Explosion Dynamics of Methane Clusters Irradiated by 38 nm XUV Laser Pulses
aa r X i v : . [ phy s i c s . a t m - c l u s ] F e b Explosion Dynamics of Methane Clusters Irradiated by 38 nm XUV Laser Pulses
A. Helal , ∗ S. Bruce, H. Quevedo, J. Keto, and T. Ditmire
Center for High Energy Density Science, The University of Texas at Austin, Austin,TX 78712 USA (Dated: Feb. 2020)We have studied the explosion dynamics of methane clusters irradiated by intense, femtosecond, 38nm (32.6 eV) XUV laser pulses. The ion time-of-flight spectrum measured with a Wiley-McLaren-type time-of-flight spectrometer reveals undissociated molecular CH +4 ions, fragments which aremissing hydrogen atoms due to the breakage of one or more C-H bonds (CH +3 , CH +2 and CH + ) andthe recombination product CH +5 . Also visible on the time-of-flight traces are atomic and molecularhydrogen ions (H + and H +2 ), carbon ions, and larger hydrocarbons such as C H +2 and C H +3 . Nodoubly-charged parent ions (CH ) were detected. The time-of-flight results show that total andrelative ion yields depend strongly on cluster size. The absolute yields of CH +5 and H + scale linearlywith the yields of the other generated fragments up to a cluster size of h N i = 70 ,
000 molecules, thenbegin to decrease, whereas the yields of the CH + n ( n = 1 −
4) fragments plateau at this cluster size.The behavior of H + may be understood through the electron recombination rate, which depends onthe electron temperature and the cluster average charge. Moreover, the CH +5 behavior is explainedby the depletion of both CH +4 and H + via electron-ion recombination in the expanding nanoplasma. I. INTRODUCTION
The first observation of high-order harmonic genera-tion (HHG) using tabletop lasers, performed by McPher-son et al., opened the door to the widespread experimen-tal study of the interactions between matter and intenseelectromagnetic radiation at ultraviolet frequencies [1].High harmonic radiation can be generated by focusing anultra-intense femtosecond laser into a rare gas medium,thereby providing an ultrafast source of intense radia-tion in the extreme ultraviolet (XUV) regime. This high-frequency source exhibits unique characteristics, such aspulse durations in the range of tens of attoseconds [2–4],while maintaining spatial and temporal coherence [4–6].These intense XUV pulses interact with matter differ-ently than visible or infrared light due to their higherphoton energies. Van der Waals-bound rare gas clustersare a commonly used model target for studies of the in-teraction of high-intensity laser pulses with nano-scalematter. Their high density and small size make thema unique target for high-intensity laser experiments - ex-hibiting properties of both gases and solids. From intensenear-infrared (IR) experiments, it is known that, depend-ing on size and electron density, clusters may explodeprimarily by Coulombic or hydrodynamic forces [7, 8].These two limits exhibit very different cluster explosiontimes and signatures. The ionization process leading tocluster explosion is strongly wavelength-dependent fromIR through XUV [9, 10] to the X-ray regime; because thekinetic energy of the released electrons determines thecharge distribution within the cluster and therefore theexplosion dynamics.When clusters are irradiated with XUV laser pulses,the ponderomotive energy imparted to the electrons is ∗ Corresponding author: [email protected]; Current affiliation:Center for Nonlinear Dynamics (CNLD), The University of Texasat Austin low, but individual photon energies easily exceed theionization potential of the cluster atoms. Thus, in thisregime, single photon ionization is the dominant ioniza-tion mechanism. As electrons are ejected from the clus-ter, the growing electric potential well results in later-ejected electrons with less kinetic energy than initially-released photoelectrons. This leaves a telltale sign of thedirect multi-step ionization in the photoelectron spec-trum [10]. Eventually, the Coulomb field induced bythe cluster charge becomes large enough to prevent elec-trons from escaping the cluster, creating a quasineutralnanoplasma [11, 12].Previous experimental investigations into intense,high-frequency laser-cluster interactions have relied onfree-electron lasers as the photon source. Several experi-ments at the free-electron lasers FLASH (DESY facility)[13, 14] and LCLS (SLAC facility) [15] used different in-tense soft X-ray energies (92 eV at FLASH, and 850 eV atLCLS) to study the explosion dynamics of CH and CD as well as xenon clusters. The results of the FLASH ex-periment showed that the explosion dynamics depend onthe cluster size, and indicated a transition from Coulombto a hydrodynamic explosion as the cluster size increased,while the SLAC experiment demonstrated the formationof a xenon nanoplasma that exploded hydrodynamically.A growing number of studies have also focused on the-oretical as well as numerical investigation of the explo-sion dynamics of these large clusters irradiated by intenseXUV pulses.In this article, we report on an experimental study ofthe explosion dynamics of methane clusters irradiated byhigh intensity 38 nm wavelength (32 eV) XUV pulses gen-erated from a tabletop laser system. We were primarilyfocused on investigating the dependence of the transi-tion from Coulomb to hydrodynamic explosions on thecluster size. We found that the yield of CH +5 and H + isqualitatively different from that of the other fragmentsdetected in the experiment, and that prominent transi-tions in yield-to-cluster-size ratio occur around a cluster FIG. 1. Diagram (not to scale) of the experimental setup.XUV pulses were generated by focusing 800 nm anular profilelaser pulses into a supersonic argon gas jet. The XUV wasthen separated from the IR using an iris followed by a 200nm thick Al-filter. The transmitted XUV pulses were thenfocused into another gas jet (the cluster target) by a spher-ical Si/Sc mirror, designed to reflect preferentially the 21 st harmonic. size of h N i = 70 ,
000 molecules, in a good agreement withprevious experiments [13, 14].This paper is organized as follows: In Sec. II we in-troduce the experimental apparatus. The experimentalresults are described in Sec. III. In Sec. IV we presentthe results, analysis, and discussion, and the conclusionsare drawn in Sec. V.
II. EXPERIMENTAL SETUP
The intense, coherent XUV pulses used in this exper-iment were generated via HHG by loosely focusing 800nm ultrafast laser pulses into a supersonic pulsed argongas jet. The front end of the system was an amplifiedTi:sapphire laser, which delivered 600 mJ, 30 fs pulsesat a repetition rate of 10 Hz. We applied a mask that,in combination with an inverse mask downstream, sepa-rated the generated XUV light from the IR. The schemeremoved 17% of the (previously flat-top profile) beamcenter, resulting in an annular beam profile with an in-ner diameter of 12.5 mm and an outer diameter of 30mm. Fig. 1 shows a schematic of the experimental setupfor both the HHG generation and the XUV interactionchamber. The annular beam was brought to a focus by a f /200 spherical mirror of focal length 6.0 m, and directedinto the supersonic argon gas jet for high-order harmonicgeneration. We used a pulsed gas source, equipped witha solenoid valve (Parker General Valve, Series 9) and anorifice of 790 µ m. An attached nozzle directed the ex-panding gas into a slit at its output (0.635 x 6.57 mm),to increase the length of the gas-laser interaction region.The IR and XUV diverge at different rates with theXUV expanding within the center hole of the IR annulus.At the mask image plane downstream, the inverse mask- an iris - blocked the IR light while allowing the XUV topass through. Any IR scattered or diffracted in the XUV direction was blocked by a 200 nm thick aluminum filterwith 63% transmission in the XUV for λ <
70 nm (LuxelCorporation). This two-stage filtering scheme for sepa-rating the IR and low harmonics from XUV harmonicsresulted in a beam with no detectable IR light on targetwhen measured with a calibrated International RadiationDetectors IRD-AXUV576C photodiode. To ensure thatthere were no defects in the aluminum filter, a standardmicroscope slide was inserted regularly into the beampath after the filter, in order to block XUV while trans-mitting any stray IR. Photodiode measurements of theenergy on the target jet indicate no observable IR leakagewithin the sensitivity of the diode ( <
50 pJ/pulse). Thiscorresponded to an IR fluence at the target jet less than13 µ J/cm − and an intensity less than 3 . × W/cm ,which yielded a measured IR attenuation (aperture + Alfilter) of better than 1 . × at the target jet.After separation from the fundamental frequency, thefiltered XUV pulse propagated into the interaction cham-ber, where it was focused by a f /12 Sc/Si multilayer,dielectric-coated, spherical mirror with a focal length of12 cm. This mirror was designed to reflect only the 21 st harmonic (38 ± o to normalincidence [16]. We measured the 1 /e diameter of the re-sulting focus to be 7 µ m using the knife-edge technique.We measured pulse energies, for the experiments reportedin this article, of (0.6 ± . × W/cm [17].The targets used in this experiment were van derWaals-bound methane gas clusters, generated via adia-batic expansion of a supersonic gas jet into the vacuum.The jet was injected using a pulsed valve with a coni-cal nozzle with a half-angle of 5 o , and a throat diameterof 790 µ m. We used the empirical Hagena scaling law[18] with the modification for larger clusters presented inArefiev et. al. [19] to estimate the desired cluster size byvarying the backing pressure and nozzle temperature.Γ = Kpd . T . (1) < N > = . Γ1000 ) . < Γ < Γ1000 ) . < Γ < Γ1000 ) . < Γ < (2)Where Γ is the Hagena parameter, K is the gas sub-limation constant (K=2360 for Methane), T is the gastemperature in kelvin and p is the gas backing pressure.The pulsed nozzle we used was outfitted with a jacketfor direct cryogenic cooling. However, for this experi-ment, the nozzle kept at room temperature and different I on S i gn a l ( m V ) Time of Flight ( µ s)
000 molecules. cluster sizes were obtained by varying the gas backingpressure (0.25 bar < p <
10 bar) allowing us to reacha wide range of cluster sizes in the range of 4 × to3 . × molecules per cluster. We used a nozzle openingtime of 1 ms to minimize the load on vacuum pumps whilereaching near steady-state flow conditions for clustering.The pulsed valve was located inside a small sub-chamberwith its dedicated vacuum pumps. As the gas exitedthe nozzle and expanded, it passed through a skimmerwith an orifice 1.2 mm in diameter to create a collimatedstream of gas at the interaction region, where the XUVpulses were focused. Particles from the interaction werestudied using a Wiley-McLaren type time-of-flight spec-trometer [20] with a drift region of about 0.5 m providingimproved mass resolution over previous experiments [9].The length of this drift region was surrounded by a Mu-metal cylinder (wall thickness of 1.575 mm), designed toshield the Earth’s magnetic field. The detection systemconsisted of two microchannel plates in a Chevron config-uration for maximum signal to noise ratio. Amplified ioncharges were collected by a 50 Ohm impedance-matchedanode, where the signals were recorded using a TektronixTDS5000B - 1 GHz bandwidth, 5 GS/s oscilloscope. III. EXPERIMENTAL RESULTS
The ion time-of-flight spectrum of methane clustersof h N i = 142 ,
000 molecules, irradiated by 38 nm XUVpulses, is shown in Fig. 2. The following species can beobserved: undissociated molecular ions CH +4 , fragmentsthat are missing hydrogen atoms due to the breakage ofone or more C-H bonds (CH +3 , CH +2 and CH + ), the re-combination product CH +5 , atomic and molecular hydro-gen ions (H + and H +2 ), carbon ions, and larger hydrocar-bons like C H +2 and C H +3 molecules. No doubly chargedparent ion (CH ) or higher charge states of any of the I on S i gn a l ( m V ) Time of Flight ( µ s)
000 molecules, then decreases withincreasing cluster size. fragments were detected.The change in the ion time-of-flight yields of themethane species as a function of cluster size is shownin Fig. 3. We observed an increase in the amplitude ofthe continuum spectra under the methane fragmentationpeaks. As found in other gas cluster experiments (Ar,Xe, and N ) [17], the increase in cluster size leads toa disproportionate increase in the tails of the kinetic en-ergy distributions. In the methane case, the close charge-to-mass ratios of the fragmentation products cause theirenergy distributions to overlap. A closer look at the ionspectra reveals that the generation of the larger hydro-carbons (C H +2 and C H +3 ) occurs only after the clustersize reaches h N i = 4 ,
000 molecules. Moreover, we no-ticed that the yield of the H + ions (Fig. 4) depends onthe cluster size, such that the yield increases with thecluster size up to h N i ≃ ,
000 molecules, then begins todecrease with further increase in the cluster size.To understand these observations we present in Fig. 5the measured ion yield, normalized to the species maxi-mum after removing the continuum spectrum, as a func-tion of the cluster size. We note that the normalized yieldof all the fragments and the undissociated CH +4 shows anincrease with cluster size up to h N i ≈ ,
000 molecules,beyond which it is constant. However, the normalizedyield of the recombined CH +5 and the hydrogen peak H + do not level off but decrease together at the same rate.This change in yield for CH +5 was observed before by B.Iwan et al. [13] and N. Tˆımneanua et al. [14] using theFLASH free-electron laser which produces 15-fs pulses ata wavelength of 13.5 nm (photon energy = 92 eV) anda focused beam fluence of 13.7 J/cm . The maximumyield in their case occurred for a cluster size of 20,000molecules. In those experiments, they also found a mono-tonic increase in the yield of atomic fragments H + andC + with increasing cluster size, unlike in this experimentat 32 eV photon energy where H + behaves similarly toCH +5 . Their trend was linear with the stagnation pres-sure used to generate the clusters, consistent with theincrease in the overall molecule density. Moreover, atthe largest cluster size, the H + fragment accounted for60% of the total ions.To help understand our experimental results, we alsoanalyzed the yield of each measured ion fragment as afraction of the total ion yield shown in Fig. 6. Therelative yields of CH + , CH +2 , CH +3 and CH +4 show asmall increase with increasing cluster size up to ≃ +5 and H + ions showeda monotonic decrease in the relative yield with increas-ing cluster size (especially for H + ). Only a small con-centration of H +2 was also observed, which also decreasedslightly as the cluster size increased. IV. DISCUSSION AND ANALYSIS
The relative abundances of the methane ion fragmentsare controlled by dissociative photoionization, dissocia-tive ionization by electron impact, and electron-ion re-combination. In this section, we discuss each of thesemechanisms separately to understand the change in thebehavior of CH +5 and H + after a cluster size of ≃ A. Dissociative photoionization
For smaller cluster sizes, the populations are explainedto first order by dissociative photoionization cross sec-tions, measured as a function of photon energy by Sam- N o r m a li z e d P eak H e i gh t ( a r b . un i t s . ) Average Cluster Size (
B. Dissociative ionization by electron impact
Dissociative ionization by electron impact also con-tributes to the ion yield fractions [24], especially as thecluster size increases. For the 20 eV photoelectrons ex-pected and measured in our experiments the mean freepath for elastic scattering is 0.73 nm and for ionizationis 5.1 nm . This range corresponds to a mean size of ∼ +4 , CH +3 , and CH +2 ions. Threshold forelectron impact dissociative ionization to form H + is 22.4eV [24]. In experiments reported here, free protons areproduced by photodissociation during the 7 fs laser pulse,and not by electron impact either during the laser pulseor at later times as the cluster explodes.The photoelectron energy is the major expected differ-ence compared to the FLASH experiments. There, thephotoelectron energy of 80 eV, much greater than 20 eVin our case, leads to a mean free path for electron impactionization of 0.28 nm, with a much greater ionizationrate than ours, particularly for H + . This partly explainsthe smaller number of H + ions produced in the currentexperiments compared with FLASH experiments, wherethe ion yield fraction for H + was near 60% for the largestclusters. For momentum transfer cross sections see [25].
C. Electron recombination
The electron recombination rate also plays an impor-tant role in the difference between experiments at differ-ent photon energies. The main recombination mechanismof H + is the three-body recombination process describedby H + + 2 e k → H + e. (4)where the recombination rate, k is given by k = 8 . × − Z T . e cm s − (5)where T e is the electron temperature in electron volts,and Z is the ionic charge state [26]. Since the frac-tional ionization approaches 2% in our experiments, theelectron-ion recombination rate is very fast at the result-ing large electron density. The ions observed in the TOFare the sum over the full explosion time for the clus-ter, and as the cluster size becomes bigger the explosiontime increases, and a greater number of ions and elec-trons recombine. For Z = 1 and T e ≈ + densitywill decrease an order of magnitude during a time of 56fs after the end of the laser pulse. This contributes tothe loss in H + yield observed in Fig. 5 as the cluster sizeis increased above 70,000 molecules. For the experimentsat FLASH, T e = 4 eV, which reduces the recombinationrate by a factor of about 500 [14]. At this higher T e , therecombination time exceeds the explosion time. The dif-ference in the H + ionization rate and recombination rateat the two photon energies explains the different rela-tionships between H + concentration and cluster size. Forphoton energies of 92 eV, the electron impact ionizationrate overcomes the slower recombination rate, so thatthe ion concentration increases with the linearly increas-ing number of methane molecules in the focal volume. Incontrast, our lower photon energy, lower photoelectronenergy, larger recombination rates, and longer expansiontimes decrease the number of surviving H + with increas-ing cluster size. D. The behaviour of CH +5 Explaining the variation in population of the largerhydrocarbon ions (CH +5 , C H +2 , and C H +3 ) with clustersize is more difficult. Because of the correlation observedin the behavior of CH +5 and H + , one is tempted to asso-ciate the decrease in CH +5 ion signal with an increased de-struction rate with cluster size, similar to the explanation In this context, explosion time is defined as the time required bythe expanding cluster to reach twice its initial diameter. for H + . The dissociation of CH +5 by electron collisions isof fundamental importance and is one of the mechanismsthat could contribute to the loss of CH +5 [27, 28]. Directdissociative excitation rates are small for electron ener-gies below 10 eV compared to dissociative recombinationrates with electrons for energies below 0.2 eV: CH +5 + e k → CH + H + 8 eV (6a) CH + H + 7 . eV (6b) CH + H + H + 3 . eV (6c) CH + H + H + 3 . eV (6d) CH + H + H + 3 . eV (6e)However, recombination of all of the molecular ions isexpected to be dominated by three-body reactions similarto Eq. (4) for electron densities greater than 2 × cm − [29]. The time required (21 ps) for the electron density todecay to this concentration exceeds the cluster explosiontime unless T e falls substantially below 1 eV. Recombina-tion is also expected to increase the electron temperature.Qualitatively, over the explosion time, all of the ions areexpected to recombine at similar rates. CH +5 in particu-lar has exactly the same dissociative recombination andthree-body rate as CH +4 [30]. Clearly, the difference inthe yields of CH +4 and CH +5 depends on their productionrates and not their recombination rates.CH +5 is formed by an association of molecular ions withneutral molecules[31, 32]: CH +4 + CH k → CH +5 + CH (7a) H + + CH + CH −→ CH +5 + CH (7b) CH +4 + H −→ CH +5 + H (7c)where the dominant reactions in our experiments are Eqs.(7a) and (7b) since here the H concentration as deter-mined from the H +2 concentration shown in Figs. 5 and6 is too small to contribute.Given the large production rate for H + in Eq. (3b) andthe correlation between the CH +5 and H + ion yields, it ispossible to suggest that the formation channel for CH +5 ismostly by the association of H + with methane describedby Eq. (7b). At solid densities, the three-body rate isexpected to be fast and the process could be two-bodycapture with rotation and vibrational excitation followedby energy loss by phonon production in the solid clus-ter. The additional loss of both ions by recombinationwith electrons as the cluster size increases would decreasethe production rate of CH +5 . Consequently, formation ofCH +5 would contribute to the loss of both H + and CH +4 .To illustrate, we can assume reaction (7a) alone con-tributes to the production of CH +5 , combine this with theloss rate controlled by three-body recombination similarto Eq. (4), and predict the concentration of CH +5 , as-suming steady-state, to be of the order:[ CH +5 ] ≈ k [ CH +4 ][ CH ] k [ e ] . (8) -2 -1 I on K i n e t i c E n e r g y ( e V ) Average Cluster size (
We would expect an increase in CH +5 yield because ofthe increasing number of CH +4 ions with increasing clus-ter size, as observed in Fig. 5. We also observe in Fig.5 that at a cluster mean size of h N i ≃ +4 ions saturate, suggesting that theirproduction rate no longer increases with the number oftarget methane molecules. Above this cluster size theproduction rate in the numerator of Eq. (8) no longer in-creases to compensate the increasing recombination rateas the cluster size and explosion time increases, and hencethe yield decreases.The average kinetic energies of ions originating fromthe photoionization of methane clusters, derived from thewidth of the time-of-flight ion peak are shown in Fig. 7.The kinetic energies of the undissociated CH +4 , the frag-ments (CH + , CH +2 , and CH +3 ), the recombined CH +5 , themolecular H +2 and H + all increase as a function of thecluster size up to h N i ≃ ,
000 molecules, indicated bythe dashed line in the figure. Above this size, the energiesremain constant as the cluster size increases, revealing achange in the cluster’s explosion dynamic at large clus-ter size. One of the characteristic differences betweena Coulomb explosion and a hydrodynamic expansion isthat the latter is characterized by the trapping of elec-trons inside the cluster, which in turn increases the elec-tron density within the cluster, leading to an increase inthe recombination rate for all ions. This change in theexplosion dynamics affects both the ion energies and ionchemistry.
V. SUMMARY
In summary, we have studied the explosion dynam-ics of methane clusters irradiated by 38 nm XUV laserpulses. The time-of-flight spectrum shows the undisso-ciated molecular ion CH +4 , fragments without hydrogenatoms due to the breakage of one or more C-H bonds(CH +3 , CH +2 and CH + ), the recombination product CH +5 ,hydrogen ions and molecules (H + and H +2 ), and carbonions and larger hydrocarbons such as C H +2 and C H +3 molecules. No doubly-charged parent ion (CH ) wasdetected. The TOF results show that total and relativeion yields depend strongly on cluster size. CH +5 and H + both show a behavior similar to the rest of the generatedfragments up to a cluster size of h N i ≃ ,
000 molecules,beyond which they exhibit a drop in the yield. In theother fragments, we observe a plateau in the yield withincreasing cluster size, beginning at this same transitionpoint.A comparison between the data presented in this ex-periment and that acquired on FLASH with a differ-ent photon energy (92 eV) provided much insight intothe effect of the photon energy on the cluster dissocia-tion behavior. We were able to explain the behavior ofH + through the electron recombination rate which de-pends on the electron temperature and the cluster aver- age charge. Moreover, the CH +5 behavior was successfullydetermined and explained by the loss of both CH +4 andH + by recombination with electrons above a cluster sizeof h N i ≃ ,
000 molecules. This increase in the recombi-nation rate could be explained by a change in the clusterexplosion dynamics from Coulomb to hydrodynamics assuggested by the kinetic energy measurement shown inFig. 7 and the scattering range for photoelectrons pro-duced by 32 eV photons.
ACKNOWLEDGMENTS
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