Efficiency of Dopant-Induced Ignition of Helium Nanoplasmas
A. Heidenreich, B. Gruener, M. Rometsch, S. R. Krishnan, F. Stienkemeier, M. Mudrich
EEfficiency of Dopant-Induced Ignition of HeliumNanoplasmas
A. Heidenreich , , B. Gr¨uner , M. Rometsch , S. R. Krishnan ,F. Stienkemeier , and M. Mudrich 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 Physikalisches Institut, Universit¨at Freiburg, 79104 Freiburg, Germany Department of Physics, Indian Institute of Technology - Madras, Chennai 600036,India
Abstract.
Helium nanodroplets irradiated by intense near-infrared laser pulses igniteand form highly ionized nanoplasmas even at laser intensities where helium is notdirectly ionized by the optical field, provided the droplets contain a few dopant atoms.We present a combined theoretical and experimental study of the He nanoplasmaignition dynamics for various dopant species. We find that the efficiency of dopants toignite a nanoplasma in helium droplets strongly varies and mostly depends on (i) thepick-up process, (ii) the number of free electrons each dopant donates upon ionization,and remarkably, (iii) by the hitherto unexplored effect of the dopant location in or onthe droplet.
1. Introduction
Plasmas formed in nanoscale matter by the interaction with intense light pulses rangingfrom near-infrared (NIR) up to hard X-rays are a focus of current research. These studiesare motivated by a large number of potential applications including the generation ofenergetic electrons and ions [1, 2] as well as intense XUV and attosecond pulses [3].Besides, in single-shot X-ray imaging experiments of large molecules [4] and clusters [5],the creation of an expanding nanoplasma generally causes severe limitations to theachievable resolution of the initial structure. Controlling the nanoplasma dynamics forthe purpose of exploiting its exceptional properties or for mitigating its detrimentaleffects requires in both cases a profound understanding of the dynamics of the ignitionand the evolution of such nanoscale atomic and molecular systems in intense light fields.In the NIR excitation regime, the remarkable properties of nanoplasmas have beenrationalized by a resonant interaction between the external light field and the dipolaroscillations in the collective electron motion driven by this field [1, 2]. The resultingefficient light absorption induces avalanche-like charging and heating of the nanoplasmafollowed by hydrodynamic expansion and Coulomb explosion. a r X i v : . [ phy s i c s . a t m - c l u s ] M a r fficiency of Dopant-Induced Ignition of Helium Nanoplasmas ignition – conspicuously varies as function of the dopants physico-chemicalproperties. The efficiency of dopant-induced ignition is assessed by comparing variousspecies – Xe residing in the droplet interior, Ca in the surface layer, and potassium (K)on the surface. A detailed analysis reveals the crucial properties of dopants which allowsus to propose principles for optimally designing dopant clusters for nanoplasma studies.
2. Experiment
The experimental setup is composed of an amplified fs laser system for generating intenseNIR laser pulses and a molecular beam apparatus for generating doped He nanodroplets.The latter has been described in detail elsewhere [28, 15]. fficiency of Dopant-Induced Ignition of Helium Nanoplasmas p = 50 bar) of high purity (He 6.0) out of a cold nozzle ( T = 18K) with a diameter of 5 µ m into vacuum. At these expansion conditions, the meandroplet size is (cid:104) N (cid:105) ≈ λ = 800 nm, pulse length t FWHM = 220 fs)are generated by chirped pulse amplification (Coherent Legend) at a repetition rate of5 kHz. The pulses are focused by a lens (focal length f = 75 mm) placed inside thedetector chamber to reach a maximum peak intensity I = 5 × W cm − in the focalvolume.
3. Theory
The MD simulation method for the interaction of a cluster with the electric and magneticfield of a linearly polarized NIR Gaussian laser pulse was described previously [31, 32,33]. All atoms and nanoplasma electrons are treated classically, starting with a cluster ofneutral atoms. Electrons enter the simulation, when the criterion for tunnel ionization(TI), classical barrier suppression ionization (BSI) or electron impact ionization (EII) ismet. This is checked at each atom at every MD time step, using the local electric fieldat the atoms as the sum of the external laser electric field and the contributions fromall other ions and electrons of the cluster. Instantaneous TI probabilities are calculatedby the Ammosov-Delone-Krainov (ADK) formula [34], EII cross sections by the Lotzformula [35] taking the ionization energy with respect to the atomic Coulomb barrier inthe cluster [36]. The effect of chemical bonding on the valence shell ionization energiesof K and Ca dopants is disregarded.Coulomb potentials between ions, smoothed Coulomb potentials for ion-electronand electron-electron interactions are used. Interactions involving neutral atoms aredisregarded except for a Pauli repulsive potential of 1.1 eV between electrons and neutralHe atoms [37] in terms of a fourth-order Gaussian function centered at every He atom.The binding potentials of He +2 and of other He + n complexes are not implemented, so thatthe simulations cannot account for the He +2 formation explicitly; we can only estimate an fficiency of Dopant-Induced Ignition of Helium Nanoplasmas +2 abundance from the remaining groundstate neutral He atomsand He + ions at the end of each trajectory. Neutral He atoms and He + ions whichare formed by three-body electron-ion recombination are Rydberg state atoms and aretherefore excluded from the estimate of the He +2 production. Electron-ion pairs whichare found within a cutoff distance of 2 ˚A at the end of each trajectory (temporal length0.7-1.8 ps) are taken to be recombined and the ion charge state abundances are correctedaccordingly.He ion and dopant ion signals are laser-intensity averaged over the three-dimensional focus volume [38] in the range 8 × -5 × Wcm − . Due to the highsensitivity of the droplet evolution to initial conditions, the results are averaged over setsof 5 to 100 trajectories per doped droplet and laser intensity. Moreover, surface-dopeddroplets (K and Ca) are averaged over their parallel and perpendicular orientations ofthe dopant-droplet axis with respect to the laser polarization axis unless mentionedexplicitly. The temporal width of the Gaussian pulse intensity envelope is τ I = 200 fs,slightly lower than in the experiment (220 fs). He 2171, K16, t=-74.4fsFrame 243 He 2171, Ca8x, t=-60.3fsTrajectory 9, frame 190
He 2171, Xe8c, t=-62.1fs
Trajectory 3, frame 170 K Ca Xe t = -74 fst = -60 fs t = -62 fs Figure 1.
Cross sectional views of the doped He droplets before (left column) andat the onset of droplet ignition 60 −
74 fs before the maximum of the laser pulse (rightcolumn). The blue, orange, purple and white bullets depict neutral He atoms, dopantatoms, ions, and electrons, respectively.
For the He droplets we assume a fcc structure with an interatomic distance of3.6 ˚A [39]. The dopant clusters are assembled according to the principle of densest fficiency of Dopant-Induced Ignition of Helium Nanoplasmas cluster) [40], Ca-Ca 3.9 ˚A (average value for Ca clusters) [41], Ca-Xe5.17 ˚A (CaXe complex) [42], Xe-Xe 4.33 ˚A (bulk), He-Xe 4.15 ˚A [43], He-K 7.13 ˚A [44],He-Ca 5.9 ˚A (HeCa diatomic complex) [45].In case of surface doping we assume a dimple depth of 7 ˚A (inferred from densityfunctional calculations of a single Ca atom on the surface of a He droplet) [23]. Accordingto Ancilotto et al. [21], a single K atom is located in a dimple of depth 2.3 ˚A. Since such ashallow dimple cannot be implemented in a fcc lattice of discrete He atoms, we neglectthe dimple for K dopants. The left column of Fig. 1 shows cross sectional views ofdopant-He complexes containing 2171 He atoms and the indicated number of dopantatoms. The right column shows snapshots of the clusters shortly after He ignition atthe indicated interaction times with respect to the maximum of the laser pulse of peakintensity I = 10 W cm − . Neutral He atoms are represented by blue spheres, dopantatoms are orange, ions are red and electrons are small white dots.
4. Results
Our simulations provide full insight into the nanoplasma ignition and charging dynamicsby giving access to all relevant microscopic and ensemble-averaged observables as theyevolve in time, including electron and ion kinetic energies as well as the yields and chargestates of He and dopant ions. As examples, Fig. 2 illustrates for selected dopant speciesthe dynamics of ionization of dopants and of the He host initiated by the ignition andavalanche-like growth of a He nanoplasma. Shown are the intensity envelope of thelaser pulse in panel a), the average charge per dopant atom b) and per He atom c), theprobability of igniting a He nanoplasma d), and the average electron kinetic energy e),for trajectory bundles of He droplets doped with clusters K and K (both on thesurface), Ca (in a dimple on the surface), as well as Xe (in the center).Ionization of the doped droplets starts with TI or BSI of the dopant in the risingedge of the laser pulse. After a time delay which we call “incubation time”, ignitionof the He droplet induced by EII occurs. The role of the dopant is to provide the seedelectrons and to assist EII by lowering of the Coulomb barrier at He by the field of thedopant cations. EII is also the by far dominating ionization channel (typically > case as compared to K doping(9.7 and 2, respectively, in units of the elementary charge e ), in spite of the much higherfirst ionization energy of Xe (12.1 eV) than for K (4.3 eV).For K dopants, a single ionization per K atom occurs early in the pulse at t ≈ − , an incubation time of 100-150 fs elapses until the average chargeof He [Fig. 2 c)] starts to rise. During this incubation time, EII of He competes witha partial drain of the seed electrons by outer ionization [46]. This competition is not fficiency of Dopant-Induced Ignition of Helium Nanoplasmas
05 x 1 0
Laser int. [Wcm-2] ( e )( d )( c )( a )( b ) K C a K K K C a C a K K Av. dopant charge [ e ] X e X e q a v e n t i r e s e t q a v i g n . o n l y n p i g n . o n l y T i m e [ f s ] Av. He charge q av, plasma electrons n p [ e ] - 3 0 0 - 2 0 0 - 1 0 0 0 1 0 0 2 0 0 3 0 002 04 06 08 01 0 01 2 0 X e Av. electron energy [eV] K Ignition probability
X e C a K Figure 2.
Simulated ionization dynamics of a He droplet doped with Xe , K , K and Ca clusters for fixed pulse peak intensity I = 10 Wcm − . (a) Temporal profileof the Gaussian pulse intensity envelope; (b) Average charge per atom of dopants and(c) of He atoms. (d) Ignition probabilities; (e) Average electron kinetic energies. Allquantities are trajectory set-averaged. always in favor of EII. It turns out that, depending on slight variations of the trajectories’initial conditions but for the same pulse parameters, either He ionization does not takeplace at all, ceases after a few He atoms, or ignition occurs, that is, ionization propagatesavalanche-like through a large part or the entire He droplet. Which factors contributeto ignition and determine the incubation time, is subject of a detailed mechanistic studyand will be published in a subsequent paper. We define an average He charge of 0.1 asan empirical criterion for the detection of the onset of ignition. The exact choice of thethreshold value is uncritical in view of the rapid charging process in the He droplet.The sensitivity to the initial conditions is high for those dopant sizes and pulseparameters for which the occurrence of ignition is on the knife’s edge. In thosetrajectories with ignition, the average charge per He atom jumps to almost 2 within fficiency of Dopant-Induced Ignition of Helium Nanoplasmas +2 formation do not occur; recombination becomes important for I (cid:46) × Wcm − .Averaging only over those trajectories with ignition also leads to a long-time average Hecharge of nearly 2 [included as dashed lines for K and Ca in Fig. 2 c)]. The ignitionprobabilities, derived as fractions of the number of trajectories with ignition, are shownin Fig. 2 d). The long-time ignition probabilities for K , Ca and Xe dopants are 0.01,0.30 and 1, respectively.The K and K examples reveal a dopant cluster size effect: The ignitionprobability increases with the number of dopant atoms as a larger dopant clusterprovides more seed electrons and a stronger electric field created by the sum of dopantion charges, thereby assisting EII by reducing the Coulomb barrier at the adjacentHe atoms. Moreover, the dopant cluster size effect is nonlinear: While for K theaverage charge per K atom remains 1 during the incubation time [Fig. 2 b)], for K it rises gradually, making via EII also up to two inner shell electrons available for seedionizations. Ca contributes by its two valence electrons per atom.With an ignition probability of 1, the Xe cluster has the highest ignition efficiencyas compared to the K and Ca dopants of the same size. For Xe , the initial seedionization begins much closer to the center of the laser pulse ( t ≈ −
100 fs) than for Kand Ca dopants. Within an incubation time of only a few fs, up to three seed electronsper atom are set free by TI, BSI and EII, in contrast to only one seed electron per atomin the K case. This can be rationalized by the relatively low second and third ionizationenergies of Xe of 21.0 and 32.1 eV, compared to 31.6 and 45.7 eV for K. Further reasonsfor the low ignition capability of K are its long incubation time and its surface location.Delaying the initial ionization of K artificially until t = −
100 fs (the instant when TIsets in for Xe), the detrimental effect of outer ionization of the seed electrons is reducedand the ignition probability increases to 0.6. Furthermore, the interior doping site ofXe brings the laser-driven cloud of quivering seed electrons in closer contact with thehost cluster. The aspect of dopant location and dopant-He interatomic distance will beaddressed later.The average dopant charge state is considerably enhanced in case of ignition [10],since EII as the almost exclusive ionization channel critically depends on the laser-drivennanoplasma electron cloud. This is demonstrated in Fig. 2 b) for K and Ca . In theseexamples the final dopant charges averaged only over trajectories with ignition (dashedlines) are by about 2 elementary charges higher than the corresponding values averagedover the entire trajectory set (solid lines).Fig. 2 e) exhibits the time-dependent average electron kinetic energies. Their time-dependent shape is determined by the instants of ignition. Trajectories without ignitionalmost do not contribute because of their small number of electrons. The averageelectron kinetic energies obtained along single trajectories are in the range of 60-150,40-150 and 140-150 eV for K , Ca and Xe doped He droplets, respectively. Thesmaller trajectory set-averaged values for K and Ca as compared to Xe doping are fficiency of Dopant-Induced Ignition of Helium Nanoplasmas q av (solid line for Xe and dashed lines for the K and Ca doped droplets) and the nanoplasma electron population n p per atom (dottedlines, obtained from the number of nanoplasma electrons within six droplet radii fromthe droplet center of mass). In all the three cases, the outer ionization amounts to about0.5 elementary charges per atom.A preliminary analysis shows that the main energy absorption takes place by thenanoplasma electrons during the avalanche EII. However, damping of the laser-drivennanoplasma electron oscillation is very strong as a large part of the absorbed energy isconsumed by EII, such that a nanoplasma resonance is unlikely to be present during thisphase. This changes only near the termination of avalanche ionization when dampingbecomes small and energy absorption is still considerable, apparently driving outerionization during this time period.A resonance also seems to be present during the incubation time, involving the seedelectrons and a limited number of electrons set free from He ionization, when energyabsorption is positive and damping is small. Although this small nanoplasma resonancedoes not carry weight in the total energy balance of the droplet, it might be important forthe ignition process. Pristine He droplets for I M ≥ × Wcm − (i. e., for intensitieswhen TI rates at He become notable) show the same behavior: (i) resonance as longas only a limited number of He atoms is ionized, (ii) strong damping during avalancheEII and (iii) a second resonance with strong energy absorption towards the completionof the nanoplasma formation. Thus, the initial phase before the onset of avalanche EIIresembles the experiment of Sch¨utte et al. [47] where the seed electrons are generatedby an XUV laser pulse. At lower pulse peak intensities (e. g., I M = 10 Wcm − ),avalanche ionization is not complete during the laser pulse, so that the only nanoplasmaresonance occurs during the incubation time. These energy absorption and nanoplasmaresonance phenomena as well as their implications for the ignition mechanism requirefurther investigations. In this context it will also be of interest to characterize thedamping of the nanoplasma in terms of the quality factor of damped oscillators.The efficiency of igniting a He nanoplasma is manifested by the appearance of Heion signals. Fig. 3 shows the experimental yield of He + , He , and He +2 ions recordedas a function of the vapor pressure of dopants. The latter is adjusted by controllingthe temperature of the heated crucible in the case of K and Ca and by leaking Xe intothe doping chamber using a dosing valve. The conspicuous result is that by far thehighest He ion yields are obtained when doping with Xe, whereas doping with Ca andK provides lower He ion yields by about one and two orders of magnitude, respectively.When increasing the doping pressure starting from zero, the He ion yields first rise dueto enhanced efficiency of the dopant-induced ignition process. The diminishing of ionyields for high doping pressures is a consequence of massive droplet beam depletion due fficiency of Dopant-Induced Ignition of Helium Nanoplasmas + H e
H e +2 K d o p i n g H e + H e
H e +2 He ion yield [ions per laser shot]
D o p a n t p r e s s u r e * c o l u m n l e n g t h [ 1 0 - 4 m b a r * c m ]X e d o p i n g H e + H e
H e +2 Figure 3.
Experimental He ion yields as a function of the vapor pressure of K, Ca,and Xe dopants multiplied by the length of the doping region (1 cm vapor cell for K,Ca, 35 cm vacuum chamber for Xe).
In an attempt to directly compare the experimental results with the simulation,the experimental data of Fig. 3 are represented on different x and y scales in Fig. 4a)-c). The rescaling of dopant pressure to the number of dopant atoms relies on thedetailed simulation of the doping process [30]. The measured yields of He + and He ions as a function of the number of dopant atoms picked up on average by one dropletattains the highest values for Xe at about 13 dopant atoms. In contrast, the highestHe + signal observed for K-doping stays below that for Xe-doping by factor 6 × − .When doping with Ca atoms, the He + ion yield comes close to the one obtained forXe-doping at low doping numbers ( n Xe ≤ ions sharply drops upon doping onlya few ( n Ca = 2-3) Ca atoms. The significant fraction of He +2 observed for n Ca = 3-6points at incomplete cluster ionization which is followed by dimer formation out of He + surrounded by neutral He atoms.A complete simulation of the ion signals requires (i) the averaging over all intensitiesin the focal volume which contribute to the He ion signal, (ii) the averaging over the sizedistribution of doped droplets, (iii) the dopant size distribution, and, for surface dopantstates, (iv) the averaging over the orientation of the dopant-droplet axis relative to thelaser polarization. For the simulated He ion signals, Figs. 4 d)-f), we have carried outonly points (i) and (iv). Therefore, we cannot expect quantitative agreement betweenexperiment and theory. As a consequence of the missing dopant size averaging, the fficiency of Dopant-Induced Ignition of Helium Nanoplasmas c ) Kb ) C a a ) X e N u m b e r o f d o p a n t s
Experimental He ion yield (ions per laser shot)
H e + H e
H e +2 f ) H e K n e ) H e C a n d ) H e X e n N u m b e r o f d o p a n t s , n Simulated He ion yield (normalized)
Figure 4. a)-c) Experimental and d)-f) simulated yields of He ions generated by Henanoplasma ignition induced by multiple dopants of the species K, Ca, and Xe. Thesimulated He ion counts in proportion to the total number of He atoms are averagedover the focus volume of the laser beam. In case of surface doping with K and Ca,the signals are also averaged over the parallel and perpendicular orientations of thedopant-droplet axis relative to the laser polarization. abscissa of Fig. 4 d)-f) represents a fixed number n of dopant atoms, whereas each valueof the abscissa of the experimental signals, Fig. 4 a)-c), is the average number of dopantatoms in a distribution.The simulated results qualitatively reproduce the experimental He ion yields forthe dopant sequence Xe > Ca > K in the regime of weak doping where the detrimentaleffects of droplet evaporation are nearly negligible. By far the largest He ion yields areobtained for Xe doping. For Ca and K doping, the small signal intensities stem fromintensities I ≥ × Wcm − for which the droplet ignites by itself because of TI ofHe. Only for n ≥ n ≥ I = 2 × Wcm − ,at which the focal volume is sampled. The experimental signal increase already for asmall number of dopant atoms is caused by the admixture of signal intensities fromlarger dopants in the dopant size distribution and therefore cannot be reproduced bythe simulations. Likewise, the decrease of the experimental signal for larger dopantsbecause of droplet evaporation cannot be accounted for. The order of the He + andHe signal intensities compared to the experimental signal is reversed which we partlyattribute to the averaging over the broad He droplet size distribution. Simulations forthe smaller He doped droplets as a sample of the droplet size distribution indeed show fficiency of Dopant-Induced Ignition of Helium Nanoplasmas + , as shown inFig. 5 d) and e). + H e
H e +2 c ) H e K n b ) H e C a n a ) H e X e n Simulated He ion yield (normalized)
N u m b e r o f d o p a n t s e ) H e
C a n d ) H e X e n N u m b e r o f d o p a n t s
Simulated He ion yield (normalized)
Figure 5.
Simulated yields of He ions as a function of the dopant species for twodifferent sizes of the He droplets, He (left column) and He (right column). Thedata are averaged over the intensity distribution of the laser focus volume and overorientations of the K and Ca-doped droplets with respect to the laser polarization.
Since simulations are not limited by droplet beam depletion, we can study thehypothetical situation of attaching larger ( >
10) K and Ca dopant clusters to the Hedroplets. For these larger dopant clusters we find strongly enhanced He ion yields evenfor doping with Ca and K, see Fig. 5. The larger number of dopant atoms supply enoughseed ionizations for He ignition at low laser intensities which make up the largest part ofthe laser focus volume. Note that, as a consequence of focal averaging, for doping with (cid:38)
11 Ca or (cid:38)
19 K atoms which make the low intensities in the periphery of the focusvolume available for ignition, the yield of the He ions even exceeds the maximum yieldreached for Xe doping. The largest considered dopants K and Ca induce partialignition already below 8 × Wcm − . The contribution of these very low intensities ison the order of 10% and is neglected here. Since TI of Xe requires I (cid:38) × Wcm − ,lower intensities remain unaccessible even for larger Xe dopants.The systems considered in this work are dissimilar in various respects, given by theexperimental boundary conditions: ionization energies and locations inside or at thedroplet surface are different. In the experiment, droplet beam depletion upon clusteraggregation is a further dopant-specific limitation. What are the crucial factors forthe observed conspicuous species-dependence of doped He nanodroplet ignition? In the fficiency of Dopant-Induced Ignition of Helium Nanoplasmas
051 01 52 02 5 X eC aK c e n t e r p a r a l l e l p e r p .
Critical dopant number for ignition, nign
I n t e n s i t y [ W c m - 2 ] Figure 6.
Simulated minimum numbers of K, Ca or Xe dopant atoms needed forignition of a He droplet as a function of the (non-focally averaged) pulse peakintensity. Results are given for interior and surface doping, the latter for the paralleland perpendicular orientation of the cluster with respect to the laser polarization.
Fig. 6 depicts the simulated minimum number n ign of dopant atoms at which theignition probability exceeds 10%. The variation of n ign is shown as a function of theintensity I , for interior and surface dopant states. The latter ones are distinguished byparallel and perpendicular orientation of the dopant-droplet complex with respect to thelinear laser polarization. The data clearly show three main trends in dopant-inducedignition:(i) A lower intensity can be compensated to a large extent by larger dopant clusters.This is due to the larger number of seed electrons available for EII and by the highersum of ion charges which assist EII by reducing the Coulomb barrier at He. In addition,for a given species the number of seed ionizations per dopant atom increases with thenumber of dopant atoms, as shown for the K and K dopants (cf. Fig. 2).(ii) Dopants which are easily multiply ionized (Xe, Ca) are considerably favored,for the same reasons as in (i).(iii) Dopants residing in the droplet interior ignite the neighboring He atoms moreefficiently, as the cloud of seed electrons quivering in the driving laser field has bettercontact with the He host droplet. For all three dopants, a significantly larger numberof dopants is needed for ignition of surface-bound dopant clusters at any laser intensity,where the parallel orientation is more favorable than the perpendicular one. Surfacedoping in parallel orientation typically requires 1-3 dopant atoms more to reach thesame ignition efficiency as interior doping; the same gradation is found for surface dopingbetween parallel and perpendicular orientation.Another parameter which may severely impact the ignition efficiency of dopantsattached to He droplets is the dopant-He interatomic distance as it affects the dopant- fficiency of Dopant-Induced Ignition of Helium Nanoplasmas .
15 ˚A) and the He-K distance (7 .
13 ˚A) for interior as well as for surface dopingin parallel and perpendicular orientation of the dopant-droplet axis relative to the laserpolarization. While the general trend is, as expected, the decrease of the ignitionprobability with increasing He-dopant separation, Xe in its interior doping state is soefficient that its ignition probability remains 1 in the entire considered distance range.In contrast, K does not reach the ignition probability of Xe , even when it is broughtto the droplet interior at the shorter He-Xe distance, confirming that geometrical effectsalone cannot account for the larger ignition capability of Xe. c e n t e r p a r a l l e l p e r p . X e K C a K Ignition probability
D i s t a n c e R [ Å ] Figure 7.
Dependence of the probability of igniting a He nanoplasma in a He dropletdoped with various dopants as a function of the interatomic distance between dopantand He atoms. The peak laser intensity is I = 10 W/cm and the He droplet size is2171 He atoms.
5. Conclusions
In conclusion, our investigations, theoretical and experimental, benchmark genericprinciples for the design of dopant clusters for efficient nanoplasma generation byexamining the ability of K, Ca, and Xe dopants to ignite He droplets. The dopants’ability to trigger ignition of He droplets induced by EII at moderate laser intensities isdetermined (i) by the ability to provide initial seed electrons to drive electron-impactionization of the He droplet, (ii) by the doping site – interior or surface state – and He-dopant distance which both determine the contact strength of the laser-driven quiveringelectron cloud with the He droplet, and (iii), as an experimental constraint, by the fficiency of Dopant-Induced Ignition of Helium Nanoplasmas I (cid:38) × W cm − . The possibility of optimizing the physico-chemicalproperties of the dopant clusters by mixing various species inside the same He dropletwill be studied in a forthcoming work. Stimulating discussions with Th. Fennel, M. Krishnamurthy and R. Gopal are gratefullyacknowledged. This work is supported by the Deutsche Forschungsgemeinschaft in theframe of the Priority Programme ”Quantum Dynamics in Tailored Intense Fields”.The dissertation of B. Gr¨uner is supported by scholarship funds from the StateGraduate Funding Program of Baden-W¨urttemberg. We are grateful to Ivan Infantefor prepublication information on inner-shell ionization energies of K and Ca. Theauthors thank for computational and manpower support provided by IZO-SGI SGIkerof UPV/EHU and European funding (EDRF and ESF).
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