From self-organization in relativistic electron bunches to coherent synchrotron light: observation using a photonic time-stretch digitizer
Serge Bielawski, Edmund Blomley, Miriam Brosi, Erik Bründermann, Eva Burkard, Clément Evain, Stefan Funkner, Nicole Hiller, Michael J. Nasse, Gudrun Niehues, Eléonore Roussel, Manuel Schedler, Patrik Schönfeldt, Johannes L. Steinmann, Christophe Szwaj, Sophie Walther, Anke-Susanne Müller
FFrom self-organization in relativistic electron bunches to coherent synchrotron light:observation using a photonic time-stretch digitizer
Serge Bielawski , ∗ , Edmund Blomley , Miriam Brosi , Erik Br¨undermann , Eva Burkard , , Cl´ement Evain , StefanFunkner , Nicole Hiller , , Michael J. Nasse , Gudrun Niehues , El´eonore Roussel , Manuel Schedler , PatrikSch¨onfeldt , , Johannes L. Steinmann , Christophe Szwaj , Sophie Walther , , and Anke-Susanne M¨uller Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers, Atomes et Mol´ecules,Centre d’ ´Etude Recherches et Applications (CERLA), F-59000 Lille, France. Karlsruhe Institute of Technology (KIT), D-76131 Karlsruhe, Germany Present address Fraunhofer Institute of Optronics,System Technologies and Image Exploitation (IOSB), D-76275 Ettlingen, Germany Present address Paul Scherrer Institute (PSI), 5232 Villigen, Switzerland. DLR (Deutsches Zentrum f¨ur Luft und Raumfahrt) Institute of Networked Energy Systems,Carl-von-Ossietzky-Str. 15, D-26129 Oldenburg, Germany Present address DESY (Deutsches Elektronen-Synchrotron), Notkestr. 85, D-22607 Hamburg, Germany ∗ (Dated: February 19, 2019) In recent and future synchrotron radiation fa-cilities, relativistic electron bunches with increas-ingly high charge density are needed for produc-ing brilliant light at various wavelengths, from X-rays to terahertz. In such conditions, interactionof electrons bunches with their own emitted elec-tromagnetic fields leads to instabilities and spon-taneous formation of complex spatial structures.Understanding these instabilities is therefore keyin most electron accelerators. However, inves-tigations suffer from the lack of non-destructiverecording tools for electron bunch shapes. Instorage rings, most studies thus focus on the re-sulting emitted radiation. Here, we present mea-surements of the electric field in the immedi-ate vicinity of the electron bunch in a storagering, over many turns. For recording the ultra-fast electric field, we designed a photonic time-stretch analog-to-digital converter with terasam-ples/second acquisition rate. We could thus ob-serve the predicted link between spontaneous pat-tern formation and giant bursts of coherent syn-chrotron radiation in a storage ring.
INTRODUCTION
Current storage ring synchrotron radiation facilities in-volve challenges in photonics, both for understanding thelight source and for realizing suitable ultrafast measure-ment devices. Generation of light for users is performedby using electron bunches in the subnanosecond to pi-cosecond range, with high charge density. This density isso high that the light emitted by the electrons affects thedynamics of neighboring electrons in a dramatic way. Inparticular, this nonlinear collective effect leads to spon-taneous formation of small-scale structures (in the sub- ∗ Corresponding author : [email protected] millimeter to centimeter range) in the longitudinal profileof electron bunches [1–17]. This is known as the mi-crobunching instability [3, 4, 18, 19] (see Figure 1) . Thiseffect is conceptually close to the universal mechanismsof pattern formation in Nature [20] due to interaction be-tween parts of the same system, such as the modulationinstability in optical fibers [21], sand ripple formation in-duced by the wind or under the sea [22], or phantomtraffic jams [23].However, besides being a fascinating phenomenon oflight and matter self-organization, latest generation lightsources must systematically consider these collective ef-fects for very practical reasons. Spontaneous formation ofsmall-scale microstructures can have a deleterious effecton electron bunch stability and emission properties, andthey are at the same time a tremendous source of coher-ent radiation in the terahertz domain [3–17], provided theinstability can be mastered. This is the reason why un-derstanding and controlling the interplay between Coher-ent Synchrotron Radiation (CSR) and the microbunchinginstability has nowadays become a central open questionin the development of synchrotron radiation facilities.To answer this question, it is essential to develop ul-trafast photonic devices for electron bunch shape char-acterization. The challenges for the photonics commu-nity is high, given the need for ultrashort (picosecondor femtosecond) temporal resolution, single-shot opera-tion, at high repetition rates (MHz and more), and giventhe particularly challenging environment near relativisticelectron bunches. Recent advances consequently pushedphotonics systems beyond the state of the art. Ultrafastelectric-field measurement techniques using femtosecondlaser pulses (electro-optic sampling [24]) have allowedsingle-shot bunch shape measurement [25], and thesetechniques have then been extensively investigated andimproved this last decade [26–30]. As these techniquesrequire compact femtosecond lasers, this also motivateda specific work on fiber-based sources, using parabolicpulse amplification [31, 32]. This even led to new recordspectral widths for parabolic pulse amplifiers [33]. a r X i v : . [ phy s i c s . acc - ph ] F e b relativisticelectrons synchrotron radiation i n t e r a c t i o n w i t h o t h e r e l e c t r o n s ( a h e a d a n d b e h i n d ) (a) q q (mm) e n e r g y ( a r b un i t . ) q (mm) l o n g i t u d i n a l d e n s i t y (b)(c) Figure 1.
Microbunching instability in a relativisticelectron bunch. (a)
Illustration: at accelerator locationswhere curved trajectories are present, each electron interactswith the coherent synchrotron radiation emitted by the oth-ers. (b,c)
Numerical simulation: resulting spontaneous ap-pearance of a pattern in phase space, which evolves in a com-plex way (computation using KARA storage ring parameters,see Method Section, and Supplementary Video 1). (c) cor-responding longitudinal density profile. Note that the fastmodulation in (c) – thought apparently small – is responsi-ble for a particularly intense emission of coherent synchrotronradiation (typically 10 –10 times the normal synchrotron ra-diation) ranging from the millimeter-wave to THz domains. Ultrafast diagnostics also recently started to use strate-gies from the emerging field of ”photonic hardware ac-celerators” [34], which aims at increasing the speed ofelectronic devices by combining them with specially de-signed photonic front-ends. In particular photonic time-stretch analog to digital converters [35, 36] opened theway to the realization of “single-shot terahertz oscillo-scopes” [30, 35, 37–39] providing up to tens of million traces per second.The availability of new ultrafast measurement systemsled to several milestones in these storage ring investiga-tions. Pioneer experiments using a streak camera couldvisualize microstructures in the several GHz range at theVUV ring [40]. More recently, electron bunch shapeshave been indirectly characterized in single-shot by us-ing new detectors based on thin films of superconductingYBCO [41], and high repetition rate electro-optic sam-pling, using photonic time-stretch [37]. Although thisprogress enabled to record structures in single-shot up tothe THz range, the obtained information concerned onlythe far-field (i.e., the synchrotron radiation) emitted bythe microstructures [37, 39, 40].In this article, we present a photonic system that en-ables to observe microstructures and their evolution in adirect way, by monitoring the electric field in the imme-diate vicinity of the electrons.
RESULTSExperimental strategy
Recording bunch shapes in a non-destructive way re-quired two open problems to be solved. The first oneconsisted in probing the electric field by approaching anelectro-optic crystal at few millimeters from the relativis-tic electron bunch (Figure 2), without losing the electronbunch or damaging the crystal. By carefully designingthe experimental setup [42, 43], we could demonstratethe possibility to operate the synchrotron facility withan electro-optic crystal at 2-18 millimeters from the elec-tron bunch. This pioneer experiment at the ANKA (nowKArlsruhe Research Accelerator – KARA) storage ringthus opened the way to real-time investigations of stor-age ring electron bunch shapes, under the condition thata suitable photonic ultrafast readout system can be de-signed.Optical readout of the crystal birefringence versus timewas the second key problem as measurements had to bebe performed: (i) in single-shot, (ii) with picosecond orsub-picosecond resolution, (iii) at several MHz acquisi-tion rate. Moreover this ultrafast readout needs to beperformed with an important dynamical range becausethe fast microstructures are expected to appear as a smallmodulation superimposed on a large slowly-varying back-ground (see Figure 1c). At KARA, we have been explor-ing two directions in parallel. We have been develop-ing a new generation of fast linear cameras (KALYPSO)with multi-MHz acquisition rates [44–47]. In parallel, wehave been developing a second direction consisting in us-ing the so-called photonic time-stretch strategy [35, 36].The latter strategy allows up to tens of MHz acquisi-tion rate, using an association of commercial detectorsand electronics. The results presented in this article areobtained with this strategy. (b) near- fi eld electro-optic sampling setup location (probe crystal and polarization optics) high charge densityrelativistic electron bunch (typ. length 5-25 ps)coherent THzemission near-fieldelectro-optic sampling setup femtosecondlaser pulsesultrafast laser pulse analysis op t i c a l f i be r op t i c a l f i be r (a) Figure 2.
Global strategy of the experiment (a), and picture of the KARA storage ring (b).
Interaction ofa relativistic electron bunch with its own emitted coherent radiation leads to the so-called microbunching instability, andformation of a pattern with few millimeter period in the longitudinal direction. For monitoring the longitudinal electron bunchshape, we record the electric field evolution in its vicinity (at few millimeters), using a specially designed picosecond-speed photonic-time-stretch analog-to-digital converter . The digitization is made in two steps: (i) laser pulses are modulated by theelectric field using an electro-optic crystal, and (ii) the modulated pulses are analyzed in single-shot, picosecond resolution, andmulti-MHz acquisition rate. Note that the crystal is actually placed above the electron beam (the whole photonic time-stretchdigitizer is detailed in Figure 3). The electron bunch microstructure is also emitting intense coherent synchrotron radiation(CSR), which is simultaneously recorded.
Photonic time-stretch Analog-to-Digital Converter
The photonic time-stretch digitizer setup is repre-sented in Figure 3. The optical front-end combines twoparts. A single-shot electro-optic sampling (EOS) sys-tem [42] imprints the electric field shape onto a chirpedlaser pulse [24, 25]. Then, the laser pulse exiting theEOS system is stretched in a 2 km dispersive fiber, sothat the picosecond information is temporally stretchedto the nanosecond range, and can be recorded using aphotodetector and a conventional oscilloscope (5 GHzbandwidth is typically used here, see Methods). If westart from a compressed laser pulse, the output signalshould be a replica of the ultrafast electric pulse, slowed-down by a factor [35, 36]: M = 1 + L L , (1)with L and L the lengths of fiber before and after thecrystal (if the fibers are identical). Since an unknownamount of extra-dispersion is also present before the fiberof length L , we also measured the stretch factor experi-mentally. We found M = 75 .
8, i.e., 1 nanosecond on theoscilloscope corresponds to a real duration of 13 . Simultaneous measurement of electron bunch shapesand resulting coherent radiation emission
A typical single-shot electro-optic signal is representedin Figure 4a. The data correspond to the longitudinaldensity profile of the electron bunch (or more precisely tothe electric field in its vicinity, see Methods and supple-mentary material). Detailed analysis reveals two compo-nents. As expected, a slowly-varying shape is systemati-cally observed, whose width is of the order of the electronbunch size. When the electron bunch is “compressed” be-low a threshold size (technically, by decreasing the mo-mentum compaction factor of the storage ring), a fastmodulation appears on the electro-optic sampling signal.In order to conclude non-ambiguously that this struc-ture corresponds to the microbunching instability, werepresented the data as a function of the revolution num-ber (Figs. 4b,c,d). High-pass filtered data reveal that therapidly evolving structure occurs in bursts (Figs. 4c), andtheir space-time evolutions (Figs. 4b) present a charac-teristic pattern. As we will see, this will be a central (cid:1) edfemtosecond Yb (cid:1) ber laser PM (cid:1) berL1=35 m PBSpicosecond electronbunch temporal stretchingin a single-mode (cid:0) ber (length L2=2 km) balancedphoto-detector
GHz oscilloscope slowed-down replica of the e-bunch near- (cid:2) eld
50% coupler Pockelscrystal(GaP)QWP andHWPPolarizer unmodulatedlaser pulse(reference) laser pulsemodulated bythe electron bunch picosecond pulse 1 picosecondpulse 2picosecond pulse 2 picosecond pulse 1nanosecondpulse 2 nanosecondpulse 1nanosecond pulse 1nanosecond pulse 2delay a cc e l e r a t o r v a c uu m c h a m b e r YDFA
Figure 3.
Photonic time-stretch analog-to-digital converter realized for recording the shape the of electronbunches at high repetition rate.
The electron bunch near-field is imprinted onto a chirped laser pulse, by using the Pockelseffect in a gallium phosphide (GaP) crystal. The laser pulse is then further chirped in a long fiber, so that the modulation isslowed down to the nanosecond range, and can be recorded by an oscilloscope. Furthermore, an additional laser pulse whichhas not interacted with the electron bunch is used as ”zero field” reference, and is subtracted from the signal by a balancedphotodetector. Note that another reference laser pulse (not shown) is also recorded and used in the offline data processing(see Methods and Supplementary Material). Blue line: polarization-maintaining (PM) fiber, green lines: single-mode non-polarization maintaining (SM) fibers. YDFA: ytterbium- doped fiber amplifer, HWP: half-wave plate, QWP: quarter-waveplate, PBS: polarizing beam splitter. The GaP crystal is placed above the electron bunch trajectory. Only the free-space optics(along the dashed line) is located near/in the vacuum chamber, the rest (laser source, YDFA and downstream components) islocated in a remote laboratory. point for comparing data with theory.Since the electro-optic sampling is performed at eachturn in the storage ring, it is possible to examine thecorrelation of the spontaneous microstructure formation,with the appearance of coherent synchrotron radiation.In Figure 4f we have plotted the data over a long timerange, together with the signal synchronously recordedwith a millimeter-wave diode detector placed at our in-frared beamline. We can clearly see the correlation be-tween the occurence of a burst of CSR, and the growth ofthe microstructure. This correlation was systematicallyobserved in the recorded data.
DISCUSSION
These new data sets can be compared to existing mod-els of electron bunch dynamics. The physics of the elec-tron bunch evolution involves essentially three ingredi-ents: (i) acceleration and energy losses at each turn,(ii) interaction of each electron with the field created bythe whole electron bunch distribution, (iii) and the rela-tion between their energy and the revolution time in thestorage-ring. The evolution equation for the distributionof the electrons in phase space may be written in the form of a Vlasov-Fokker-Planck equation [18, 19]: ∂f∂θ − p ∂f∂q + [ q − I c E wf ( f, q )] ∂f∂p = 2 (cid:15) ∂∂p (cid:18) pf + ∂f∂p (cid:19) , (2)where f ( q, p, θ ) is the distribution of the electrons attime θ in phase space ( q, p ). θ is a continuous and di-mensionless variable associated to the number of turnsin the storage ring: θ = 2 πf s t , where t is the time (inseconds) and f s is the synchrotron frequency (here inthe tens of kilohertz range). The longitudinal position q and relative momentum p are the deviation from theso-called synchronous electron (with position z and en-ergy E ). q and p are expressed in units of the equi-librium bunch length σ z and energy spread σ E at zerocurrent. I c E wf ( f, q ) corresponds to field created by thewhole bunch at the location q . We use here only shieldedCSR impedance. Details are given in the Methods sec-tion.In Figure 5, we have represented the simulated evolu-tion of the electron bunch shape versus number of turnsin the storage ring. We can see that this type of rep-resentation can be used directly for performing severetests of theoretical model versus experimental data. Inour case, we can see that the model can reproduce partof the spatio-temporal features, as e.g., structures mov-ing towards the bunch head, and bunch tail. Evolution T H z de t e c t o r ( V ) Numbers of round-trips01234567 W a v enu m be r ( c m - ) -2 -1 T i m e ( p s ) -0.0400.04 E O S s i gna l ( V ) E O S s i gna l ( V ) Time (ps) 01020304050 T i m e ( p s ) E O S s i gna l ( V ) T i m e ( p s ) Numbers of round-trips -0.06-0.0300.030.06 E O S s i gna l ( V ) (b)(c)(d)(f)(a)(e) Figure 4.
Simultaneous recording of the electron bunch shape at each turn and associated emission of coherentsynchrotron radiation (CSR). (a) single-shot recording of an electron bunch shape that passes near the detection electro-optic crystal (electric near-field recorded using time- stretch electro-optic sampling). Red: electro-optic signal (over the 0-250 GHz bandwidth). Green: high frequency part between 90 and 250 GHz. Blue: low frequency part below 80 GHz. (b,c,d)
Single-shot bunch shapes versus turns in the storage ring: (b)
Total electro-optic sampling signal (unfiltered), (c) and (d) :high frequency part (90-250 GHz) revealing the microbunching structure [ (c) is a zoom of (d) ]. (e) Power spectrum of eachbunch shape versus turn number. (f )
Emitted coherent synchrotron radiation recorded simultaneously at the KARA infraredbeamline using a THz diode detector (the pulse height is represented at each turn). Note the correlation between the increasein coherent synchrotron radiation emission in (f ) and the spontaneous formation of microstructures (d,e) . versus number of turns also reveals interesting discrep-ancies between model predictions and experimental data.These types of measurements should allow in due courseto refine the models of the wakefiels created by each elec-tron (whose Fourier transform is known as the machineimpedance ).In conclusion, we present a strategy enabling a simul-taneous measurement of the “shape” of electron bunchesin a non-destructive manner at each turn in a storagering, by monitoring their electric fields. This new mea- surement possibility enables to directly observe the corre-lation, at each turn, between the charge modulation andthe underlying coherent synchrotron radiation emission,and was predicted for storage rings more than a decadeago [18, 19]. This type of strategy will enable to startvery stringent tests of theoretical models of relativisticelectron bunch dynamics, that were not possible before.We believe that this direct access to the microbuchinginstability and coherent synchrotron radiation propertiesmay provide an important milestone on the way to mas- T i m e ( p s ) (a) 0.00.10.220020 T i m e ( p s ) (b) 0.00.10.220020 T i m e ( p s ) (c) 0.030.000.039000 9500 10000 10500 11000Number of turns0.00.51.0 T H z p o w e r ( a r b . un i t s ) (d) Figure 5.
Numerical simulation of the electron bunch dynamics. (a) and (b) electron bunch shape at each turn inthe storage ring (b) is a zoomed view of one of the bursts of (a) . (c) filtered data (in the 90-250 GHz range), revealing themicrostructure evolution. (d) Coherent synchrotron radiation emitted by the microstructure. See Figure 1 for the associatedlongitudinal density profile and phase-space at turn 9742, and Supplementary Video 1 for the corresponding phase spaceevolution. ter the instabilities, either for suppressing them, or makethem usable as a stable source of THz radiation.In a general way, needs for electron bunch shape di-agnostics are expected to address challenging questionsto the photonic community. An important (and related)open question concern the non-destructive characteriza-tion of electric field oscillations, when the time-scales arein the few to tens of microns range. This is an impor-tant question for studies of microbunching instabilitiesin lastest generation Free-Electron Lasers, and wouldrequire to perform single-shot electro-optic sampling ofmid-infrared pulses. This may represent one of the nextmilestones in the development of photonic systems des-tined to relativistic electron bunch characterization.
METHODSLaser system
The 1030 nm probe pulses are produced by amode-locked ytterbium-doped fiber laser, operating at 62.5 MHz, and synchronized on the RF reference of theKARA storage ring. An acousto-optic pulse picker selects3 pulses per turn in the storage ring. The pulses are com-pressed and then amplified in a polarization-maintainingytterbium-doped fiber parabolic pulse amplifier [43]. Theoutput pulses have a typical bandwidth of 80 nm FWHM.
Near-field electro-optic sampling setup
The laser pulses are then transported in a 35 m-longpolarization maintaining fiber to the electro-optic mea-surement system installed in the storage ring. Thanksto a Treacy compressor placed before the fiber, outputpulses can be adjusted in the few tens of ps range. Theelectro-optic sampling is performed by an 5 mm-long GaPcrystal placed inside the vacuum chamber, above the elec-tron beam. The crystal can be moved towards the elec-tron beam orbit and was placed – for the data shown –at a distance of ≈ Amplified photonic time stretch system
The modulated chirped laser pulses are first amplifiedusing a home-made ytterbium-doped fiber preamplifier,and then stretched by propagation in a 2 km-long single-mode fiber (Corning HI 1060). The fiber’s output is thensplit using a thin-film 3 dB splitter (see Figure 3), andthe two ports are delayed by exactly one repetition pe-riod of the mode-locked laser (16 ns). Thus a reference(i.e., unmodulated) laser pulse is subtracted from thelaser pulse which carries the ultrafast modulation usingthe balanced photodetector. The balanced photodetectoris an InGaAs amplified photoreceiever (DSC-R412 fromDiscovery Semiconductors), with a 20 GHz bandwidth.The photoreceiver specifications for gain and noise are2800 V/W and 40 pW/ √ Hz (both being specified at1550 nm). The precise delay and relative power levelsbetween the two photodetector inputs are adjusted usingan adjustable delay line and a variable optical attenuator.Data are recorded using a Lecroy Labmaster 10 Zi oscil-loscope (with an – overdimensioned – 30 GHz bandwidthand 80 Gs/s acquisition rate), and the acquired data arenumerically low-passed filtered at 5 GHz before signalanalysis (corresponding to 380 GHz at the electro-opticcrystal location).Each recorded pulse is a replica of the electric field inthe near-field of the electron bunch, which is “stretchedin time” by a factor M = 75 .
8. In other words, 1 ns atoscilloscope input corresponds to 13.2 ps at the electro-optic crystal. The oscilloscope’s 80 gigasamples/s ac-quisition rate corresponds to an effective sampling rateof 6.06 terasamples/s. The post-processing filtering to5 GHz corresponds to an input analog bandwidth limi-tation of 380 GHz.
Data processing
At each turn in the storage ring, three consecutivepulses are emitted by the laser, and only the last oneinteracts with the electron bunch near-field. Thus, atturn n , the balanced detector signal contains four pulses:(i) the raw balanced EOS signal V EOSn ( t ), (ii) a referencebalanced signal without EOS modulation V REFn ( t ), andtwo saturated pulses corresponding to unbalanced pulses(see supplementary Figures 1-2). The EOS signal rep-resented here corresponds to V EOSn ( t ) − V REFn ( t ). Thespectra of the EOS signal (as in Figure 4e) show that areasonable signal-to-noise ratio is observed up to 5 GHzbandwidth (i.e., 380 GHz at input). Hence raw data werefirst low-pass filtered at 5 GHz, before data analysis (i.e., a 5 GHz oscilloscope would be sufficient for the presentrecording). Then we proceeded to further filtering forexamining the different parts of the spectra. In particu-lar, high frequency structures of Figs. 4c,d (and the greencurve in Fig. 4a) are obtained by filtering the data in the1.19 GHz-3.30 GHz band (i.e., 90-250 GHz at the input).Unfiltered data are represented in Fig. 4b.The electro-optic sampling signals (as represented inFig. 4a-e) hence represent the electric field evolution,multiplied by the laser pulse shape, (see Supplementarymaterial for the signal details). Coherent sychrotron radiation analysis
The THz pulses are detected at KARA’s IR1 infraredbeamline, using an amplified 140-220 GHz Schotty bar-rier diode detectector (Virginia Diodes Inc. WR5.1ZBD)connected to a 6 GHz oscilloscope (Lecroy SDA760ZI-A).Figure 4e represents the recorded detector pulse heightversus revolution number.
Accelerator parameters
The results presented in this article are performed insingle bunch operation, at E = 1 .
287 GeV energy, for acurrent I = 1 .
625 mA, an acceleration voltage of 1500 kVand a momentum compaction factor of α = 0 . × − .The storage ring revolution frequency is 2.716 MHz. Numerical simulations
Numerical simulations have been performed using thesemi-Lagrangian scheme [50], and the shielded CSRwakefield as in Refs. [37, 41]. Calculations have beenmade and cross-checked using two independently devel-oped codes. One code is a parallel implementation of theWarnock scheme [50] using MPI (Message Passing Inter-face), and the other code is INOVESA which has beendeveloped by the KIT group [51]. Figure 5 is providedby the first code, parameters are summarized in the Sup-plementary material.
Data availability
The data that support the findings of this study areavailable from the corresponding author upon reasonablerequest.
ACKNOWLEDGMENTS
This work has been supported by the German Fed-eral Ministry of Education and Research (contract no.05K16VKA) and by the Initiative and Networking Fundof the Helmholtz Association (contract no. VH-NG-320).On the PhLAM side, the work has been supported by theMinistry of Higher Education and Research, Nord-Pas deCalais Regional Council and European Regional Develop-ment Fund (ERDF) through the Contrat de Projets ´Etat-R´egion (CPER photonics for society), and the LABEXCEMPI project (ANR-11- LABX-0007). This workwas performed using HPC resources from GENCI-IDRIS(Grants i2015057057, i2016057057, A0040507057).
AUTHOR CONTRIBUTIONS
Main project management has been peformed by ASM.The association of the EOS system with photonic time-stretch has been developed by NH, EBlo, SF, EBru,MJN, GN, PS, MS, JLS, SW, and ASM on the EOS side. The amplified time-stretch readout has been devel-oped by CE, ER, CS, SB. Time-stretch data analysis hasbeen performed by CS and CE. Measurement of the THzradiation has been performed by JLS and MB. EBlo andMS prepared the KARA fill with low-alpha optics. Nu-merical simulations have been performed by EBur, PS,CE, SB, and simulation code development by ER, CE,SB (MPI implementation of the Warnock scheme), andPS (INOVESA code). All authors participated in themanuscript redaction.
COMPETING INTERESTS
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