Desorption/ablation of lithium fluoride induced by extreme ultraviolet laser radiation

NUKLEONIKA 2016;61(2):131138 doi: 10.1515/nuka-2016-0023 ORIGINAL PAPER Introduction Understanding the interactions of soft X-ray (SXR) and extreme ultraviolet (XUV) radiation with solid targets is challenging for fundamental physics of warm dense matter (WDM) state, which is relevant to laser ablation and various approach to inertial Desorption/ablation of lithium fl uoride induced by extreme ultraviolet laser radiation Tomáš Blejchař, Václav Nevrlý, Michal Vašinek, Michal Dostál, Milada Kozubková, Jakub Dlabka, Martin Stachoň, Libor Juha, Petr Bitala, Zdeněk Zelinger, Peter Pira, Jan Wild T. Blejchař, M. Kozubková Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava-Poruba, CZ 708 33, Czech Republic V. Nevrlý, J. Dlabka, P. Bitala Faculty of Safety Engineering, VŠB-Technical University of Ostrava, Lumírova 13, Ostrava-Výškovice, CZ 700 30, Czech Republic, Tel.: +420 597 322 872, Fax: +420 597 322 980, E-mail: vaclav[email protected] M. Vašinek, M. Stachoň Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava-Poruba, CZ 708 33, Czech Republic M. Dostál Faculty of Safety Engineering, VŠB-Technical University of Ostrava, Lumírova 13, Ostrava-Výškovice, CZ 700 30, Czech Republic and J. Heyrovský Institute of Physical Chemistry ASCR, Dolejškova 3, Praha 8, CZ 182 23, Czech Republic Abstract. The availability of reliable modeling tools and input data required for the prediction of surface removal rate from the lithium fl uoride targets irradiated by the intense photon beams is essential for many practical aspects. This study is motivated by the practical implementation of soft X-ray (SXR) or extreme ultraviolet (XUV) lasers for the pulsed ablation and thin fi lm deposition. Specifi cally, it is focused on quantitative description of XUV laser-induced desorption/ablation from lithium fl uoride, which is a reference large band-gap dielectric material with ionic crystalline structure. Computational framework was proposed and employed here for the reconstruction of plume expansion dynamics induced by the irradiation of lithium fl uoride targets. The morphology of experimentally observed desorption/ablation craters were reproduced using idealized representation (two-zone approximation) of the laser fl uence profi le. The calculation of desorption/ablation rate was performed using one-dimensional thermomechanic model (XUV-ABLATOR code) taking into account laser heating and surface evaporation of the lithium fl uoride target occurring on a nanosecond timescale. This step was followed by the application of two-dimensional hydrodynamic solver for description of laser-produced plasma plume expansion dynamics. The calculated plume lengths determined by numerical simulations were compared with a simple adiabatic expansion (blast-wave) model. Key words: desorption • fl uid dynamics • lithium fl uoride • numerical simulation • plume expansion • pulsed laser ablation L. Juha Institute of Physics ASCR, Na Slovance 2, Prague 8, CZ 182 21, Czech Republic Z. Zelinger J. Heyrovský Institute of Physical Chemistry ASCR, Dolejškova 3, Praha 8, CZ 182 23, Czech Republic P. Pira J. Heyrovský Institute of Physical Chemistry ASCR, Dolejškova 3, Praha 8, CZ 182 23, Czech Republic and Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, Praha 8, CZ 180 00, Czech Republic J. Wild Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, Praha 8, CZ 180 00, Czech Republic Received: 30 September 2015 Accepted: 27 November 2015 Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 132 T. Blejchař et al. confi nement fusion (ICF). Quantitative description of laser ablation phenomena is critically important for practical implementation of pulsed laser deposition (PLD) technique when utilizing radiation sources at this spectral range. The behavior of optical dielectrics upon SXR/XUV-laser irradiation is the subject of particular attention and lithium fl uoride (LiF) is often studied in this context as a reference large band-gap material [1–4]. Moreover, LiF is a feasible precursor of lithium atoms and ions for the purpose of tokamak diagnostics [5]. Therefore, phenomenology of pulsed laser ablation (PLA) and adequacy of models describing laser-produced plasma (LPP) plume expansion dynamic and laser blow-off (LBO) process needs to be well known in order to increase the performance of such kind of diagnostics. Effective computational strategies and approaches with wide applicability for numerical simulation of LPP plume expansion dynamics under various experimental conditions is still desirable for many experimentalists as well as engineers in material science and fusion research. Extensive efforts were previously done concerning the LPP plume expansion in vacuum as well as in the presence of different background gases [6, 7]. Various experimental techniques and modeling approaches were employed for obtaining qualitative as well as quantitative information on the related physical phenomena. One-dimensional (1D) and quasi-two-dimensional (2D) numerical simulations of LPP expansion dynamics enabled to gain the fundamental understanding of the experimental observations, for example concerning of plume splitting phenomenon. However, multidimensional numerical simulations of fl uid dynamics can bring yet unexplored insight into such complex physical phenomena. For example, shock-wave propagation after pulsed laser irradiation of Al targets under the atmospheric pressure conditions was studied by Harilal et al. [8] employing unsteady solver of Navier-Stokes equations in a two-dimensional axially symmetric geometry. To best of author’s knowledge, no attempts have been made yet in order to describe spatio-temporal evolution of plasma plume induced by ablation or desorption from solid targets irradiated by the pulsed SXR/XUV laser beams. In the given context, basic concepts and phenomenology of laser ablation and desorption, as well as experimental data related to SXR/XUV ablation threshold for LiF, are summarized briefl y in the next section. SXR/XUV laser ablation and desorption of lithium fl uoride Depending on the incident laser fl uence F [J/cm2] radiation-induced damage can proceed in the regime of ablation or desorption. In Ref. [9] Haglund describes laser-induced desorption as a process resulting in the emission of ions, atoms and molecules without any substantial disturbance in the surrounding surface, while laser ablation is to be associated with large- -scale disruption of surface. Mechanistic criterion is also given implicitly in Ref. [9], which defi nes the ablation threshold as the radiation intensity (laser fl uence), which causes at least a half of monolayer of the material to be eroded form the target surface by a single laser pulse. Following the analysis of ablation/desorption craters in molecular solids irradiated by the short pulses of XUV free-electron laser [10], it was recognized that desorption is at least one order of magnitude more effi cient for soft X-rays than for UV-Vis laser light. Therefore, the above mentioned Haglund’s criterion was reconsidered and phenomenological model describing nonthermal desorption/ablation was proposed in Ref. [10]. The depth of crater in desorption region is defi ned by this model as being linearly proportional to: (i) attenuation length (latt); (ii) the ratio of incident laser fl uence (F) and the laser ablation threshold fl uence (Fth), and fi nally (iii) effi ciency of desorption (des). On the other hand, laser ablation is traditionally recognized as a threshold phenomenon described by the logarithmic dependence of the depth of ablation crater (dabl) on the incident laser fl uence (normalized by the ablation threshold). Linear proportionality of dabl to latt implies nanometer-scale ablation rate for optical materials strongly absorbing the photons in SXR/XUV range (latt  10 nm for LiF). The threshold value of XUV laser ablation for LiF crystals was fi rst determined by Ritucci et al. [4], employing capillary-discharge Ne-like Ar laser operating at  = 46.9 nm wavelength (26.4 eV) with the pulse duration of about 1.5 ns. Microsized cracks were identifi ed at low-fl uence (subthreshold) region, which was explained by the strong thermoelastic stress on the surface and to the brittleness of the materials. Less evident cracks and a cleaner condition of ablation were found above threshold fl uence due to more effi cient evaporation of material. Important measurements reported in Refs. [2, 3] revealed very low ablation threshold (~0.01 J/cm2) for LiF exposed to picosecond SXR laser pulses, reasoned out by the occurrence of spallative ablation [1]. The ablation threshold for LiF irradiated by UV excimer laser [11] (1 J/cm2) is strongly affected by the value of latt, which is much higher compared to SXR/XUV spectral region meaning that laser energy is deposited into larger volumes. Taking these fi ndings into consideration, we could conclude that the laser ablation threshold is dependent on the photon energy, pulse length as well as optical properties of the target material (mainly latt as a function of wavelength ) (see Fig. 1). More recent experiments on LiF ablation [12] are based on utilization of a  = 46.9 nm capillary- -discharge laser (CDL) source [13], which is a compact experimental apparatus with broad range of practical applications. This instrument based on stimulated emission of neon-like argon (Ar8+) ions from a 21-cm long Al2O3 capillary (internal diameter  = 3.2 mm) fi lled with 400 mTorr of Ar will be further abbreviated in this text as XUV-CDL. The XUV-CDL delivers a pulsed beam of 26.4 eV photons with an average energy of 10 J/pulse, 1.5 ns pulse duration and 3 Hz repetition rate. Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 133Desorption/ablation of lithium fl uoride induced by extreme ultraviolet laser radiation Implementation of XUV-CDL for PLA experiments performed by our group uses multilayer (Sc/Si) mirror with refl ectivity R  30% at the  = 46.9 nm for focusing the laser beam onto the desired target surface. Therefore, the total energy in the focused XUV-CDL beam reaches about 3 J (e.g., depending on working time of Al2O3 capillary and other factors related to optical setup). Craters in LiF targets irradiated by the multiple pulses (multishot exposure) of focused XUV-CDL beam are characterized by presence of signifi cant rim around the laser spot footprint of the low-fl uence region, which is found at the periphery of the ablation crater. This feature was assigned to desorption regime of radiation-induced damage. The surface of LiF exposed to 10 shots of focused XUV-CDL beam, under an incidence angle of 20°, is shown in Fig. 2. Samples were investigated after an irradiation (post-mortem) by the white light interferometry (WLI, Zygo) profi ler. Desorption and ablation regimes can be distinguished also in vertical crater profi le (see Fig. 3) where it is shown together with the idealized profi le considering the results of prediction given by the thermodynamic model, which is described in the following section. Modeling ns-XUV laser heating of LiF target and surface evaporation Quantitative description of LiF desorption/ablation rate is based on modifi ed version of thermomechanic model, which was originally written by A.T. Anderson [14]. This code (ABLATOR) was developed at Lawrence Livermore National Laboratory (LLNL) in order to predict the radiation-induced damage and feasibility of materials considered as fi rst wall of inertial confi nement fusion reactors. Modifi cations of the original code were carried out previously taking into account relatively short attenuation lengths in the case of XUV ablation as well as the radiation-induced chemical decomposition occurring in ablated materials. The modifi ed version of the code called XUV-ABLATOR, which was reported in more details elsewhere (Ref. [15]), was used for our recent study. Briefl y, XUV-ABLATOR is the Lagrangian code solving the energy balance equation along one axis (normal to the surface) employing fi nite difference method. It uses explicit scheme for advancing in time. Deposition of laser energy in near surface zones is governed by the Lambert-Beer law. Temperature in each zone is estimated by iterative procedure considering equations of state for condensed phase (Mie-Gruneisen) and gas phase (ideal gas law) together with enthalpy and mass conservation. The transient form of Fourier equation is used for treatFig. 1. Ablation threshold fl uence relevant to LiF for selected lasers given here as a function of photon energy in log-log scale. Ablation threshold (symbols) for various pulsed UV/XUV/SXR laser systems with different wavelengths (specifi ed above the symbol) and pulse lengths (given in parentheses) correspond to values reported in Refs. [2–4] (for XUV/SXR) and in Ref. [11] (for UV). Fig. 3. The experimental crater profi le (gray dash-dot line) measured along the beam propagation direction in LiF target after an exposure of 10 CDL pulses and corresponding contours of idealized desorption/ablation (blue/red) crater as predicted by XUV-ABLATOR model in two-zone approximation of laser fl uence profi le, that is, equivalent to relevant representative desorption and ablation rate (ddes  5 nm/pulse and dabl  22 nm/pulse, respectively) multiplied by the factor of 10, accounting for 10 CDL pulses. Fig. 2. Image of LiF target surface with multishot damage pattern after exposure of 10 CDL pulses in tight focus distance of target surface to mirror plane as obtained by white light interferometry (WLI) technique. The zero-level coordinate on the LiF target surface, which belongs to plane given by direction of laser beam propagation and normal to target surface, is depicted by the black line with color segments corresponding to desorption (blue) and ablation (red) region. Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 134 T. Blejchař et al. ing the heat conduction between individual zones. Mechanical response is solved by one-dimensional fi nite-difference hydrodynamic model in order to predict the stress wave and material motion after the deposition of XUV-laser radiation. Material properties of lithium fl uoride serving as the input data for the given study were determined based on bibliographic survey. Computational grid size was defi ned by the size of the fi rst (initial surface) zone, which was set as equal to l0 = 1 nm. The total number N = 100 cells were included in the numerical simulations employing a XUV-ABLATOR code. The thickness lz of the computational grid cells (z is the index ranging from 1 to N – 1 in relevance to position of z-th zone below the initial target surface) is growing with a geometrical factor, following the formula lz = q × lz–1, where q = 1.06 was used as a default value proposed by Anderson [14]. Attenuation length (latt = 13.6 nm), appropriate to normal incidence angle of laser beam to LiF target, was utilized for modeling purposes. It should be pointed out that only cold opacities are considered by the recent version of XUV-ABLATOR code. Rectangular (fl at-in-time) profi le specifying temporal dependence of laser power within pulse duration (p = 1.5 ns) was assumed at the given level of approximation. Total energy available in single pulse of the focused XUV-CDL beam Etot = 3 J was assumed to be deposited on the laser spot area of Stot = 2500 m2, which was divided equally into desorption and ablation region presuming the ratio of their respective area Sdes/Sabl = 3/1. Following this criteria, the fi rst part of laser energy Edes = 1.5 J was considered to irradiate the area Sdes = 1875 m2 (yielding Fdes = 70 mJ/cm2) and the second part of laser energy Eabl = 1.5 J on the area Sabl = 625 m2 (yielding Fabl = 240 mJ/cm2). These conditions were set as an idealized representation of observed experimental crater profi les and its typical morphology. Temporal evolution of vertical temperature profi le within the LiF target during XUV-CDL pulse is presented in Fig. 4, as obtained from the 1D numerical simulations performed by XUV-ABLATOR code under the given circumstances. The vertical position of the interface between condensed (liquid/solid) and vaporized (gaseous) LiF decreases in time under the initial target surface (below zero-level coordinate) due to material removal process, mainly occurring in laser pulse duration period (p). The resulting depth at the end of simulation ( = 200 ns) is equal to dabl = 21.5 nm for the ablation region. This value correlates well with the ablation rate at the peak (absolute minimum) of experimental crater profi le (see Fig. 3). For the desorption rate is equal to ddes = 4.5 nm, which corresponds to desorption rate observed at the periphery of experimental crater profi le, in spite of relatively high surface roughness of the sample. Further details concerning implementation of output parameters (predicted by XUV-ABLATOR) into multidimensional fl uid dynamics simulation of LPP plume expansion dynamics are given below. Numerical modeling of LiF plume expansion The element-based fi nite volume method (EbFVM) [16], as implemented in Ansys CFX software suite, was used for numerical modeling of LPP plume expansion dynamics. Whereas the problem of high-speed plume expansion is unsteady and there exists supersonic fl ow, then second order schemes and double precision solver has to be used. The LiF plume expansion was simulated as multispecies fl ow because the effect of background gas was investigated. The basic set of equations describing the unsteady compressible fl ow of gas mixtures can be written as follows: (1) (2) Fig. 4. Contour plots showing temporal evolution of temperature profi le below the surface of the LiF target as predicted by XUV-ABLATOR code (1D thermomechanic model) for the ablation region (Fabl = 240 mJ/cm2) depicted in (a) and desorption region (Fdes = 70 mJ/cm2) depicted in (b). Dashed white line in (a) and dotted white line in (b) describes instantaneous vertical positions of surface layer, that is, interface between condensed (liquid/ solid) and vaporized (gaseous) LiF relative to initial target surface (zero-level coordinate).  3 kg 0 ms j j u tx           22 kg ms ij ii jijj uu uu p tx xxx                Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 135Desorption/ablation of lithium fl uoride induced by extreme ultraviolet laser radiation (3) (4) Equation (1) represents the law of conservation (continuity equation), Eq. (2) represents the momentum equation (Navier-Stokes equation), Eq. (3) represents the law of energy conservation and Eq. (4) defi nes the mass fraction of component of mixture. Here  [kg/m3] is density, u [m/s] is velocity, t [s] is time, x [m] is the position in Cartesian coordinate system, p [Pa] is pressure,  [Pa·s] is dynamic viscosity, E [J] is the total energy, T [K] is temperature,  [W/m·K] is thermal conductivity, jl [Pa] is shear stress tensor, YLiF [–] is mass fraction of lithium fl uoride in the plume, and D [m2/s] is diffusion coeffi cient. This set of equations was closed by the perfect gas equation (p/) = R·T/M where R [J/K·mol] is universal gas constant and M [g/mol] is molar mass. Since the mixture of LiF (as plume constituent) and He (as a background gas) was assumed to be present in the computational domain during the entire simulation time, the equation (YLiF + YHe = 1) closes the defi nition of gaseous mixture. The above mentioned set of equations was solved by EbFVM with coupled solver and second-order discretization scheme, which solves the hydrodynamic Eqs. (1)–(4) as a single system. This solution uses a fully implicit discretization of equations at any given time step. Computational domain was defi ned in two-dimensional axisymmetric geometry with dimensions 200 m × 500 m consisting of 35 000 quadrilateral elements. The LPP plume expansion is expected to be initiated from the circular laser spot consisting of inner ablation region (having the radius rabl = 14.1 m) and the outer annulus with inner radius equal to rabl = 14.1 m and outer radius rdes = 28.2 m). Therefore, two independent inlets are defi ned with nonstationary boundary conditions given as total pressure expressed from relevant pressure and temperature histories predicted by the XUV- -ABLATOR code (1D thermomechanic model), as shown in Fig. 5. A multiexponential curve fi t of the temperature data was performed in order to obtain continuous temporal profiles. These algebraic expressions, that is, functions defi ning pressure dependence on the simulation time  ( = 0 corresponds to the beginning of the XUV-CDL pulse) were set as nonstationary boundary condition in two-dimensional fl uid dynamics simulations. The effect of the surface regression rate and geometrical shape of the crater (10 nm) was neglected in the given case with respect to the spatial resolution of computational grid near the inlet (100 nm). The entire domain was initially assumed as being fi lled with He as a background gas at the moderate pressure. Two scenarios were investigated separately in frame of this study: (a) simulation of LPP plume expansion dynamics at the background pressure P0 = 1 Torr (further referred as case A) and (b) simulation of LPP plume expansion dynamics at the background pressure P0 = 10 Torr (further referred as case B). It is worth noting here that such moderate background pressures are not relevant to our recent PLA experiments performed under high vacuum conditions (P0  10–8 Torr). However, selected conditions (mostly typical for PLD experiments) were assumed in order to explore the effect of background gas pressure on XUV-LPP plume expansion dynamics and to consider further possibilities of setup adjustments. Transient simulation of ns-XUV-LPP plume expansion dynamics was detached into three time intervals: (I) laser pulse duration and afterglow period (0–5 ns); (II) fast, that is, supersonic expansion period (5–200 ns); (III) slow, that is, subsonic, expansion (200–1000 ns). Adequate time step was assigned for these intervals on the basis of Currant number, giving 1 ps for the period (I), 5 ps for sec-    3 kg ms j jjj jjl l uE EpT txtxx u x                LiF LiF LiF 3 kg ms j j jj uY Y tx Y D xx                 Fig. 5. Temporal evolution of surface temperature at the instantaneous interface of condensed and gas phase LiF (a) and corresponding saturation vapor pressure (b) calculated by the XUV-ABLATOR code for fl uences relevant to desorption (blue dotted line) and ablation (red dashed line) region, according to Fig. 4. Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 136 T. Blejchař et al. ond for the period (II), and 100 ps for the period (III). Such approach was chosen as a compromise between the size of total computational time and effi cient convergence (with the criteria set as 10–6 for all variables) in each time step. Results and discussion The results of hydrodynamic simulations characterizing the spatio-temporal evolution of plume expansion dynamics are presented in Fig. 6. A noticeable expansion (<10 m) is observed within the period of laser pulse duration (~1 ns) in the case A as well as in the case B. After this initial period of time, visibly different plume expansion dynamics evolves for two cases studied here. In the case A, nearly spherical plume expansion behavior can be recognized (mostly at   1 s). The level of deceleration during the given period can be deduced from Fig. 7. The temporal change of a plume front distance (R- plot) can be effi ciently fi tted by a viscous drag model (see e.g. Ref. [17]) in order to extract the relevant plume stopping length. On the contrary, very poor performance of drag model as well as shock model can be concluded when we aimed at fi tting the R- plot given by the numerical simulation for the case B. Apparently, we can link this feature of R- plot to loss of spherical expansion behavior, which can be clearly identifi ed in Fig. 6. A nearly adiabatic free expansion behavior demonstrated by the quasi-spherical plume dynamics can be observed for the given condition up to about P0 = 1 Torr He background gas pressure. At elevated background pressure (P0 = 10 Torr), collisional effects start to dominate, leading to spatial confi nement of the plasma and mushroom-like plume shape accompanying shock-wave propagation. The compression of the background gas can be considered as a shock compression process involving kinetic energy transfer. The shock front (high-density peaks of the background gas) propagates forward ahead of the ablated species. At the plume periphery, where the normal-to-target component of the velocity vector is vanishing, nonlinear terms corresponding to magnitude of viscous shear stress tensor are of pronounced importance. It was observed previously [6] that as the background pressure increases from vacuum, there exists a transition regime, where the plume is characterized by a strong interpenetration of the ablated species and background gas, leading to plume splitting and sharpening. The results of our numerical simulations predicting quasi-spherical expansion at reduced pressure and the formation of mushroom-like plume shape at elevated background pressures are in qualitative agreement with these observations. The pressure range of the transition regime depends on several factors corresponding to given experimental setup. The molar mass of ambient gas and target material vapors, laser intensity, laser spot size, and also the laser beam profi le are the main parameters infl uencing LPP plume shape in the presence of background gas. Fig. 6. Spatio-temporal evolution of ns-XUV-LPP plume at background pressures P0 of helium relevant to the simulation of case A (a) and case B (b) described in text. Instantaneous shape of plume is characterized at selected delays times (specifi ed below image) by the contours plot of volume number density [cm–3] relevant to LiF monomer obtained from fl uid dynamics simulations. Fig. 7. R- plot of the expansion front boundary for the numerical simulations at the helium background pressure of P0 = 1 Torr (a) and P0 = 10 Torr (b). Instantaneous position of plume front was evaluated based on number density of LiF at the vertical axis of symmetry (normal to target surface) assuming the limit value of nLiF = 10–15 cm–3. Fits of these data obtained by utilizing shock model (dashed line) and viscous drag model (dotted line) are also included. Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 137Desorption/ablation of lithium fl uoride induced by extreme ultraviolet laser radiation From Fig. 6 (at   10 ns), it is also obvious that difference in propagation speed of the initial volume of LiF ejected from the ablation and desorption region can play a role. Such difference is much more pronounced for case B compared to the simulation for case A. The ‘faster’ mass of LiF from ablation region is confi ned in very narrow expansion angle and with prolonged time after the initial phase ( ~ 100 ns), it can interact with the vortical structures accompanying the propagation of ‘slower’ component desorbed from the outer annulus of the laser spot. In order to further explore the effect of geometrical factors on the modeling output, we performed an additional numerical simulations assuming the same fl uence profi le as being applied at the smaller laser spot (with radii rdes and rabl reduced by the factor of 2). In that case, more compact behavior of the shock front is observed at (P0 = 10 Torr), resulting in less pronounced lateral compression of the central column compared to the case B and relatively slower expansion dynamics compared to the case A as well as compared to simulation performed at P0 = 1 Torr with spot size reduction. Based on these fi ndings, we suggest that application of a more realistic laser beam profi le is required in order to resolve the onset of the ablation near the tails of a low-fl uence region, where the laser desorption occurs with considerably different dynamics of the surface evaporation. It is also evident that the results of numerical simulations at elevated background pressures leading to formation of hydrodynamic instabilities are strongly affected by the actual setup of the initial and boundary conditions. The applicability of simple mathematical models (e.g., an adiabatic expansion; i.e., a blast-wave model [18]) for the estimation of a target to substrate distance was previously proven mostly against the specifi c set of experimental data on LPP plume expansion dynamics. Nevertheless, several examples showing reduced predictive capabilities in relevance to PLD applications were also reported in the literature, e.g. [19]. When we compare the results of our numerical simulations with the estimated plume lengths Lp obtained from adiabatic expansion model [18] (see Fig. 8), some qualitative disagreement can be remarked. The reversed trend of plume length with increasing background gas pressure can be reasoned out by the transition to nonspherical plume expansion behavior occurring probably in the range of background pressure 1 Torr > P0 > 10 Torr for the given laser and target parameters. Nevertheless, it should be pointed out here that quantitative evaluation of plume stopping length for the case with the loss of spherical expansion behavior would require much longer simulation time as the propagation of the confi ned ablated/desorbed mass is expected to continue for a prolonged period (10–100 s or more). Therefore, we have to consider the perfect match with adiabatic expansion model obtained for the case B as the accidental agreement only. For a nearly spherical plume expansion observed in the case A (also obtained from the simulations with a reduced spot size) underprediction of plume length Lp by the factor of 3 have to be concluded. The effect of viscous forces considered implicitly by the solver of Navier-Stokes equations can be identifi ed as possible source of the given discrepancy. Our recent results can thus be regarded as promising step toward realistic simulation of LPP plume expansion dynamics at the level of detail feasible for practical purposes (e.g., designing of PLD experiments) as well as for model-based interpretation of the related experiments. Conclusions The capability to estimate the plume stopping length based on predictive modeling at the broad range of feasible conditions is highly desirable when setting up or optimizing PLD experiment. Multidimensional numerical simulations of LPP plume expansion following ablation/desorption of XUV laser-illuminated LiF target was performed. The specifi c tools of continuum hydrodynamics were employed for the given purpose. It can be concluded that the system of Navier-Stokes equations can be successfully solved considering the initial and boundary conditions representative for PLD experiments (P0 ~ 1 Torr of helium). We suggest that characteristic features of LPP plume expansion dynamics in different background gases can be effi ciently investigated following the computational procedure described here. Finally, we would like to show the application of the ABLATOR code [14] as a demonstrative example how the models built through inertial confi nement fusion related research can be used, for example, for solving some practical issues in material sciences. Acknowledgment. This work was supported by the Czech Science Foundation (GAČR) via the project no. P108/11/1312. This work was performed in Czech Republic at the J. Heyrovský Institute of Physical Chemistry of the Academy of Sciences of the Czech Republic, the Fig. 8. Plume stopping lenght Lp estimated from adiabatic expansion (blast-wave) model (green dashed line) as a function of the background pressure in the log-log scale assuming expansion into monoatomic gas (specifi c heat ratio  = 1.67) with initial velocity of v0 = 104 m/s and expansion angle equals to 35°. For the results of numerical simulations (symbol ), plume length was determined by least-square fi tting of the R- plot to the viscous drag model, i.e., R = Lp(1 – e–). Brought to you by | Technicka Univerzita Ostrava Authenticated Download Date | 7/21/16 1:39 PM 138 T. Blejchař et al. Institute of Physics of the Academy of Sciences of the Czech Republic, the VŠB-Technical University of Ostrava and the Charles University in Prague, Czech Republic. References 1. Inogamov, N. A., Zhakhovsky, V. V., Faenov, A.Y., Khokhlov, V. A., Shepelev, V. V., Skobelev, I. V., Kato, J., Tanaka, M., Pikuz, T. A., Kishimoto, M., Ishino, M., Nishikino, M., Fukuda, Y., Bulanov, S. 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