection of coherent XUV radiation emitted by the excited clusters.For driver and heater with parallel polarizations, we observed continuous XUV spectraemitted in a very limited delay range, compatible with the duration of the pulses cross-correlation. This emission was interpreted as enhanced high-order harmonics generatedwhen the two pulses are overlapped in time [26] and was exploited for determining thezero delay between the pulses. We could not observe generation of high-order harmonicsin CO clusters neither by one of the two pulses nor when the pulses were not overlappedin time. Moreover, harmonic generation was never observed at any time delay for driverand heater pulses with orthogonal polarizations.Since we will focus this work on incoherent emission from ions excited inside the clusters,we will consider hereafter only those experimental results we obtained with pulses havingperpendicular polarization directions.
3. Results
A typical pump-probe scan performed in CO clusters is shown in Figure 2 as a functionof temporal delay and fluorescence wavelength. According to the Hagena model ofclustering in supersonic gas expansion [22] the average number of molecules per clusterwas N = 6100 (see Table 1 for the corresponding experimental conditions).Several emission lines are clearly observed; the lines appear only for positive delays, i.e.O exploding clusters dynamics probed by XUV fluorescence I p (eV) Investigated lines (nm) Lower level Upper levelC I 11.26O I 13.61C II 24.38O II 35.12C III 47.88 38.62(*) 2s S P O III 54.93 37.38-37.444 2s P j P j ′ C IV 64.49 38.403-38.418(*) 1s P j D j ′ O IV 77.41 23.836-23.857 2s P j D j ′ O V 113.90 19.2751-19.2906 2s2p P j D j ′ O VI 138.12 17.2935-17.3095 1s P j D j ′ C V 392.09C VI 489.99O VII 739.33O VIII 871.41
Table 2.
Ionization potential I p , investigated spectral lines and correspondingtransitions for Carbon and Oxygen ions [25]; data are ordered for increasing I p . Thelines from Carbon, marked with (*), appear overlapped in our setup. when the heater pulse comes after the driver one. This behaviour is consistent with theso called nanoplasma model [27], which provides a qualitative description of the laser-cluster interaction: the driving pulse prepares the cluster in a mild ionization state byoptically-induced electron tunneling; afterwards, the ionized cluster starts expandinguntil it interacts with the heater pulse. Provided that the cluster plasma density is in aproper range (which corresponds to an optimal delay range), a very efficient absorptionof the heater pulse takes place. During such interaction, efficient collisional ionizationoccurs and the new ionic species can readily be transferred to an excited state, fromwhich they decay to the ground state by fluorescence emission.It is worth to stress that the time-resolved experiment we performed must not beinterpreted as a usual pump-probe measurement, in which the probe pulse does notperturb the excited state induced by the pump one in the sample. On the contrary,here the heater pulse ignites the clusters that are pre-ionized by the driver one, henceit strongly interacts with the sample.Another important aspect to be considered is that the ionic fluorescence is inducedby the heater, but evolves on temporal scales much longer than its duration since itinvolves ionization and excitation by thermal electrons as well as radiative electron-ionrecombination processes. Hence the observed spectra are the integrated emission overall the temporal evolution of the excited plasma. This aspect must be kept in mindwhen considering the measurements we report in this work: when we consider a time-resolved fluorescence dynamics, we refer to the dependence of the fluorescence signal onthe driver-heater delay, not to the duration of the fluorescence emission.O exploding clusters dynamics probed by XUV fluorescence , O III, perp. pol. N=31000N=17000N = 8200N = 6100N = 3200 N o r m a li z ed i n t en s i t y Delay (ps)
Figure 4.
Normalized fluorescence traces of the O III ion as a function of the delaybetween driver and heater, for different CO cluster sizes: N = 3200 (stars), N = 6100(down triangles), N = 8200 (up triangles), N = 17000 (filled dots), N = 31000 (filledsquares); the dash-dotted lines are guides to the eye showing the almost linear decayof the ionic fluorescence. The driver and heater polarizations were perpendicular; thecross-correlation between the pulses is shown as solid line. By comparing the emission spectra with the NIST Atomic Spectra Database [25], itis possible to assign each fluorescence line to the corresponding ionic emitting speciesand to the involved radiative transition. Figure 3 shows the identification of the mostintense lines we observed; the experimental conditions are reported in the caption.Several emitting species are identified, in particular C III, C IV, O III, O IV, O V andO VI. The presence of relatively high ionization stages is not surprising by itself, since itis a fingerprint of laser-cluster interaction [1]. However it is instructive to recall in Table2 the ionization potentials that must be overcome in order to observe such ions. On thebasis of those parameters and of the Ammosov-Delone-Krainov model [28], it is foundfor instance that isolated O VI ions could be generated by tunnel ionization of O V ionsby exploiting driving pulses with a peak intensity three order of magnitude larger thanthe experimental one. This striking result reveals the strong importance of the clusterenvironment on the ionization processes during and after the interaction with the laserpulses.Molecular clusters, as the ones considered in this work, are more complex systemsthan atomic clusters. For instance in carbon dioxide several molecular orbitals liein the energy region between 13.78 eV and 22 eV under the vacuum level, henceO exploding clusters dynamics probed by XUV fluorescence O III O IV O V O VI CO , perp. pol.Average cluster size (10 molecules) E m i ss i on pea k ( p s ) Figure 5.
Driver-heater delay corresponding to the peak of the ion emission as afunction of the cluster size N for the following ions: O III (empty squares), O IV(empty dots), O V (filled triangles) and O VI (filled stars). electrons colliding with moderate kinetic energy on CO molecules could trigger severalphenomena, like the generation of molecular ions and the molecular fragmentationalong several pathways. Those phenomena may play important roles in the earlystages of the cluster excitation. Since fluorescence from excited CO molecules andmolecular fragments does not appear in the spectral region we considered, we willlimit the investigation to the fate of atomic ions that are likely to be generated aftercomplete molecular fragmentation. In the following we will refer to some of the observedfluorescence lines; the last three columns in Table 2 report the spectral range, the lowerand the upper levels of the transitions we will investigate hereafter. For each of thechosen set of lines, the temporal evolution of the fluorescence signal is obtained as theintegral of the emission in the corresponding spectral range. It is worth noting thatemission from C III and C IV ions cannot be disentangled owing to the limited spectralresolution of our setup. Once the principal ionic lines are identified, one can determine the fluorescence growingand decay dynamics for each ionic species as a function of the driver-heater delay. Figure4 shows the normalized fluorescence traces corresponding to the emission of the O IIIion for different average cluster sizes. It is worth noting that the driver and heaterdurations are substantially shorter than the time scale of the observed dynamics, ascan be seen by comparing the fluorescence signals (symbols) with the calculated pump-O exploding clusters dynamics probed by XUV fluorescence N O III O IV O V O VI CO , perp. pol.Average cluster size (10 molecules) D e c a y s l ope ( p s - ) Figure 6.
Decay slope of the O III (empty squares), O IV (empty dots), O V (filledtriangles) and of the O VI (filled stars) normalized fluorescence as a function of thecluster size N . The solid and dashed lines are fitting traces both proportional to N − .See text and Figure 4 for more details. probe cross-correlation (solid line). The fluorescence dynamics on the leading edge ofthe pump-probe traces shows an initial fast rise, which then slows down for larger clustersizes; also the decay of the fluorescence signal is slower for larger clusters. This trendis a general feature in the measured spectra, as it is observed also for the other ionicspecies (not shown). It is worth noting that the fluorescence decay can be very wellfitted by a linear law for all the average cluster sizes, as shown by the dash-dotted linesreported in Figure 4.In order to provide a more quantitative description of the size dependence of thefluorescence dynamics, we report in Figure 5 the driver-heater delay at which theemission from each ionization stage is maximum; this optimal delay is shown as afunction of the cluster size N . The error bars for the cluster sizes are chosen as equalto the relative width δR/R of the size distribution in the cluster jet, which has beenfound in [29] to be of the order of 12%; the error on the optimal emission delay hasbeen determined as the sampling step used in the pump-probe measurement. As canbe seen from the figure, in small clusters the emission peak occurs almost at the samedelay for all the considered ionic species. This behavior is not observed in large clusters,where the fluorescence emitted by low ionization stages reaches the maximum muchearlier than high stages; in particular in the largest clusters the optimal delay for O VIemission is almost double the one for O III emission.As previously mentioned, the ionic fluorescence dynamics can be fitted with a lineartemporal decay; Figure 6 shows the decay rates calculated for all the Oxygen ions; theO exploding clusters dynamics probed by XUV fluorescence Cross corr. O VI O V O IV O III C III-C IV CO , N=3200, perp. pol. Delay (ps) CO ,N=31000, perp. pol. N o r m a li z ed i n t en s i t y Delay (ps)
Figure 7.
Temporal evolution of the normalized fluorescence of O III (down triangles),O IV (up triangles), O V (filled dots) and O VI (filled squares) for an average clustersize N = 3200 (upper panel) and N = 31000 (lower panel); the fluorescence from C IIIand C IV is shown as stars. The driver and heater polarizations were perpendicular;the cross-correlation between the pulses is shown as dashed line. Solid lines are B-splinefittings of the data and are displayed only as a guide to the eye. error bars on the decay slope are determined from data fitting. The decay rates areinversely proportional to the cluster size, as confirmed by the 1 /N curves plotted in thefigure (solid and dashed lines, which respectively fit emission decay from O III and O VIions, differing only by a constant multiplication factor). As a consequence, the clusterfluorescence persists for a delay range proportional to N , thus larger clusters emit forlonger delay intervals. The agreement between measurement and fitting is fair for largecluster sizes, whereas becomes less satisfactory for small ones. In particular, the decayrate of the O VI fluorescence traces saturates to about 2.1 ps − in small clusters; suchvalue is still well below the limit imposed by the pump-probe temporal resolution. Atendency in saturation, though less evident, is found for O V emission whereas is notobserved for O III and O IV decay rates. On the basis of findings shown in Figures 5 and6 we infer that the physical processes involved in ionic fluorescence emission depend onthe cluster size, because one cannot reproduce all the emission processes with a uniquescaling law. As already mentioned in the previous section, the dynamics of ionic XUV fluorescencedepends on the emitting species. In order to better clarify this peculiarity, we showO exploding clusters dynamics probed by XUV fluorescence N = 31000; symbols show theacquired data, whereas solid lines are B-spline fittings of the data and are reported onlyas a guide to the eye. The calculated cross-correlation between the two pulses is shownas dashed line.Limiting initially the data analysis to Oxygen contributions, one finds that ionic specieswith lower ionization potential appear earlier than species with higher I p (see Table 2for comparison); moreover, the growing dynamics is steeper for the former species andsmoother for the latter ones. As can be seen, the Carbon contribution seems to followan intermediate dynamics between the O III and the O IV traces. Assuming that theordering by ionization potential can be applied to Carbon as well, one can concludethat the line is dominated by the C IV contribution, at least for delays larger than 250fs. It is worth noting that the ordering in fluorescence traces is confirmed for all theaverage cluster sizes we explored, although the overall growing dynamics becomes fasterfor smaller clusters. This trend can be seen for instance in the upper panel of Figure 7,which shows the fluorescence dynamics for an average cluster size N = 3200.A close inspection to the fluorescence scan shows that a temporal ordering is alsoobserved in the decay of the ionic emission, where emission from ions with higher I p seems to persist more than fluorescence emitted by ions with lower ionization potential.This ordering in the fluorescence decay was observed in the majority of cases but it wasless evident for N = 17000 and N = 6100, probably owing to a larger noise amplitude.However, as will be clarified in the following, the departures in fluorescence decay amongdifferent ionic species is only apparent. This can be already understood from Figure 6:for large clusters, the fluorescence decay rates behave according to the same scaling lawas a function of cluster size (i.e. as 1 /N ). Moreover all the traces show a linear temporaldecay and, as can be seen from Figure 7, at a fixed cluster size the fluorescence emittedby all the ionic species goes to zero at the same delay. A consequence of this finding isthat fluorescence decay traces from different ionic species can be rescaled in a suitableway in order to be overlapped and to show the same dynamics.
4. Discussion
As already mentioned, in order to discuss the experimental data one has to keep in mindthat the pump-probe measurement here presented are deeply in the non-perturbativeregime. Hence a suitable way of analyzing the results is to divide the cluster dynamicsin two stages: (a) the first stage is triggered by the mid-IR driver pulse and consists in amild ionization ad expansion of the clusters. The ionization and excitation rates can beassumed to be low since no ionic line emission was observed in the considered spectralrange when the heater pulse was blocked. (b)
In the second stage, the heater pulseignites the clusters, which undergo a complex dynamics giving rise to ionic fluorescenceemission.In the following, we will discuss these two stages separately.O exploding clusters dynamics probed by XUV fluorescence A long-standing debate in the interpretation of laser-cluster interaction concerns themechanisms of cluster expansion; two main phenomena are in general considered:hydrodynamic expansion or Coulomb explosion [1, 27]. The first mechanism is morelikely to dominate in large clusters and for relatively cold electrons; in this case thefreed electrons expand as a gas pulling ions outwards. Under suitable conditions thenanoplasma expansion can be represented by a self-similar model [30, 31] where thekey parameters governing the expansion are the initial electron temperature and thedeparture from charge neutrality inside the cluster. The second mechanism dominatesin small clusters or for extremely high laser intensities and takes place when ions are notscreened any more by the stripped electrons. In this case the repulsive forces dominateand the key parameter of the expansion process is the initial ion density and meancharge [32]. As a matter of fact, numerical simulations reveal that there is a faint borderbetween the two mechanisms [33]. Moreover, when nonuniform expansion processes areconsidered, the cluster dynamics becomes extremely complicated since shock ion shellscan be predicted [34] and have been also indirectly observed in the ion kynetic energydistribution of exploding clusters [35]. Further complications in the modelling of clusterdynamics come from transient phenomena like inner three-body recombination [17] andmacroscopic effects as the interaction among ions and Rydberg excited clusters [36].Even if the detailed theoretical study of CO cluster expansion is beyond the scopeof this work, we note that in our experimental conditions a hydrodynamic expansionmechanism is likely to occur. In such a case, in the framework of a self-similar expansionmodel and assuming a uniform electron temperature inside the cluster, the characteristicsize R of the system should evolve in time according to the equation [30]: d ˜ Rd ˜ t = 2 q − ˜ R − (1)where R is the initial size, ˜ R = R/R is the normalized size and ˜ t = tc s /R is thenormalized time. The quantity c s = q ZkT e /m i is the ion sound speed in t = 0, where k is the Boltzmann constant, Z the ionization stage, T e the initial electron temperatureand m i the ion mass. The solution of the equation takes the form:2˜ t = r ˜ R (cid:16) ˜ R − (cid:17) + ln (cid:18)q ˜ R + q ˜ R − (cid:19) (2)The evolution of the normalized size is shown in the inset of Figure 8. Although self-similar solutions imply a non-uniform electron density inside the cluster, we will assumea constant density for the sake of discussion. One expects that the fluorescence peak isreached when the plasma density is about three times the critical density at the heaterwavelength [27]; this allows one to estimate the order of magnitude of ZT e . In thecase of CO clusters, we assume an average ion mass of 14.67 atomic units and an iondensity at t = 0 three times larger than the number of molecules per unit volume in thesolid state. We took into account the peak of the O VI fluorescence traces as a reference(see Figure 5) and we calculated the value of ZT e , which is reported in Figure 8 as aO exploding clusters dynamics probed by XUV fluorescence , perp. pol. T e m pe r a t u r e ( e V ) Average cluster size (10 molecules) R / R tc s0 /R Figure 8.
Initial electronic temperature ZT e of the clusters after driver excitation,calculated as a function of the cluster size N (filled dots); the temperature follows adependence on the cluster size as N − (fit shown as solid line). Inset: evolution of thenormalized cluster size ˜ R = R/R as a function of the normalized time ˜ t = tc s /R calculated in the framework of a self-similar expansion model [30]. function of the average cluster size N . One can see that for small clusters ZT e is in theorder of tens of eV but decreases suddenly to a few eV for large clusters; the estimatedinitial temperature depends on the cluster size according to ZT e ∝ N − , as shown bythe solid line in Figure 8. A small departure of the estimated ZT e from the fitting isobserved for N = 31000, which could be attributed to a non-vanishing asymptotic valueof the electron temperature for very large clusters.The decrease in ZT e for increasing cluster size is consistent with the findings of the nanoplasma model [27], which attributes this behavior to the more rapid expansion rateof smaller clusters that brings them near resonance earlier along the driver laser pulse.It is however important to stress that the the ionization stage Z could be higher than 1in small clusters owing to the mentioned resonance mechanism, hence for those clustersthe effective electron temperature T e could be lower than what is shown in Figure 8.Indeed this would also be consistent with the lack of ionic emission when the heaterpulse was blocked, since too high values of the electron temperature would produceefficient ion impact excitation followed by radiative decay.A noticeable consequence of the temperature estimation we report is that the assump-tion of a relatively cold electron gas in the nanoplasma is confirmed. It is worth stressingthat such result is not trivial at first sight, since mid-IR driver pulses are expected totransfer a large ponderomotive energy to freed electrons with respect to standard 800-nm laser sources [21]. In particular, in our experimental conditions the maximum energyacquired by electrons ionized from a single molecule is expected to be in the order ofO exploding clusters dynamics probed by XUV fluorescence The interaction of the expanding cluster with the heater pulse leads to strongenergy absorption, which results in high collisional excitation and ionization rates andsubsequent fluorescence emission. The way this energy is transferred to the nanoplasmais however still not completely understood. The model proposed by Ditmire et al. in1996 assumed a uniform electron density and temperature inside the cluster duringits expansion [27], so that the resonance condition for efficient energy absorptioncould be reached only for a very limited amount of time, when the electron densityreaches the condition n e ≈ n c with n c the critical density at the laser wavelength.Milchberg et al. questioned this assumption and proposed that the non uniformplasma density in the cluster may play a key role in laser-cluster interaction [37];moreover the cluster dynamics was found to be intrinsically bidimensional in natureeven for spherical clusters, with further complications in the understanding of the energycoupling mechanisms [33, 37]. Recent theoretical models concerning ultracold expandingplasmas revealed that the absorption mechanisms depend on the departure of the clusterfrom neutrality [38]. In the framework of a self-similar description, collective energyabsorption is in general peaked inside the cluster where the laser frequency matches thelocal plasma frequency; however in charged clusters there is also a second absorptionpeak which is localized at the plasma edge and occurs at light frequencies related to thedegree of charge imbalance [38].Although we are not aiming at a detailed understanding of cluster absorptionmechanisms, we would like to exploit the experimental results for a qualitativedescription of the excitation and emission processes undergoing in the clusters. Asalready mentioned, in our experiments on CO clusters different ionization stages ofOxygen show different fluorescence temporal evolutions. In order to discuss in moredetail such finding, we show in Figure 9 the polynomial fittings F i ( i = 3 , , , N = 31000 molecule per cluster. Thefitting curves were rescaled in order to show that, in the delay range between 2 and4 ps, the fluorescence presents the same dynamics irrespective of the emitting species.This is also shown in the inset of Figure 9, where we plot the ratios among fitting curvesO exploding clusters dynamics probed by XUV fluorescence F F F F CO , N=31000perp. pol. I n t en s i t y ( a r b . un i t s ) Delay (ps)
F4 /F3 F5 /F4 F6 /F5 R a t i o Delay (ps)
Figure 9.
Rescaled polynomial fittings of fluorescence traces already shown in thelower panel of Figure 7 (corresponding to N = 31000 molecule per cluster) emitted byO III (F , solid line), O IV (F , dashed line), O V (F , dash-dotted line) and O VI(F , dotted line) ions. Inset: ratios between rescaled fittings; solid line: F / F ; dashedline: F / F ; dash-dotted line: F / F . corresponding to adjacent ionization stages; one can see that such ratios saturate atunity in the same delay range.This finding allows us to speculate that, in a delay range comprised between 2 and 4ps, the ratios among number of photons emitted from different ionic populations stayconstant. On the other hand, for small driver-heater delays those ratios change andlower ionization stages always show higher F i . Such behavior was observed for all theexperimental conditions we analysed and it is consistent with the general dynamicalscaling reported in Figure 6. A tentative explanations for the observed dynamics canbe the following: at small delays, when the cluster density is still overcritical, theheater absorption is moderate; for this reason the generation of high ionization stagesis inefficient and low-charged ions predominate in fluorescence emission. Moreoverelectron-ion recombination would be at this stage very efficient, hence further reducingthe contribution from highly charged ions.At large delays almost all Oxygen atoms undergo efficient ionization up to O VI; theseions emit fluorescence but then undergo recombination with surrounding electrons. Suchrecombination is however less efficient with respect to small delays, owing to the lowerelectron and ion densities; hence the fluorescence we observe is a remnant of the variousintermediate ionization stages, which have enough time for decaying to their groud stateby photon emission before recombining with electrons. Thus at large pump-probe delaysO exploding clusters dynamics probed by XUV fluorescence Conclusions
The interaction of clusters with intense and ultrashort laser pulses presents a very richphenomenology. In this work we have shown that the fluorescence emitted by ions canbe used as a sensitive probe of the expansion and excitation of molecular clusters. Theefficient triggering of cluster expansion by 1.45- µ m pulses demonstrate that ultrashortmid-IR pulses can be effectively used in this investigation. We found that fluorescencedynamics is a function of both the ionization stage and the cluster size. The scalinglaw we determined in the fluorescence traces points to a physical picture that cannot beeasily related to simple models and calls for much more complex theories.Our outcomes also demonstrate that mid-IR drivers leave the photoionized clusterswith an almost solid-state density and a relatively cold electron temperature, allowingto reproduce warm and dense states of matter in a laser laboratory. The method weadopted for determining the initial temperature of the ionized cluster could be extendedto study the effect of the driving wavelength on the cluster ionization and expansionrate and to fully determine the role of the ponderomotive energy and of the peak electricfield on the initial stages of the laser-cluster interaction. Acknowledgments
The research leading to the results presented in this work has received fundingfrom LASERLAB-EUROPE (grant agreement n. 284464, EC’s Seventh FrameworkProgramme), from the European Research Council (ERC grant agreement n. 307964-UDYNI, EC’s Seventh Framework Programme) and from the Italian Ministry ofResearch and Education (ELI project - ESFRI Roadmap).
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