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
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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.
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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.
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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
 
 
 



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  


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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.
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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.
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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°. Fo he esul s o nume ical
simula ions (symbol ), plume leng h was de e mined
by leas -squa e i ing o he R- plo o he iscous d ag
model, i.e., R = Lp(1 – e–).
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138 T. Blejchař e al.
Ins i u e o Physics o he Academy o Sciences o
he Czech Republic, he VŠB-Technical Uni e si y
o Os a a and he Cha les Uni e si y in P ague, Czech
Republic.
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