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 In oduc ion Unde s anding he in e ac ions o so X- ay (SXR) and ex eme ul a iole (XUV) adia ion wi h solid a ge s is challenging o undamen al physics o wa m dense ma e (WDM) s a e, which is ele an o lase abla ion and a ious app oach o ine ial Deso p ion/abla ion o li hium l uo ide induced by ex eme ul a iole lase adia ion Tomáš Blejchař, Václa Ne lý, Michal Vašinek, Michal Dos ál, Milada Kozubko á, Jakub Dlabka, Ma in S achoň, Libo Juha, Pe Bi ala, Zdeněk Zelinge , Pe e Pi a, Jan Wild T. Blejchař, M. Kozubko á Facul y o Mechanical Enginee ing, VŠB-Technical Uni e si y o Os a a, 17. lis opadu 15/2172, Os a a-Po uba, CZ 708 33, Czech Republic V. Ne lý, J. Dlabka, P. Bi ala Facul y o Sa e y Enginee ing, VŠB-Technical Uni e si y o Os a a, Lumí o a 13, Os a a-Výško ice, CZ 700 30, Czech Republic, Tel.: +420 597 322 872, Fax: +420 597 322 980, E-mail: acla [email p o ec ed] M. Vašinek, M. S achoň Facul y o Elec ical Enginee ing and Compu e Science, VŠB-Technical Uni e si y o Os a a, 17. lis opadu 15/2172, Os a a-Po uba, CZ 708 33, Czech Republic M. Dos ál Facul y o Sa e y Enginee ing, VŠB-Technical Uni e si y o Os a a, Lumí o a 13, Os a a-Výško ice, CZ 700 30, Czech Republic and J. Hey o ský Ins i u e o Physical Chemis y ASCR, Dolejško a 3, P aha 8, CZ 182 23, Czech Republic Abs ac . The a ailabili y o eliable modeling ools and inpu da a equi ed o he p edic ion o su ace emo al a e om he li hium l uo ide a ge s i adia ed by he in ense pho on beams is essen ial o many p ac ical aspec s. This s udy is mo i a ed by he p ac ical implemen a ion o so X- ay (SXR) o ex eme ul a iole (XUV) lase s o he pulsed abla ion and hin i lm deposi ion. Speci i cally, i is ocused on quan i a i e desc ip ion o XUV lase -induced deso p ion/abla ion om li hium l uo ide, which is a e e ence la ge band-gap dielec ic ma e ial wi h ionic c ys alline s uc u e. Compu a ional amewo k was p oposed and employed he e o he econs uc- ion o plume expansion dynamics induced by he i adia ion o li hium l uo ide a ge s. The mo phology o expe imen ally obse ed deso p ion/abla ion c a e s we e ep oduced using idealized ep esen a ion ( wo-zone app oxima ion) o he lase l uence p o i le. The calcula ion o deso p ion/abla ion a e was pe o med using one-dimensional he momechanic model (XUV-ABLATOR code) aking in o accoun lase hea ing and su ace e apo a ion o he li hium l uo ide a ge occu ing on a nanosecond imescale. This s ep was ollowed by he applica ion o wo-dimensional hyd odynamic sol e o desc ip ion o lase -p oduced plasma plume expansion dynamics. The calcula ed plume leng hs de e mined by nume ical simula ions we e compa ed wi h a simple adiaba ic expansion (blas -wa e) model. Key wo ds: deso p ion • l uid dynamics • li hium l uo ide • nume ical simula ion • plume expansion • pulsed lase abla ion L. Juha Ins i u e o Physics ASCR, Na Slo ance 2, P ague 8, CZ 182 21, Czech Republic Z. Zelinge J. Hey o ský Ins i u e o Physical Chemis y ASCR, Dolejško a 3, P aha 8, CZ 182 23, Czech Republic P. Pi a J. Hey o ský Ins i u e o Physical Chemis y ASCR, Dolejško a 3, P aha 8, CZ 182 23, Czech Republic and Facul y o Ma hema ics and Physics, Cha les Uni e si y in P ague, V Holešo ičkách 2, P aha 8, CZ 180 00, Czech Republic J. Wild Facul y o Ma hema ics and Physics, Cha les Uni e si y in P ague, V Holešo ičkách 2, P aha 8, CZ 180 00, Czech Republic Recei ed: 30 Sep embe 2015 Accep ed: 27 No embe 2015 B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 7/21/16 1:39 PM 132 T. Blejchař e al. con i nemen usion (ICF). Quan i a i e desc ip ion o lase abla ion phenomena is c i ically impo an o p ac ical implemen a ion o pulsed lase depo- si ion (PLD) echnique when u ilizing adia ion sou ces a his spec al ange. The beha io o op ical dielec ics upon SXR/XUV-lase i adia ion is he subjec o pa icula a en ion and li hium l uo ide (LiF) is o en s udied in his con ex as a e e ence la ge band-gap ma e ial [1–4]. Mo eo e , LiF is a easible p ecu so o li hium a oms and ions o he pu pose o okamak diagnos ics [5]. The e o e, phenomenology o pulsed lase abla ion (PLA) and adequacy o models desc ibing lase -p oduced plasma (LPP) plume expansion dynamic and lase blow-o (LBO) p ocess needs o be well known in o de o inc ease he pe o mance o such kind o diagnos ics. E ec i e compu a ional s a egies and app oaches wi h wide applicabili y o nume ical simula ion o LPP plume expansion dynamics unde a ious expe imen al condi ions is s ill desi able o many expe imen alis s as well as enginee s in ma e- ial science and usion esea ch. Ex ensi e e o s we e p e iously done conce n- ing he LPP plume expansion in acuum as well as in he p esence o di e en backg ound gases [6, 7]. Va ious expe imen al echniques and modeling app oaches we e employed o ob aining quali a i e as well as quan i a i e in o ma ion on he ela ed physical phenomena. One-dimensional (1D) and quasi- wo-dimensional (2D) nume ical simula ions o LPP expansion dynamics enabled o gain he undamen al unde s anding o he expe imen al obse a ions, o example conce ning o plume spli ing phenomenon. Howe e , mul idimensional nume ical simula ions o l uid dynamics can b ing ye unexplo ed insigh in o such complex physical phenomena. Fo example, shock-wa e p opaga ion a e pulsed lase i adia ion o Al a ge s unde he a mosphe ic p essu e condi ions was s udied by Ha ilal e al. [8] employing uns eady sol e o Na ie -S okes equa ions in a wo-dimensional axi- ally symme ic geome y. To bes o au ho ’s knowledge, no a emp s ha e been made ye in o de o desc ibe spa io- empo al e olu ion o plasma plume induced by abla ion o deso p ion om solid a ge s i adia ed by he pulsed SXR/XUV lase beams. In he gi en con ex , basic concep s and phenomenology o lase abla ion and deso p ion, as well as expe imen al da a ela ed o SXR/XUV abla ion h eshold o LiF, a e summa- ized b ie l y in he nex sec ion. SXR/XUV lase abla ion and deso p ion o li hium l uo ide Depending on he inciden lase l uence F [J/cm2] a- dia ion-induced damage can p oceed in he egime o abla ion o deso p ion. In Re . [9] Haglund desc ibes lase -induced deso p ion as a p ocess esul ing in he emission o ions, a oms and molecules wi hou any subs an ial dis u bance in he su ounding su ace, while lase abla ion is o be associa ed wi h la ge- -scale dis up ion o su ace. Mechanis ic c i e ion is also gi en implici ly in Re . [9], which de i nes he abla ion h eshold as he adia ion in ensi y (lase l uence), which causes a leas a hal o monolaye o he ma e ial o be e oded o m he a ge su ace by a single lase pulse. Following he analysis o abla ion/deso p ion c a- e s in molecula solids i adia ed by he sho pulses o XUV ee-elec on lase [10], i was ecognized ha deso p ion is a leas one o de o magni ude mo e e i cien o so X- ays han o UV-Vis lase ligh . The e o e, he abo e men ioned Haglund’s c i e ion was econside ed and phenomenological model desc ibing non he mal deso p ion/abla ion was p oposed in Re . [10]. The dep h o c a e in deso p ion egion is de i ned by his model as being linea ly p opo ional o: (i) a enua ion leng h (la ); (ii) he a io o inciden lase l uence (F) and he lase abla ion h eshold l uence (F h), and i nally (iii) e i ciency o deso p ion (des). On he o he hand, lase abla ion is adi ionally ecognized as a h eshold phenomenon desc ibed by he loga i hmic dependence o he dep h o abla ion c a e (dabl) on he inciden lase l uence (no malized by he abla ion h eshold). Linea p opo ionali y o dabl o la implies nanome e -scale abla ion a e o op ical ma e ials s ongly abso bing he pho ons in SXR/XUV ange (la  10 nm o LiF). The h esh- old alue o XUV lase abla ion o LiF c ys als was i s de e mined by Ri ucci e al. [4], employing capilla y-discha ge Ne-like A lase ope a ing a  = 46.9 nm wa eleng h (26.4 eV) wi h he pulse du a- ion o abou 1.5 ns. Mic osized c acks we e iden i- i ed a low- l uence (sub h eshold) egion, which was explained by he s ong he moelas ic s ess on he su ace and o he b i leness o he ma e ials. Less e iden c acks and a cleane condi ion o abla ion we e ound abo e h eshold l uence due o mo e e i cien e apo a ion o ma e ial. Impo an measu emen s epo ed in Re s. [2, 3] e ealed e y low abla ion h eshold (~0.01 J/cm2) o LiF exposed o picosecond SXR lase pulses, easoned ou by he occu ence o spalla i e abla ion [1]. The abla ion h eshold o LiF i adia ed by UV excime lase [11] (1 J/cm2) is s ongly a ec ed by he alue o la , which is much highe compa ed o SXR/XUV spec al egion meaning ha lase ene gy is deposi ed in o la ge olumes. Taking hese i nd- ings in o conside a ion, we could conclude ha he lase abla ion h eshold is dependen on he pho on ene gy, pulse leng h as well as op ical p ope ies o he a ge ma e ial (mainly la as a unc ion o wa eleng h ) (see Fig. 1). Mo e ecen expe imen s on LiF abla ion [12] a e based on u iliza ion o a  = 46.9 nm capilla y- -discha ge lase (CDL) sou ce [13], which is a compac expe imen al appa a us wi h b oad ange o p ac ical applica ions. This ins umen based on s imula ed emission o neon-like a gon (A 8+) ions om a 21-cm long Al2O3 capilla y (in e nal diame e  = 3.2 mm) i lled wi h 400 mTo o A will be u he abb e ia ed in his ex as XUV-CDL. The XUV-CDL deli e s a pulsed beam o 26.4 eV pho ons wi h an a e age ene gy o 10 J/pulse, 1.5 ns pulse du a ion and 3 Hz epe i ion a e. B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 7/21/16 1:39 PM 133Deso p ion/abla ion o li hium l uo ide induced by ex eme ul a iole lase adia ion Implemen a ion o XUV-CDL o PLA ex- pe imen s pe o med by ou g oup uses mul ilaye (Sc/Si) mi o wi h e l ec i i y R  30% a he  = 46.9 nm o ocusing he lase beam on o he desi ed a ge su ace. The e o e, he o al ene gy in he ocused XUV-CDL beam eaches abou 3 J (e.g., depending on wo king ime o Al2O3 capilla y and o he ac o s ela ed o op ical se up). C a e s in LiF a ge s i adia ed by he mul iple pulses (mul isho exposu e) o ocused XUV-CDL beam a e cha ac e ized by p esence o signi i can im a ound he lase spo oo p in o he low- l uence egion, which is ound a he pe iphe y o he abla- ion c a e . This ea u e was assigned o deso p ion egime o adia ion-induced damage. The su ace o LiF exposed o 10 sho s o ocused XUV-CDL beam, unde an incidence angle o 20°, is shown in Fig. 2. Samples we e in es iga ed a e an i adia ion (pos -mo em) by he whi e ligh in e e ome y (WLI, Zygo) p o i le . Deso p ion and abla ion e- gimes can be dis inguished also in e ical c a e p o i le (see Fig. 3) whe e i is shown oge he wi h he idealized p o i le conside ing he esul s o p e- dic ion gi en by he he modynamic model, which is desc ibed in he ollowing sec ion. Modeling ns-XUV lase hea ing o LiF a ge and su ace e apo a ion Quan i a i e desc ip ion o LiF deso p ion/abla ion a e is based on modi i ed e sion o he momechanic model, which was o iginally w i en by A.T. Ande - son [14]. This code (ABLATOR) was de eloped a Law ence Li e mo e Na ional Labo a o y (LLNL) in o de o p edic he adia ion-induced damage and easibili y o ma e ials conside ed as i s wall o ine ial con i nemen usion eac o s. Modi i ca ions o he o iginal code we e ca ied ou p e iously aking in o accoun ela i ely sho a enua ion leng hs in he case o XUV abla ion as well as he adia ion-induced chemical decomposi- ion occu ing in abla ed ma e ials. The modi i ed e sion o he code called XUV-ABLATOR, which was epo ed in mo e de ails elsewhe e (Re . [15]), was used o ou ecen s udy. B ie l y, XUV-ABLATOR is he Lag angian code sol ing he ene gy balance equa ion along one axis (no mal o he su ace) employing i ni e di e ence me hod. I uses explici scheme o ad ancing in ime. Deposi ion o lase ene gy in nea su ace zones is go e ned by he Lambe -Bee law. Tem- pe a u e in each zone is es ima ed by i e a i e p o- cedu e conside ing equa ions o s a e o condensed phase (Mie-G uneisen) and gas phase (ideal gas law) oge he wi h en halpy and mass conse a ion. The ansien o m o Fou ie equa ion is used o ea - Fig. 1. Abla ion h eshold l uence ele an o LiF o selec ed lase s gi en he e as a unc ion o pho on ene gy in log-log scale. Abla ion h eshold (symbols) o a ious pulsed UV/XUV/SXR lase sys ems wi h di e en wa e- leng hs (speci i ed abo e he symbol) and pulse leng hs (gi en in pa en heses) co espond o alues epo ed in Re s. [2–4] ( o XUV/SXR) and in Re . [11] ( o UV). Fig. 3. The expe imen al c a e p o i le (g ay dash-do line) measu ed along he beam p opaga ion di ec ion in LiF a ge a e an exposu e o 10 CDL pulses and co - esponding con ou s o idealized deso p ion/abla ion (blue/ ed) c a e as p edic ed by XUV-ABLATOR model in wo-zone app oxima ion o lase l uence p o i le, ha is, equi alen o ele an ep esen a i e deso p ion and abla ion a e (ddes  5 nm/pulse and dabl  22 nm/pulse, espec i ely) mul iplied by he ac o o 10, accoun ing o 10 CDL pulses. Fig. 2. Image o LiF a ge su ace wi h mul isho damage pa e n a e exposu e o 10 CDL pulses in igh ocus dis ance o a ge su ace o mi o plane as ob ained by whi e ligh in e e ome y (WLI) echnique. The ze o-le el coo dina e on he LiF a ge su ace, which belongs o plane gi en by di ec ion o lase beam p opaga ion and no mal o a ge su ace, is depic ed by he black line wi h colo segmen s co esponding o deso p ion (blue) and abla ion ( ed) egion. B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 7/21/16 1:39 PM 134 T. Blejchař e al. ing he hea conduc ion be ween indi idual zones. Mechanical esponse is sol ed by one-dimensional i ni e-di e ence hyd odynamic model in o de o p edic he s ess wa e and ma e ial mo ion a e he deposi ion o XUV-lase adia ion. Ma e ial p ope ies o li hium l uo ide se ing as he inpu da a o he gi en s udy we e de e mined based on bibliog aphic su ey. Compu a ional g id size was de i ned by he size o he i s (ini ial su ace) zone, which was se as equal o l0 = 1 nm. The o al numbe N = 100 cells we e included in he nume ical simula ions employ- ing a XUV-ABLATOR code. The hickness lz o he compu a ional g id cells (z is he index anging om 1 o N – 1 in ele ance o posi ion o z- h zone below he ini ial a ge su ace) is g owing wi h a geome i- cal ac o , ollowing he o mula lz = q × lz–1, whe e q = 1.06 was used as a de aul alue p oposed by Ande son [14]. A enua ion leng h (la = 13.6 nm), app op i- a e o no mal incidence angle o lase beam o LiF a ge , was u ilized o modeling pu poses. I should be poin ed ou ha only cold opaci ies a e conside ed by he ecen e sion o XUV-ABLATOR code. Rec angula ( l a -in- ime) p o i le speci ying empo al dependence o lase powe wi hin pulse du a ion (p = 1.5 ns) was assumed a he gi en le el o app oxima ion. To al ene gy a ailable in single pulse o he o- cused XUV-CDL beam E o = 3 J was assumed o be deposi ed on he lase spo a ea o S o = 2500 m2, which was di ided equally in o deso p ion and abla- ion egion p esuming he a io o hei espec i e a ea Sdes/Sabl = 3/1. Following his c i e ia, he i s pa o lase ene gy Edes = 1.5 J was conside ed o i adia e he a ea Sdes = 1875 m2 (yielding Fdes = 70 mJ/cm2) and he second pa o lase ene gy Eabl = 1.5 J on he a ea Sabl = 625 m2 (yielding Fabl = 240 mJ/cm2). These condi ions we e se as an idealized ep esen a- ion o obse ed expe imen al c a e p o i les and i s ypical mo phology. Tempo al e olu ion o e ical empe a u e p o- i le wi hin he LiF a ge du ing XUV-CDL pulse is p esen ed in Fig. 4, as ob ained om he 1D nume i- cal simula ions pe o med by XUV-ABLATOR code unde he gi en ci cums ances. The e ical posi ion o he in e ace be ween condensed (liquid/solid) and apo ized (gaseous) LiF dec eases in ime unde he ini ial a ge su - ace (below ze o-le el coo dina e) due o ma e ial emo al p ocess, mainly occu ing in lase pulse du a ion pe iod (p). The esul ing dep h a he end o simula ion ( = 200 ns) is equal o dabl = 21.5 nm o he abla ion egion. This alue co ela es well wi h he abla ion a e a he peak (absolu e mini- mum) o expe imen al c a e p o i le (see Fig. 3). Fo he deso p ion a e is equal o ddes = 4.5 nm, which co esponds o deso p ion a e obse ed a he pe iph- e y o expe imen al c a e p o i le, in spi e o ela i ely high su ace oughness o he sample. Fu he de ails conce ning implemen a ion o ou pu pa ame e s (p edic ed by XUV-ABLATOR) in o mul idimensional l uid dynamics simula ion o LPP plume expansion dynamics a e gi en below. Nume ical modeling o LiF plume expansion The elemen -based i ni e olume me hod (EbFVM) [16], as implemen ed in Ansys CFX so wa e sui e, was used o nume ical modeling o LPP plume expansion dynamics. Whe eas he p oblem o high-speed plume expansion is uns eady and he e exis s supe sonic l ow, hen second o de schemes and double p ecision sol e has o be used. The LiF plume expansion was simula ed as mul ispe- cies l ow because he e ec o backg ound gas was in es iga ed. The basic se o equa ions desc ibing he uns eady comp essible l ow o gas mix u es can be w i en as ollows: (1) (2) Fig. 4. Con ou plo s showing empo al e olu ion o empe a u e p o i le below he su ace o he LiF a ge as p edic ed by XUV-ABLATOR code (1D he momechanic model) o he abla ion egion (Fabl = 240 mJ/cm2) de- pic ed in (a) and deso p ion egion (Fdes = 70 mJ/cm2) depic ed in (b). Dashed whi e line in (a) and do ed whi e line in (b) desc ibes ins an aneous e ical posi ions o su ace laye , ha is, in e ace be ween condensed (liquid/ solid) and apo ized (gaseous) LiF ela i e o ini ial a ge su ace (ze o-le el coo dina e).  3 kg 0 ms j j u x           22 kg ms ij ii jijj uu uu p x xxx                B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 7/21/16 1:39 PM 135Deso p ion/abla ion o li hium l uo ide induced by ex eme ul a iole lase adia ion (3) (4) Equa ion (1) ep esen s he law o conse a- ion (con inui y equa ion), Eq. (2) ep esen s he momen um equa ion (Na ie -S okes equa ion), Eq. (3) ep esen s he law o ene gy conse a ion and Eq. (4) de i nes he mass ac ion o componen o mix u e. He e  [kg/m3] is densi y, u [m/s] is eloci y, [s] is ime, x [m] is he posi ion in Ca e- sian coo dina e sys em, p [Pa] is p essu e,  [Pa·s] is dynamic iscosi y, E [J] is he o al ene gy, T [K] is empe a u e,  [W/m·K] is he mal conduc i i y, jl [Pa] is shea s ess enso , YLiF [–] is mass ac- ion o li hium l uo ide in he plume, and D [m2/s] is di usion coe i cien . This se o equa ions was closed by he pe ec gas equa ion (p/) = R·T/M whe e R [J/K·mol] is uni e sal gas cons an and M [g/mol] is mola mass. Since he mix u e o LiF (as plume cons i uen ) and He (as a backg ound gas) was assumed o be p esen in he compu a ional domain du ing he en i e simula ion ime, he equa ion (YLiF + YHe = 1) closes he de i ni ion o gaseous mix u e. The abo e men ioned se o equa ions was sol ed by EbFVM wi h coupled sol e and second-o de disc e iza ion scheme, which sol es he hyd odynamic Eqs. (1)–(4) as a single sys em. This solu ion uses a ully implici disc e iza ion o equa ions a any gi en ime s ep. Compu a ional domain was de i ned in wo-di- mensional axisymme ic geome y wi h dimensions 200 m × 500 m consis ing o 35 000 quad ila e al elemen s. The LPP plume expansion is expec ed o be ini ia ed om he ci cula lase spo consis ing o inne abla ion egion (ha ing he adius abl = 14.1 m) and he ou e annulus wi h inne adius equal o abl = 14.1 m and ou e adius des = 28.2 m). The e o e, wo independen inle s a e de- i ned wi h nons a iona y bounda y condi ions gi en as o al p essu e exp essed om ele an p essu e and empe a u e his o ies p edic ed by he XUV- -ABLATOR code (1D he momechanic model), as shown in Fig. 5. A mul iexponen ial cu e i o he empe a u e da a was pe o med in o de o ob ain con inuous empo al p o iles. These algeb aic exp essions, ha is, unc ions de i ning p essu e dependence on he simula ion ime  ( = 0 co esponds o he beginning o he XUV-CDL pulse) we e se as non- s a iona y bounda y condi ion in wo-dimensional l uid dynamics simula ions. The e ec o he su ace eg ession a e and geome ical shape o he c a e (10 nm) was neglec ed in he gi en case wi h e- spec o he spa ial esolu ion o compu a ional g id nea he inle (100 nm). The en i e domain was ini ially assumed as being i lled wi h He as a backg ound gas a he mode a e p essu e. Two scena ios we e in es iga ed sepa a ely in ame o his s udy: (a) simula ion o LPP plume expansion dynamics a he backg ound p essu e P0 = 1 To ( u he e e ed as case A) and (b) simula ion o LPP plume expansion dynamics a he backg ound p essu e P0 = 10 To ( u he e- e ed as case B). I is wo h no ing he e ha such mode a e backg ound p essu es a e no ele an o ou ecen PLA expe imen s pe o med unde high acuum condi ions (P0  10–8 To ). Howe e , selec ed condi ions (mos ly ypical o PLD expe i- men s) we e assumed in o de o explo e he e ec o backg ound gas p essu e on XUV-LPP plume expansion dynamics and o conside u he pos- sibili ies o se up adjus men s. T ansien simula ion o ns-XUV-LPP plume expansion dynamics was de ached in o h ee ime in e als: (I) lase pulse du a ion and a e glow pe iod (0–5 ns); (II) as , ha is, supe sonic expan- sion pe iod (5–200 ns); (III) slow, ha is, subsonic, expansion (200–1000 ns). Adequa e ime s ep was assigned o hese in e als on he basis o Cu an numbe , gi ing 1 ps o he pe iod (I), 5 ps o sec-    3 kg ms j jjj jjl l uE EpT x xx u x                LiF LiF LiF 3 kg ms j j jj uY Y x Y D xx                 Fig. 5. Tempo al e olu ion o su ace empe a u e a he ins an aneous in e ace o condensed and gas phase LiF (a) and co esponding sa u a ion apo p essu e (b) cal- cula ed by he XUV-ABLATOR code o l uences ele an o deso p ion (blue do ed line) and abla ion ( ed dashed line) egion, acco ding o Fig. 4. B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 7/21/16 1:39 PM 136 T. Blejchař e al. ond o he pe iod (II), and 100 ps o he pe iod (III). Such app oach was chosen as a comp omise be ween he size o o al compu a ional ime and e i cien con e gence (wi h he c i e ia se as 10–6 o all a iables) in each ime s ep. Resul s and discussion The esul s o hyd odynamic simula ions cha ac e - izing he spa io- empo al e olu ion o plume expan- sion dynamics a e p esen ed in Fig. 6. A no iceable expansion (<10 m) is obse ed wi hin he pe iod o lase pulse du a ion (~1 ns) in he case A as well as in he case B. A e his ini ial pe iod o ime, isibly di e en plume expansion dynamics e ol es o wo cases s udied he e. In he case A, nea ly sphe ical plume expansion beha io can be ecognized (mos ly a   1 s). The le el o decele a ion du ing he gi en pe iod can be deduced om Fig. 7. The empo al change o a plume on dis ance (R- plo ) can be e i cien ly i ed by a iscous d ag model (see e.g. Re . [17]) in o de o ex ac he ele an plume s opping leng h. On he con a y, e y poo pe o mance o d ag model as well as shock model can be concluded when we aimed a i ing he R- plo gi en by he nume ical simula ion o he case B. Appa en ly, we can link his ea u e o R- plo o loss o sphe ical expansion beha io , which can be clea ly iden i i ed in Fig. 6. A nea ly adiaba ic ee expansion beha io dem- ons a ed by he quasi-sphe ical plume dynamics can be obse ed o he gi en condi ion up o abou P0 = 1 To He backg ound gas p essu e. A ele a ed backg ound p essu e (P0 = 10 To ), collisional e - ec s s a o domina e, leading o spa ial con i ne- men o he plasma and mush oom-like plume shape accompanying shock-wa e p opaga ion. The com- p ession o he backg ound gas can be conside ed as a shock comp ession p ocess in ol ing kine ic ene gy ans e . The shock on (high-densi y peaks o he backg ound gas) p opaga es o wa d ahead o he abla ed species. A he plume pe iphe y, whe e he no mal- o- a ge componen o he eloci y ec o is anishing, nonlinea e ms co esponding o magni ude o iscous shea s ess enso a e o p onounced impo ance. I was obse ed p e iously [6] ha as he back- g ound p essu e inc eases om acuum, he e exis s a ansi ion egime, whe e he plume is cha ac e ized by a s ong in e pene a ion o he abla ed species and backg ound gas, leading o plume spli ing and sha pening. The esul s o ou nume ical simula ions p edic ing quasi-sphe ical expansion a educed p essu e and he o ma ion o mush oom-like plume shape a ele a ed backg ound p essu es a e in quali- a i e ag eemen wi h hese obse a ions. The p essu e ange o he ansi ion egime depends on se e al ac o s co esponding o gi en expe imen al se up. The mola mass o ambien gas and a ge ma e ial apo s, lase in ensi y, lase spo size, and also he lase beam p o i le a e he main pa ame e s in l uencing LPP plume shape in he p esence o backg ound gas. Fig. 6. Spa io- empo al e olu ion o ns-XUV-LPP plume a backg ound p essu es P0 o helium ele an o he simula ion o case A (a) and case B (b) desc ibed in ex . Ins an aneous shape o plume is cha ac e ized a selec ed delays imes (speci i ed below image) by he con ou s plo o olume numbe densi y [cm–3] ele an o LiF monome ob ained om l uid dynamics simula ions. Fig. 7. R- plo o he expansion on bounda y o he nume ical simula ions a he helium backg ound p essu e o P0 = 1 To (a) and P0 = 10 To (b). Ins an aneous posi ion o plume on was e alua ed based on numbe densi y o LiF a he e ical axis o symme y (no mal o a ge su ace) assuming he limi alue o nLiF = 10–15 cm–3. Fi s o hese da a ob ained by u ilizing shock model (dashed line) and iscous d ag model (do ed line) a e also included. B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 7/21/16 1:39 PM 137Deso p ion/abla ion o li hium l uo ide induced by ex eme ul a iole lase adia ion F om Fig. 6 (a   10 ns), i is also ob ious ha di e ence in p opaga ion speed o he ini ial olume o LiF ejec ed om he abla ion and deso p ion e- gion can play a ole. Such di e ence is much mo e p onounced o case B compa ed o he simula ion o case A. The ‘ as e ’ mass o LiF om abla ion egion is con i ned in e y na ow expansion angle and wi h p olonged ime a e he ini ial phase ( ~ 100 ns), i can in e ac wi h he o ical s uc u es accompany- ing he p opaga ion o ‘slowe ’ componen deso bed om he ou e annulus o he lase spo . In o de o u he explo e he e ec o geome ical ac o s on he modeling ou pu , we pe o med an addi ional nume i- cal simula ions assuming he same l uence p o i le as being applied a he smalle lase spo (wi h adii des and abl educed by he ac o o 2). In ha case, mo e compac beha io o he shock on is obse ed a (P0 = 10 To ), esul ing in less p onounced la e al comp ession o he cen al column compa ed o he case B and ela i ely slowe expansion dynamics com- pa ed o he case A as well as compa ed o simula ion pe o med a P0 = 1 To wi h spo size educ ion. Based on hese i ndings, we sugges ha applica- ion o a mo e ealis ic lase beam p o i le is equi ed in o de o esol e he onse o he abla ion nea he ails o a low- l uence egion, whe e he lase deso p- ion occu s wi h conside ably di e en dynamics o he su ace e apo a ion. I is also e iden ha he esul s o nume ical simula ions a ele a ed back- g ound p essu es leading o o ma ion o hyd ody- namic ins abili ies a e s ongly a ec ed by he ac ual se up o he ini ial and bounda y condi ions. The applicabili y o simple ma hema ical models (e.g., an adiaba ic expansion; i.e., a blas -wa e model [18]) o he es ima ion o a a ge o subs a e dis ance was p e iously p o en mos ly agains he speci i c se o expe imen al da a on LPP plume expansion dynamics. Ne e heless, se e al examples showing educed p edic i e capabili ies in ele ance o PLD applica ions we e also epo ed in he li e a u e, e.g. [19]. When we compa e he esul s o ou nume i- cal simula ions wi h he es ima ed plume leng hs Lp ob ained om adiaba ic expansion model [18] (see Fig. 8), some quali a i e disag eemen can be ema ked. The e e sed end o plume leng h wi h inc easing backg ound gas p essu e can be easoned ou by he ansi ion o nonsphe ical plume expan- sion beha io occu ing p obably in he ange o backg ound p essu e 1 To > P0 > 10 To o he gi en lase and a ge pa ame e s. Ne e heless, i should be poin ed ou he e ha quan i a i e e alu- a ion o plume s opping leng h o he case wi h he loss o sphe ical expansion beha io would equi e much longe simula ion ime as he p opaga ion o he con i ned abla ed/deso bed mass is expec ed o con inue o a p olonged pe iod (10–100 s o mo e). The e o e, we ha e o conside he pe ec ma ch wi h adiaba ic expansion model ob ained o he case B as he acciden al ag eemen only. Fo a nea ly sphe ical plume expansion obse ed in he case A (also ob ained om he simula ions wi h a educed spo size) unde p edic ion o plume leng h Lp by he ac o o 3 ha e o be concluded. The e - ec o iscous o ces conside ed implici ly by he sol e o Na ie -S okes equa ions can be iden i i ed as possible sou ce o he gi en disc epancy. Ou e- cen esul s can hus be ega ded as p omising s ep owa d ealis ic simula ion o LPP plume expansion dynamics a he le el o de ail easible o p ac ical pu poses (e.g., designing o PLD expe imen s) as well as o model-based in e p e a ion o he ela ed expe imen s. Conclusions The capabili y o es ima e he plume s opping leng h based on p edic i e modeling a he b oad ange o easible condi ions is highly desi able when se ing up o op imizing PLD expe imen . Mul idimensional nume ical simula ions o LPP plume expansion ol- lowing abla ion/deso p ion o XUV lase -illumina ed LiF a ge was pe o med. The speci i c ools o con inuum hyd odynamics we e employed o he gi en pu pose. I can be concluded ha he sys em o Na ie -S okes equa ions can be success ully sol ed conside ing he ini ial and bounda y condi ions ep esen a i e o PLD expe imen s (P0 ~ 1 To o helium). We sugges ha cha ac e is ic ea u es o LPP plume expansion dynamics in di e en back- g ound gases can be e i cien ly in es iga ed ollow- ing he compu a ional p ocedu e desc ibed he e. Finally, we would like o show he applica ion o he ABLATOR code [14] as a demons a i e example how he models buil h ough ine ial con i nemen usion ela ed esea ch can be used, o example, o sol ing some p ac ical issues in ma e ial sciences. Acknowledgmen . This wo k was suppo ed by he Czech Science Founda ion (GAČR) ia he p ojec no. P108/11/1312. This wo k was pe o med in Czech Republic a he J. Hey o ský Ins i u e o Physical Chemis y o he Academy o Sciences o he Czech Republic, he Fig. 8. Plume s opping lengh Lp es ima ed om adiaba ic expansion (blas -wa e) model (g een dashed line) as a unc ion o he backg ound p essu e in he log-log scale assuming expansion in o monoa omic gas (speci i c hea a io  = 1.67) wi h ini ial eloci y o 0 = 104 m/s and expansion angle equals o 35°. 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