Single-shot temporal characterization of XUV pulses with duration from ~10 fs to ~350 fs at FLASH

Jou nal o Physics B: A omic, Molecula and Op ical Physics
PAPER • OPEN ACCESS
Single-sho empo al cha ac e iza ion o XUV pulses wi h du a ion om
∼10 s o ∼350 s a FLASH
To ci e his a icle: Rosen I ano e al 2020 J. Phys. B: A . Mol. Op . Phys. 53 184004
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Jou nal o Physics B: A omic, Molecula and Op ical Physics
J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 (12pp) h ps://doi.o g/10.1088/1361-6455/ab9c38
Single-sho empo al cha ac e iza ion o
XUV pulses wi h du a ion om ∼10 s o
∼350 s a FLASH
Rosen I ano 1, I e e J Be múdez Macias1,JiaLiu
2, Gün e B enne 1,
Juliane Roensch-Schulenbu g1, Gabo Ku di3, Ul ike F ühling4,5,
Ka ha ina Wenig4, Sophie Wal he 4,5, Anas asios Dimi iou4,5,Ma kus
D esche 4,5, I ina P Sazhina6, And ey K Kazansky7,8,9,NikolayM
Kabachnik1,2,6andS e anDüs e e
1
1Deu sches Elek onen-Synch o on (DESY), No kes asse 85, D-22603 Hambu g, Ge many
2Eu opean XFEL GmbH, Holzkoppel 4, D-22869 Schene eld, Ge many
3Ele a-Sinc o one T ies e, 34149 Baso izza, T ies e, I aly
4Ins i u e o Expe imen al Physics, Uni e si y Hambu g, Hambu g, Ge many
5The Hambu g Cen e o Ul a as Imaging, Lu upe Chaussee 149, Hambu g, Ge many
6Skobel syn Ins i u e o Nuclea Physics, Lomonoso Moscow S a e Uni e si y, Moscow 119991, Russia
7Depa amen o de Fisica de Ma e iales, Uni e si y o he Basque Coun y UPV/EHU, E-20018 San
Sebas ian/Donos ia, Spain
8Donos ia In e na ional Physics Cen e (DIPC), E-20018 San Sebas ian/Donos ia, Spain
9IKERBASQUE, Basque Founda ion o Science, E-48011 Bilbao, Spain
E-mail: osen.i ano @desy.de
Recei ed 17 Ap il 2020, e ised 29 May 2020
Accep ed o publica ion 12 June 2020
Published 17 July 2020
Abs ac
Ul a-sho ex eme ul a iole pulses om he ee-elec on lase FLASH a e cha ac e ized
using e ahe z- ield d i en s eaking. Measu emen s a di e en ul a-sho ex eme ul a iole
wa eleng hs and pulse du a ions as well as nume ical simula ions we e pe o med o explo e
he applica ion ange and accu acy o he me hod. Fo he simula ion o s eaking, a s anda d
classical app oach is used which is compa ed o quan um mechanical heo y, based on s ong
ield app oxima ion. Va ious ac o s limi ing he empo al esolu ion o he p esen ed e ahe z
s eaking se up a e in es iga ed and discussed. Special a en ion is paid o he cases o e y
sho (∼10 s) and long (up o ∼350 s) pulses.
Keywo ds: empo al diagnos ic, XUV pulses, SASE FEL, FLASH, THz s eaking, single
cycle e ahe z pulse
(Some igu es may appea in colou only in he online jou nal)
1. In oduc ion
F ee-elec on lase s (FELs) wo king in he ex eme ul a io-
le (XUV) and x- ay egion deli e un i alled in ense pulses
O iginal con en om his wo k may be used unde he e ms
o he C ea i e Commons A ibu ion 4.0 licence. Any u he
dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and he i le
o he wo k, jou nal ci a ion and DOI.
o s-du a ion [1–6]. They allow he in es iga ion o basic
ligh –ma e in e ac ions a high pho on in ensi ies such as
mul ipho on ioniza ion o a oms and molecules. The mos
p omising applica ion o he XUV FELs is he in es iga ion o
he ime e olu ion o elec onic p ocesses by applying pump-
p obe echniques. Fo he ealiza ion o his me hod i is c ucial
o know he empo al cha ac e is ics o he XUV pulses deli -
e ed by he FEL such as a i al ime, pulse du a ion and—a
bes — he empo al shape o he pulses.
0953-4075/20/184004+12$33.00 1 ©2020 The Au ho (s). Published by IOP Publishing L d P in ed in he UK
J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
Mos FELs in he XUV and x- ay ange ope a e in he
sel -ampli ied spon aneous emission (SASE) egime elying
on s ochas ic p ocesses, esul ing in pulses a ying on a sho -
o-sho basis [7,8]. Each pulse is composed o independen ,
empo ally cohe en spikes, wi h he du a ion o hese spikes
anging om hund eds o a oseconds o ens o em osec-
onds depending on he wa eleng h and cohe ence leng h o
he FEL p ocess. The s ochas ic na u e o he FEL adia ion
leads o la ge sho - o-sho luc ua ions in he empo al cha -
ac e is ics o he pulses. Mos o he known empo al cha ac-
e iza ion me hods a e based on a e aging o e many pulses
[9], which s ongly limi s he accu acy o he pump-p obe
expe imen s. The necessi y o know he du a ion and em-
po al p o ile o each indi idual pulse s imula ed he de el-
opmen o di e en me hods ha a e sui able o single-sho
empo al cha ac e iza ion. Besides e ahe z (THz) s eaking,
he e a e mainly h ee di e en echniques a ailable: (1)— he
obse a ion o op ical p ope ies changes in solid hin ilms
upon XUV pumping (e.g. [10,11]). This me hod howe e
only wo ks wi hin a e y limi ed dynamic ange in he XUV
and i is ques ionable how he me hod can be scaled o he
MHz high- epe i ion a e o FLASH. (2) A di e en app oach
in es iga es he empo al p o ile modula ion o he elec on
bunch du ing he XUV/x- ay c ea ion p ocess using a adio e-
quency ans e se de lec o de ice [12]. I has been shown ha
hese measu emen s can p o ide pho on pulse du a ions wi h
e y high empo al esolu ion, howe e , cu en ly canno be
scaled o he bu s mode s uc u e o FLASH. (3) A simila
app oach using an op ical eplica o he elec on bunch mod-
ula ion (‘op ical a e bu ne ’) [13] is po en ially also able o
deli e single-sho pulse du a ion in o ma ion bu has so a
no been demons a ed expe imen ally.
THz s eaking [14–19] on he o he hand can o e come
hese limi s and has he po en ial o deli e single-sho pulse
du a ion in o ma ion basically wa eleng h independen and
o e a la ge dynamic ange (in pulse du a ion and FEL ene gy).
I can be ope a ed wi h epe i ion a es up o se e al hund ed
kHz (po en ially e en MHz). In addi ion, i can p o ide a i al
ime in o ma ion o he FEL pulse wi h espec o he lase
d i ing THz gene a ion o each single pulse wi h an accu acy
well below 10 s [18]. Due o i s wide wo king ange he con-
cep can no only be used a so x- ay FEL like FLASH, bu
also a ha d x- ay FELs [17,20].
Recen ly a THz- ield d i en s eaking se up has been
ins alled a FLASH1 [18] deli e ing pho on pulse du a ion
as well as a i al ime in o ma ion o each indi idual XUV
pulse. In his pape , we epo on measu emen s pe o med
wi h his s eaking se up and heo e ical simula ions de o ed
o he in es iga ion o i s accu acy and limi a ions. P e ious
THz s eaking expe imen s [14,15,17,19] ha e been pe -
o med a ixed FEL se ings whe e he a e age XUV wa e-
leng h, pulse du a ion and pulse ene gy we e essen ially s able.
He e, o he i s ime, a comp ehensi ecollec ion o measu e-
men s eco ded a a ious FEL pa ame e s go e ning he pulse
du a ion a e p esen ed. F om sho es possible FLASH SASE
pulses in he sub 10 s ange (single longi udinal mode) wi h
only ew μJ o pulse ene gy o in ense >100 μJ pulses con ain-
ing a la ge numbe o longi udinal modes ex ending o pulse
du a ions >300 s (FWHM) ha e been in es iga ed.
The pape s uc u e is as ollows: he nex sec ion is de o ed
o he heo e ical desc ip ion o he s eaking p ocess which
is used in he simula ions and he econs uc ion o he em-
po al p o iles om he elec on ime-o - ligh (eTOF) mea-
su emen s. In sec ion 3 he expe imen al se up a FLASH1 is
b ie ly desc ibed p o iding necessa y in o ma ion abou he
pa ame e s o he XUV and he THz ields. In subsec ion 3.2
he analysis o he possible e o sou ces as well as limi a ions
o he desc ibed s eaking se up is gi en. Sec ion 4p esen s
expe imen al esul s o di e en XUV pulse du a ions and
a ious pa ame e s o he THz ield. Finally, we conclude in
sec ion 5.
2. Theo e ical backg ound
2.1. S eaking p inciple. Classical desc ip ion
We conside he pho oioniza ion o an a om by a sho ( em-
osecond) XUV pulse in he p esence o a co-p opaga ing THz
adia ion ield. Bo h ields a e linea ly pola ized in he same
di ec ion.In he scope o he cu en pape , we assume a single-
cycle THz pulse wi h du a ion much longe han ha o he
XUV pulse [15]. The XUV pulse p oduces a dis ibu ion o
pho oelec ons ia ioniza ion ha ca ies he empo al in o -
ma ion o he ionizing XUV pulse. The kine ic ene gy o he
pho oelec ons is modi ied by he in e ac ion wi h he THz
elec ic ield, and hei inal ene gy is de e mined by he ins an
THz- ield ec o po en ial a he momen o ioniza ion. Thus,
he empo al s uc u e o he elec on wa e packe is mapped
on o he kine ic ene gy dis ibu ion o he pho oelec ons.
Classically, one can w i e he inal ene gy Wo pho oelec-
ons emi ed a he ins an o ime as (a omic uni s (a.u.) a e
used in his sec ion unless o he wise indica ed)
W( )=W0+qATHz ( )cos θ−(ATHz( ))2/2, (1)
whe e W0is he ini ial ene gy o he ejec ed elec on wi h-
ou THz ield, q=√2Wis i s inal linea momen um di ec ed
a angle θ o he pola iza ion di ec ion o bo h pulses, and
ATHz ( )=−∞
ETHz( )d is he THz- ield ec o po en ial,
wi h ETHz( ) being he THz elec ic ield. No e ha he THz
ield is weak and he quad a ic e m in equa ion (1) can
be igno ed. One can u he simpli y he THz ield-induced
pho oelec on ene gy modula ion o ΔWs eak =W−W0∼
=
qATHz ( ) by assuming θ=0 (de ec ing only elec ons along
he pola iza ion di ec ion). Thus, he shi o he kine ic ene gy
peaks p o ides he a i al ime o he XUV pulse.
The ela ion be ween he ime in e al δ and he ene gy
in e al δ(ΔWs eak)isas ollows:
δ(ΔWs eak)=sδ =qdATHz( )
d δ ,(2)
whe e sis he so-called s eaking speed. As a i s app oxima-
ion, he alue smay be se o be a cons an p opo ional o he
de i a i e o he ec o po en ial a he cen e o he slope. The
pulse du a ion τXUV can hus be ex ac ed om he b oadening
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J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
o he pho oelec on spec um due o he p esence o he THz
ield. Fo a Fou ie limi ed Gauss-shaped peak he ollowing
equa ions apply:
σ2
s eak =σ2
e +s2τ2
XUV,(3a)
τXUV =s−1σ2
s eak −σ2
e , (3b)
wi h σs eak and σ e being he wid hs o he peak wi h and
wi hou he THz ield, espec i ely.
I he XUV pulse has a linea chi p, e.g. EXUV ( )
=˜
EXUV ( )cosω +c 2whe e ˜
EXUV ( ) is he en elope and
ωis he cen e equency o he XUV ield, equa ion (3a)
becomes σ2
s eak =σ2
e +τ2
XUV s2+4cswhich may be used
o expe imen al de e mina ion o he chi p [14,19,21].
As he THz pulse is ocused he phase o he THz ield
changes con inually along he p opaga ion di ec ion. This
e ec , o en called Gouy phase, changes he phase by 180◦
ac oss he Raleigh ange. Thus, elec ons gene a ed a di e -
en posi ions wi hin he in e ac ion egion a e accele a ed by a
sligh ly di e en THz ield and he e o e expe ience a di e -
en ene gy modula ion. This leads o an addi ional b oadening
σGouy o he pho oelec on line independen o he XUV pulse
du a ion [21]. The b oadening can, a leas app oxima ely, be
de e mined om he THz ocusing geome y and he accep-
ance olume om which he elec ons a e collec ed. This
Gouy phase b oadening has o be sub ac ed om he ac ually
measu ed wid h:
τXUV =s−1σ2
s eak −σ2
e −σ2
Gouy.(4)
2.2. Quan um mechanical simula ion
A mo e accu a e desc ip ion o he s eaking p ocess can be
achie ed by a quan um mechanical app oach. Fo calcula ions
o he double di e en ial c oss sec ion o he pho oioniza ion
(in ene gy and angle), he s ong ield app oxima ion (SFA)
can be used [22] since i is alid o medium s ong s eaking
ields and ela i ely as elec ons (kine ic ene gies o mo e
han 1 a.u. (27.2 eV)). Realiza ion o he SFA in he con-
ex o s eaking was discussed in e e ences [23–26]. Wi hin
his app oxima ion, pulse du a ion, empo al p o ile, kine ic
ene gy, a ge gas, s eaking ield and s eng h can be indepen-
den ly a ied o s udy he ole o each pa ame e in he s eak-
ing p ocess. As a esul , he simula ion p o ides he ene gy
and angula esol ed double di e en ial c oss sec ions o he
s eaked pho oelec ons. Se e al examples will be discussed
la e .
The SFA app oach, howe e , is compu a ionally a he
demanding limi ing i s applicabili y in as (on-line) sho - o-
sho analysis o expe imen al spec a. The desc ip ion o he
p ocess can be signi ican ly simpli ied wi hin a quasi-classical
app oach using he s a iona y phase me hod as sugges ed in
[24,25]. Recen ly, a e y simple and as me hod o FEL pulse
e ie al om he THz s eaking spec um has been sugges ed
in e e ence [26]. The me hod is based on SFA and uses he s a-
iona y phase app oxima ion. As shown in e e ence [26] he
double di e en ial c oss sec ion (DDCS) o XUV ioniza ion
in he p esence o he THz ield can be p esen ed as:
dσ
dWdΩ(W,θ)=2πE2
XUV ( s)
ETHz ( s)q2
0−2Wsin2θ
dσ(0)
dWdΩ˜
Ws,˜
θs,
(5)
whe e he las ac o is he common DDCS o pho oioniza ion
o he l0shell o he a om by he XUV pulse alone which can
be p esen ed in a s anda d o m:
dσ(0)
dWdΩ(˜
Ws,˜
θs)=σl0
(0) ˜
Ws
4π(1 +β˜
WsP2(cos θs)), (6)
he e σl0
(0)(˜
Ws)andβ˜
Wsa e he c oss-sec ion and aniso opy
pa ame e o he pho oioniza ion o he l0shell o he a om
by he XUV pulse alone, P2(x)is he second Legend e polyno-
mial. The ene gy ˜
Wsand angle ˜
θsa e de ined as:
˜
Ws=1
2q−
ATHz( s)
2
,(7)
˜
θs=a ccos cos θ−ATHz ( s)/q.(8)
They ha e he meaning o he elec on ene gy and emission
angle be o e en e ing he THz ield. The s a iona y poin s
( he ime o ioniza ion p o iding he inal ene gy (W=q2/2)
is gi en by he equa ion:
(qcos θ−ATHz ( s))2+q2sin2θ−q2
0=0, (9)
wi h q0=√2W0and W0being he ini ial ene gy o he
pho oelec ons.
Equa ion (9) has wo solu ions qcos θ−ATHz ( s)
=±q2sin2θ−q2
0. The expe imen implies ha he
momen a q0and qin ol ed a e subs an ially la ge han he
magni ude o he ec o po en ial o he THz ield ATHz. Thus,
i one conside s he case cos θ>0, he solu ion wi h he plus
sign should be chosen while he solu ion wi h he minus sign
should be chosen o cos θ<0. I only complex oo s so
equa ion (9) exis , o compu a ion o he SFA ampli ude he
saddle poin me hod should be used ins ead o he s a iona y
phase me hod. The saddle poin me hod allows one o ob ain
he Ai y unc ion ep esen a ion o he SFA ampli ude which
exponen ially dec eases wi h inc ease o he absolu e alue o
he imagina y pa o s. Fo he p esen p oblem his case is
no ele an .
The exp ession (5) can be di ec ly used o e ie e he em-
po al XUV pulse p o ile om a measu ed elec on ene gy
spec um:
E2
XUV ( s)=
ETHz ( s)q2
0−2Wsin2θ
2π
×dσ
dWdΩ(W,θ)dσ0
dWdΩ˜
Ws,˜
θs−1
.(10)
The e ie al s a egy is he ollowing: o each ene gy
W=q2/2, angle θand a gi en ime-dependence o he THz
ec o po en ial ATHz( ), he emission momen sis ound om
he ela ion (9). Then he ene gy ˜
Wsand angle ˜
θsa e calcula ed
acco ding o equa ions (7)and(8), espec i ely. Finally using
3
J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
Figu e 1. (a) Geome y o he THz s eaking se up used a he PG0 beamline o FLASH. (b) THz s eaking p inciple. Pho oelec ons a e
emi ed om ee (noble gas) a oms ionized by sho XUV pulses in he p esence o a s ong linea ly pola ized THz ield, hus modi ying he
momen um componen o he pho oelec ons. (c) Mapping o he empo al in o ma ion o he kine ic ene gy dis ibu ion om he THz
ec o po en ial (s eaking ace).
equa ion (10) he XUV pulse is e alua ed, p o ided he c oss
sec ion dσ0/dWdΩis known.
Since exp ession (10) is algeb aic, he pulse e ie al is as
as as using he classical exp ession (1) wi h linea app oxi-
ma ion o he ec o -po en ial. The o me exp ession (10)has
he ad an age ha i can be used o any shape o he ec o
po en ial and he e o e is sui able also o compa a i ely long
XUV pulses. The only limi a ion is ha he THz ec o po en-
ial mus be a mono onous unc ion in ime du ing he XUV
pulse du a ion.
3. Expe imen
3.1. THz-s eaking se up and da a acquisi ion
The expe imen s we e pe o med a he plane g a ing (PG)
monoch oma o beamline [27,28] o he ee-elec on lase
in Hambu g (FLASH) [1]. The PG beamline was ope a ed in
he so-called pa allel con igu a ion. This con igu a ion enables
he u iliza ion o he 0 h di ac ion o de (a he PG0 beamline
b anch) o expe imen s o diagnos ics (THz s eaking in ou
case) while he dispe sed adia ion is simul aneously used o
measu e he XUV FEL spec um wi h high esolu ion.
Va ious se ings o he accele a o we e used o es he
applicabili y o he s eaking diagnos ic o e a wide ange o
FEL pa ame e s. The FEL was ope a ed in single bunch mode
a 10 Hz, wi h elec on bunch cha ges al e ed om 0.08 nC
up o 0.44 nC, leading o di e en XUV pulse du a ions om
∼10 s o ∼350 s (FWHM) as well as o XUV pulse ene gies
anging be ween only a ew μJa 7nm o>100 μJ pe pulse
a 20 nm.
An 80 s, 800 nm, 6.5 mJ, 10 Hz Ti:Sapphi e lase [29]
wi h a sub 10 s synch oniza ion o he op ical mas e oscilla-
o [30] was used o gene a e single-cycle THz s eaking pulses
based on pulse on il op ical ec i ica ion in a li hium nio-
ba e (LiNbO3)c ys al[31]. The ob ained THz pulse ene gy
was on he o de o 15 μJ leading o a THz ield s eng h up o
300 kV cm−1(see igu e 3 in [18]). A de ailed desc ip ion o
he expe imen al se up and he wo king p inciple can be ound
in e e ence [18]. In b ie , he XUV pulses a e ocused in o a
noble gas a ge (see igu e 1) and c ea e pho oelec ons ia
ioniza ion. The XUV ocus size is chosen o be su icien ly
smalle (∼300 μm diame e (FWHM)) as compa ed o he THz
ocus size o 2.1 mm (FWHM). A Ce:YAG sc een and as
pho odiode we e used o ind he coa se spa ial and empo al
o e lap be ween he XUV and THz pulses [32].
Neon was chosen as he a ge gas p o iding he 2p and 2s
pho oelec onspec al lines in he ene gy ange o in e es . The
elec on binding ene gies a e 21.7 eV (2p) and 48.5 eV (2s),
espec i ely[33]. A he FEL wa eleng h o 6.8 nm (182.3 eV),
wo single, well sepa a ed spec al lines wi h kine ic ene gies
o 160.6 eV and 133.8 eV we e measu ed. A 20 nm (62.0 eV)
XUV wa eleng h he pho oelec on kine ic ene gies a e 40.3
eV and 13.5 eV, espec i ely.
As will be shown below, he ange o XUV pulse du a ions
om 30 s <τXUV <150 s can be e alua ed o XUV wa e-
leng hs up o abou 30 nm. Fo longe wa eleng hs, pulse du a-
ions o 30 s app oach he ew-mode ope a ion and ha e o be
ea ed mo e ca e ully. Fu he mo e, he pho oelec on kine ic
ene gy ge s smalle , hus making i inc easingly mo e di i-
cul o each su icien s eaking s eng h (see equa ion (2)).
Ne e heless, pulse du a ion measu emen s using a simila
se up ha e been success ully measu ed a 34 nm seeded VUV
adia ion [19].
The mapping be ween he s eaked kine ic pho oelec on
ene gy and he ime is gi en by ΔW( )≈eATHz( )2W0/me.
The igh -hand side o his equa ion is usually called ‘s eaking
ace’ and p o ides he maximum ene gy shi o pho oelec-
ons o a gi en THz ield. By i ing he linea pa o he
ec o po en ial we can e alua e he s eaking speed ‘s’which
ela es he ene gy shi and emission ime [14,21].
3.2. Possible sou ces o e o s and limi a ions
One o he main challenges o pulse du a ion diagnos ics is
he de e mina ion o measu emen e o ba s. The e a e se -
e al di e en sou ces o inaccu acy ha ha e al eady been
discussed in [14–16,34]. He e we summa ize he ac o s ha
limi he accu acy and he empo al esolu ion o THz s eak-
ing in gene al. In sec ion 4we ocus on he speci ic in luence
o he e o sou ces o he di e en pulse du a ion anges and
p o ide expe imen al esul s om FLASH.
3.2.1. Spec al luc ua ions o he SASE FEL pulse. As ol-
lows om equa ion (2) he sho e he XUV pulses a e, he
smalle he b oadening induced by he s eaking o a ce ain
THz ield is. Ul ima ely, o he sho es pulses a ailable a
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J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
Table 1. B oadening o he s eaking signal in s (FWHM)
calcula ed o 300 kV cm−1THz ield and di e en ho izon al
posi ions (along he FEL p opaga ion) o he eTOF wi h espec o
he THz ocus and o di e en accep ance olumes-sou ce size
(ho izon al leng h) o he eTOF [18].
eTOF posi ion Sou ce Phase Gouy b oadening
(mm) size (mm) ( ad) FWHM ( s)
0 0.25 0.023 6.2
0 0.5 0.047 13
0 0.75 0.071 19
6 0.25 0.017 4.7
6 0.5 0.033 10
6 0.75 0.053 14
FLASH he b oadening app oaches he spec al wid h luc-
ua ions caused by he SASE p ocess (see e.g. igu e 6). In
addi ion, o sho pulses only a ew o e en ually one spec al
mode is p esen [35]. Thus, he spec al dis ibu ion changes
signi ican ly om sho o sho while he in luence o he b oad-
ening due o s eaking is dec easing, leading o a mo e chal-
lenging da a analysis. Fo his wo k i is manda o y o use
he in o ma ion o e e ence spec a om each XUV pulse
measu ed ei he by a second eTOF [14]o byanXUVspec-
ome e . In he p esen case, he XUV spec al dis ibu ion is
measu ed o each FEL pulse simul aneously o he THz
s eaking by he PG monoch oma o beamline ope a ing in
spec ome e mode [27]. These spec a can hen be used o
p o ide he e e ence ene gy wid h on a single-sho basis wi h
signi ican ly highe esolu ion as compa ed o an eTOF [27].
In o de o c osscheck he app oach, a se o un-s eaked pho-
oelec on spec a we e eco ded and he de e mined wid h
o hese eTOF spec a we e ound o co ela e well wi h he
spec al wid h de e mined by he XUV spec ome e . Since
he ew-spec al-mode subs uc u e is also isible in he eTOF
spec a an analysis based on a single-peak Gaussian app oxi-
ma ion has se e e limi a ions and he analysis has o be adap ed
indi idually o each pulse as has been shown in [14,15].
An al e na i e way o cope wi h he spec al luc ua ions o
he SASE pulses is he u iliza ion o Auge emission p ocesses.
He e he SASE pulses ejec an inne shell elec on o noble
gas a oms. The exci ed ions will la e decay ia he emission
o Auge elec ons. The ene gy o he Auge elec ons only
depends on he in ol ed a omic s a es and is independen o he
ene gy o he ionizing pho ons. The spec al wid h o he Auge
elec ons is de e mined by he li e ime o he exci ed s a e and
is ypically abou 100 meV o smalle [36]. Thus, he spec-
a o he Auge elec ons a e ex emely na ow and s able as
compa ed o di ec pho oelec on spec a a SASE FELs. The
measu ed empo al dis ibu ion o he Auge -elec on wa e-
packe s is a con olu ion o he empo al p o ile o he ionizing
ligh pulse and he exponen ial Auge decay. The XUV pulse
du a ion can be ex ac ed om he s eak-measu emen s by a
simple decon olu ion. The Auge li e imes a e usually well
known and ypically lie in he ange o a ew em oseconds.
The e o e hey do no pose a se e e limi o he a ge pulse
du a ion ange.
3.2.2. Gouy phase b oadening. The THz phase shi be o e
and a e he ocus leads o an addi ional b oadening o he
eTOF signal esul ing in a longe e ie ed XUV pulse. Ou
eTOF spec ome e has a ∼0.5 mm FWHM accep ance ange
[18]. In able 1we p esen he Gouy b oadening calcula ed o
ou THz sou ce [18] o di e en accep ance olumes, sou ce
size (ho izon al leng h) and in e ac ion poin posi ion ega d-
ing he THz ocus. In o de o educe he Gouy phase induced
b oadening, one can ei he mo e he in e ac ion poin away
om he THz ocus posi ion o minimize he in e ac ion ol-
ume. The la e could be achie ed by using a mo e na ow gas
a ge and a es ic ed eTOF accep ance ange.
3.2.3. eTOF spec ome e esolu ion, accep ance angle and
signal o noise a io (SNR). The ene gy esolu ion o he used
eTOF (Kaesdo ETF11) is app oxima ely 1% o he ini ial
elec on kine ic ene gy simila o he pho on ene gy band-
wid h o he XUV pulse. Thus, in he case o 7 nm XUV
wa eleng h, he un-s eaked peak wid h is on he o de o
1.0–1.5 eV. I should be no ed ha o a gi en eTOF spec om-
e e , he empo al esolu ion can be imp o ed ei he by apply-
ing a mo e in ense THz ield o by s eaking mo e ene ge ic
pho oelec ons.
Ne e heless, he inc eased ene gy esolu ion usually leads
o a educed collec ion e iciency, and i is challenging o
achie e high ene gy esolu ion and high collec ion e iciency
simul aneously. The single-sho s eaked pho oelec on signal
has o be in ense enough o de e mine he s eaking o each
single XUV pulse, i.e. o collec a su icien numbe o elec-
ons pe pulse while a oiding unwan ed spec al b oadening
due o space cha ge esul ing om oo many ions c ea ed in he
FEL ocal olume [37]. By inc easing he a ge gas p essu e
un il a signi ican b oadeningo he un-s eakedpho o-linewas
obse ed, we could de e mine ha a o al numbe o collec ed
elec ons in he ange o ew hund ed pe XUV pulse does no
lead o signi ican space cha ge b oadening. Conside ing he
45◦collec ion angle his co esponds o a o al numbe o a
ew en housand elec ons wi hin he FEL ocus olume.
The collec ed elec ons a e dis ibu ed by he ime-o - ligh
p inciple o he spec ome e o a ce ain ime in e al which is
ypically ew imes longe han he signal p oduced by a single
elec on (1.2 ns (FWHM) o he used se up).
Thus he eco ded ampli ude o an eTOF ace a a ce ain
poin is ypically composed o a ew ens o elec ons only.
The ini e numbe o elec ons con ibu ing o he signal
leads o a s a is ical unce ain y o he signal shape [21]. In
he case o a Gaussian dis ibu ion he unce ain y due o he
Poisson s a is ics can be easily calcula ed. Fo nelec ons
con ibu ing o he ampli ude o he pho oelec on signal, he
unce ain y o he ampli ude is gi en by Poisson s a is ics: √n.
Thus he unce ain y ange o he no malized ampli ude is 1
±1/√nas shown in igu es 5,7and 9.
A simula ion o he s eaked eTOF signal dependence on
he accep ance angle was pe o med o e i y he addi ional
b oadening due o he a he la ge accep ance angle o he used
eTOF spec ome e . Using equa ion (5) he DDCS was calcu-
la ed o he model case o six 5 s XUV pulses in h ee pai s
5
J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
Figu e 2. SFA simula ion acco ding o equa ion (5). The 2D igu e
shows he double di e en ial c oss-sec ion simula ed o he neon
2p ioniza ion (a an inciden pho on ene gy o 182 eV/6.8 nm) using
h ee pai s o 5 s (FWHM) XUV pulses which a e spaced by 15 s
while he pai s a e 200 s sepa a ed. A 250 kV cm−1s eaking ield
was chosen. The middle pai was se a he ze o c ossing o he
ec o po en ial. The s eaking ield ac s s onges a 0 deg ees
(elec ons emi ed pa allel o he THz pola iza ion) and i s e ec is
dec easing o highe angles. In he angula ange o ±22.5 deg ees
o he used spec ome e he e is al eady a ce ain change isible in
he angula dis ibu ion. The lineou s (b) and (c) show he in eg a ed
pho oelec on signal o he angula accep ance o ±22.5 deg ees
( ed) and o he e e ence signal aking only he emission a 0
deg ees in o accoun —(blue). Two cases a e shown: o a THz ield
o (b) 150 kV cm−1and (c) 250 kV cm−1. While he e is a
signi ican di e ence in he esolu ion o he empo ally shi ed
peaks (∼190 eV), he di e ence be ween he la ge accep ance angle
and he e e ence is almos negligible o he s eaked signals a he
ze o c ossing o he ec o po en ial (∼160 eV). One can also see
he be e esolu ion a 250 kV cm−1compa ed o 150 kV cm−1.
Figu e 3. XUV pulse e ie al simula ions using equa ion (10).
Figu e 3(a) shows h ee s eaked Gaussian pulses o di e en XUV
du a ions in he ene gy domain (wi h a cen al ene gy o 68 eV). The
lowe panel igu e 3(b) displays he co esponding e ie ed XUV
pulses. The dashed lines deno e he linea (L) econs uc ion o he
pulse (assuming a linea beha io o he main slope o he ec o
po en ial); he solid lines deno e he econs uc ion o he same
s eaked pulse bu using equa ion (10) (NL) wi h a measu ed THz
po en ial (s eaking ace). The s eaking ace is shown in black
do s. Fo pulses <150 s, he econs uc ion gi es a Gaussian-like
pulse. As he pulse du a ion inc eases, he shape o he THz ec o
po en ial has a g ea e in luence, leading o a conside able change in
he shape o he XUV pulse.
spaced by 200 s andeach o he pai s sepa a ed by a 15 s in e -
al. The calcula ion was pe o med o neon 2p ioniza ion a an
XUV wa eleng h o 6.8 nm (elec on ene gy 160 eV) in a THz
ield o 250 kV cm−1. As shown in igu e 2(a) he s onges
e ec o he s eaking ield is o elec ons mo ing along he
pola iza ion di ec ion ( he a =0 deg ees).
Fo elec ons mo ing pe pendicula o he THz ield (90
deg ees) he e is p ac ically no ene gy shi . I is in e es ing
o no e ha he pho oelec on lines do no c oss he ini ial
pho oelec on ene gy o 160 eV bu he elec ons no emi -
ed a he ze o c ossing o he s eaking ace end up wi h
less kine ic ene gy a 90 deg ees han he un-s eaked elec-
ons. In equa ion (1) he e a e wo e ms depending on he
ield (pATHz ( )cos θ)andATHz( )2.The e mATHz( )2is
ypically e y small and can be neglec ed, howe e , i causes
he asymme ic shi a 90 deg ees.
The angula dis ibu ion a he ze o c ossing o he THz ec-
o po en ial has almos no angula dependence. The e o e, a
6
J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
la ge accep ance angle does no limi he esolu ion signi i-
can ly. On he o he hand, a s eaking posi ions ou side he
ze o c ossing (yielding an ene ge ic shi a 0 deg ees), a sig-
ni ican e ec o he accep ance angle can be obse ed (see
igu es 2(b) and (c)).
In ou case, he accep ance angle o 45 deg ees ( ull solid
angle) shows only an addi ional b oadening o <1 sa he
ze o c ossing o he ec o po en ial and <5 s measu ed 200
s away om he c ossing. Reducing he ield o 150 kV cm−1,
he wo pulses loca ed 200 s away om he c ossing canno
be esol ed anymo e showing he impo ance o he co ec
se ing o he ela i e iming be ween XUV and THz ields.
3.2.4. In luence o he non-linea i ies o he THz ec o po en-
ial. Usually he analysis o he s eaking spec a is pe o med
assuming a linea slope in he THz ec o po en ial (cons an
s eaking speed). Howe e , he ec o po en ial is non-linea
and he s eaking speed depends on he a i al ime. Fo e y
sho pulses and o a i al imes close o he ze o-c ossing
o he THz ield ec o po en ial he di e ence is negligible.
Ne e heless, o longe pulses his di e ence may be consid-
e able. We in es iga ed he in luence o he non-linea amp by
e ie ing Gaussian s eaked XUV pulses using equa ion (10)
o di e en pulse du a ions. The esul s a e shown in igu e 3.
When he pulses a e almos as long as he ange o he ec o
po en ial slope, he non-linea i y is e lec ed as a change in he
shape o he pulse as well as a small shi in he a i al ime.
3.2.5. SASE induced e o sou ces. Ano he sou ce o
unce ain y esul s om adia ion p ope ies o he SASE pulse
i sel . Measu emen s o he elec on phase space and he spec-
al wid h o he XUV adia ion gi e s ong hin s ha he SASE
adia ion can be chi ped due o he in luence o space cha ge
and adio equency (RF) slopes [38–41]. The ene gy chi p
esul s in an SASE pulse whose leading pa has a sligh ly
di e en a e age wa eleng h as compa ed o he ailing pa .
This leads o di e en measu ed pulse du a ions depending on
he ela i e sign o he THz s eaking ield and he chi p as
explained e.g. in [21]. To es ima e he in luence o he e ec ,
one can compa e he pulse du a ions e ie ed om he posi-
i e and nega i e THz slopes (compa e s eaking ace shown
in igu e 1(c), i only one eTOF is used. Fo wo eTOFs ac-
ing each o he see [14,21]) he chi p can be de i ed o each
measu ed XUV pulse.
4. Measu emen s and discussion
4.1. S eaking in he ‘s anda d’ XUV pulse ange (30 s <
τXUV <150 s)
Be o e ocusing on he limi s o he me hod, we ha e in es-
iga ed he ‘s anda d’ pulse du a ion egime o FLASH. No e
ha he e o sou ces discussed abo e a e in a ole able ange
and he pulse du a ion can be de e mined a he accu a ely. A
de ailed in es iga ion o he pulse du a ion luc ua ions and
hei co ela ions o o he pulse pa ame e s such as pulse
ene gy and spec al dis ibu ion was discussed in [42]. Fo
his pulse du a ion egion he in luence o he di e en e o
sou ces is compa a i ely small.
Figu e 4. (a) Single-sho pulse du a ion measu emen s shown o
h ee housand FLASH pulses. The ed line indica es he mean alue
o ∼102 s FWHM. The e o ba s o each measu ed pulse du a ion
(no shown in he plo ) is ±20% including all di e en con ibu ions
discussed in he ex . (b) His og am o pulse du a ions.
Figu e 4shows he single-sho pulse du a ion wi h he
una oidable and expec ed luc ua ions due o he SASE p o-
cess poin ing again on he need o p o ide a single-sho diag-
nos ic o SASE based FELs.
4.1.1. Re e ence spec a-SASE luc ua ions. Fo he used
expe imen al se up, he s eaked pho oelec on spec a a e sig-
ni ican ly b oadened as compa ed o he un-s eaked ones
( igu es 5and 6(b)). We he e o e can simpli y he analysis by
eco ding he a e aged un-s eaked e e ence spec al wid h by
blocking he THz beam e e y ew minu es.
Since he eTOF esolu ion is no good enough o esol e
he empo al sub-s uc u e in he s eaked spec um, we used
a Gaussian i o de e mine he line wid h (FWHM) o bo h
s eaked and un-s eaked spec a. In o de o ge an es ima e
o he e o in oduced by aking he a e aged e e ence, he
esul ing XUV pulse du a ion was calcula ed by using he
smalle and la ge FWHM alues o he e e ence spec um
wid h his og am. The wid hs o he e e ence spec a his-
og am shown in igu e 6(b) is 0.9 ±0.1 eV which leads (using
equa ion (3b)) o an unce ain y o <1% o de e mina ion o
he pulse du a ion and he e o e negligible.
4.1.2. Gouy phase b oadening. The in luence o he Gouy
phase was aken in o accoun o he THz beam shape a ound
he in e ac ion poin (see also igu e 4 in e e ence [18]).
7
J. Phys. B: A . Mol. Op . Phys. 53 (2020) 184004 R I ano e al
Figu e 5. S eaked ( ed) and un-s eaked (blue) pho oelec on
spec a o ∼60 s (FWHM) XUV FEL pulses a e shown ( hick lines)
including he 1/σ e o ba s (shaded a ea) caused by he Poisson
s a is ics due o he limi ed numbe (abou 80–100 elec ons in he
peak) o elec ons in he spec um. The s eaking speed swas 0.05
eV s−1. FEL pho on ene gy was 70.2 eV (wa eleng h 17.6 nm).
S eaked spec um o Ne 2p was aken a he 0-c ossing o he
THz- ec o po en ial.
Acco ding o able 1, he Gouy b oadening is (13 ±2 s)
o he THz ocus posi ion and ∼0.5 mm sou ce size (ho i-
zon al leng h). The unce ain y in he Gouy b oadening s ems
om he no p ecisely known sou ce size. Due o he quad a ic
dependence, he in luence on he acqui ed pulse du a ion is
a he small (see equa ion (3)) and he unce ain y in he
knowledge o he Gouy phase leads o an e o o <5%.
4.1.3. eTOF spec ome e esolu ion, accep ance angle and
signal o noise a io (SNR). As shown in igu e 2 he b oaden-
ing by a la ge angula accep ance is (a he ze o c ossing o he
ec o po en ial) only a ew s and hus leads, in he conside ed
pulse du a ion ange, o an e o o less han 5%.
The pho oelec on peak wid h/shape has an unce ain y due
o he limi ed numbe o elec ons in a sho (∼200–500 elec-
ons). The ini e numbe o elec ons con ibu ing o he sig-
nal, leads o a s a is ical unce ain y o he signal shape. The
s a is ical e o o he wid h de e mina ion oge he wi h he
Gaussian i ing leads o an unce ain y o 10%–25% as illus-
a ed in igu e 5. Typically, he eTOF esolu ion in combina-
ion wi h coun ing s a is ics shows an e o ha is oo la ge
o a de ailed analysis o he pulse shape. Thus, only he
pulse du a ion is analyzed. Howe e , o longe pulses some
in o ma ion abou he ough o e all pulse s uc u e can be
de e mined as shown in sec ion 4.2.
4.1.4. In luence o he non-linea i ies o he THz ec o po en-
ial. In he conside ed pulse du a ion ange, he SASE pulses
consis o se e al sub pulses which canno be esol ed by he
cu en eTOF spec ome e , hus we only apply a Gaussian i .
Asshownin igu e3 he in luence o he non-linea THz ield
is only a ew pe cen and hus o he s anda d analysis, he
linea app oach (equa ion (4)) can be applied.
4.1.5. SASE induced e o sou ces. Po en ially, a s ong
ene gy chi p in he elec on bunch gene a ing he XUV pulse,
can lead o a co esponding equency chi p o he XUV pulse
which is no de ec able on a single sho basis wi h he p esen
se up due o he gi en s a is ical unce ain y. Howe e , he
a e age amoun o equency chi p was de e mined by com-
pa ing he a e age s eaking wid h on he posi i e and nega i e
ec o po en ial slope, simila o how i was done in e e ence
[19]. In e es ingly, we did no ind an indica ion o chi p (la ge
han he e o ba s) o he whole la ge ange o measu ed FEL
pa ame e s.
In summa y, o pulse du a ions in he ange 30 s <τXUV
<150 s we can s a e a ypical unce ain y o ±20% o he
de e mina ion o he single-sho pulse du a ion.
4.2. Explo ing he uppe limi : ‘long’ (τXUV >150 s) XUV
pulses
Fo pulses ha co e a signi ican ac ion o he s eaking
slope, he THz s eaking induced b oadening is so la ge ha
he XUV pulse shape de ia es om he ini ial Gaussian shape
and shows a con olu ion o he e e ence line shape wi h he
ac ual XUV pulse shape (see igu e 6(c)). In his case, we can
de e mine no only a alue (FWHM) o he pulse du a ion bu
econs uc he pulse shape o he indi idual XUV pulses, mak-
ing a decon olu ion o s eaked and e e ence spec a using
he non-linea equa ion (10) (see igu e 7). No e, ha he e he
in luence o he a ious e o sou ces is di e en as compa ed
o he s anda d s eaking case (sec ion 4.1).
4.2.1. Re e ence spec a-SASE luc ua ions. One can see
om igu e 6(c) ha he wid h dis ibu ion o he e e ence
spec a (no THz) and o he ac ual s eaked spec a a e su -
icien ly well sepa a ed. Thus, he SASE luc ua ions show
almos no con ibu ion o he pulse du a ion unce ain ies
(<0.1%).
4.2.2. Gouy phase b oadening. Gouy co ec ion leads o
<1% change o he pulse du a ion and does no ha e o be
conside ed.
4.2.3. eTOF spec ome e esolu ion, accep ance angle and
signal o noise a io (SNR). The maximum s eaking ield
s eng h has o be adjus ed o p o ide su icien s eaking
s eng h o clea ly b oaden he pho oelec on peaks in compa -
ison o he e e ence wid h. This allows one o de e mine he
ac ual XUV pulse shape, while keeping he signal le el s ill
la ge enough wi hin he ime bins o he eTOF signal. I he
s eaked pho oelec on line is b oadened oo much, he e a e
only ew elec ons pe ime bin le leading o a la ge Poisson
unce ain y and hus a la ge e o in he de e mina ion o he
pulse shape.
We ound ha 30–40 elec ons con ibu ing o he maxi-
mum signal a e su icien o educe he e o o he signal
ampli ude o <20%. Figu e 7shows he e ie ed XUV pulses
including he s a is ical e o bands.
4.2.4. In luence o he non-linea i ies o he THz ec o po en-
ial. The econs uc ion o he XUV pulse shape om he
measu ed pho oelec on dis ibu ion needs o ake he mea-
su ed ec o po en ial in o accoun i he pulses co e la ge
pa s o he slope. The XUV pulses we e econs uc ed using
8