N Blanchot

G Béhar

J C Chapuis

C Chappuis

S Chardavoine

J F Charrier

H Coïc

C Damiens-Dupont

J Duthu

P Garcia

J P Goossens

F Granet

C Grosset-Grange

B. HEBRARD P Guerin

L Hilsz

L Lamaignere

T Lacombe

E Lavastre

T Longhi

J Luce

F Macias

M Mangeant

E Mazataud

B Minou

T Morgaint

S Noailles

J Neauport

P Patelli

E Perrot-Minnot

C Present

B Remy

C Rouyer

N Santacreu

M Sozet

D Valla

F Laniesse

.15 PW-850 J compressed beam demonstration using the PETAL facility

The Petawatt Aquitaine Laser (PETAL) facility was designed and constructed by the French Commissariat à l'énergie atomique et aux énergies alternatives (CEA) as an additional PW beamline to the Laser MegaJoule (LMJ) facility. PETAL energy is limited to 1 kJ at the beginning due to the damage threshold of the final optics. In this paper, we present the commissioning of the PW PETAL beamline. The first kJ shots in the amplifier section with a large spectrum front end, the alignment of the synthetic aperture compression stage and the initial demonstration of the 1.15 PW @ 850 J operations in the compression stage are detailed. Issues encountered relating to damage to optics are also addressed.

Introduction

The invention of optical pulse compression with diffraction gratings by Treacy [START_REF] Treacy | Optical pulse compression with diffraction gratings[END_REF] and the advent of the Chirped Pulse Amplification (CPA) technique in 1985 [START_REF] Strickland | Compression of amplified chirped optical pulses[END_REF] paved the way to ultra-high intensity large laser facilities devoted to the study of light-matter interactions. Since the end of the nineties, several ultra-high intensity systems have been built and commissioned around the world as upgrades of older systems or new facilities to reach the PW [START_REF] Danson | Petawatt class lasers worldwide[END_REF]. The Petawatt Aquitaine Laser (PETAL) beamline has been designed and constructed by the French Commissariat à l'énergie atomique et aux énergies alternatives (CEA) to deliver laser pulses in the kJ-picosecond range at a wavelength of 1053 nm [START_REF] Blanchot | Overview of PETAL, the multi-Petawatt project in the LMJ facility[END_REF]. PETAL will allow for experiments in the field of ultrahigh intensity sciences, extreme plasma physics, astrophysics, radiography, and for fast ignition by a combination of its own multipetawatt kilojoule beam and the nanosecond multikilojoule beams of the Laser Megajoule (LMJ) [START_REF] Batani | Development of the PETawatt Aquitaine Laser system and new perspectives in physics[END_REF][START_REF] Miquel | The Laser Mega-Joule: LMJ & PETAL status and Program Overview[END_REF]. The PETAL beamline hence joins kJ-ps range, Petawatt to multi-Petawatt facilities such as OMEGA-EP [START_REF] Waxer | High-energy petawatt capability for the OMEGA laser[END_REF], LFEX [START_REF] Kitagawa | Prepulse-free petawatt laser for a fast ignitor[END_REF][START_REF] Miyanaga | Precision performance for full-scale operation of LFEX PW laser[END_REF] or NIF-ARC [START_REF] Barty | An overview of LLNL high-energy short-pulse technology for advanced radiography of laser fusion experiments[END_REF]. In this paper, we present the laser commissioning of the PETAL beamline and its main current performances. In particular, we detail the front-end performance ( front end (Se compression compression s powerful sing vacuum optic applied to imp the laser oper will be reache

Front-end

The front-end stages pumpe temporal shap pulses at a w reflective Öff amplifier sect pump pulse i OPA gain and The saturation amplified sign the beam is s diffusion [START_REF] Dorrer | Design and analysis of binary beam shapers using error diffusion[END_REF] aperture beam energy of the

Amplifier

The PETAL a µm. The amp (Section 2), the ection 3), and scheme (Sect stage performe gle beams in o cs operating in prove this dam ration due to th ed when workin d performanc d of PETAL [F ed by a 4.5 ns, ping. A seed p wavelength of fner system. To tion, the 16 nm s then signific d spectral narro n of the param nal of 4.5 ns @ shaped using a ] is then used m into a squar front-end injec on (OPA) th spationg 100 fs nd an alleeding the 9 ns. The the large neglected. elivers an g. Finally, sing error he 4 subeme. The h of 1.053 r section, however the 4x2 beams amplifier section mechanical structure of the LMJ is modified to handle a single beam (37.1 x 35.6 cm 2 ). The architecture comprises a four-pass system with angular multiplexing and a reverser [Fig. 3]. It uses 16 amplifier laser slabs arranged into two sets. The front-end pulse is injected into the transport spatial filter, passes into two amplifier groups separated by the cavity spatial filter, bounces off the M1 deformable mirror, and passes through the 16 slabs a second time. The beam is then reflected off the Mdt1 mirror, enters the reverser, reflects off the M2 mirror and goes back to M1 to exit the amplifier section after L4, the last transport spatial filter lens.

The two sets of amplifiers can accept up to 9 slabs. For 6.4 kJ operations, only 16 slabs are required. Therefore, PETAL uses 7 (cavity amplifier) and 9 (transport amplifier) Phosphate Nd:glass slabs, 8 from HOYA (LHG-8) and 8 from SCHOTT (LG-770) to optimize the spectral bandwidth taking benefit of the small fluorescence peak difference (0.4 nm). These spatial filters (pair of refractive lenses) are used to clean the beam of unwanted intensity modulations at high spatial frequencies and also to extend and/or to image the spatial profile for each amplifier stage. As glass index depends on wavelength, when a polychromatic light goes through a refractive lens, this light is focused in multiple foci along the lens axis, each corresponding to a given wavelength. This aberration is known as longitudinal chromatic aberration or Pulse Front Curvature. This chromatic aberration is equivalent to a delay in the time domain and the addition of the delays induced by traversing the various lenses of the Amplifier Section (equivalent to 1520 fs) will prevent the system from reaching sub-picosecond compression if uncorrected. We have consequently fitted a chromatism corrector [START_REF] Néauport | Chromatism compensation of the PETAL multipetawatt high-energy laser[END_REF] in the reverser. This chromatism corrector (CROCO) uses a diffractive Fresnel lens with a focal length of 2.523 m, in combination with a divergent refractive lens allowing for a correction of -1520 fs.

The amplifier section was commissioned in two steps. The first step was performed with an LMJ front-end delivering monochromatic pulses and a full aperture, to qualify the gain of the different slabs in the single-beam configuration. The second step was performed with the PETAL front end (large spectrum and sub-aperture beam) to study the effect of spectral gain narrowing and observe the evolution of the sub-aperture beam profiles.

Monochromatic commissioning demonstrated energy of 4.9 kJ in 5 ns, corresponding to LMJ pulse duration operation. To remain within the range of PETAL in terms of pulse duration and energy, 1.9 kJ in 1.7 ns was qualified.

Large spectrum commissioning demonstrated energy of 1.4 kJ in 2 ns with a 3.5 nm spectral bandwidth and a sub-aperture shaped beam. The decrease in pulse duration is due to spectral gain narrowing in the Nd:glass amplifiers. This output energy value corresponds to the current operating point since 1.4 kJ corresponds to 1 kJ after compression. This is the maximum energy level we can compress due to the damage threshold after the compressor. This large spectral bandwidth was commissioned with 13 slabs, to limit the energy stored in the amplifiers corresponding All the sh figures. The f which allowe 2D-gain profi Commissioning results with a sub-aperture beam are presented in Fig. 6 with the evolution of the temporal and spatial profiles for the 1.15 PW shot. 14 slabs were used to amplify the beam from 20 mJ to 1240 J. These commissioning processes have indicated [Fig. 7] that the holes in the beam are affected neither by the ASE in the amplifiers nor by amplification saturation. We observe a deformation of the spatial profile along the sub-apertures due to the amplifier gain. A new phase plate has been designed to compensate for this shape and will be implemented in PETAL for future shots to obtain a top hat spatial profile and extract more energy for the same maximum fluence.

Compression performance

Compression scheme

The PETAL compressor scheme [START_REF] Blanchot | Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers[END_REF] is based on the coherent addition of beams instead of grating mosaic phasing. The initial beam is divided into sub-apertures, which are independently compressed and synchronized with classical (micrometric range) precision. Finally, these sub-apertures are coherently combined using only one segmented mirror with three interferometric displacements for each sub-aperture. To limit the volume of the vacuum compressor, compression is applied in two stages [Figs. 8 and9]. First, a compressor in air reduces pulse duration from a few nanoseconds to a few hundred picoseconds in an unfolded double pass compression configuration (gratings G11, G12, G13 and G14). The relatively long pulse duration allows for the use of 83 cm monolithic gratings by decreasing the grating incidence angle. Second, a compressor in a vacuum finalizes the compression of the pulse down to a duration of 500 fs. The second compression stage is designed with a small compression factor to limit transverse chromatism in a single-pass configuration. This allows us to consider this compressor as four independent units, each one addressing one subaperture. Each independent compressor (G21/G22, G23/G24, G25/G26 and G27/G28) may even have different characteristics such as groove density or incidence angle. Finally, a segmented mirror between the two compression stages compensates the spatial phase shift induced by the separation of the gratings in the final compressor. The first compressor has a groove density of 1680 g/mm, an incidence of 56° and a grating distance of 2.62 m. The second compressor has a groove density of 1780 g/mm, an incidence of 77.2° and a grating distance of 2 m. The transmission is 81% for the first stage of compression and 91% for the second stage.

Compression diagnostics

All compression diagnostics are performed after a pair of leaky mirrors, MT5 (transport mirror #5) and MT5bis [Figs. 8 and9]. These 2 mirrors have 3 configurations: shot on target ( + 45°, -45°), shot on the compression calorimeter (-45°, + 45°), and alignment ( + 1°, -1°). These configurations allow for transmission to be adjusted while maintaining the same beam centering. MT5 has 0.16% transmission at an incidence of 45° and more than 60% at 0°. MT5bis has 3% transmission at 45° and more than 60% at 0°.

Spatio-temporal effects are some of the key issues for the ultra-high intensity beam [START_REF] Walmsley | Characterization of ultrashort electromagnetic pulses[END_REF][START_REF] Pariente | Space-time characterization of ultra-intense femtosecond laser beams[END_REF]. Therefore, many efforts were made in terms of image relay and beam propagation prior to the diagnostics. A diffractive lens is used to compensate for longitudinal chromatism in the diagnostic pickup and the beam is imaged in the different diagnostics. Multiple characteristics of this attenuated beam are measured on the compression diagnostics table (TDC): the near field, the far field, the pulse duration with a second order autocorrelator, the spectrum, the spectral phase with a SPIRITED [START_REF] Bigourd | Direct spectral phase measurement with spectral interferometry resolved in time extra dimensional[END_REF], spectral phase differences and the synchronizations between sub-aperture pulses with a 2D spectral interferometer (2D-SI) [START_REF] Blanchot | Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers[END_REF] and the relative energy. An absolute calorimeter for energy (RECO) is installed in a specific vacuum box to calibrate the relative energy. All diagnostics can be performed in single-shot operation.

The 2D-SI [START_REF] Blanchot | Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers[END_REF] uses a bi-prismatic plate, a cylindrical lens for one-direction focusing along the slit axis (vertical axis), and a spectrograph with a 0.05 nm spectral resolution. The temporal delay between the sub-apertures is visually deduced and precisely adjusted by analysing the interference pattern using a 1D-Fourier transform along the slit axis. Moreover, a visual 2D-SI pattern observation allows the differential spectral phase shift to be quantified and qualified: delay, chirp difference between sub-apertures, temporal distortion and also residual unwanted dispersion.

Figure 10 shows the 2D-SI for the full beam, with 4 sub-apertures corresponding to the 4 independent compressors of the second stage of compression. In the first image, sub-apertures are not synchronized, therefore we observe a complex system of vertical fringes. After adjusting the grating distances of the 3 sub-apertures to be synchronized, we observe only one system of vertical fringes, which corresponds to one independent compressor not synchronized with the 3 others. By finally adjusting the distance of this 4th independent compressor, we suppressed the last vertical fringes. A small curvature (SMILEY) was observed in the horizontal fringes due to residual chirp difference, horizontal fringes are due to the bi-prismatic plate.

Compressor alignments

First, each grating in the compressors (1st and 2nd stages) is pre-aligned with a monochromatic alignment laser to adjust the parallelism of the face and the grooves. The oscillator (16 nm and 77.76 MHz) from the front end is then used to precisely correct all residual angular dispersions (groove parallelism, grating face parallelism, groove density mismatch and longitudinal chromatism) [START_REF] Blanchot | High precision alignment of PW compressor system for kJ-PW class laser[END_REF][START_REF] Fiorini | Temporal aberrations due to misalignments of a stretcher-compressor system and compensation[END_REF].

The sub-aperture PETAL compression scheme requires a specific alignment procedure. Indeed, the second stage is equivalent to 4 independent compressors that must be compressed and synchronized. The sub-aperture synchronization cannot be adjusted with the segmented mirror, its correction range in delay is too limited.

Since the compression is optimized (pulse duration) with a few 100 µm of grating distance adjustments and synchronization (precision 50 fs) is achieved with a few 10 µm, the PETAL compressor can be optimized in 3 steps:

• Step A: optimization of the 4 independent compressors with the second order autocorrelator. At this step, the sub-apertures have time delays T D between each other. Vertical fringes are observed on the 2D-SI [START_REF] Blanchot | Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers[END_REF] due to the delay between subapertures [Fig. 11(a)];

• Step B: one sub-aperture is taken as a reference and a second compressor is synchronized (T D = 0) with this reference by adjusting the grating distance δL B using the 2D-SI measurement for these 2 sub-apertures. At this step, the second compressor is no longer compressed due to the grating distance displacement. A SMILEY is observed on the 2D-SI due to residual chirp [Fig. 11(b)];

• Step C: starting from step A, the gratings of the second compressor are tilted to an angle Δi C and the grating distance changed by δL C to compensate for both the delay and the chirp. Only horizontal fringes are observed on the 2D-SI due to the bi-prismatic plate [Fig. 11(c)]. Using the second stage compressor characteristics (N = 1780 g/mm, i = 77.2°), the adjustment of each independent compressor is given by the following equations [START_REF] Blanchot | High precision alignment of PW compressor system for kJ-PW class laser[END_REF][START_REF] Fiorini | Temporal aberrations due to misalignments of a stretcher-compressor system and compensation[END_REF]:

( ) ( ) 2.71 C B L m L m δ μ δ μ = ⋅ (1) ( ) ( ) 0.26 C B i rad L m μ δ μ Δ = ⋅ ( 2
)
Figure 11 shows the 2D-SI results observed in the 3 alignment steps with compensation of residual chirp difference while maintaining synchronization. A small global residual chirp may persist after these 3 steps. This global chirp is then suppressed using a monolithic grating in the 1st stage of compression to correct the 4 subapertures at the same time. This fine adjustment is measured using the SPIRITED [START_REF] Bigourd | Direct spectral phase measurement with spectral interferometry resolved in time extra dimensional[END_REF].

Experimental results to demonstrate a peak power of 1.15 PW

Compression

Compression can be optimized by changing the grating distances of each independent compressor. Pulse duration is measured with a second order autocorrelator. Figure 12 shows the autocorrelation between the 4 independent compressors on a 219 J shot with a pulse duration between 540 fs and 570 fs for a 3 nm spectral bandwidth. Fig. 12. Autocorrelation plots for a 219 J @ 3nm shot and pulse durations at FWHM.

Synchronization of sub-aperture pulses with compression maintained

Figure 13 presents the experimental results obtained for 2 independent compressors (G25/G26, G27/G28) by taking compressor G23/G24 as a reference. First, the 2D-SI measurements [Fig. 13(a)] give SMILEY at best synchronization, which is an indication of residual chirp difference. The formula given by Eq. ( 1) and Eq. ( 2) are used to correct this chirp difference and to maintain synchronization [Fig. 13(b)]. The improvements for autocorrelation plots are shown in Figs. 13(c) and 13(d). The 2D-SI is more precise (interferometric precision Δφ 2nd order (ω) << 2π) to optimize the relative chirp between independent compressors than the second order autocorrelator. Moreover 2D-SI has the advantage to allow measurement with the oscillator pulse train instead of the mJ front-end pulse (1 shot / 4 min). Synchronization better than +/-50 fs between sub-apertures could be obtain thanks to this 2D-spectral interferometer.

1.15 PW shot

During the first PW campaign in may 2015, the measurements on the TDC was biased by Kerr effect due to the propagation in the diagnostic pick-up and by an imperfect relay imaging on the diagnostics. All these points are now improved [Fig. 12]: imaging systems are under vacuum, near fields are imaged on diagnostics, energy on the TDC is limited to 3 mJ (15 mJ on the 1.15 PW shot). Moreover, we have decided to completely model the diagnostics using Miró code to take into account the residual Kerr effect and the spatiotemporal effects on measurements. This point is crucial since the maximum peak power is less than the direct ratio of the energy divided by the pulse duration deduced from the autocorrelation measurement.

Before the maximum energy shot, we delivered a front-end shot [Figs. 14 and 15] to validate the compression performance (400 fs for the 8 nm supergaussian profile). The input for Miró simulations come from experimental measurements of the beam at the amplifier section injection (spatial, temporal, spectral profiles). We find a quite good agreement between the experimental results and the simulations. The Miró code allows us to add the residual synchronization of the sub-apertures [Fig. 15(d)] to estimate the pulse duration with more accuracy. The 1.15 PW shot was then run with the activation of 14 slabs in the amplifier section. These 14 slabs amplify energy from 20.3 mJ @ 4.3 ns up to 1.24 kJ @ 3.7 nm. The experimental and associated simulated profiles are shown in Figs. 16 and17. We observe a Kerr effect on the measurements and on the simulations due to the level of energy injected at TDC, 15 mJ instead of 3 mJ (value for optimal diagnostics). The duration of the compressed pulse, with synchronization, is equal to 700 fs for an energy level of 850 J, corresponding to 1.15 PW. Energy is measured using the RECO calorimeter. Moreover this shot was also measured with a damaged leaky mirror [Fig. 18(a)] inducing a reflection decrease of 8.8% for the calorimeter. Hence, the real energy on this shot was 925 J instead of 850 J, which corresponds to 1.25 PW.

Damage issues

Visual inspections were carried out during the PETAL beamline commissioning process to check for potential laser damage. Pulse compression gratings and the MT5 leaky mirror after were pictured after compression using observation windows located in the vicinity of these optical components. We particularly focused on leaky and transport mirrors. Pulse compression gratings are used at a 77.2° incidence while mirrors operate at 45°. The latter are therefore likely to be the first to exhibit laser damage, the beam size on the component surface is 3 times higher for the gratings due to the incidence angle.

Initial damage was detected on the MT5 leaky mirror above a power of approximately 0.8 PW (F max ≈ 1.3 J/cm 2 , in beam normal) during the first PW campaign where the MT5 was oriented using the RECO calorimeter and no damage was observed for gratings. Damage occurred at a relatively low energy level due to both the excessive beam spatial modulations and a non-optimized early coating design. We then first worked on the mirror coating design. We also decided to test the transport mirror MT6 (transport mirror next to MT5). To this end, the MT6 component was placed in the MT5 position. Figure 18 shows the damage pattern observed for these optical components. Rather large areas of each sub-aperture exhibit damage morphology typical of intrinsic material damage, suggesting that the mirror damage threshold was locally exceeded. Moreover, the high spatial frequency patterns observed in Fig. 18 are likely to be induced by the diffraction gratings and their manufacturing process.

Based on these results, we modified the coating design to enhance the laser induced damage threshold (LIDT) of the mirror while maintaining the same reflectivity. This basically involves reducing the electric field in the first layers of the coating by changing the stack design. The LIDT of samples representative of both the early and the updated design were damage tested using both a 1:1 damage procedure [23] and a mono-shot protocol using the DERIC damage tester [START_REF] Sozet | Assessment of mono-shot measurement as a fast and accurate determination of the laser-induced damage threshold in the sub-picosecond regime[END_REF]. Two improvements were revealed, for example, for the MT5 leak mirror, raising the LIDT from 1.7 J/cm 2 to 3.7 J/cm 2 at 1.053 µm, 770 fs, 45°, S-pol in the beam normal. The MT5 leaky mirror was consequently replaced with a mirror coated with this updated design and used in the next commissioning steps. A visual inspection after a 1 PW shot on the MT5 leaky mirror confirmed the trend observed for samples. As seen on Fig. 19, the mirror is now sustaining this high intensity. A complete optical inspection was performed in the metrology lab on the MT6 early design mirror after replacement. This inspection confirmed that most damage was intrinsic, with damage sites growing during successive laser shots [START_REF] Sozet | Study of the laser damage growth on components for high power[END_REF]. Nevertheless, sparse localized coating defects, induced damage, were also observed. Their morphology is similar to that already seen on mirror samples and these are also growing sites, as reported elsewhere [START_REF] Sozet | Laser damage growth with picosecond pulses[END_REF]. While the intrinsic damage threshold can be measured with a 1:1 damage testing protocol, coating defect induced damage (which remained well below the 1:1 threshold) is measured using a raster scan testing protocol [START_REF] Sozet | Laser damage density measurement of optical components in the sub-picosecond regime[END_REF]. Both intrinsic threshold and damage density must be improved to reach the multi-PW regime.

Finally, we report that during the beamline commissioning process, we observed very few localized damage sites on the pulse compression gratings. The high incidence of the gratings used in the PETAL compressor is very favorable in terms of damage resistance compared to mirrors.

Damage to optics can be induced by inadequate design or a local initiator. Beam spatial quality also has to be improved to reach a higher intensity. Knowledge of the uniformity of the beam profile, beam modulations and beam size must be improved.

All of these contributions are options in order to reach the 2 PW target.

Fig. 2 .

 2 Fig. 2. r section perf amplifier sectio plifier section

Fig. 1

 1 Fig. 1. Fron

Fig. 3 .

 3 Fig. 3. Amplifier section scheme.

  Fig. 4 activa simula The next f Gaussian fron shots into acc 14 nm Lorent (LHG-8 or LG with fewer sla the spectrum amplifier sect Lorentzian [1 fluctuation (s with the preci

  Fig. 5 activa and lin

Fig. 6 .

 6 Fig. 6. Sub-apertures beam amplification up to 1.24 kJ.

Fig. 7 .

 7 Fig. 7. Profiles of the injected and the amplified beam.

Fig. 8 .

 8 Fig. 8. Implementation of the compression stage and diagnostics table (TDC); MT5 and MT5bis are drawn in target shot configuration.

Fig. 9 .

 9 Fig. 9. 1st stage of compression in air (left), 2nd stage of compression in the vacuum vessel (center) and compression diagnostics table (right).

Fig. 10 .

 10 Fig. 10. 2D-spectral interferometry with 4 non-synchronized sub-apertures (a), 3 out of 4 subapertures synchronized (b), all sub-apertures synchronized (c).

Fig. 11 .

 11 Fig. 11. Step A: 2D-spectral interferometry with 4 non-synchronized sub-apertures (a), Step B: observation of a SMILEY after synchronization of G23/G24 pulse with G25/G26 (b), Step C: reduction of the SMILEY with changes of incidence angle and grating distance of G25/G26 (c).

Fig. 13 .

 13 Fig. 13. (a) 2D-SI with the residual chirp; (b) 2D-SI after modifications of gratings angle and grating distance; (c) and (d) 2nd order autocorrelation traces corresponding to (a) and (b).

Fig. 14 .

 14 Fig. 14. Spatial experimental (top) and simulated (bottom) profiles for the front-end shot.

Fig. 15 .

 15 Fig. 15. Experimental (a, b) and simulated (c) 2nd order autocorrelation plots at TDC, simulated energy front profile at the output of the compressor (d) and peak power (e) for the front-end shot

Fig. 16 .

 16 Fig. 16. Spatial experimental (top) and simulated (bottom) profiles for the 1.15 PW shot.

Fig. 17 .

 17 Fig. 17. Experimental (a, b) and simulated (c) 2nd order autocorrelation plots at TDC, simulated energy front profile at the output of the compressor (d) and peak power (e) for the 1.15 PW shot.

Fig. 18 .

 18 Fig. 18. MT5 leaky mirror, early design, after a 572 J, 700 fs shot May 2015 (a) MT6 transport mirror, early design, after a 1004 J, 1 ps shot, October 2015 (b). Damage to sub-apertures (red arrows)

Fig. 19 .

 19 Fig. 19. MT5 leaky mirror with updated design (a) and pulse compression grating after a 1 PW shot (1030 J, 1 ps) (b). October 2015. No damage observed visually.

Vol. 25, No. 15 | 24 Jul 2017 | OPTICS EXPRESS 16963

Funding

This work is being performed by the Commissariat à l'énergie atomique et aux énergies alternatives under the financial auspices of the Aquitaine Region in France (project owner), the French Government and the European Union.

Summary

The PETAL beamline was commissioned over a 2-year period up to the end of the compressor stage. During this commissioning process, the amplifier section demonstrated its ability to deliver energy up to 5 kJ and a spectral bandwidth up to 3 nm, compatible with 500 fs operation. Spatial beam shaping was managed with a phase plate in the front-end to create the 4 sub-apertures required for the compression stage. This beam shaping process is not affected by the ASE during the high energy amplification process. A PW campaign was then carried out on the PETAL beamline in May 2015. A 1.15 PW shot was obtained with 700 fs pulse duration and 850 J energy at the output of the PETAL compressor. Attention was paid to the compressor alignment, on beam pickup and during diagnostics to limit non-linear and spatio-temporal effects. Full-scale optics (transport mirrors in particular), visual monitoring and sample damage testing indicated that the first transport mirror design was limited to 1.7 J/cm 2 . The new coating design with a damage threshold of 3.7 J/cm 2 has been validated in transport allowing for the future transport of 1 kJ in the target chamber. Furthermore, works are in progress to optimize the spatial beam profile to obtain a more uniform beam.


Reza Vosooghi

Jakob Puchinger

Marija Jankovic

Göknur Sirin

A Critical Analysis of Travel Demand Estimation for New One-Way Carsharing Systems

Keywords: Carsharing, Shared Autonomous Vehicle, Shared Mobility, Free-floating, Station-based, Travel demand estimation, Agent-base simulation, Autonomous Mobility-on-Demand, Shareduse vehicle systems

Technologic advancements have contributed to the spread of sharing economy concepts, a developing phenomenon that favors the shift from private mobility to service-use (shared mobility). One-way carsharing is a most recent and popular kind of shared mobility, that is growing and developing rapidly in various forms. These systems are considered to have a transformative impact on future urban transportation. Despite all of the benefits that have been reported from the use of new one-way carsharing (e.g. Autonomous Mobility-on-Demand systems), their impacts on the mobility are not certain yet. This comes from the fact that in such services supply and demand influence each other in a significant way in short-, mid-, and long-term. Also service characteristics at the level of each vehicle strongly affect the demand. In this paper methods, paradigms, toolkits and platforms used in the literature for the demand estimation of the new one-way carsharing systems, as well as their potential drawbacks are discussed. A review of the literature reveals that despite the considerable number of studies related to balancing vehicle stocks across stations in one-way systems, the investigation about demand estimation of such services for which the complex relationship between supply and demand is considered, remain very limited. The majority of current platforms and toolkits used for demand estimation of new one-way carsharing systems are based on activity-based multi-agent simulations. In these simulations several main components are not yet taken into account, which could dramatically change the results. Data detail, accessibility and reliability, high computational time, calibration and validation still remain major challenges for travel demand estimation for one-way carsharing systems.

I. INTRODUCTION

In the last years the growth of service-oriented transport alternatives is shifting the private mobility from ownership to service access/use. Carsharing is one of the first concepts for such alternatives, introduced for the first time in Switzerland in the middle of 20th century and gained worldwide popularity in the 1990s [START_REF] Shaheen | Carsharing in Europe and North America: past, present, and future[END_REF]. Developing the strategy for enabling users to gain short-term access to any other conventional private modes (such as bicycle) results gradually in the increase of popularity of "shared-use vehicle systems". Nowadays car producers are also directly involved in vehicle-sharing operations with the scope of finding new channels to market the produced cars and to gain the financial benefits of new car rental service systems [START_REF] Ferrero | Car-sharing services -part A taxonomy and annotated review[END_REF].

Technologies including social networking, location-based services, the Internet, electric vehicles, keyless vehicle access, invehicle and mobile global positioning system (GPS) receivers have played a major role in the growth of carsharing over time [START_REF] Shaheen | Shared mobility: current practices and guiding principles[END_REF]. Due to the development of technologies related to automated vehicle, it is expected that next generation of carsharing systems will be based upon these vehicles [START_REF] Litman | Autonomous vehicle implementation predictions implications for transport planning[END_REF], [START_REF] Fagnant | Preparing a nation for autonomous vehicles: opportunities, barriers and policy recommendations[END_REF]. Shared autonomous vehicles (SAVs) have the potential to take over a significant amount of traffic handled nowadays by conventionally driven vehicles, especially taking in consideration that these new services could potentially be integrated with public transportation by solving the "last mile problem" [START_REF] Shaheen | Autonomous carsharing / taxi pathways[END_REF]. In addition SAVs can anticipate future demand and relocate in advance to better match vehicle supply and travel demand [START_REF] Fagnant | Operations of shared autonomous vehicle fleet for Austin, Texas, market[END_REF].

New carsharing systems are considered to have a transformative impact on many cities by enhancing transportation accessibility, increasing multimodality, changing vehicle ownership rate, and providing new ways to access services [START_REF] Shaheen | Shared mobility: current practices and guiding principles[END_REF]. To predict this impact before placing any services in operation, it is necessary to estimate the eventual travel demand. This is usually done by travel models. Travel models produce quantitative information about travel demand and transportation system performance that can be used to evaluate alternatives and make informed decisions.

The aim of this paper is to give a holistic view into the existing methods of travel demand estimation for one-way carsharing systems. We outline also the identification of appropriate platforms (travel models) to model innovative carsharing services when they are applied for a multimodal integrated transportation system. To the authors' best knowledge this paper presents for the first time a through comparison of all methods, platforms and toolkits used to estimate the demand of new one-way carsharing systems and discusses their potential drawbacks. Another important contribution of this study is the illustration of why and how activity-based multi-agent simulations are often used to demand estimation of such new systems and which limitations they have. This paper is structured as follows. Initially different types of carsharing systems are classified. Then all travel demand estimation methods for one-way services are described, as well as existing literature on this subject is reviewed. After that application of these methods is analyzed and criticized. Finally, the conclusion as a base for future work is provided.

II. CARSHARING CLASSIFICATION

Carsharing is generally defined as short-term vehicle access among a group of members who share a vehicle fleet that is maintained, managed, and insured by a third-party organization [START_REF] Shaheen | One-way carsharing's evolution and operator perspectives from the Americas[END_REF]. With respect to the operating model carsharing systems can be classified in two general types: (1) round-trip, in which users must return the car to its departing point, and (2) one-way, in which users may drop off the car to a different location from where they started [START_REF] Shaheen | Carsharing and personal vehicle services: worldwide market developments and emerging trends[END_REF]. In the last decade round-trip carsharing systems were more common, but over the last years with the important development on electric vehicles, smart phones and information technologies there has been a significant growth of one-way systems [START_REF] Shaheen | Innovative mobility carsharing outlook 2013[END_REF], [START_REF] Shaheen | Innovative mobility carsharing outlook worldwide carsharing growth continues[END_REF].

One-way carsharing systems could fall in three general types:

(1) station-based, (2) free-floating, and (3) shared autonomous vehicles (SAVs). One-way station-based carsharing provide short term car rentals enabling users to take a car from the initial station and return it to any other station. The advantages of such services include the reliability and predictability of car locations and parking, as well as the ability to reserve cars in advance. However, this comes for the price of less freedom of movement and spontaneity for members. Free-floating carsharing -where cars may be picked up by members wherever they are available and parked anywhere on the street, within the service area -has appeared afterwards. This type of carsharing is more financially attractive for short trips and allows greater flexibility [START_REF]Car share fact sheet[END_REF].

One-way carsharing present new and important operational challenges, such as vehicle rebalancing and parking management [START_REF] Shaheen | One-way carsharing's evolution and operator perspectives from the Americas[END_REF], [START_REF] Brandstätter | Overview of optimization problems in electric carsharing system design and management[END_REF]. It's expected that with autonomous vehicle technology there will be no more such challenges in the future. This is the reason why self-driving capability has the potential for more vehicles sharing, including robotaxis, and more sharing of private vehicles [START_REF] Litman | Autonomous vehicle implementation predictions implications for transport planning[END_REF]. It should be mentioned that concerning park space problem for free-floating services as the vehicle can be parked anywhere on the street, there won't be any problem related to the limitation of park space in the contrary to station-based services. But comparing to SAVs there will be more limitation for finding park space in congested areas.

Table I illustrates all types of carsharing systems. A complete classification of carsharing and more overall "shared-use vehicle systems" is described in [START_REF] Barth | Shared-use vehicle systems: framework for classifying carsharing, station cars, and combined approaches[END_REF]. One-way carsharing services are the ones in the focus of this paper. Various economic models of station-based and free-floating carsharing are under development nowadays and considerable efforts are being made for the planning of future SAVs. Thus, the estimates of travel demand for these new innovative systems turn more and more important.

III. DEMAND ESTIMATION

A. Approaches

To estimate travel demand of one-way carsharing systems several approaches might be applied depending on data availability, expected accuracy and study scale. In general, these approaches fall into three categories or better say evolutionary levels: (1) survey and analysis, (2) discrete choice modeling, and (3) agent-based simulation.

Less precise methods are based on survey and analysis. These methods are designed to produce rough estimations of potential demand and range from demand elasticity analysis (e.g. pivotpoint) to modal diversion estimation [15]. These approaches have been developed when one can have already existing data, thus hindering the prediction when it comes to new innovative systems. It is nevertheless important to take this approach into account because by coupling with regression or logit models it may be used for service membership prediction [START_REF] Kortum | Free-floating carsharing systems: innovations in membership prediction, mode share, and vehicle allocation optimization methodologies[END_REF].

The second group of methods are discrete choice models. They have been employed widely in travel demand analysis with the most common application being in the choice of travel mode, aim and destination [15]. Within this approach stated-preference (SP) surveys are also required. One of the most important parameters used in discrete choice models is travel time (indoor, waiting, etc.). The time (commonly converted to equivalent cost) is usually calculated by separate traffic simulators.

More sophisticated and common solutions for estimating the travel demand of one-way carsharing systems are agent-based transport simulations. Their roots lay on activity-based travel demand models and are commonly characterized by a similar feature [START_REF] Zheng | A primer for agent-based simulation and modeling in transportation applications[END_REF]. An agent-based simulation is developed in which travel demand emerges from the interactions of four types of agents in the transportation system: node, arc, traveler and vehicle. This approach is mostly used for demand estimation of one-way carsharing, ridesharing SAVs, and Autonomous Mobility-on-Demand (AMoD) systems.

B. Challenges

In general, three major challenges facing travel demand estimation of innovative one-way carsharing systems have been found in the literature: (1) data detail, accessibility and reliability, (2) high computational time, and (3) calibration and validation.

The most important challenge is data. As various types of these systems are not yet in operation issue-specific SP surveys are needed. Such surveys are costly and might not necessarily result in reliable and complete models. Also in order to assign travelers to the right alternative, travel needs to be modeled at the individual level with explicit modeling of the modal choice, which requires individual socio-demographic data. Likewise, in order to create a model sensitive to short-distance trips (trips in which new carsharing services are more interesting for travelers) extremely fine-grained spatial information at the parcel level is needed. All these data are not necessarily accessible and available.

A second challenge is computation time. In theory there are two major components of transportation models: travel demand (represented classically by the trip matrix) and traffic assignment (estimates the traffic flows on a network). Traffic assignments can be either static -as in most four step trip-based models (FSM) -or dynamic, as recently applied especially in activity-based models. The assignment outputs -mainly traffic volumes and travel times-in their turn are used as inputs to the travel demand models. The big challenges for coupling these two components of modeling is that the models typically compute probabilities for a large number of alternatives at the individual level, which demands an explicit choice set. To account for such alternative sets in assignment or simulation procedures for real size networks and huge number of individuals would result in very long computation times.

Finally, there is be a big challenge regarding to calibration and validation of models. For innovative one-way carsharing forms (e.g. SAVs) there are no real data on hand, so it is difficult to validate if the model runs correctly or not.

C. Application in Literature

Significant literature can be found on the topic of carsharing, especially describing how to explore the demand of real roundtrip services. Jorge and Correia [START_REF] Jorge | Carsharing systems demand estimation and defined operations: a literature review[END_REF] have reviewed all the studies where car-sharing has been modelled after 2000 and they concluded that despite the considerable number of studies related to demand modeling for round-trip systems, there is a clear predominance of studies about balancing vehicle stocks across stations in one-way systems, mainly through relocation operations performed by the company or the users. However, there are some studies concerning travel demand estimation of one-way carsharing.

Catalano et al. [START_REF] Catalano | Car sharing demand estimation and urban transport demand modelling using stated preference techniques[END_REF] estimated the potential demand for oneway car-sharing and car-pooling in Palermo, Italy. They used a SP survey for calibrating a multinomial logit model and applied it to a future scenario characterized by some transport policy actions. Kouwenhoven et al. [START_REF] Kouwenhoven | Estimating potential demand for Autolib' -a new transport system for Paris[END_REF] used SP and discrete choice modeling (IMPACT4) to estimate the potential demand for the Autolib' service (one-way station-based carsharing) in Paris. In this study service membership was modeled separately. Several other works have been done, proposing the use of spatial and temporal disaggregate models. Ciari et al. [START_REF] Ciari | Modeling one-way shared vehicle systems: an agent-based approach[END_REF] used for the first time an agent-based approach to model one-way carsharing. Their research used the open source multi-agent simulation tool MATSim [START_REF]MATSim | Multi-Agent Transport Simulation[END_REF] and was based on their previous research aimed to simulate classic two-ways carsharing. In this research demand is considered as independent from the supply and vice-versa. Ciari et al. [START_REF] Ciari | Modeling station-based and freefloating carsharing demand[END_REF] used the same platform later to consider station-based and free-floating carsharing in both their demand and supply side case-study in Berlin. Balac et al. [START_REF] Balac | Carsharing demand estimation[END_REF] used also MATSim to investigate the effects of supply on the demand of the existing round-trip service in Zurich and compared the results with those of one-way station-based systems. They concluded that there is still untapped potential for round-trip carsharing.

The more complex supply-demand relationship has been studied by Martínez et al. [START_REF] Martínez | Insights into carsharing demand dynamics: outputs of an agent-based model application to Lisbon, Portugal[END_REF] by using a different agent-based simulation tool applied to Lisbon. They propose a new agentbased model that simulates a one-way carsharing system as part of the transport supply in a city, accurately describing the demand mode choice and the operation of the system. In their simulation travel times were obtained from AIMSUN [START_REF]Aimsun traffic modelling software | TSS-Transport Simulation Systems[END_REF] for each arc of the network, varying with the time of the day. Also an optimization model was developed to estimate the location and relative dimension of the stations, based on the mobility patterns of Lisbon. Heilig et al. [START_REF] Heilig | Multiple-day agent-based modelling approach of station-based and freefloating car-sharing[END_REF] used a travel demand model (tripbased) based on the principle of agent-based simulation, to model both round-trip and one-way (free-floating) carsharing systems.

In their work for the first time carsharing usage was simulated for more than one day.

The demand for SAVs also have been recently explored by using activity-based multi-agent simulation tools. Fagnant et al. [START_REF] Fagnant | Operations of shared autonomous vehicle fleet for Austin, Texas, market[END_REF] used MATSim to estimate the demands for a fleet of SAVs (with a low level of market penetration: 1.3% of regional trips) serving travelers in Austin, Texas. Hörl et al. [START_REF] Hörl | Simulation of autonomous taxis in a multimodal traffic scenario with dynamic demand[END_REF] explored the demand for autonomous taxis with the same tool by simulation of different scenarios. Azevedo et al. [START_REF] Azevedo | Microsimulation of demand and supply of autonomous mobility on demand[END_REF] used an integrated agentbased traffic simulator built on disaggregated behavior models in both demand and supply (SimMobility [START_REF]SimMobility -Integrated Simulation Platform | Intelligent transportation systems lab[END_REF]) to study the potential impacts of introducing of an AMoD service in a carrestricted zone of Singapore. In their work individual preferences to use autonomous vehicle were kept unchanged and only cost of the service was assumed as 40% less than the regular taxi service in Singapore.

Table II presents a summary of the studies where travel demand of one-way carsharing systems has been estimated. For each study the demand estimation approach used, the type of carsharing and the case study are indicated. The references are in chronological order. As mentioned before in the literature the largest attention was given to the possibility of fleets to become unbalanced and the works on travel demand estimation of this services are limited [START_REF] Jorge | Carsharing systems demand estimation and defined operations: a literature review[END_REF], [START_REF] Balac | Carsharing demand estimation[END_REF]. However there are some studies about the influence of different factors on demand related to one-way station-based and free-floating services [START_REF] Schmöller | Empirical analysis of free-floating carsharing usage: the Munich and Berlin case[END_REF], or membership prediction [START_REF] Kortum | Free-floating carsharing systems: innovations in membership prediction, mode share, and vehicle allocation optimization methodologies[END_REF], [START_REF] Zheng | Carsharing in a university community[END_REF]. Also there are many works in which the preferences of travelers to use SAVs have been studied [START_REF] Krueger | Preferences for shared autonomous vehicles[END_REF]- [START_REF] Zmud | Consumer acceptance and travel behavior impacts of automated vehicles final report consumer acceptance and travel behavior impacts of automated vehicles[END_REF]. All these studies do not focus on whole travel demand model but their results could potentially be useful for model calibration.

IV. ANALYSIS

A. Travel Model

As shown in the table II most of the above mentioned studies use an activity-based approach for estimating travel demands for one-way carsharing. Activity-based travel demand estimation is the application of discrete choice analysis methods to model the decision making process that motivates daily trip tours. A trip tour is the sequence or chain of trips in time and space throughout a particular day. However, in transportation modelling trip-based models are more popular. These models are often referred to as "four step models (FSMs)" because they commonly include four primary components: (1) trip generation, (2) trip distribution, (3) mode choice, and (4) traffic assignment. FSMs have evolved over many decades and are widely used and the question is why for demand forecasting of one-way carsharing systems, activity-based models are employed? There are some reasons for that: Firstly, FSMs do not consider the entire tour made by an individual and typically have high numbers of non-home-based trips, which do not include important information such as trip purpose, traveler income, or relation to other trips in the person's day. These trips are considered to be captured more by one-way systems [START_REF] Barth | Shared-use vehicle systems: framework for classifying carsharing, station cars, and combined approaches[END_REF]. That has been approved in the literature. Heilig et al. [START_REF] Heilig | Implementation of free-floating and station-based carsharing in an agentbased travel demand model[END_REF] use a trip-based aggregated model for simplification and ignored sub-tours. They admitted in their revised paper that this simplification could be the reason why their modeled outputs do not match the real data. Martínez et al. [START_REF] Martínez | Insights into carsharing demand dynamics : outputs of an agent-based model application to Lisbon , Portugal[END_REF] also used trip-based approach in their first simulation for Lisbon city but they developed afterwards an activity-based model to simulate shared mobility systems in larger area (Lisbon Metropolitan Area).

Secondly, the mode choice functionality in FSMs is based on behavioral models that usually rely on revealed preferences (RP) data, which for new services -as these new systems are not in operation yet-is not available, especially in the case of SAVs.

Thirdly, to model one-way carsharing both spatial and temporal location of vehicles are needed which aggregated FSMs cannot provide.

Fourthly, typically FSMs are not sensitive to short-distance trips. This is because in any FSMs some aggregated spatial zoning (traffic analysis zone) are used. Heilig et al. [START_REF] Heilig | Implementation of free-floating and station-based carsharing in an agentbased travel demand model[END_REF] pointed that in their model access and egress trips to the carsharing are not modeled explicitly due to the zone-based spatial resolution. Martínez et al. [START_REF] Martínez | Insights into carsharing demand dynamics: outputs of an agent-based model application to Lisbon, Portugal[END_REF] used extremely fine-grained spatial zoning (homogeneous grid of 200 m x 200 m cells) for their simulation.

Finally, activity-based models are more sensitive to pricing policies. Therefore, for one-way carsharing systems it would be of more use in order to study the financial and economic aspects of the services.

B. Agent-based Simulation

In activity-based approaches, every individual is a decision maker who confronts a huge choice set of various activity patterns in the time-space domain. Each combination of activities and their locations, starting and ending points, and durations forms a unique activity pattern. Individuals select the patterns that maximize their utilities by somehow solving a large-scale combinatorial optimization problem conditional on others' decisions. Thus such disaggregate models require faster solution algorithms. One solution is agent-based simulation. It typically refers to a computational method and simulation for studying the actions and interactions of a set of autonomous entities. It is also called a multi-agent system or agent-based system [START_REF] Zheng | A primer for agent-based simulation and modeling in transportation applications[END_REF]. Agentbased transport simulations usually derive travel demand from activity-based modeling approaches but employ microscopic and completely time-dynamic traffic simulation of each agent's individual demand based on system constraints given by the transport network and its attributes [START_REF] Balmer | Agent-based demand-modeling framework for large-scale microsimulations[END_REF].

C. Activity-based Multi-agent Simulation: Overall Framework

Within most of the reviewed literature, demand estimation frameworks of one-way carsharing systems are structured as follows: (1) a "synthetic population" (synthetic individuals) is created from demographic data, (2) activity plans and activity locations are generated (selected) for each synthetic individual, also mode and route choice decisions are done for each individual, (3) the traffic simulation (particularly micro simulation) and plan execution are done to find performance measures, (4) activity planning, route and mode decisions are revised for each individual, and (5) iteration process is repeated until average performance measures for all agents stabilize.

For the first step of this framework some generators have been used in different studies. In fact, each activity-based model does require the development of a synthetic population that represents a region's travelers and their detailed attributes. Population generator or synthesizer generate detailed household or traveler characteristics in a way that is consistent with known aggregate population or travel characteristics. The generation of synthetic population in the most cases rely on PUMS (Public Use Microdata Sample) availability and details. To draw synthetic population from samples some methods (e.g. IPF, IPU, CO) have been employed. Activity chains are also extracted from micro census and travel surveys. The most important challenge in this steps is data detail and availability. The more data is inserted to the generator, the more synthetic individuals and its activity plan is accurate.

In the second step for every traveler in the synthetic population, a fully descriptive daily activity plan, including locations of daily activities such as work or education needs to be derived (the activities' location, its durations, start and end time, and the trips connecting two activities, including mode and route). The main process is related to a discrete choice approach that is based on the assumption of random utility maximization. In fact, almost all agent-based transport simulations do not involve discrete choice models as they are used in conventional transport demand models, but these simulations are more based on finding stochastically the maximized utility for various choices sets. In agent-based simulation every agent has the ability to learn and adapt its behaviors based on experience, which requires some form of memory. Discrete choice capability provides agents to select one plan from their memory. For this aim, in the first stage an initial set of individual choices or plans has to be determined. Then during the plan execution these set of choices would be examined.

The third step is focused on plan execution and traffic simulation. It can be done with other tools integrated to the model either by agent-based tools oneself. In the latter case it's observed that the traffic theory integrated to the model have been simplified to reduce computational time and complexity (e.g. in the case of MATSim). For instance, it couldn't be concluded if this simplification results in the important changes on outputs or not. In some agent-based tools a plugin is created to import especially the network to the model (e.g. from Open Street Map). But in almost all cases this imported network has been modified and cleaned manually. The performance measures are estimated in the end of each plan execution. In SimMobility time-variable measures (e.g. waiting time, travel time) and costs are used for this aim. The performance measure in the case of MATSim is commonly a score (the sum of activity and travel utility scores).

In the fourth step, an activity plan for each individual and respected mode and route choice (set of individual choices) are revised, regenerated and modified in the closed loop. MATSim applies genetic algorithm (GA) to revise activity plans.

Finally the model(s) will iterate many times until a systematic relaxation reached [START_REF] Balmer | Travel demand modeling for multi-agent transport simulations: algorithms and systems[END_REF]. Computational time is one of the challenges that can be observed during the simulation. Usually this term depends on the number of agents and network's size. Some others challenges could be met during demand estimation process of new services dependent on service type (e.g. validation and calibration in the case of SAVs).

D. Platforms

Among the well-known activity-based multi-agent platforms, MATSim, SimMobility, and MobiTopp [START_REF]MobiTopp[END_REF] are used to model new carsharing systems.

MATSim (Multi-Agent Transport Simulation

) is the open source platform implemented in Java that is designed to run millions of agents in a metropolitan area. MATSims' framework consists of several modules which can be combined or used stand-alone. Network simulation in this platform is queue-based. MATSim is currently considered to be the most widely applied model for new innovative services [START_REF] Fagnant | Operations of shared autonomous vehicle fleet for Austin, Texas, market[END_REF], [START_REF] Hörl | Simulation of autonomous taxis in a multimodal traffic scenario with dynamic demand[END_REF], [START_REF] Fagnant | Dynamic ride-sharing and fleet sizing for a system of shared autonomous vehicles in Austin, Texas[END_REF], [START_REF] Boesch | Autonomous vehicle fleet sizes required to serve different levels of demand[END_REF].

SimMobility is the multi-modal multi-scale platform that considers land-use, transportation, and communication interactions. This platform consists of three different sub-models: (1) short-term, (2) mid-term, and (3) long-term; and is designed to run millions of agents from second-by-second to year-by-year [START_REF] Adnan | SimMobility: a multiscale integrated agent-based simulation platform[END_REF]. SimMobility particularly focuses on impacts on transportation networks, intelligent transportation services and vehicular emissions, thereby its objectives and applications are wider than MATSim.

MobiTopp is the first activity-based multi-agent platform that has been intended for an analysis period of one week when it was initially designed. This platform does not contain an internal traffic assignment procedure and relies on external tools [START_REF] Mallig | Modeling travel demand over a period of one week: the mobitopp model[END_REF].

E. Limitations

During travel demand estimation of one-way carsharing using activity-based multi-agent simulation, several main components are not yet taken into account, which could dramatically change the results:

Firstly, despite their emphasis on activities the majority of the activity-based multi-agent simulators are essentially microsimulation tour based models using a random utility choicemodelling framework. So long-term decisions of the household and its members, as well as mid-term schedules for each individual are not taken into account in the simulations (except SimMobility).

Secondly, to speed up the computation all traffic simulators used in comprehensive multi-agent platforms or those that are coupled with activity demand models have simplified microscopic rules. For instance, MATSim utilizes parallel computation of the spatial queue model in microsimulationbecause the queue model needs less data and computing resources and it runs much faster-but a noticeable shortcoming of this model is that the traffic dynamics may not be realistic, and the speed of the backward wave may not be modeled correctly. However, MATSim is designed to run millions of agents in a metropolitan area and in this regard, it is computationally fast.

Thirdly, all service operational characteristics are not taken into account in these simulations. For example, initial distribution of vehicles in the network or redistribution strategy during services are the terms that have not been yet introduced to the simulations but they could result in important changes of demand.

Finally, as innovative carsharing systems (i.e. SAVs or AMoD) are expected to be used collectively, it is necessary to make these simulations sensitive to sharing strategies of rides, which is not well investigated yet.

V. CONCLUSION

In this paper methods and approaches used in the literature to estimate demands for one-way carsharing systems were presented, illustrated and analyzed. Also potential drawbacks in particular with regard to demand estimation of new innovative one-way carsharing systems were discussed. In today's literature, the investigation about demand estimation of such systems in which the complex relationship between supply and demand is considered, remain very limited. In this paper also platforms and toolkits used for the modeling process were presented and criticized. Almost all of these platforms are based on activitybased multi-agent simulation. Activity-based approach provides the feedback of travel time to a multidimensional decision domain, including not only travelers' route and mode choice decisions but also a set of activity decisions (e.g. activity location, schedule, etc.). Above mentioned simulations adopt heuristic rules in feedbacks to achieve approximate convergence and consistency. To estimate travel demand of innovative services (such as SAVs or AMoD) several components specially related to supply side are not yet taken into account. This comes from the fact that the simulation takes a huge time to run millions of agents. Therefore it is practically only possible to evaluate a limited number of pre-determined scenarios. One solution could be to reduce the number of agents (as in the case of MATSim for several cities). But to study multi-modal transportation systems, network and public transport capacities should be reduced similarly. This requires more investigations especially that the accuracy of this approach is not yet approved in the literature. The study area could be also reduced but in this case the potential demand from the agents who live out of the area or those who cross the area would be neglected. Data detail, accessibility and reliability still remain the major challenges. These data are required first to generate synthetic population and secondly to calibrate the simulation. Some local or international sources could be useful to this aim (e.g. IPUMS). To simulate innovative one-way carsharing systems such as SAVs or AMoD, as there are no real data on hand, it would be difficult to validate the simulation outputs.

Future work will involve investigations on how to integrate feasibly supply characteristics of new carsharing systems (riding and redistribution strategies of operation, fleet specification, service quality etc.) at the fine level of detail to the travel demand models.

TABLE I . CLASSIFICATION OF CARSHARING SYSTEMS Carsharing types Round-trip One-way Station- based Free- floating SAVs

 I

	Pick-up	Specified points	Any rental station	Anywhere available	Anywhere
	Drop-off	Same point	Any station	Anywhere authorized	Anywhere
	Park space problem	No	Yes	No/Yes	No
	Rebalancing problem	No	Yes	Yes	No

TABLE II .

 II SUMMARY OF THE STUDIES ON TRAVEL DEMAND ESTIMATION FOR ONE-WAY CARSHARING SYSTEMS

	Authors		Year	Case study	Demand estimation approach	Type of shared-use vehicle services
	Catalano, Lo Casto and Miglior	2008	Palermo urban area	SP + random utility model	One-way station-based
	Kouwenhoven, Kroes, Gazave and Tardivel	2011	Autolib	SP + discrete choice model	One-way station-based
	Ciari, Dobler, and Axhausen	2012	Zurich area	Activity-based multi-agent simulation (MATSim)	One-way station-based
	Ciari, Bock and Balmer		2014	Berlin	Activity-based multi-agent simulation (MATSim)	One-way station-based and free-floating
	Balac, Ciari and Axhausen	2015	Zurich area	Activity-based multi-agent simulation (MATSim)	Round-trip and one-way station-based
	Heilig, Kagerbauer, & Vortisch Mallig,	Schroder,	2015	Greater Stuttgart area	Aent-based simulation (MobiTopp) + Traffic simulation (VISUM)	Round-trip and one-way free-floating
	Fagnant, Kockelman and Bansal	2015	Austin	Activity-based multi-agent simulation (MATSim)	SAVs
	Hörl, Earth and Axhausen	2016	Sioux Falls	Activity-based multi-agent simulation (MATSim)	Free-floating and SAVs
	Azevedo et al.		2016	Singapore	Multi-scale integrated activity-, agent-based Simulation (SimMobility)	SAVs (non-carpooling)
	Martínez, Almeida Correia, Moura and Lopes	2017	Lisbon	Agent-based modeling + Traffic simulation (AIMSUN)	One-way station-based

ACKNOWLEDGMENT

This research work has been carried out in the framework of IRT SystemX, Paris-Saclay, France, and therefore granted with public funds within the scope of the French Program "Investissements d'Avenir".


V Brunel

Marc Bocquet

Th Jolicoeur

Edge NMR as a probe of boundary conformal field theories

HAL is

Semi-infinite quantum spin chains display spin autocorrelations near the boundary with powerlaw exponents that are given by boundary conformal field theories. We show that NMR measurements on spinless impurities that break a quantum spin chain lead to a spin-lattice relaxation rate 1/T edge 1 that has a temperature dependence which is a direct probe of the anomalous boundary exponents. For the antiferromagnetic S=1/2 spin chain, we show that 1/T edge 1 ∝ T log 4 T instead of log 1/2 T for a bulk measurement. We show in the case of a one-dimensional conductor described by a Luttinger liquid, a similar measurement lead to a relaxation rate 1/T edge 1 ∝ T , independent of the anomalous exponent Kρ. 75.10.Jm, 75.40.Gb ] Impurity effects in quantum spin chains are a subject of much interest since they are a sensitive probe of the peculiar correlations that develop in these magnetic systems. For example it has been shown recently [1] that an external uniform magnetic field creates a staggered magnetization near impurities in the antiferromagnetic (AF) spin chain compound Sr 2 CuO 3 , in agreement with theoretical predictions [2]. In S=1 AF spin systems with a Haldane gap in the bulk there are effective free spins S=1/2 at the end [3] of the chain that are revealed by the coupling to an impurity.

One-dimensional quantum systems like the S=1/2 AF chain or the electron gas -the "Luttinger liquid" -are critical systems with an effective low-energy physics which is a conformal field theory. In both cases it is the massless Gaussian model that is at the heart of the correct description. When boundaries are introduced in such problems, then it has been shown by Cardy that there are boundary operators with nontrivial scaling dimensions [4]. This means that if we measure the spin autocorrelation in time S(t) • S(0) for the spin at the end of a chain, it decays with a power law which is different from that of the bulk. Measurements with a local probe like the 1/T 1 relaxation rate in NMR experiments are sensitive to this power law.

Conventional NMR is performed on nuclear spins that are coupled by hyperfine interactions to the atomic spin of the same atom : for example in the S=1/2 antiferromagnetic spin chain Sr 2 CuO 3 one may use 63 Cu resonance [1]. While this is a local measurement, it involves the time autocorrelation of a bulk spin. We show in this Letter that by NMR measurements on nuclei belonging to spinless impurities that break the chain (or the 1D conductor) one measures the anomalous boundary exponents of the boundary conformal field theory. We call this "edge NMR". In the case of the spin-1/2 chain we show that the bulk marginal operator manifests itself by a logarithmic factor in 1/T 1 which is different from the bulk case.

In the case of a spin chain, our main idea is illustrated in fig. 1. Impurities that are spinless but do have a nuclear spin are introduced at a low concentration level in the spin chain. The nuclear spin of the impurity in fig. 1 has substantial coupling only with its two neighboring spins if we are dealing with a magnetic insulator. The coupling may be dipolar or transferred hyperfine : its precise nature does not matter for our reasoning. When impurities are very dilute, the nuclear spin is surrounded by two essentially semi-infinite spin chains. So measurement of the relaxation rate T 1 of the impurity nuclear spin involve only the fluctuations of the two end spins and these spins give the same contribution. If there is no exchange through the impurity, then we have exactly a probe of a boundary critical phenomena since the relaxation rate is given by the following formula [5] :

1/T 1 = A 2 lim ω→0 +∞ -∞ dt e iωt S 0 (t) • S 0 (0) T . (1)
In this equation A is the (hyperfine) coupling, S 0 is the end spin of the semi-infinite chain and . . . T stands for thermal averaging. An example would be a S=1/2 spin chain realized by Cu 2+ ions and the impurity may be Zn which is a possible substitution for Cu in the cuprate family of materials. So Zn doping effectively cuts the chains. The isotope 67 Zn has a nuclear spin so NMR may be performed on this nucleus selectively.

In the case of the S=1/2 AF chain we show that (1/T 1 ) edge ∝ T log 4 T is the universal low-temperature behavior instead of log 1/2 T as predicted [6,7] and measured in the case of bulk NMR [8]. In the case of a one-dimensional conductor, one can perform the same kind of measurement by using an impurity which is insulating, i.e. which breaks the chain. Similarly one has now a relaxation rate that scales as (1/T 1 ) edge ∝ T while in the bulk it is given by [START_REF]the contribution by D. Jérome[END_REF] DSM/SPhT-T99/003 http://www-spht.cea.fr/articles/T99/003/ Impurity with nuclear spin on FIG.

1. An NMR 1/T1 measurement performed on an impurity with a nuclear spin but no atomic spin (white dot) is a probe of the time autocorrelation of the end spins of the spin chain (black dots).

(1/T 1 ) bulk ∝ T + T Kρ where K ρ is the anomalous exponent that characterizes the Luttinger liquid behavior of the system.

We first discuss the S=1/2 AF spin chain described by the Heisenberg hamiltonian :

H = J n S x n S x n+1 + S y n S y n+1 + ∆S z n S z n+1 . (2)
In this equation, we have introduced the exchange anisotropy ∆ which is convenient for the bosonization description of the low-energy physics. In most materials that are known to be reasonably well described by a S=1/2 AF chain like KCuF 3 or Sr 2 CuO 3 , in fact there is isotropy, i. e. ∆ = 1. If ∆ = 0 we have the XY chain which maps onto a system of free spinless fermions in a band of dispersion E(k) = -J cos k and two Fermi points at k F = ±π/2. There are particle-hole excitations with small momentum transfer, i.e. staying on the same side of the Fermi "surface" and also excitations across the Fermi surface with momentum transfer 2k F = π. In the spin language, they correspond respectively to ferro and antiferromagnetic fluctuations. In the bosonic language [10] we have :

S z x = - 1 √ π ∇ x φ(x) + (-) x πα cos( √ 4πφ(x)). (3)
The effective theory in the infrared limit for the boson φ is a free theory given by the following Lagrangian density :

L φ = 1 2 (∂ t φ) 2 -(∂ x φ) 2 . ( 4
)
For anisotropies ∆ ≤ 1, the chain is in a massless phase which is still described by Eq.( 4) after a rescaling of the boson φ → φ/ √ K where K = K(∆) is a parameter that contains the effects of interactions induced by z-exchange. At the isotropic point ∆ = 1 we have K = 1/2. This massless effective theory leads to power laws in the spin fluctuations. The local correlations of a spin S in an infinite chain can be computed at nonzero temperature T with the result :

S z (t)S z (0) ∝ T sinh πT t + ( T 2 sinh 2 πT t ) K , (5)
DSM/SPhT-T99/003 http://www-spht.cea.fr/articles/T99/003/

S + (t)S -(0) ∝ ( T 2 sinh 2 πT t ) 1/4K + ( T sinh πT t ) 2K+1/2K , (6)
(omitting constant prefactors). In the isotropic case both spin correlations are equal to T / sinh πT t and this behavior leads to a relaxation 1/T 1 calculated from Eq. ( 1) which is ∝ T 0 . This is essentially the behavior observed by Takigawa et al. [8]. There is an additional logarithmic correction log 1/2 T due to the presence of Umklapp processes for the fermions [6].

If we now consider a spin at the end of an open chain, we must supply our bosonic description with a boundary condition. It is a Dirichlet condition which is appropriate [START_REF] Eggert | [END_REF]. The condition S z (x = 0) = 0 in the bosonic theory leads to φ(0) = √ π/2 √ 2 by use of Eq. ( 3). This boundary condition can then be used to relate the chiral components φ L and φ R . Indeed φ R may be regarded as the analytic continuation of φ L on the negative axis by φ R (x, t) = -φ L (-x, t) + √ π/2 √ 2. The Green's function can then be expressed in terms of the L field only and this field does not feel the existence of the boundary.

The edge autocorrelations have now a different behavior from the bulk. We find that the uniform and staggered part of the correlation functions have the same behavior at the edge, given by :

S z (t)S z (0) ∝ T 2 sinh 2 πT t (7)
S + (t)S -(0) ∝ ( T sinh πT t ) 1/K , (8)
where we have kept the leading behavior. This is due to the fact that spin operators have boundary scaling dimensions 1 instead of 1/2 in the bulk. In the isotropic case these correlations leads to contributions to 1/T 1 that scale as T instead of T 0 in the bulk. So the boundary critical behavior influences directly the NMR relaxation rate. The leading behavior is thus (1/T 1 ) edge ∝ T . We now turn to the influence of the marginal operator. Indeed it is known that there are logarithmic corrections to the power-law behavior of the spin-1/2 chain [12,13]. In fact the effective theory given by Eq. ( 4) contains an additional marginal operator that is allowed in the isotropic case : it is due to Umklapp scattering of the fermions and can be written as cos( √ 16πφ). The complete effective theory is given by :

L φ = 1 2 (∂ t φ) 2 -(∂ x φ) 2 + g cos( √ 16πφ). ( 9
)
The set of the two coupling constants K and g flows under renormalization group according to the Kosterlitz-Thouless equations. There is a single line that reaches the fixed point K * = 1/2 and which corresponds to an isotropic spin chain. Along this line, the flow of the couplings is marginal. This operator leads to a multiplicative logarithmic correction to the bulk magnetic susceptibility, as predicted theoretically [14] and observed experimentally [15]. In the relaxation rate it leads to a correction [6] ∝ (log T ) 1/2 which is a possible explanation for the experimental upturn of 1/T 1 at low temperature [8]. Many numerical studies have been devoted to demonstrate ab initio its existence in the spin-1/2 chain. In fact it is responsible for the extremely slow approach to the thermodynamic limit [16,17]. This bulk marginal operator still exists in the theory with a boundary. In addition, some new operators are permitted at the edge. Note that the surface term ∂ x φ L , while forbidden in the bulk of the chain, is a perfectly allowed operator in the boundary theory. If we now classify all possible marginal operators at the boundary fixed point, there are only two such operators ∂ x φ L and exp(i √ 8πφ L ). They have boundary scale dimension 1 and thus are marginal on the edge.

But it is easy to see that they are forbidden by the symmetry of the problem. The rotational invariance around z-axis forbids exp(i √ 8πφ L ) whereas it is rotation around x-axis that forbids ∂ x φ L . As a consequence, there are no extra marginal operators. Thus the Green's function defined by :

G(t) edge = S + 0 (t)S - 0 (0) , (10)
obeys the following edge renormalization group equation :

t ∂ ∂t + β bulk (g) ∂ ∂g + 2γ edge (g) G(t, g) edge = 0. ( 11
)
In this equation, g is the coupling of the marginal operator. Since it is a bulk operator its β-function is that of the bulk : β(g) ≡ β bulk (g). The anomalous dimension γ edge (g) however is related to the short-distance singularity of the bulk marginal operator with an operator that lies at the boundary. Hence it is modified with respect to its bulk value.

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We compute γ edge (g) by a Coulomb gas technique similar to that used by Singh, Fisher and Shankar [13], expressing all the Coulomb gas quantities in terms of φ L only. We find :

β bulk (g) = -2πg 2 + O(g 3 ), ( 12
)
γ edge (g) = 1 -4πg + O(g 2 ). ( 13
)
The result for γ edge is different from the bulk result γ(g) = 1/2 -πg/2 : the constant term is due to the edge scaling dimension of the spin operator which is twice the bulk value. The O(g) coefficient leads directly to the logarithmic correction. The solution of Eq. ( 11) by the method of characteristics leads to an asymptotic behavior which includes a logarithmic correction :

G(t) edge ∝ 1 t 2 (log t) 4 . (14)
This is the peculiar law of time decay for the autocorrelation of the end spin of the chain (in the bulk it is log 1/2 t/t). This result holds for the staggered as well as the uniform part of the correlation function. We have checked that Eqs. (12,13) are consistent with isotropy : S + 0 (t)S - 0 (0) and S z 0 (t)S z 0 (0) have the same behavior. To treat the effect of a nonzero temperature we impose periodic conditions in Euclidean time with period 1/T . The system lives then on a half-cylinder. The Callan-Symanzik equation ( 11) is unchanged, though the Green's function depends upon an additional argument which is the temporal extent 1/T . A standard finite-size scaling argument leads then to a solution of the form :

G(t, T ) edge ∝ T 2 sinh 2 (πT t) (log t) 4 . (15)
Such a behavior leads to a relaxation rate (1/T 1 ) edge ∝ T log 4 T strikingly different from the bulk. Experimental check of this result seems feasible with the possible complication that if the nearest-neighbor coupling needed in edge NMR is dipolar then it may be that there are parasitic effects due to the other neighboring chains.

The Luttinger liquid. We now apply the same line of arguments to the one-dimensional Luttinger liquid. There are many examples of physical systems including quantum wires, carbon nanotubes or one dimensional organic conductors that belong to the universality class of the "Luttinger liquid". In such systems, the spin and charge degrees of freedom are decoupled in the low-energy long-wavelength limit and can be described in a bosonization framework by two bosonic fields, φ σ for the spin and φ ρ for the charge. For isotropic systems, the effective theory for φ σ is a free field theory like Eq. ( 4). The theory for φ ρ is also a free theory but with a nontrivial constant K ρ which encapsulates all low-energy long-distance properties of the system. The rate 1/T 1 is a probe of the spin fluctuations through the spin density wave (SDW) correlations SDW z (t) SDW z (0) where the SDW z operator is given by c † nα σ z αβ c nβ (we consider the isotropic case). In a translationally invariant system these correlations have a uniform part with q ≈ 0 and a q ≈ 2k F part. They both contribute to (1/T 1 ) bulk leading to a law T + T Kρ which involves explicitly the coupling K ρ . In the case of edge NMR, we use the bosonized form of the SDW operator :

SDW z staggered ∼ sin 2πK ρ φ ρ sin √ 2πφ σ . (16)
The condition S z = 0 on the last spin of the chain leads to the Dirichlet boundary conditions φ σ (0) = 0 and φ ρ (0) = √ π/2 2K ρ . The staggered part contributes then to 1/T 1 through the product :

sin √ 2πφ σ (t) sin √ 2πφ σ (0) φσ (0)=0 × sin 2πK ρ φ ρ (t) sin 2πK ρ φ ρ (0) φρ (0)= √ π 2 √ 2Kρ . (17)
The spin part in Eq. ( 17) is exactly the same as in a quantum spin chain while the charge part is different due to the presence of K ρ but also due to the peculiar boundary condition. As a consequence, when we compute these correlations each factor involves four nonzero contributions instead of two in the bulk (the electric neutrality of Coulomb gas calculations is affected by the boundary). Let us compute the charge correlator between two arbitrary points (x 1 , t 1 ) and (x 2 , t 2 ). We give some details in the zero temperature case, a conformal mapping can be used afterwards to obtain the corresponding expressions valid for low T . The left and right components of the charge Boson are related by φ ρR (x, t) = -φ ρL (-x, t) + √ π/2 2K ρ and the charge part C ρ of the correlator Eq. ( 17) is thus equal to :

DSM/SPhT-T99/003 http://www-spht.cea.fr/articles/T99/003/

cos 2πK ρ (φ ρL (x 1 , t 1 ) -φ ρL (-x 1 , t 1 )) × × cos 2πK ρ (φ ρL (x 2 , t 2 ) -φ ρL (-x 2 , t 2 )) . (18)
Evaluation of this correlation function leads to the following expression :

C ρ = ( 1 x 1 x 2 ) Kρ/2 (I + 1 I ), (19)
where I is equal to :

(t 1 -t 2 ) 2 -(x 1 + x 2 ) 2 (t 1 -t 2 ) 2 -(x 1 -x 2 ) 2 Kρ/2 . ( 20
)
When approaching the edge of the system, i.e. x 1 and x 1 are O(a) where a is the lattice spacing, the expression I of Eq. ( 20) goes to a constant and the correlator C becomes independent of time and the charge part in Eq. ( 17) does not contribute to the time decay. This is to be contrasted with the spin correlator in Eq. ( 17). There the boundary condition is simply φ σ (0) = 0 and thus in the expression corresponding to Eq. ( 19), we find the difference I -1/I (with now K ρ replaced by 1) that decays in time according to a power law ∼ 1/t 2 We thus obtain a law of the form T 2 / sinh 2 πT t at nonzero temperature leading to a "superuniversal" behavior 1/T edge 1 ∝ T independent of K ρ . We note that it has also been proposed recently [18][19][20] to use photoemission spectroscopy on the open end of a Luttinger liquid to probe the boundary effects. In this case the physical measurement is sensitive to the boundary spectral properties of the Luttinger liquid and also involves novel exponents that differ from those of the bulk.

In this Letter, we have shown how edge NMR can be used as a probe of some boundary conformal field theories. For the S=1/2 AF spin chain, the relaxation rate scales like T log 4 T at the edge instead of T 0 log 1/2 T . For a Luttinger liquid with gapless spin and charge degrees of freedom it scales as T . This universal behavior is independent of the correlation exponent K ρ which rules all 1D behavior through anomalous power laws.

ACKNOWLEDGMENTS

We thank I. Affleck for a useful correspondence and F. David, J. F. Jacquinot, J. P. Renard for useful discussions