Single-shot electron imaging of dopant-induced nanoplasmas
C. Medina, D. Schomas, N. Rendler, M. Debatin, D. Uhl, A. Ngai, Ben Ltaief, M. Dumergue, Z. Filus, B. Farkas, R. Flender, L. Haizer, B. Kiss, M. Kurucz, B. Major, S. Toth, F.Stienkemeier, R. Moshammer, T. Pfeifer, S. R. Krishnan, A. Heidenreich, M. Mudrich
SSingle-shot electron imaging of dopant-induced nanoplasmas
C. Medina, D. Schomas, N. Rendler, M. Debatin, L. Ben Ltaief, M. Dumergue, Z.Filus, B. Farkas, R. Flender, L. Haizer, B. Kiss, M. Kurucz, B. Major, S. Toth, F.Stienkemeier, R. Moshammer, T. Pfeifer, S. R. Krishnan, A. Heidenreich,
6, 7 and M. Mudrich
2, 8 Physikalisches Institut, Universit¨at Freiburg, 79104 Freiburg, Germany Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark ELI-ALPS, ELI-HU Non-Profit Ltd., Wolfgang Sandner utca 3., Szeged, H-6728, Hungary Max-Plank-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany Department of Physics and QuCenDiEM-group,Indian Institute of Technology Madras, Chennai 600036, India Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and DonostiaInternational Physics Center (DIPC), P.K. 1072, 20080 Donostia, Spain IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain Indian Institute of Technology Madras, Chennai 600036, India ∗ (Dated: February 26, 2021)We present single-shot electron velocity-map images of nanoplasmas generated from doped heliumnanodroplets and neon clusters by intense near-infrared and mid-infrared laser pulses. We report alarge variety of signal types, most crucially depending on the cluster size. The common feature isa two-component distribution for each single-cluster event: A bright inner part with nearly circularshape corresponding to electron energies up to a few eV, surrounded by an extended backgroundof more energetic electrons. The total counts and energy of the electrons in the inner part arestrongly correlated and follow a simple power-law dependence. Deviations from the circular shapeof the inner electrons observed for neon clusters and large helium nanodroplets indicate non-sphericalshapes of the neutral clusters. The dependence of the measured electron energies on the extractionvoltage of the spectrometer indicates that the evolution of the nanoplasma is significantly affectedby the presence of an external electric field. This conjecture is confirmed by molecular dynamicssimulations, which reproduce the salient features of the experimental electron spectra. I. INTRODUCTION
The generation of nanoplasmas in clusters andnanoparticles by intense femtosecond laser pulses is be-ing widely studied, both for exploring fundamental light-matter interactions under extreme conditions, and inview of potential applications. Nanoplasmas absorb laserlight very efficiently and convert it into fast electrons [1],highly-charged ions [2], and energetic radiation [3, 4].Therefore, nano- and microplasmas bear the potential toserve as sources of extreme-ultraviolet (XUV) and x-rayradiation [5], as compact accelerators for charged andneutral particles [4, 6], and for high-harmonic genera-tion [7, 8].The ionization dynamics of clusters and nanodropletsinduced by intense near-infrared (NIR) pulses is fairlywell understood, owing to dedicated experiments and de-tailed model calculations [3, 4, 9, 10]. Initiated by tunnelionization [11], an ionization avalanche is launched withina few optical cycles mainly by electron-impact ioniza-tion, thereby releasing a large fraction of electrons fromtheir parent atoms or ions (inner ionization) [12]. Thesequasi-free electrons remain trapped in the space-chargepotential of the cluster and mainly determine the opticalresponse of the resulting nanoplasma. Some electrons aredirectly emitted by the combined action of the laser andthe Coulomb field of individual ions (outer ionization).Depending on the pulse duration or the delay between short pulses in a dual-pulse scheme, resonant absorp-tion occurs, thereby further enhancing the yield, chargestate and kinetic energy of emitted ions [13, 14]. As thenanoplasma heats and charges up, it starts expandingand electrons evaporate out of the collective Coulombpotential of the cluster core. This leads to a thermaldistribution of free electrons characterized by an essen-tially exponential energy dependence [15–19]. Finally,slow electrons and ions partly recombine in the course ofthe expansion. Highly excited neutral and ionic speciesformed during this phase can decay by correlated elec-tronic decay processes, as recently observed [18–21].Helium (He) nanodroplets are a special type of rare-gas clusters due to the extremely high ionization energyof He atoms and the unique superfluid nature of Hedroplets [22]. When doping He droplets with impurityatoms or molecules, the latter tend to aggregate insidethe droplet or at the surface where they form a clus-ter. Electrons emitted from this dopant cluster by tun-nel ionization then act as seeds to ignite a nanoplasma inthe entire He droplet [23, 24]. Thus, doping He dropletswith various types of atoms or molecules in an adjustablequantity offers an additional control knob to tune thesusceptibility of the droplets to intense NIR pulses [23–25]. In particular, the addition of a few dopant atomswith low ionization energy such as xenon (Xe) can dras-tically reduce the intensity threshold for nanoplasma ig-nition [23–26]. Furthermore, electron spectra of ionized a r X i v : . [ phy s i c s . a t m - c l u s ] F e b He droplets are relatively simple to interpret due to thesimple electronic structure of He and the large spacingbetween atomic levels [19].Experimentally, He nanodroplets can be created ina wide range of sizes spanning many orders of magni-tude [27, 28]. Dopant clusters formed by aggregationare mostly located inside the nanodroplets, the onlyexception being alkali metals [26]. In contrast, neon(Ne)clusters are present in the solid phase. The loca-tion of dopants picked up by Ne clusters inside or at thesurface of the clusters is less well defined [29, 30].He nanoplasmas have mainly been studied using iondetection techniques [24–26, 31]. Recently, time-of-flight (TOF) spectroscopy of electrons has revealed ad-ditional details about the dynamics of He nanoplas-mas [19, 21, 32]. However, so far only averaged dataover many laser shots and nanoplasma hits have beenreported. In this paper, we present for the first timesingle-shot electron images from individual He nanoplas-mas driven by intense NIR and mid-infrared (MIR) fem-tosecond laser pulses. We show typical examples of indi-vidual velocity-map images (VMIs) recorded under differ-ent conditions, and we systematically analyze large setsof VMIs to identify important trends and dependencies.By simultaneously detecting electrons and ions, we showthat electron VMIs and ion TOF mass-over-charge spec-tra can be recorded simultaneously.The salient feature of the VMIs is a mostly centro-symmetric intensity distribution with greatly fluctuatingsize and brightness for each plasma explosion. We showthat this feature can be described by a simple heuris-tic model based on a homogeneously charged sphericalelectron cloud. A more complete classical molecular dy-namics (MD) simulation shows that the external elec-tric field applied in the VMI spectrometer for extractingelectrons and ions influences the electron energy distri-butions. Simulated velocity distributions and electronspectra are compared with the experimental data.
II. METHODSA. Experimental setup
The nanodroplet apparatus resembles the one we haveused previously [14, 24, 26]. The main novelty is theimplementation of a combined VMI and TOF detector,capable of detecting energetic electrons and ions, seeFig. 1, [33]. The He nanodroplets, respectively Ne clus-ters, were produced by a supersonic expansion at highstagnation pressure ( p = 20-50, 10 bar) and low tem-perature ( T = 9-15 K, 37-41 K) through a thin-wallednozzle with a diameter of 5 µ m for He and 20 µ m forNe. The size of He nanodroplets was estimated basedon literature data [27]; the Ne cluster size was calculatedusing Hagena’s scaling law [34]. Doping with Xe atoms Figure 1. Schematic illustration of the experimental setup.The He droplet source, doping cell and spectrometer are con-tained in differentially-pumped vacuum chambers separatedby beam skimmers. Electrons are imaged on imagin detectoron the top of the spectrometer; ions are detected by a Dalytype time-of-flight (TOF) detector on the bottom. The laserbeam is back focused into the He droplet beam at right anglesby a spherical mirror ( f = 75 mm). is achieved by passing the clusters through a doping cellcontaining Xe gas at adjustable pressure, see Fig. 1. Thesize of the Xe dopant cluster is estimated based on thePoissonian pick-up statistics while taking into accountthe shrinkage of the He droplets induced by the aggrega-tion of a dopant cluster [35].NIR (800 nm) laser pulses of 35 fs duration (FWHM)with a repetition rate of 3 kHz are focused into the clusterbeam using a back-focusing mirror with a focal length of75 mm. With a pulse energy of up to 200 µ J, the peakintensity ranges up to 1 . × Wcm − as inferred fromthe distribution of charge states of strong-field ionizedxenon atoms [36]. Most of the measurements presented inthis work were measured at a pulse energy of 80 µ J. A fewexperiments were carried out using a high-repetition-rate(100 kHz) MIR laser centered at a wavelength of 3 . µ mwhich provides pulses with energy up to 100 µ J and alength of about 6 optical cycles (50 fs) [37], yielding peakintensities up to 4 × Wcm − . This laser system waslocated at the ELI-ALPS Research Institute in Szeged,Hungary.The detector consists of a compact VMI spectrome-ter capable of detecting high-energy electrons [33], anda TOF ion spectrometer placed on the opposite sidewhich is based on a Daly type detector [38], see Fig. 1.The VMI and TOF spectrometers were synchronized tothe laser trigger using a delay generator. One advan-tage of the single-shot VMI technique is that very shortexposure times in the microsecond range can be used,which reduces the background level. In most of the mea-surements we adjusted the experimental parameters suchthat on average less than 10 % of the images containeda nanoplasma hit to ensure that the rate of images con-taining two or more hits remained low. Given the tightfocusing of the laser beam and the low number density ofdoped He droplets in the interaction region, multiple hitsinduced by the same laser pulse can be safely excluded. B. Molecular dynamics simulations
The molecular dynamics (MD) simulation method forthe interaction of a cluster with the electric and magneticfield of a linearly polarized NIR Gaussian laser pulse wasdescribed previously [9, 39, 40]. Starting from neutralatoms, electrons enter the MD simulation, when the cri-teria for tunnel ionization (TI), classical barrier suppres-sion ionization (BSI) or electron impact ionization (EII)apply. This is checked at each atom in the course of thetrajectory, using the local electric field at the atoms asthe sum of the external laser electric field and the contri-butions from all ions and nanoplasma electrons. Instan-taneous TI probabilities are calculated by the Ammosov-Delone-Krainov (ADK) formula [41], EII cross sectionsby the Lotz formula [42], calculating the ionization en-ergy with respect to the local atomic Coulomb barrier inthe nanoplasma environment [43]. The electron dynam-ics is treated relativistically. Three-body electron-ion re-combination (TBR) is automatically accounted for in theMD simulations.Ion-ion interactions are described by Coulomb poten-tials, ion-electron and electron-electron interactions bysmoothed Coulomb potentials. Interactions involvingneutral atoms are disregarded except for a Pauli repulsivepotential between electrons and neutral He atoms. ThePauli repulsive potential is taken as a sum of pairwiseforth-order Gaussian functions located at every neutralHe atom, V ( r ij ) = V exp (cid:0) − r ij /σ (cid:1) , where r ij is theHe-electron distance, V = 1 . σ = 1 . V ij is about half of the He-He distance (3 . .
33 ˚A (bulk),He-Xe distances 4 .
15 ˚A[45]. The simulations are car-ried out for He Xe , NIR pulse peak intensities I =2 × Wcm − , and a FWHM pulse duration of 35 fs.For these laser parameters, the He droplet is nearly com-pletely ionized; the ionization degree depends very littleon the initial conditions of the trajectories, so that aver-aging over a set of trajectories that is usually necessaryin case of doped He droplets [39, 40] is not needed.Simulations are carried out for static homogenous elec-tric field strengths of 1, 2 and 10 kV/cm. To mimic theVMI detection, a plane is placed perpendicular to thedirection of the static electric field, and the Cartesiancoordinates and velocities of the extracted electrons arerecorded upon passing the plane. The plane is placedin a sufficient distance (5 mm) from the droplet centerto avoid that ions reach the plane during nanoplasmaexpansion. To achieve simulation times of 10 ns and more, necessary for the electrons (including latecomers)to reach the plane, each trajectory is subdivided intoparts. The first 4 ps covering the laser-cluster interac-tion, initial nanoplasma expansion and the vast major-ity of three-body electron-ion recombinations (TBR) iscarried out with a short time step of 10 − fs. Afterthis initial part, the recombined electrons are removedfrom the simulation by unifying them with their corre-sponding host ions, reducing the ion charges accordingly.This “recombination step” not only reduces the numberof electrons to be further propagated but is also a nec-essary prerequisite to increase the MD time step, sincethe recombined electrons with tight orbits around theirhost ions and binding energies on the order of several eVwould otherwise require to continue the simulation withthe small time step to guarantee energy conservation. Inthe subsequent parts of the simulation, the MD time stepis increased successively up to about 0.1 fs, as the inter-particle distances increase. III. RESULTS
In usual photoionization experiments of atomic ormolecular beams, the ionization probability per laser shotis kept well below one to avoid blurring of electron VMIsand broadening of TOF peaks by space-charge effects. Incontrast, in this experiment a single laser pulse creates alarge number of electrons and ions when the nanoplasmais formed; consequently, we may expect that the detectedelectron distributions are dominated by Coulomb repul-sion between the electrons. Only electrons directly emit-ted by outer ionization during the laser pulse produce anextended distribution that is not affected by the spacecharge. Thus, we may expect to measure two main com-ponents in the electron VMIs; a dominant structure atlow energies due to the extraction of nanoplasma elec-trons by the static electric field, and a more energeticone due to direct laser-induced outer ionization.Indeed, all measured VMIs containing nanoplasmaelectrons feature a two-component distribution, as shownin Fig. 2. It is important to note that the brightness andstructure of the electron distributions greatly vary fromshot to shot. The top panels a)-d) show selected VMIsfor large He droplets composed of 2 × He atoms onaverage, whereas the middle panels e)-h) are for smalldroplets composed of 2 × He atoms. The bright innercircular spot mostly has a rather flat intensity profile anda well-defined outer edge for the case of large droplets.The intensity level inside the inner spot is nearly con-stant irrespective of the spot size, resulting in high totalbrightness for large spots.For small droplets, a great shot-to-shot variation ofthe structure of the bright inner spot and the ratio ofinner spot vs. the diffuse outer distribution is observed.This can be seen in the kinetic energy spectra inferred
Figure 2. Selected single-shot electron VMIs of He nanoplasmas induced by intense NIR laser pulses. a-b) Typical VMIs forlarge droplets consisting of 2 × He atoms doped with 40 Xe atoms. e-h) Typical electron VMIs for smaller droplets (2 × He and 8 Xe atoms). The arrows in e) indicate the direction of propagation of the laser ( (cid:126)k ) and its polarization parallel to thedetector plane ( (cid:126)E field ). The He beam propagates parallel to (cid:126)E field . The bottom row shows electron spectra inferred from thesmall-droplet images (middle row). from panels e-h) by an inverse Abel transformation [46],see lower panels Fig.2. The peaks at energies (cid:46) (cid:38) N Ne = 6 × atoms wereirradiated by intense MIR laser pulses; panels e-h) showVMIs of Ne clusters of size N Ne = 2 × irradiatedby NIR pulses. The general structure of the VMIs is Figure 3. Selected single-shot electron images of Ne clusters.a-d) Large Ne clusters consisting of on average 6000 Ne atomsdoped with 10 Xe atoms ionized by a MIR laser pulses. e-h)Ne Xe and their respective electron spectra (bottom row)ionized by NIR pulses. very similar to that of He droplets: a bright inner spotsurrounded by a diffuse cloud of more energetic electronswith variable brightness and radius. While small Ne clus-ters mostly generated circular inner spots, for large Neclusters the inner feature tends to significantly deviatefrom the circular shape. This is likely a direct mani- Figure 4. Selected single-shot electron VMIs of Xe-dopedHe droplets irradiated by MIR pulses and ion time-of-flightmass-over-charge spectra measured simultaneously. festation of a non-spherical shape of the Ne clusters andshould be studied in more detail both experimentally andtheoretically. The nonuniform shape of the diffuse cloudaround the inner spot in a)-d) is due to technical issueswith the spectrometer present in these measurements.Likewise, the low-brightness region in the upper part ofthe inner spot is due to a reduced sensitivity of the de-tector. When bright nanoplasma VMIs are recorded at ahigh repetition rate, degradation of the detector is a se-rious issue. The electron spectra inferred from the VMIsin e)-h), shown in the bottom row, have a similar struc-ture as the electron spectra of small He nanodroplets.This indicates that single-shot VMIs of nanoplasma elec-trons are not particularly element specific but rather re-flect the generic dynamics of electron emission out of ananometer-sized quasi-neutral expanding plasma.One advantage of the electron VMI technique is thepossibility to combine it with ion detection. To demon-strate this capability, we ignited He nanoplasmas withintense MIR pulses and measured electron VMIs and ionTOF traces for every hit. Fig 4 shows typical data. Thebright feature in the VMI (large number of emitted elec-trons) clearly correlates with an intense and broadenedHe + peak indicative for high ion kinetic energies. Evenfully ionized He atoms, He , are visible as a small peakin the TOF spectrum shown in the top right panel. Thefact that it appears at a value of m/q slightly below 2is due to the high He kinetic energy causing peak de-formations [14, 24–26]. In contrast, low-intensity VMIscorrelate with narrow He + and He +2 peaks in the TOF Figure 5. Electron spectra of averaged VMIs for differentHe cluster sizes compared to Ne clusters. The inset shows anexample of the averaged VMIs for He droplets of size 3 × He atoms doped with on average 40 Xe atoms. The outermostwhite circle indicates the edge of the imaging detector. trace, indicating low ion kinetic energies and incompletefragmentation or ion dimerization occurring in a nan-odroplet that is only partly ionized (bottom panels). Inthe future, a systematic analysis of the correlated elec-tron and ion signals may help to disentangle the two maincontrol parameters, droplet size and local laser intensity.Assuming that the VMI technique is in principle appli-cable to imaging of nanoplasma electrons, we can convertthe measured radial intensity profile into an electron ki-netic energy distribution according to electron-trajectorysimulations validated by calibration measurements [33].Fig. 5 shows electron spectra obtained in this way fromaveraged VMIs recorded for various mean sizes of Hedroplets and Ne clusters. For every cluster size, around100 images containing nanoplasma signals were averaged.As an example, the inset displays the resulting averageimage for He droplets of mean size N He = 3 × atoms.The electron spectra show a pronounced peak structurewhere the peak position shifts from 0.1 up to 3 eV asthe mean He droplet size increases from N He = 3 × × . The electron spectrum for Ne clusters dopedwith on average 8 Xe atoms closely resembles the one ofHe doped with 10 Xe atoms. Thus, by varying themean cluster size in the shown range, the kinetic energyof emitted nanoplasma electrons shifts by more than afactor of 10.More detailed information should be obtained by an-alyzing the individual single-shot VMIs. This was donein two steps. First, those images containing clear signalsfrom nanoplasma electrons were identified by integratinga small area around the center of the image and com-paring the result with a fixed threshold value. In mostof the measurements, a maximum of 10 % of images con-tained hits and the rest contained only small numbersof electrons emitted from the residual gas or from smallHe clusters in the size range 100-1000 atoms. Second, Figure 6. a) Histograms of the electron peak energies E max of the single-shot VMIs that were averaged in Fig. 5. Thedata points are the energies for the different He and Ne clus-ters sizes. The solid lines are Gaussian fits. b) Cluster sizedependence of the mean peak energy for the He data found ina) including additional cluster sizes. The red line is a linearfit of the experimental data. the radius of the inner bright spot was determined bya simple algorithm that computes the derivative of theradial intensity profile. The radius is then defined by thelargest negative value of the radial derivative. This ra-dius value is directly converted into energy correspondingto the maximum of the distribution, E max . The integralof the area within the radius is converted into the totalnumber of electrons by analyzing the brightness of singleelectron hits on the detector measured in the backgroundimages.Fig. 6 a) shows the resulting histograms of E max valuesfor the individual shots used in Fig. 5. The solid linesare fits by a Gaussian function. Overall, both analysismethods are in good agreement. For large He droplets,the peaks in Fig. 6 a) are slightly narrower than thosein Fig. 5. This is expected, as in the histogram anal-ysis [Fig. 6 a)], the peak width is solely determined bythe scatter of E max , whereas the shape of each individ-ual electron spectrum is not accounted for. For smallclusters, the peaks extend further towards low energies E max < . E max distributions shown in a) and from additional mea-surements are depicted as squares in Fig. 6 b). As shownby the solid line, these mean values (cid:104) E max (cid:105) closely followa linear dependence of the number of He atoms. Figure 7. Dependence on the number of dopant atoms.a) Fraction of VMIs containing nanoplasma electrons for dif-ferent He and Ne cluster sizes ionized by NIR pulse. b)Mean electron peak energy. The blue symbols correspondto He droplets of different sizes, the red symbols correspondto Ne . When we apply the same procedure to VMIs recordedfor varying Xe partial pressure in the doping cell, we ob-tain the data shown in Fig. 7 b) for He and Ne clustersof different sizes. The data shows no significant variationof the nanoplasma electron energy as a function of thenumber of Xe dopant atoms embedded into the clusters.Thus, the nanoplasma is primarily determined by thesize of the He or Ne host cluster, whereas the Xe dopantcluster only facilitates the ignition of the nanoplasma, aspreviously shown [24–26, 50]. This can be clearly seenfrom the fraction of VMIs that contain nanoplasma sig-nals, shown in Fig. 7 a). The rate of nanoplasma VMIssteeply rises when increasing the number of Xe dopantsfrom 0 to 25. For higher doping levels, the signal slowlydrops again because of scattering and destruction of theHe droplets by multiple collisions with Xe atoms in thedoping cell [26]. A minimum of about 5 Xe atoms isneeded to ignite a He nanoplasma, whereas Ne nanoplas-
Figure 8. Laser intensity dependence. a) Nanoplasma hitrate for He droplets irradiated by NIR and MIR pulses atdifferent intensities. b) Electron peak energy for the two lasertypes. Notice that the blue axis (bottom and left) correspondsto the NIR data and the red (top and right) to the MIR data. mas are measured even at the lowest doping levels of 1 Xedopant atom per cluster on average. This is due to thelower ionization energy of Ne, which makes pure Ne clus-ters more prone to strong-field ionization as comparedto He nanodroplets. The overall similar behavior of Neclusters and He nanodroplets with respect to their dopingdependence of the nanoplasma ignition indicates that thestructure of the cluster (solid vs. superfluid) is not deci-sive for the dopant-induced activation of a nanoplasma.Similar to the doping dependence, the intensity ofthe laser pulses significantly influences the abundance ofnanoplasma events, whereas the mean electron energy isonly weakly affected. Fig. 8 shows the intensity depen-dence for He nanodroplets doped with Xe atoms exposedto NIR laser pulses and for He droplets, doped with wa-ter, exposed to MIR pulses at different intensities (notethe colored axes on the top and bottom of the figure). Inboth cases, the signal rates follow a nearly linear risewith the laser intensity. However, the mean electronenergy remains nearly constant within the experimen-tal uncertainty. This is due to intensity averaging overthe volume of the laser focus; while a few droplets arehit by the laser in the center of the focus and generatemore energetic electrons at higher laser intensity, a largenumber of droplets in the periphery of the focal volumeexperience a reduced local intensity, which may still besufficient for igniting a nanoplasma. These droplets leadto an enhanced signal rate with rising laser intensity but contribute mostly low energies. Owing to the single-shotmethod, we can select only the brightest nanoplasma im-ages thereby selecting events where the largest dropletsare exposed to the peak intensity. These selected images(not shown) clearly display enhanced electron numbersand energies when the intensity increases.
DISCUSSION
The evolution of a laser-induced nanoplasma is a com-plex dynamical phenomenon that involves various pro-cesses of light-matter interactions and collisions on thelength scale of atoms and of the cluster as a whole.These include tunnel ionization, inverse bremsstrahlung,electron-impact ionization, plasmon-enhanced resonantabsorption, three-body recombination, etc. [3, 4]. Ac-cordingly, sophisticated numerical model calculations,such as MD simulations, are usually required to capturethe most important aspects of the nanoplasma dynamics.Nevertheless, we attempted to come up with a simpleanalytic model to reproduce the most pronounced corre-lation visible in the VMIs despite their strong shot-to-shot variation, namely that of size and brightness of theinner spot. This model is based on the expansion of ahomogeneous spherical distribution of charges of radius R (electrons in our case) driven by Coulomb repulsion.According to Islam et al. [51], the initial radial chargedensity distribution dPdr = 3 r R Θ( R − r ) (1)transforms into a final kinetic energy distribution dPdE = 32 (cid:114) E R E R √ E · Θ (cid:18) − EE R (cid:19) , (2)where E R = e π(cid:15) (cid:18) πρ (cid:19) / N / (3)is the cut-off energy. Here, Θ is the Heaviside step func-tion, N is the number of electrons in the sphere and e isthe elementary charge. In this way, we obtain a simplepower law dependence E R ∝ N / under the assumptionof a constant initial density ρ = 3 N/ (4 πR ). Here, E R can be identified with E max in the experimental electronspectra and N is derived from the integrated brightnessof the inner spot.The correlation of E max and N is represented in Fig. 9.The data points are obtained by binning E max and N val-ues from a total of about 1000 VMIs for every He andNe cluster size. The error bars indicate the dispersionof the data within each bin, resulting from 10-200 VMImeasurements per data point. The solid lines are fits of Figure 9. Peak electron energies as a function of the numberof nanoplasma electrons. The data points represent the meanvalues of the distributions of electron peak energies for differ-ent He and Ne cluster sizes. The solid lines represent the fitsbased on Eq. 3. The inset shows a closeup of the low-energyregion where the Ne data points are concentrated.
Eq. 3 to the data. Surprisingly, despite of the simplic-ity of our model, the experimental data for both He andNe clusters are well reproduced by the fits. Due to thelimited range of sizes of Ne clusters accessible in the ex-periment, the Ne data were constrained to N (cid:46) × .The inset shows an overview of the data and fits at lowenergies.The only free fit parameter is the prefactor in Eq. 3which yields ρ = 0 . . e µ m − for He nanodroplets,where e is the electron charge. The smallest valueis obtained for small droplets at low NIR intensity I ∼ × Wcm − , the largest value is obtained forlarge droplets and I (cid:38) Wcm − . These values aremuch smaller than the atom density of He nanodroplets,0.022 ˚A − . This is expected in view of our tentative in-terpretation that the relevant electron density responsi-ble for the lower-energy component is the one in the moredilute electron beam extracted by the external static elec-tric field of the VMI spectrometer, see below. In the hot-ter nanoplasma created by more intense pulses in largedroplets, the electrons appear to be extracted more eas-ily, i. e. at an earlier stage of the nanoplasma expansionwhen the electron density is higher. While the insightinto the physics of nanoplasmas gained from this modelcertainly is rather limited, it is still useful for predictingthe energy of nanoplasma electrons merely based on thedetection of their yield. Figure 10. Dependence of the mean electron peak energy onthe extractor voltage for He Xe irradiated by NIR pulses.The red line is a linear fit of the data. Up to this point we have discussed our results assumingthat the VMI technique applies when detecting electronsemitted from a nanoplasma. However, we find indica-tions that the evolution of a nanoplasma, in particularthe emission of electrons, is affected by the static electricfield present in the VMI spectrometer. Fig. 10 shows themean electron peak energies as a function of the voltageapplied to the extractor electrode of our spectrometer.The electric field (in V/cm) in the interaction region isgiven by a factor 0 . × Wcm − was applied to a Henanodroplet consisting of 2171 He atoms doped with 23Xe atoms. The polarization of the laser is horizontal,and the electric field F = 1000 V/cm points upwards.Electrons, neutral He and Xe atoms as well as ions arerepresented by differently colored beads.In the early stage t (cid:46)
430 ps (top frames), electrons(white dots) are emitted in two rather distinct distri-butions; a diffuse and nearly isotropic cloud is createdshortly after the laser pulse (see frame at 61 ps), and
Figure 11. Theoretical time-evolution of a nanoplasma ig-nited by an intense NIR laser pulse in the presence of anexternal homogeneous electric field ( F = 1000 V/cm). Thelaser polarization is horizontal and the electric field pointsupwards. one highly directional component of electrons is extracteddownwards along the electric field axis at t (cid:38)
100 ps. At t > F = 0, 1, 2, and 10 kV/cm as coloredlines. Clearly, an increasing electric field gives rise to Figure 12. Comparison of theoretical and experimen-tal results. a) Simulated velocity distribution for a dopeddroplet, He Xe , exposed to a NIR pulse in an electricfield of F = 1000 V/cm. b) Selected experimental VMIs forHe Xe ionized by NIR pulses in the presence of an elec-tric field of 25 V/cm in the interaction region. c) Kineticenergy distributions from the simulation (colored lines) andthe experiment (black line). a growing shoulder structure extending up to 0.6 eV at F = 10 kV/cm (blue dashed line), which is not presentwithout electric field (red line). Electron energies inferredfrom this shoulder are depicted in the inset. The blackline depicts the electron spectrum obtained from the Abelinversion of the average of 5 images of the same type asthat shown in panel b), arbitrarily scaled in intensity. Itqualitatively resembles the simulated spectra at low elec-tric field. However, the electron energies inferred fromthe simulated spectra fall significantly below the averageof experimentally determined electron energies (Fig. 10),despite the higher electric fields used in the simulation.Clearly, this study should be further extended tofully characterize the electric-field dependence of elec-tron emission from a nanoplasma in various regimes oflaser intensity and droplet size. The fact that the simu-lated spectra do not reproduce the exact peak structureat energies exceeding 1 eV observed in most of the ex-perimental spectra (Fig. 2 and 3) is likely due to therelatively small size of the He droplet used in the simula-tion (He Xe ). Larger droplets emit larger amountsof electrons at higher densities which likely give rise toa more pronounced shoulder in the spectra, eventuallyevolving into a peak. Unfortunately, simulations of largeHe droplets are prohibitively costly for this work. Ad-0ditionally, the inhomogeneous electric field of the VMIspectrometer may cause distortions of the velocity distri-butions due to the coupling of longitudinal and transversedegrees of freedom with respect to the electric field. IV. CONCLUSION
In conclusion, we presented the first dedicated exper-imental study of single-shot VMI of electrons emittedfrom He and Ne nanoplasmas induced by intense NIR andMIR laser pulses. The images are characterized by largeshot-to-shot fluctuations of the brightness and structuredue to the large variation of cluster sizes and of laser in-tensities seen by each cluster as it is hit at different posi-tions within the laser focus. This puts some demands onthe data storage capacities, sorting and analysis meth-ods to cope with the large amount of image data. Toclearly map systematic dependencies, typically a mini-mum of about 100 images have to be recorded per setof parameters. Despite the rather high intensities usedto strong-field ionize the clusters, the electron emissionpatterns are circularly symmetric to a high degree. Onlyslight dents and elongations along the laser polarizationwere observed for the highest intensities (cid:38) Wcm − .The VMIs of both He and Ne clusters feature a generictwo-component structure consisting of a central brightspot and a diffuse cloud of electrons around it. Likewise,VMIs measured for MIR and NIR laser pulses are verysimilar, which supports the concept that electron emis-sion is mostly determined by the intrinsic dynamics ofthe nanoplasma. The initial structure of the clusters (su-perfluid, solid) and the characteristics of the laser pulsesonly play minor roles once the threshold for avalancheionization is reached. The most sensitive parameter thatdetermines the yield and energy of emitted electrons isthe cluster size.We have demonstrated the possibility to record elec-tron VMIs and ion TOF traces simultaneously on a shot-to-shot basis. Bright electron images clearly correlatewith large yields of singly and doubly charged He atomicions, whereas low nanoplasma electron yields correlatewith singly charged He + and He +2 ions. Despite the largeshot-to-shot variations, a clear correlation of the bright-ness (number of nanoplasma electrons) and size of theinner spot (maximum electron energy) is found. It isconsistent with a simple power law derived for an ex-panding spherical cloud of electrons. A more realisticMD simulation including a static electric field unravelsthe mechanism of electron extraction out of the expand-ing nanoplasma. It shows that the resulting transversekinetic energy distributions of electrons significantly dif-fer from the electron spectrum obtained in the case offield-free expansion in that they feature a shoulder struc-ture around 0 . ∗ E-mail me at: [email protected][1] Y. Shao, T. Ditmire, J. Tisch, E. Springate, J. Marangos,and M. 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