Development of ion recoil energy distributions in the Coulomb explosion of argon clusters resolved by charge-state selective ion energy spectroscopy
aa r X i v : . [ phy s i c s . a t o m - ph ] F e b Development of ion recoil energy distributions in the Coulombexplosion of argon clusters resolved by charge-state selective ionenergy spectroscopy
D. Komar , L. Kazak , K.-H. Meiwes-Broer , , and J. Tiggesb¨aumker , University of Rostock, Albert-Einstein-Strasse 23, 18059 Rostock, Germany Department ”Life, Light, and Matter”,Universit¨at Rostock, 18059 Rostock, Germany
Abstract
The laser intensity dependence of the recoil energies from the Coulomb explosion of small argonclusters has been investigated by resolving the contributions of the individual charge states to theion recoil energy spectra. Between 10 and 10 W/cm the high-energy tail of the ion energyspectra changes its shape and develops into the well-known knee feature, which results from thecluster size distribution, laser focal averaging, and ionization saturation. Resolving the contribu-tions of the different charge states to the recoil energies, the experimental data reveal that the basicassumption of an exploding homogeneously charged sphere cannot be maintained in general. Infact, the energy spectra of the high- q show distinct gaps in the yields at low kinetic energies, whichhints at more complex radial ion charge distributions developing during the laser pulse impact. NTRODUCTION
Recent developments in ultrafast laser technology provide opportunities to study light-matter interactions in the regime, where the energy absorption depends on the field strengthrather than on the photon energy. Laser-produced plasmas from optically ionized solid den-sity matter have been widely explored over the past years as potential sources for energeticparticles [1] and short wavelength radiation [2]. Small particles can be utilized as a replace-ment for solid targets as they provide debris-free conditions in the experiment as well asyet retain solid-like properties. Measurements on clusters are appealing since they act asnm-sized model systems to study base issues of strongly non-linear many-body interactionswith light [3–5], such as the impact of collective effects on the charging dynamics [6–8].Emission of highly energetic ions in various charge states [9, 10] and fast electrons [11] wasobserved from laser heated clusters. Moreover, the control of fast electron emission on theattosecond timescale through modification of the collective oscillations of the nanoplasmaby two-color laser field has been reported [12].The ionization dynamics of rare gas clusters are in the focus of experimental stud-ies [10, 13–19]. To date, only a few experiments aimed to resolve the underlying charge-statedistributions upon exposure to strong optical laser fields [10, 13, 14]. In these measurements,however, laser intensities above 10 W/cm have been utilized, which is about two ordersof magnitude higher than the atomic barrier suppression intensity threshold I BSI [20]. I BSI can be taken as a measure for the onset of extreme cluster charging [21]. The thresholdregime is appealing since one can expect to resolve, e.g., the transition from a partially to afully ionized plasma.Experimental data of the Coulomb explosion of clusters were analyzed by Islam et al. [22],to explain the recoil energy spectra of laser-exposed clusters on the basis of an analyticalmodel. Compared to other approaches [23–30], the model is strongly simplified. But as a keybenefit, different contributions, such as cluster size distribution, laser intensity distributionsin the focus, and ionization saturation can be separated. That allows visualizing their impacton the experimental recoil energy spectra.In the model, the cluster is represented as a uniformly charged sphere of constant densityand the cluster explosion occurs solely due to Coulomb repulsion forces. The correspondingion recoil energy spectrum is shown in Fig. 1 (black solid line). The yield increases with2
IG. 1. ( color online ) Ion recoil energy spectra of homogeneously charged Ar N clusters calculatedaccording to the model of Islam et al. [22]. black solid line: Single-sized clusters exposed to a givenlaser intensity. blue dashed line:
Including a log-normal cluster size distribution and a Gaussianlaser beam profile. red dash-dotted line:
Taking ionization saturation into account. Note, that theenergy spectra are presented on double-logarithmic scales. recoil energy E R up to a maximum energy E max . The low-velocity ions originate from thecenter of the cluster, whereas ions with E R = E max are released from the surface. In theexperiment, however, the spectra differ for several reasons: (i) the size distribution of theclusters in the interaction region and (ii) exposure of clusters to different intensities due tothe spatial profile of the focused laser beam. The resulting energy spectrum calculated byconsidering a log-normal cluster size distribution and a Gaussian laser beam profile is shownin Fig. 1 (blue dashed line). Large volumes in the focus illuminated by intensities lowerthan the maximum laser intensity lead to a steep decrease of the yields with energy. Thevolumetric weighting reflects in a strong contribution of low energy ions to the spectrum.The cluster size distribution results in recoil energies exceeding E max . Finally, considerationof ionization saturation leads to a high energy cut-off ( knee -feature, see Fig. 1 (red dash-dotted line). The simplified modeling can reasonably fit different experimental data [31–36],but the considerable change in the energy spectrum due to the impact of target and laserconditions permits to draw conclusions from the resulting spectrum on the single cluster ion3 lustersource Slit apertures y x ionsElectromagnetDelay line detectorCharge-state Resolving Ion Energy Analyzer FIG. 2. (color online)
Experimental setup to measure charge-state selective ion recoil energyspectra from the Coulomb explosion of argon clusters, according to [37]. recoil energy distribution.In the present work, we extend former studies by resolving the impact of the different ioncharge states on the recoil energy spectra. The intensities of the laser pulses were chosenin order to monitor the development of the energy spectra with respect to the phenomenonof ionization saturation. The analysis will be conducted in two steps. In order to putthe results into the context of previous measurements and the predictions of the model,the individual findings on the recoil energy spectra and the charge-state distribution arepresented first. The experimental data show that ionization saturation limits the maximumion recoil energies already at laser intensities of 10 W/cm . In the second step, the analysisof the charge-state resolved energy spectra will uncover, that with respect to the highest q , the simplified assumption of an expanding homogeneously charged sphere made in themodel cannot be retained. EXPERIMENTAL SETUP
The experimental setup to obtain charge-state resolved ion recoil energy spectra fromthe Coulomb explosion of clusters is schematically shown in Fig. 2. Briefly, argon clustersof mean size N =3800 are produced by supersonic expansion using a pulsed Even-Lavievalve [38]. About 40 cm behind the nozzle, the particles are exposed to intense 180 fs near-infrared laser pulses ( λ = 793 nm). The laser radiation is focused by a lens (f=30 cm) to a4 IG. 3. (color online)
Time-of-flight deflection histogram, obtained from argon clusters with amean size of N =3800 exposed to laser pulses having peak intensities of 7.3 · W/cm . Thesignal strength is represented by a color scale. Due to different charge states, signals from Ar q + ( q = 1–9) form lines with different slopes. spot diameter of 30 µ m. An attenuator, based on a λ /2 plate and a pair of Brewster typepolarizers, allows to adjust the intensity between 10 -10 W/cm . In the interaction region,a charge-state resolving ion energy analyzer (CRIEA) is installed [37]. Energetic fragmentsemitted from the Coulomb explosion are collimated by two slit apertures and pass througha region with a homogeneous magnetic field, and detected by a time- and position-sensitivedelay-line detector. The commissioning of the detector system includes a calibration withrespect to the actual ion impact position. For this purpose, a specially prepared maskis attached in front of the detector. From the resulting spatially and temporally resolvedsignals, charge-state resolved ion recoil energy spectra are extracted.Compared to other charge-state resolving energy analyzers used in the field like Thomsonparabola [35] or time-of-flight spectrometers with magnetic deflection [10], CRIEA features(i) a high transmission, since slit apertures are used instead of pinholes. (ii) a high energy5esolution even for MeV ions, as instead of the spacial deflection the ion time-of-flight isevaluated. (iii) a delayline detector system, which is characterized by an extended dynamicrange with respect to camera based systems and the capability to record data on a shot-toshot basis. (iv) a significant reduction of residual gas signals, since no extraction fields areused. For more detailed information on the CRIEA design and the procedure to obtaintime-of-flight deflection histograms from the delayline detector events, we refer to [37].A typical time-of-flight–deflection histogram recorded at a laser intensity of I L =7.3 · W/cm is shown in Fig. 3. Charge states from q =1 to 9 contribute to the spec-trum. The signals from Ar q + for each q form a line due to the different recoil energies E R . Summing up the yields for given q gives the corresponding abundance. Thus, the ioncharge-state distribution (CSD) after the Coulomb explosion of the clusters can be obtained.The dependence of the total ion yields as function of time-of-flight t T OF allows to determinethe charge integrated ion recoil energy spectrum (IRES), whereas the t T OF of each Ar q + isused to extract the charge-state resolved ion energy spectra (CR-IRES). RESULTS AND DISCUSSION
Charge-state integrated recoil ion energy spectra corresponding to selected laser intensi-ties are presented in Fig. 4 (top panels) on a double logarithmic scale. At 4 · W/cm the IRES spreads from zero to about E max = 2 keV. Up to about 100 eV the signal is al-most constant and falls off rapidly at higher energies. When increasing the pulse intensityto 10 W/cm the recoil energies reach values up to 18 keV. Hence, doubling the intensityleads to a nearly 10-fold increase in the maximum recoil energy E max .The substantial increase in E R between 4 · W/cm and 1 · W/cm can be tracedback to resonant charging due to plasmonic excitations [6, 39]. In the nanoplasma formation,charging of the cluster induces an ion pressure which triggers the Coulomb explosion of thesystem. The rapid inner and outer ionization [40] shifts the corresponding Mie plasmon toenergies far higher than the laser frequency. In the later expansion, the Mie frequency lowersas a result of the decreasing ion density. Only for the higher laser intensities, the expansionrate is sufficient that the collective mode can effectively adapt to the frequency of the drivinglaser field. Thus, the efficient charging of the nanoplasma reflects in a substantial increasein E R . Since the ratio between inner and outer ionization reduces with size, we expect that6 RESCSD
14 2 ·
15 2
FIG. 4. ( color online ) Ion recoil energy spectra (top panels) and charge-state distributions (bottompanels) at selected laser peak intensities I L = 4 . · W/cm (left) and 1 . · W/cm (right).The IRES are presented on double logarithmic scales. Note the different energy ranges. TheCSD shows an enhanced signal near q =7 at 1 . · W/cm providing evidence for charge-statesaturation. small clusters are mainly responsible for the increase of the recoil energies.In addition to the increase of E max at higher intensities, the envelope of the IRES changessubstantially, as shown in Fig. 4, top right. Up to about 8 keV the yield follows an exponen-tial fall off. But between E R =8 and 20 keV the yield decreases by several orders of magnitude,7iving a pronounced knee feature. Additional information on the development of the IREScan be obtained from an analysis of the charge-state distributions, see Fig. 4 (bottom pan-els). At 4 · W/cm the CSD extends up to q =7 with a maximum at around q =2, whichsuggests that ionisation saturation hardly plays a role. Therefore, the corresponding IREShas to be compared to the result of the model calculation shown in Fig. 1, (blue dashedline). Qualitatively, the calculation reproduces the experimental result. However, at lowkinetic energies, the IRES, shown in Fig. 4 (top left), differs from the theoretical result. Thedifference can be attributed to the reduced detection probability of the multichannel platedetector for ions with a low kinetic energy [41].Ions with charge states up to q =9 contribute to the IRES at the higher fluence, seeFig. 4 (bottom right). But the shape of the CSD changes, too. Up to q =4 the Ar q + yieldsare almost constant, followed by a steep increase, a maximum at Ar and a marked dropbeyond. The development of the CSD represents an indication of ionization saturation. ForAr the corresponding feature is expected to stand out through a kink in the CSD at q =8due to the pronounced increase of the ionization potential caused by the 3 s p shell closing.The underlying charging mechanism, i.e., laser-assisted electron impact ionization, requiressignificantly higher energies and thus leads to a strong reduction of the efficiency to producehigher charges states ( q > q =7, whereas the yield of Ar is reduced relative to Ar . We treat this as an indication of three-body recombination(TBR) [42] during the nanoplasma disintegration [29]. Taking ionization saturation intoaccount, the shape of the energy spectrum shown in Fig. 4 (top right) qualitatively matchesthe result of the model, see Fig. 1 (red dash-dotted line).So far the data have been analyzed by considering either the IRES or the CSD. Theion energy analyzer, however, enables us to extract charge-state resolved ion recoil energyspectra, as shown in Fig. 5 for both laser intensities. In general, none of the spectra issimilar to the IRES, as presented in Fig. 4. For Ar , the recoil energies range from zeroup to about 1 keV. With increasing q , the spectra develop into distinct peaks with themaxima shifting towards higher E R . Notably, no ions with low recoil energies are detectedfor higher charge states. In addition, the energy spectra overlap for given q , although thelaser intensities differ by more than a factor of two. Most likely, this effect arises as a result8 r Ar Ar Ar Ar Ar Ar Ar Ar Recoil energy [keV] l og ( Y i e l d ) [ a r b . u .]10 FIG. 5. (color online)
Dependence of the recoil energy spectra on the Ar ion charge state recordedat intensities of 4 . · W/cm (blue) and 1 . · W/cm (red). In contrast to the energyspectra obtained for Ar q + ( q =1-3), the CR-IRES for the higher charge states show pronouncedgaps in the ion signals at low kinetic energies. of focal averaging [43]. When increasing the laser power an additional volume is illuminatedby the higher I L , while the volume illuminated by lower intensities remains constant. Hence,if ions of selected Ar q + are not emitted from regions of higher I L , no change in the yieldsis expected. The corresponding behavior is observed for Ar to Ar , see Fig. 5, whichsuggests that these charge states are produced mainly in the low-intensity regions of thefocus. For q =4-7, focal averaging may be responsible for the peaks obtained at around 1keV, as the position of the maxima are similar at both intensities.Whereas the CR-IRES of Ar -Ar show strong contributions from slow-moving ions,the spectra beyond exhibit pronounced low energy cut-offs. For example, the spectrum ofAr taken at I L = 4 . · W/cm shows recoil energies up to E max = 3.1 keV. At thesame time, the energy distribution exhibits a sudden onset of the signal at E min =600 eV.9his behavior and the development of the distinct peaks with increasing q , cannot obvi-ously be represented as being the sum of q -dependent recoil energy spectra stemming fromhomogeneously exploding charged spheres as assumed in [22]. Since ions at the surface ofthe cluster gain the highest kinetic energy, the experimental observation implies, that thehigher charged ions reside predominantly near the cluster surface. Since cluster ionization ismainly caused by laser-assisted electron impact ionization, an excessive charging of surfaceatoms compared to the interior is not expected. Hence, in order to reproduce the experi-mental results, non-trivial spatial charge distributions have to be assumed. Inhomogeneitiesof the spatial charge distribution as a result of the oscillating quasifree electron cloud maybe responsible for the effect [32, 44, 45]. But an impact of the electron motion has onlybeen observed for the highest recoil energies [32]. Plasmon-induced charge fluctuations can,therefore, be ruled out to explain the small contribution of low energy ions in the spectra ofAr q + .Most probably, TBR is responsible and plays an essential role in the temporal develop-ment of the charge-state distribution [29, 46]. Initially, laser-assisted avalanche charging ofthe cluster produces ions in high charge states. However, in the expansion of the nanoplasma,ions primary near the cluster core recombine with quasi-free electrons, whereas for Ar q + nearthe plasma surface TBR is less effective. This results in a spatial imbalance of the charge-state distribution, i.e., surface ions will have a higher charge state and experience a largerCoulomb pressure.Note, that the CSD spectrum comprises information about the contribution of electron-ion recombination to the final ion charge state. Hence, the full expansion period is mappedwithout temporal resolution. In contrast, the CR-IRES spectra are sensitive to the periodwhen the ions accumulate most of their kinetic energy, which roughly ties to the laserpulse duration. The low-energy cutoffs indicate that TBR contributes markedly from thevery beginning of the interaction. Although the nanoplasma temperatures during the laserpulse impact are expected to be high, hence suppressing TBR, the CR-IRES suggest, thatrecombination has to be taken into account on all timescales. A related computationalstudy on the recoil energy distributions is appealing to obtain more detailed information.Conducting corresponding simulations, however, are beyond the scope of the contribution.The charge-state distribution of larger argon clusters, i.e. Ar N , N = 36 000 at intensitiesof 7 · W/cm has been studied by Rajeev et al. [41]. The authors obtained an envelope10f the CSD similar to the one observed in the present work at I L = 10 W/cm , but theCSD shift and peaks at q =8 due to the larger size and the higher pulse intensity. Hence, theobserved trend is found to be in accordance with our measurements. However, in contrast toour study, those experiments show no signals from the lower charge states, i.e., q ≤
4. Withrespect to the slight increase in the intensity conditions, the absence of ions in low q -statesin the CSD remains surprising. Irrespective on the chosen laser intensity, one would expectto obtain ion signals from the lower charge states due to focal averaging. Hence, in orderto resolve the contradictory results e.g., intensity-selective scanning experiments have to beconducted [47]. In view of the need to finally compare the results to molecular dynamicscalculations, such a treatment is appealing, since the simulations, are typically conductedat only a single laser intensity [48].Finally, the resulting spectra have to be linked to simulations on Ar
40 000 [49]. At I L =10 W/cm , the calculations show that the CSD peaks at q =6, whereas at 3 · W/cm the maximum of the distribution shifts to q =7. The computational result concurs with ourfindings. However, the corresponding energy spectra show that the knee energy exceeds theexperimental value obtained in the present work by more than a factor of four. As a possiblecause, a lower plasma electron temperature T e could be responsible as TBR strongly dependson T e , i.e., ( T − / e ) [50]. Further, the size of the argon particles may play a role. According tothe model of Islam, the lower knee -energy can be explained by the smaller clusters exposedto the laser field. In addition, one can expect that as function of cluster radius, the averagenanoplasma charge state decreases. Hence, intensity dependent measurements in this regimeare then again appealing, since, e.g., the CSD has been found to be quite sensitive to smallchanges in laser power. Moreover, the CR-IRES results will allow for a more in-depthanalysis. CONCLUSIONS
Recoil ion energy distributions from the Coulomb explosion of small Ar clusters exposed tostrong laser pulses have been studied by charge and energy-resolved spectroscopy. The recoilenergy spectra taken at the highest laser intensities of 10 W/ cm exhibit a high-energycut-off. The corresponding charge-state distribution indicates, that the feature stems fromionization saturation. The envelope of the recoil energy spectrum can be well-described11y a model, which takes into account ionization saturation as well as details of clustersize and laser intensity distributions. At lower laser intensities, the in-depth informationprovided by resolving the contributions of the individual charge states to the ion energyspectra reveal distinct low-energy gaps for the higher charge states. Since the ions gain asubstantial fraction of their recoil energy within a short period of time, the charge-stateresolved energy spectra are sensitive to the nanoplasma condition in the early expansionperiod. The experiments give evidence that the corresponding charge-state distributiondeveloping during the laser pulse impact has to be assumed to be inhomogeneous in orderto match the experimental results. The presence of low-energy gaps point out the relevanceof three-body recombination already during the laser pulse impact. ACKNOWLEDGMENTS
The Deutsche Forschungsgemeinschaft (TI210-8) is gratefully acknowledged for financialsupport.
AUTHOR CONTRIBUTIONS
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