Lionel G Vacher
email: lionel.vacher@univ-grenoble-alpes.fr

Wataru Fujiya
email: wataru.fujiya.sci@vc.ibaraki.ac.jp

Recent Advances in our Understanding of Water and Aqueous Activity in Chondrites

Keywords: asteroids, chondrites, aqueous alteration, secondary minerals, isotopes, sample return missions

Water played a critical role in the evolution of rocky material and planetesimals in the early Solar System. Many primitive asteroids (the sources of chondrites) accreted a significant amount of water ice and were affected by aqueous alteration and/or fluid-assisted metamorphism. These secondary parent body processes have strongly modified the primary mineralogy of chondrites in favor of a wide diversity of secondary phases that formed by interaction with water. The mineralogical and isotopic characterization of these secondary phases in chondrites and returned samples from hydrous asteroids Ryugu and Bennu can help us reconstruct the dynamical evolution of water in the early Solar System and understand the timing and mechanisms of aqueous alteration on hydrous asteroids.

INTRODUCTION

Chondritic meteorites are rocks from undifferentiated asteroids. They represent an important record of the Solar System's early geological history ~4.6 billion years ago. Chondrites account for >80% of the total meteorite population and consist of three dominant components accreted together to form chondritic parent bodies: chondrules; Ca,Al-rich refractory inclusions (CAIs); and fine-grained matrix (FIG. 1A). The matrix material consists of an assemblage of diverse materials that incorporated a significant proportion of water ice grains, at least ~10-15 wt.% H2O. After their accretion, chondrites experienced aqueous alteration and/or metamorphism on their parent bodies, resulting in important modifications to their mineralogy and chemical and isotopic compositions. These "secondary" characteristics form the basis of the classification system for chondrites, in which seven petrologic types are recognized (from 1 to 7), where type 1 is assigned to the most aqueously altered chondrites, and type 7 represents the most thermally metamorphosed chondrites (see [START_REF] Weisberg | Systematics and evaluation of meteorite classification[END_REF] for a review).

Among chondrites, carbonaceous chondrites (subset of chondrites, divided into nine groups, namely CI, CM, CR, CY, CO, CV, CK, CB, and CH) of types 1 to 3 have experienced different aqueous alteration histories: (1) low-temperature hydrothermal alteration for petrologic types 1-2 (CI-CM-CR-CY groups); and (2) fluid-assisted metamorphism for petrologic type 3 (CO-CV groups) (FIG. 1B). Most of the hydrated carbonaceous chondrites with petrologic types 1-3 have preserved their secondary mineralogy and, therefore, offer the unique opportunity to study aqueous alteration processes that started ~4-5 million years after the birth of the Solar System.

A combination of mineralogical, experimental, modeling, and isotopic studies on these secondary minerals can be achieved to reconstruct the source of water accreted by chondritic asteroids, their accretion time, and the physicochemical conditions of aqueous alteration that affected these hydrated asteroids.

ORIGINS OF WATER IN CHONDRITES

Stable water isotopes ( 16 O, 17 O, 18 O, H, and D) in chondrites are powerful tools to trace the origin of chondritic water and track the chemical processes that occurred on their asteroidal parent bodies. At present, almost all of the water in chondrites is now retained as hydroxyl (OH) groups or atomic O in various hydrated minerals. Therefore, the hydrogen (D/H) and oxygen (𝛿 17,18 O; see glossary) isotopic composition of chondritic water is usually inferred indirectly from bulk and in situ measurements of secondary minerals that formed from water-rock interaction.

At least two main water ice reservoirs with distinct H and O isotopic compositions are commonly inferred for the origin of water in chondrites: (1) locally derived water, directly condensed from the nebular gas; and (2) outer disk water ice, formed in the coldest part of the disk and/or inherited from the parent solar molecular cloud [START_REF] Alexander | The provenances of asteroids, and their contributions to the volatile inventories of the terrestrial planets[END_REF]) (FIG. 2A). Due to its lowtemperature chemistry, interstellar ice is enriched in D by ~2-3 orders of magnitude compared to the solar nebular H2. In the early stages of the protoplanetary disk evolution, D-rich pre-solar ice was transported into the warm regions of the inner Solar System and subsequently reequilibrated with the D-poor nebular H2. Thus, it is thought that the D/H isotopic ratio of water ice in planetary bodies increases with increasing heliocentric distance [START_REF] Jacquet | Water transport in protoplanetary disks and the hydrogen isotopic composition of chondrites[END_REF].

Similarly, the wide range of mass-independent O isotopic anomalies (∆

Hydrogen Isotopes

Deciphering the origin of chondritic water using H isotopes is challenging because hydrated chondrite matrices consist essentially of a complex mixture of hydrated minerals and organic matter (the two main H-carrier phases), which are intimately mixed at the sub-micrometer scale.

To solve this problem, [START_REF] Alexander | The provenances of asteroids, and their contributions to the volatile inventories of the terrestrial planets[END_REF] proposed that the D/H composition of chondritic water can be approximated from whole-rock D/H and C/H measurements by subtracting the organic-derived D/H from their bulk H isotopic compositions. They showed that the D/H ratios of C-free phyllosilicate are D-poor (D/H = 70 to 100 × 10 -6 ) relative to D-rich comets (up to 530 × 10 -6 ). This result implies that chondrite parent bodies accreted a dominant D-poor local water ice without a significant influx of D-rich outer disk water ice in the inner Solar System (FIG. 2B).

However, given that some members of carbonaceous, ordinary (OC), and Rumuruti (R) chondrites (two other subsets of chondrites) also record slightly or very D-rich water in their hydrated minerals relative to carbonaceous chondrites (D/H up to ~1800 × 10 -6 ), it was also proposed that the D-rich signature of outer disk or interstellar water ice has been preserved in some chondrite parent bodies (e.g., [START_REF] Piani | Micron-scale D/H heterogeneity in chondrite matrices: a signature of the pristine solar system water?[END_REF].

Current debates consider whether the presence of D-rich signatures for chondritic water represents the influx of outer disk or interstellar water into the asteroid accretion region or the role of isotopic fractionation on asteroidal parent bodies. For instance, [START_REF] Alexander | Deuterium enrichments in chondritic macromolecular material-implications for the origin and evolution of organics, water and asteroids[END_REF] suggested that the H isotopic composition of water in chondrites could have been modified on the asteroidal parent body and become isotopically heavier due to (1) metal oxidation and subsequent loss of isotopically light H2 and/or (2) the isotopic exchange of H between D-poor liquid water and D-rich organic components. Process (1) would have preferentially enriched in D the most metamorphosed chondrites. In process (2), only chondrites that experienced sufficiently high temperatures (>200 °C) and/or a long duration of aqueous alteration could have been affected by this process [START_REF] Piani | Origin of hydrogen isotopic variations in chondritic water and organics[END_REF].

Oxygen Isotopes

The variation in O isotopic compositions of secondary minerals is much smaller than that for H isotopes (FIG. 2C). For instance, the ∆ 17 O values of carbonate, magnetite, phyllosilicate, and fayalite (Fe-rich olivine) in carbonaceous and ordinary chondrites only show modest massindependent O isotopic variations, ranging from ~ -5‰ to +7‰ (see Yurimoto et al. 2008 for review). However, it should be noted that the O isotopic compositions of secondary minerals are essentially controlled by isotopic exchange between 16 O-poor initial water with 16 O-rich anhydrous minerals prior to their formation. Thus, these ∆ 17 O values likely represent lower limits on the initial water composition accreted by chondrite parent bodies. Although high-Δ 17 O values are predicted by fluid flow models in carbonaceous chondrites (up to ~ +16‰, [START_REF] Young | Fluid flow in chondritic parent bodies: deciphering the compositions of planetesimals[END_REF], the initial O isotopic compositions of chondritic water do not seem to show significant 16 O depletion (up to ~ +7‰ in OC chondrites, Yurimoto et al., 2008), in contrast to what is observed for H isotopes.

Outer disk water ice is predicted to be extremely heavy, but there have only been a few reports of very heavy O isotopic signatures in chondrites. The heaviest O isotopic signature of water (∆ 17 O ≈ up to +85‰) was found in cosmic symplectite (COS, an assemblage of 16 O-poor magnetite and pentlandite) in the primitive carbonaceous chondrites Acfer 094 [START_REF] Sakamoto | Remnants of the early solar system water enriched in heavy oxygen isotopes[END_REF]). Although CO self-shielding models predict very extensive 16 O-depletion in the outer water ice (∆ 17 O up to ~ +300‰), the O isotopic composition of the 16 O-poor reservoir is still poorly known and needs to be better constrained. Consequently, the lack of significant 16 O depletion in chondritic water suggests that chondrite parent bodies preferentially accreted a locally derived water ice with near-terrestrial ∆ 17 O values. An alternative explanation could be that mass-independent O isotopic anomalies of chondritic water ice may have been erased before their incorporation into the chondritic parent bodies due to reprocessing in the protoplanetary disk [START_REF] Fujiya | Oxygen isotopic ratios of primordial water in carbonaceous chondrites[END_REF].

CONDITIONS OF AQUEOUS ALTERATION IN CHONDRITES

Stable Isotope Geothermometry

Even though much progress has been made in understanding the alteration conditions of chondrites (see [START_REF] Brearley | The action of water[END_REF] for review), the physicochemical conditions under which aqueous alteration took place remain only partially understood. Among secondary minerals, carbonate, magnetite, and fayalite minerals are of primary importance because their O isotopic composition can be used as a paleothermometer to constrain the temperatures of aqueous alteration (FIG. 3A,C). Their temperatures of formation can be estimated using either (1) the mass-dependent O isotopic fractionation between a secondary mineral and water, which requires knowing the initial O isotopic composition of the parent fluid, or (2) the mass-dependent O isotopic fractionation between two coexisting phases that precipitated from the same parent fluid in isotopic equilibrium.

In types 1-2 carbonaceous chondrites, most studies have focused on carbonate minerals and the data are in good agreement with low-temperature alteration (≲250 °C). For example, the relatively high 𝛿 18 O fractionation determined in situ for calcite-magnetite assemblages in CR chondrites indicates alteration temperatures in the range of ~60-90 °C [START_REF] Huss | Low-temperature aqueous alteration on the CR chondrite parent body: implications from in situ oxygen-isotope analyses[END_REF].

Similarly, the small 𝛿 18 O fractionation for bulk calcite, phyllosilicate, and magnetite minerals in CI chondrites suggests slightly higher alteration temperatures, in the range of ~50-150 °C [START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF]. In CM chondrites, bulk O isotopic measurements of carbonate and serpentine from several CM chondrites suggest that these two minerals are not in isotopic equilibrium (i.e., did not precipitate from the same fluid), but recorded, instead, a change in composition of the fluid with increasing alteration [START_REF] Benedix | Carbonates in CM2 chondrites: constraints on alteration conditions from oxygen isotopic compositions and petrographic observations[END_REF]. In fact, carbonate precipitation in CM chondrites was probably complex and episodic, resulting in the formation of two main populations of carbonate: (1) an early 16 O-poor generation formed before serpentine; and (2) a later 16 O-rich generation formed after serpentine. Considered separately, the first generation appears to form at lower temperature (~0-70 °C) than the second generation (~100-250 °C), suggesting that the O isotopic compositions of CM carbonates likely recorded an increase of the alteration temperature with time (see [START_REF] Suttle | The aqueous alteration of CM chondrites, a review[END_REF] for review).

In type 3 chondrites, determining the alteration temperatures of CO and CV chondrites are more complex because these chondrites experienced only limited aqueous alteration. However, the low mass-dependent O isotopic equilibrium reported for fayalite-magnetite in the CO and CV chondrites suggests a significantly higher alteration temperature than that of types 1-2 chondrites, from ~150 °C for CV chondrites to 500 °C for CO chondrites [START_REF] Marrocchi | Origin and abundance of water in carbonaceous asteroids[END_REF].

Mineralogy and Stability Fields of Secondary Phases

The restricted stability fields of hydrous minerals, such as serpentine and clays in types 1-2 chondrites, are particularly sensitive indicators of aqueous alteration and can place limits on the physicochemical conditions during aqueous alteration. In less-altered CM chondrites (petrologic subtype CM2.9-2.7 in the Rubin et al. 2007 classification), the most abundant alteration products are tochilinite-cronstedtite intergrowth (TCIs) (FIG. 3B), whereas chrysotile-greenalite serpentine solid solution dominates in more altered occurrences (subtypes CM2.2-2.1) [START_REF] Velbel | Replacement of olivine by serpentine in the Queen Alexandra Range 93005 carbonaceous chondrite (CM2): reactant-product compositional relations, and isovolumetric constraints on reaction stoichiometry and elemental mobility during aqueous alteration[END_REF]. Thermodynamic simulations and hydrothermal experiments indicate that TCIs formed under reducing conditions (low fO2 fugacity), at moderate temperatures (~50-150 °C) and neutral to alkaline pH (pH ≈ 7-12) (e.g., [START_REF] Pignatelli | Multiple precursors of secondary mineralogical assemblages in CM chondrites[END_REF]. As alteration progressed, the fluid composition evolved to become more reducing, as indicated by the presence of Fe 2+ in the greenalite solid-solution end-member in CM2.2 and 2.1 chondrites [START_REF] Velbel | Replacement of olivine by serpentine in the Queen Alexandra Range 93005 carbonaceous chondrite (CM2): reactant-product compositional relations, and isovolumetric constraints on reaction stoichiometry and elemental mobility during aqueous alteration[END_REF]. The alteration conditions of CI-CR chondrites are less constrained than those of CM chondrites because of their scarcity, but these two groups of chondrites probably shared similar alteration conditions, as suggested by the presence of serpentine interlayed with saponite in their matrices.

Constraints provided by mineralogical observations and thermodynamic modeling indicate that aqueous alteration in CI chondrites occurs at high water/rock ratio relative to CM chondrites, neutral to alkaline pH (pH ≈ 7-12), and moderate temperature (~20-150 °C) [START_REF] Brearley | The action of water[END_REF].

Although type 3 carbonaceous chondrites do not contain a high abundance of hydrous minerals, CV and CO chondrites contain a wide diversity of secondary anhydrous phases, such as Ca-Ferich silicates (i.e., hedenbergite associated with andradite; Fig. 3D), magnetite, Fe-Ni sulfide, and Na-Al-Cl-rich feldspathoids. Recent mineralogical studies on Ca-Fe-rich and Na-Al-Cl-rich secondary silicates in CV and CO chondrites argue for a formation in fumarolic-like reduced environment from hot hydrothermal vapor (~200-600 °C) [START_REF] Ganino | Fumarolic-like activity on carbonaceous chondrite parent body[END_REF].

MODELING OF AQUEOUS ALTERATION AND FLUID CIRCULATION IN CHONDRITE PARENT BODIES

Chronology of Aqueous Activity and Thermal Modeling

Combined physical and chemical models of aqueous alteration on carbonaceous parent bodies have been constructed. These models aim to account for the characteristics of aqueously altered carbonaceous chondrites, especially in terms of their mineralogy and isotopic compositions.

These physical models have simulated the thermal evolution associated with fluid flow in carbonaceous asteroids, which is required to satisfy the chronological constraints from carbonaceous chondrites. For example, carbonates in carbonaceous chondrites formed ~4-5 My after the birth of the Solar System, placing a constraint on the time when aqueous alteration initiated. In most models, thermal conduction is calculated within asteroids of a few tens of km in diameter heated by the decay of radionuclides (e.g., [START_REF] Fujiya | Evidence for the late formation of hydrous asteroids from young meteoritic carbonates[END_REF]). If the ambient temperatures of such small asteroids are assumed to be low (~ -100 °C), they cool quickly within millions of years by thermal conduction. Thus, radioactive nuclides with half-lives comparable to the cooling timescale were effective heat sources in the early Solar System. Among short-lived radionuclides, 26 Al was the major heat source because of its short half-life of ~700,000 years, high decay energy of 4 MeV per atom, and abundance in the early Solar System. Thermal models have concluded that the carbonaceous parent bodies of aqueously altered carbonaceous chondrites likely formed 3-4 My after the birth of the Solar System to satisfy the carbonate age constraints and achieve a relatively low peak temperature of 250 °C under which aqueous alteration took place (FIG. 4).

Fluid Flow Models

Some models have incorporated fluid flow in asteroids either as exhalation flow from the interior to the surface driven by vapor pressure or as fluid convection driven by buoyancy (e.g., [START_REF] Palguta | Fluid flow and chemical alteration in carbonaceous chondrite parent bodies[END_REF]. The extent of fluid flow is controlled by the asteroid permeability. Permeability is a measure of the ability of a porous material to transmit fluid, and is not unambiguously determined for "initial" carbonaceous asteroids. The models invoking fluid flow often assume a relatively high permeability (up to 10 -11 m 2 ), consistent with that of terrestrial sediments. However, the extremely fine grain size observed in primitive carbonaceous chondrites suggests that these asteroids may have had a much lower permeability than previously estimated (down to 10 -19 m 2 ) [START_REF] Bland | Why aqueous alteration in asteroids was isochemical: high porosity ≠ high permeability[END_REF]). As a result, the distances of fluid flow in carbonaceous asteroids would have been limited to only hundreds of microns at most. Thus, whether fluid flow in carbonaceous asteroids actually occurred still remains unclear. The limited fluid flow may be consistent with the apparent isochemical nature of CM chondrites, i.e., their chemical compositions are as expected from aqueous alteration in a closed system. Furthermore, carbonates with a wide variety of C isotopic compositions (𝛿 13 CPDB = ~20‰-80‰) are observed within mm-sized thin sections of CM chondrites, suggesting heterogeneous fluid compositions, which reflect varying physicochemical conditions and, thus, limited mobility of the aqueous fluids (see [START_REF] Suttle | The aqueous alteration of CM chondrites, a review[END_REF] for a review). On the other hand, the depletion of thermally mobile trace elements in hydrated and then metamorphosed chondrites provides evidence for open system loss and fluid-assisted escape of these elements.

An alternative asteroid model describes the structure of the carbonaceous parent bodies as giant convecting mud balls [START_REF] Bland | Giant convecting mud balls of the early solar system[END_REF]. In this model, it is assumed that solid materials making up the parent bodies were not lithified when liquid water circulated through the asteroid.

Consequently, solid materials in the parent bodies could have behaved as a mobile mud moving together with aqueous fluids, rather than a rigid, spatially fixed rock. One important implication from this model is that the chemical compositions of aqueously altered carbonaceous chondrites will necessarily be kept because the system is thoroughly mixed. The individual mud particles are predicted to have undergone aqueous alteration under varying physicochemical conditions, such as temperatures and redox states during convection, and to have subsequently been brought together to form the aqueously altered carbonaceous chondrites. Thus, this model potentially explains the heterogeneous O and C isotopic compositions of carbonates observed in single CM chondrite specimens. Finally, this model predicts the size-sorting of particles during mud convection. This means that large particles (>100 μm) could have sunk to the core of the parent bodies, and that the mantle would have been dominated by fine particles. CI chondrites are the most aqueously altered chondrites and do not contain chondrules, which are mm-to sub-mmsized silicate spherules of olivine and pyroxene once melted in the solar nebula. Therefore, CI chondrites may represent the mantle of their mud-ball parent body from which chondrules sank to the parent body's center. It is argued that the mineralogy and geochemistry of dwarf planet Ceres are consistent with CM/CI-like chondrites. However, Ceres has experienced more advanced alteration, likely due to convection, which increased the effective water/rock ratios [START_REF] Mcsween | Carbonaceous chondrites as analogs for the composition and alteration of Ceres[END_REF].

POSSIBLE TESTS ON AQUEOUS ALTERATION MODELS BY SAMPLE RETURN MISSIONS

Sample Return

Recently, two space missions aiming to bring extraterrestrial samples back to Earth, so-called sample return missions, have successfully collected surface materials from volatile-rich, primitive carbonaceous asteroids. The Hayabusa2 spacecraft of the Japan Aerospace Exploration Agency (JAXA) reached the near-Earth CB-type (see glossary) carbonaceous asteroid (162173) Ryugu in June 2018 [START_REF] Watanabe | Hayabusa2 arrives at the carbonaceous asteroid 162173 Ryugu-a spinning top-shaped rubble pile[END_REF]. This spacecraft carried out touch-down operations twice in February and July 2019 and acquired ~5.4 g of material from the surface of Ryugu. The second touch-down site on Ryugu was located ~20 m from the artificial crater (~2.7 m depth) created by the Small Carry-on Impactor (SCI) in April 2019. Thus, it is likely that not only surface materials but also subsurface materials were acquired. The Hayabusa2 spacecraft delivered its collected samples to Earth in December 2020. NASA's OSIRIS-REx spacecraft also reached another near-Earth B-type (a subcategory of C-type) carbonaceous asteroid (101955) Bennu in December 2018 [START_REF]The unexpected surface of asteroid (101955) Bennu[END_REF]. The spacecraft collected a plentiful amount of surface materials, expected to be >60 g. The OSIRIS-REx spacecraft began its two-year journey back to Earth in May 2021 and will return with its samples to Earth in September 2023.

Aqueous Alteration on the Ryugu and Bennu Parent Bodies

Asteroids Ryugu and Bennu both have a spinning top-shape (i.e., a pronounced equatorial ridge) (FIG. 5A), low density of ~1.2 g/cm 3 consistent with a rubble-pile structure with a high porosity, and a low geometric albedo of approximately 4.4%-4.5%. The rubble-pile structure and high porosity suggest that these asteroids are re-accreted fragments generated by catastrophic disruption of their original, larger parent bodies. The Near-Infrared Spectrometer (NIRS3) boarded on the Hayabusa2 spacecraft has detected a weak and narrow absorption feature at ~2.7 μm in the surface materials across the entire surface of Ryugu (FIG. 5B), corresponding to OHbearing minerals (phyllosilicates) that resemble those observed in CI chondrites experimentally heated to 500 °C [START_REF] Kitazato | The surface compositions of asteroid 162173 Ryugu from Hayabusa2 near-infrared spectroscopy[END_REF]) (FIG. 5C). Similarly, the SCI experiment of Hayabusa2 also revealed a slightly stronger -OH absorption of the excavated materials found nearby the artificial impact. It is likely that both the surface and subsurface materials of Ryugu contain hydrous minerals, but underwent heating in the range of ~300-700 °C (temperatures where phyllosilicates dehydrate), and that surface processes, such as space weathering and radiative heating, have induced subtle spectral changes of the uppermost surface. Overall, these observations suggest that (1) hydrous minerals are ubiquitous on Ryugu's subsurface, (2) Ryugu materials are likely thermally metamorphosed, and (3) the primary thermal metamorphism occurred on the original, larger parent body of Ryugu.

An apparent absorption feature at ~2.7 μm, similar to that observed for CM and CI chondrites, can be found for all of the spectra of Bennu acquired by the OSIRIS-REx Visible and InfraRed Spectrometer (OVIRS). It is known that the exact position of the ~2.7-μm band minimum varies with mineral and chemical composition. The band center of Bennu occurs at 2.74 μm, consistent with petrologic subtype CM2.1-2.2 and corresponding to the most aqueously altered CM chondrites. The detection of spectral absorption at 0.55 μm, corresponding to magnetite, also supports the affinity of Bennu with heavily altered CM or CI chondrites. These observations suggest that Bennu materials have a phyllosilicate-dominated composition. The deeper 2.7-μm band of Bennu than that of Ryugu indicates that Bennu is less heated than Ryugu and that their materials differ from each other [START_REF] Ve | Evidence for widespread hydrated minerals on asteroid (101955) Bennu[END_REF].

The returned samples from Ryugu and Bennu will first tell us whether their spectra actually correspond to carbonaceous chondrites in our collection, and whether they are asteroidal materials we have not yet obtained as meteorites. The variability of the sample's mineralogy and chemistry will provide crucial information about the structure of their original, larger parent bodies. The timescales of heating by 26 Al are much shorter than the timescales of cooling determined by the thermal conductivity. Therefore, we can expect that the peak temperatures experienced by large asteroids do not drastically vary from the center to the subsurface regions of the asteroids. Thus, if we find diverse mineralogy and chemistry among individual specimens in the returned samples, then the original asteroids may have been relatively small. Moreover, we may find evidence for fluid flow in the returned samples, such as carbonate veins filling fractures.

It should be noted that centimeters-thick, roughly meter-long bright carbonate veins were found from remote sensing observations on Bennu [START_REF] Kaplan | Bright carbonate veins on asteroid (101955) Bennu: implications for aqueous alteration history[END_REF]. The analyses of the returned samples will unveil the evolution of the carbonaceous asteroids, and help to understand the fate of the water that these asteroids accreted in the early history of our Solar System.

GLOSSARY

Delta notation -The delta notation (𝛿) represents a per mil (‰: 10 -3 ) deviation of the isotopic ratio of a given sample from a terrestrial standard value. The isotopic ratios of an elements are often expressed by the delta notation because their natural variation is commonly small, on the order of 1% or less.

CO self-shielding -Carbon monoxide (CO) molecules at the surface of the parent molecular cloud or protoplanetary disk are dissociated by UV irradiation. The intensity of UV with the wavelengths of dissociation lines for abundant C 16 O rapidly attenuates at the surface, which is referred to as self-shielding. This process can produce a selective enrichment in 16 O for CO gas in the deeper region, because less abundant C 17 O and C 18 O can still be dissociated by UV there.

Asteroid taxonomy -Classification of asteroids according to their reflectance spectra, i.e., the change in reflectance with wavelength. C-complex asteroids, including Ryugu and Bennu, tend to have weak UV features and relatively flat to bluish spectra at longer wavelengths. The average visible albedo of C-complex objects is ~6 %, and ~60% of observed C-complex objects have 3-μm bands, indicating hydrated silicates on their surfaces.

FiguresFIGURE 1 .

 1 Figures

FIGURE 2 .

 2 FIGURE 2. Spatial distribution and isotopic compositions of the different water reservoirs in the early Solar System. (A) Simplified view of the repartition of the water ice reservoirs in the protoplanetary disk. The snow line represents the distance from the Sun where the temperature is low enough (≤170 K) for water ice grains to form. (B) Distribution of D/H ratios for water in ordinary (OC) and carbonaceous (CV, CO, CM, CR, CI) chondrites, comets, and interstellar water ice. (C) Distribution of mass-independent oxygen isotopic anomalies (∆ 17 O) recorded by secondary minerals in chondrites. Cosmic symplectite (COS) is an assemblage of 16 O-poor magnetite and pentlandite.

FIGURE 3 .FIGURE 4 .FIGURE 5 .

 345 FIGURE 3. Backscattered-electron images of secondary phases in carbonaceous chondrites. (A) Cacarbonate (Cc) from the CM Maribo. (B) Tochilinite-cronstedtite intergrowth (TCI) from the CM Boriskino. (C) Fayalite (Fa) from the CV Kaba. IMAGE COURTESY OF YVES MARROCCHI. (D) Hedenbergite (Hd) and andradite (Adr) from the CV Allende. IMAGE COURTESY OF CLEMENT GANINO.

  17 O = 𝛿 17 O -0.52 × 𝛿 18 O) observed in most Solar System materials is interpreted as the result of isotopic mixing between inner Solar System material (∆ 17 O ≈ 0‰) with the influx of 16 O-poor H2O ice (∆ 17 O >> 0‰) formed by a CO self-shielding process (see glossary) in the outer part of the protoplanetary disk or in the parent molecular cloud (see Yurimoto et al. 2008 for a review).

ACKNOWLEDGMENTS

The authors wish to thank Guest Editors Yves Marrocchi and Pierre Beck, and Principal Editor Richard J. Harrison for the invitation to contribute to this thematic issue. We are very grateful to Martin D. Suttle, Michael A. Velbel, and Ryan C. Ogliore for constructive comments and suggestions. Lionel Vacher acknowledges funding by the McDonnell Center for Space Sciences at Washington University in St. Louis (USA).


N Zaïm

F Böhle

M Bocoum

A Vernier

S Haessler

X Davoine

L Videau

J Faure

R Lopez-Martens

Few-cycle laser wakeeld acceleration on solid targets with controlled plasma scale length

We measure the emission of energetic electrons from the interaction between relativistic-intensity ultrashort laser pulses and a solid density plasma with tunable density gradient scale length. We detect an electron beam that only appears with few-cycle pulses (< 10 fs) and large plasma scale lengths (L > λ 0 ). Numerical simulations, in agreement with the experiments, reveal that these electrons are accelerated by a laser wakefield. Plasma waves are indeed resonantly excited by the few-cycle laser pulses in the near-critical density region of the plasma. Electrons are then injected by ionization into the plasma waves and accelerated to relativistic energies. In this laser wakefield acceleration regime, the plasma waves are rotated by the plasma density gradient which results in the electrons not being emitted in the same direction as the driving laser pulse.

I.

INTRODUCTION

Since the recent advent of ultrahigh intensity lasers, bright particle and radiation sources with femtosecond duration have been developed from relativistic laser-plasma interactions. These new sources are expected to find applications in various fields including medicine, imaging and ultrafast probing of matter [START_REF] Malka | Principles and applications of compact laser-plasma accelerators[END_REF][START_REF] Albert | Applications of laser wakefield acceleratorbased light sources[END_REF] . Laser wakefield acceleration (LWFA) is an efficient process for driving relativistic electron beams with few femtosecond durations [START_REF] Lundh | Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator[END_REF] and energies in the 100 MeV to multi-GeV range [START_REF] Faure | A laser-plasma accelerator producing monoenergetic electron beams[END_REF][START_REF] Wang | Quasi-monoenergetic laser-plasma acceleration of electrons to 2 GeV[END_REF][START_REF] Leemans | Multi-GeV electron beams from capillary-discharge-guided subpetawatt laser pulses in the self-trapping regime[END_REF] , or more recently in the few-MeV range with kHz lasers [START_REF] Guénot | Relativistic electron beams driven by khz single-cycle light pulses[END_REF][START_REF] Gustas | High-charge relativistic electron bunches from a khz laser-plasma accelerator[END_REF][START_REF] Salehi | Mev electron acceleration at 1khz with < 10mj laser pulses[END_REF] . In this scheme, the laser pulse ponderomotive force drives a high amplitude plasma wave that is able to trap and accelerate electrons over very short distances [START_REF] Esarey | Physics of laserdriven plasma-based electron accelerators[END_REF] . Usually, LWFA takes place in mm-scale underdense plasmas (gas jets) but is quite inefficient with solid targets. Indeed, for solid-density plasmas, the processes responsible for transferring the laser energy to particles and radiation are radically different. Understanding the pathways and mechanisms of energy transfer to the plasma electrons is a complex and fundamental question that has implications for ion acceleration [START_REF] Macchi | Ion acceleration by superintense laser-plasma interaction[END_REF] and high harmonic generation [START_REF] Thaury | High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms[END_REF] .

It is well known that the plasma density profile at the front surface is a key parameter that can dramatically transform the nature of the interaction [START_REF] Wilks | Absorption of ultrashort, ultra-intense laser light by solids and overdense plasmas[END_REF][START_REF] Sentoku | High-energy ion generation in interaction. of short laser pulse with high-density plasma[END_REF][START_REF] Mckenna | Effects of front surface plasma expansion on proton acceleration in ultraintense laser irradiation of foil targets[END_REF][START_REF] Kemp | Hot-electron energy coupling in ultraintense laser-matter interaction[END_REF][START_REF] Kahaly | Direct observation of density-gradient effects in harmonic generation from plasma mirrors[END_REF][START_REF] Scott | Optimization of plasma mirror reflectivity and optical quality using double laser pulses[END_REF] . When the plasma scale length is short compared to the laser wavelength (L < λ 0 /10), the physics is now fairly well understood. At moderate intensity, vacuum heating [START_REF] Brunel | Not-so-resonant, resonant absorption[END_REF] is the dominant mechanism for energy transfer to the electrons. At relativistic intensities, the physics becomes more complex: the laser field triggers a periodic push-pull motion of the front surface that follows the sign of the laser field [START_REF] Gonoskov | Ultrarelativistic nanoplasmonics as a route towards extremeintensity attosecond pulses[END_REF][START_REF] Thévenet | On the physics of electron ejection from laser-irradiated overdense plasmas[END_REF] . This nonlinear periodic motion leads to high harmonic generation via the relativistic oscillating mirror mechanism [START_REF] Lichters | Short-pulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity[END_REF][START_REF] Baeva | Theory of high-order harmonic generation in relativistic laser interaction with overdense plasma[END_REF] and also results in electron ejection from the front surface [START_REF] Thévenet | On the physics of electron ejection from laser-irradiated overdense plasmas[END_REF][START_REF] Thévenet | Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator[END_REF]25 . These electrons are subsequently injected a) Electronic mail: neil.zaim@ensta-paristech.fr into the reflected laser field where they can directly gain large amounts of energy [START_REF] Thévenet | Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator[END_REF] . In this regime, electron emission has been reported to be optimal when the gradient scale length is on the order of ∼ λ 0 /10, with electron energies ranging from 100 keV to multi-MeV, depending on laser intensity [START_REF] Thévenet | Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator[END_REF][25][START_REF] Bastiani | Experimental study of the interaction of subpicosecond laser pulses with solid targets of varying initial scalelengths[END_REF][START_REF] Mordovanakis | Quasimonoenergetic electron beams with relativistic energies and ultrashort duration from laser-solid interactions at 0.5 khz[END_REF][START_REF] Tian | Electron emission at locked phases from the laser-driven surface plasma wave[END_REF][START_REF] Bocoum | Anticorrelated emission of high harmonics and fast electron beams from plasma mirrors[END_REF] .

For longer gradient scale lengths, interaction in the nearcritical density part of the plasma, which has also been investigated in the context of ion acceleration [START_REF] Yogo | Laser ion acceleration via control of the nearcritical density target[END_REF][START_REF] Henig | Enhanced laser-driven ion acceleration in the relativistic transparency regime[END_REF][START_REF] Bin | Ion acceleration using relativistic pulse shaping in near-critical-density plasmas[END_REF][START_REF] Powell | Proton acceleration enhanced by a plasma jet in expanding foils undergoing relativistic transparency[END_REF] , becomes significant. The physics gets extremely complex and there is no unified description of energy transfer and electron acceleration. There is a wide disparity of experimental results and various mechanisms have been proposed, including resonant absorption [START_REF] Li | Hot electrons in the interaction of femtosecond laser pulses with foil targets at a moderate laser intensity[END_REF][START_REF] Cai | Double-peak emission of hot electrons generated by femtosecond laser interaction with solid targets[END_REF] , J×B heating [START_REF] Malka | Experimental confirmation of ponderomotiveforce electrons produced by an ultrarelativistic laser pulse on a solid target[END_REF] , ponderomotive acceleration [START_REF] Zhang | Emission direction of fast electrons in laser-solid interactions at intensities from the nonrelativistic to the relativistic[END_REF] , stochastic heating [START_REF] Tommasini | Generation of monoenergetic ultrashort electron pulses from a fs laser plasma[END_REF][START_REF] Feister | Relativistic electron acceleration by mj-class khz lasers normally incident on liquid targets[END_REF] , acceleration by surface quasistatic fields [START_REF] Li | Observation of a fast electron beam emitted along the surface of a target irradiated by intense femtosecond laser pulses[END_REF] or direct laser acceleration [START_REF] Toncian | Non-maxwellian electron distributions resulting from direct laser acceleration in near-critical plasmas[END_REF][START_REF] Ma | Ultrahighcharge electron beams from laser-irradiated solid surface[END_REF] . However, it is still unclear what mechanisms actually arise in experiments and the precise experimental conditions under which they appear are not known. This may be due to the lack of control and measurement of the density gradients, which makes the interpretations difficult. In this article, we show that by using few-cycle laser pulses with durations as short as 3.5 fs, we find a regime where LWFA occurs in the near-critical density region of the plasma. Even though this mechanism was previously suggested to explain experimental results with thick solid targets [START_REF] Cai | Double-peak emission of hot electrons generated by femtosecond laser interaction with solid targets[END_REF][START_REF] Mao | Highly collimated monoenergetic target-surface electron acceleration in nearcritical-density plasmas[END_REF] , LWFA is here clearly identified by varying and precisely controlling the key parameters of the interaction, namely the gradient length and the pulse duration, and by performing PIC simulations with realistic plasma density profiles. We find that this regime, which results in the emission of a ≈ 25 • -wide stable electron beam, only occurs with few-cycle laser pulses.

II. EXPERIMENTAL SETUP AND RESULTS

The experiments are performed with the Salle Noire laser system at the Laboratoire d'Optique Appliquée (LOA). The laser delivers 2.6-mJ pulses at 1-kHz repetition rate with an extremely high temporal contrast (> 10 10 ) [START_REF] Jullien | Carrier-envelope-phase stable, high-contrast, double chirped-pulse-amplification laser system[END_REF] . The 800 nm, FIG. 1. Schematic of the experimental setup. The laser pulses interact at 1-kHz repetition rate with a fused silica rotating target. Inset: superimposition of the on-target prepulse (white) and main pulse (color) focal spots.

24 fs laser pulses are post-compressed in a helium-filled stretched hollow-core fiber [START_REF] Böhle | Compression of cep-stable multi-mj laser pulses down to 4 fs in long hollow fibers[END_REF][START_REF] Ouillé | Relativisticintensity near-single-cycle pulses at 1 kHz[END_REF] . The pulse duration can be tuned by changing the pressure in the fiber, thereby providing near Fourier transform limited pulses from 3.5 fs to 24 fs. The laser beam is focused down to a 1.75 µm FWHM spot resulting in peak intensities ranging from 2.3 × 10 18 W/cm 2 (a 0 1) for 24 fs pulses to 1.6 × 10 19 W/cm 2 (a 0 2.7) for 3.5 fs pulses. Here, a 0 is defined as the normalized amplitude of the peak laser field: a 0 = E MAX /E 0 with E 0 = m e cω 0 /e where ω 0 is the laser frequency, c is the speed of light in vacuum and m e and e are the electron mass and charge respectively. In this experiment, represented in Fig. 1, p-polarized pulses impinge on an optically flat fused silica (SiO 2 ) target with an incidence angle θ i = 55 • . A spatially overlapped prepulse, created by picking off ≈ 4% of the main pulse through a holey mirror, is focused to a much larger 13 µm FWHM spot (see inset of Fig. 1) in order to generate a transversely homogeneous plasma that expands into vacuum. The plasma density profile during the interaction is controlled by varying the delay, ∆t, between the prepulse and the main pulse. The density scale length is estimated experimentally using spatial domain interferometry and assuming isothermal expansion [START_REF] Bocoum | Spatial-domain interferometer for measuring plasma mirror expansion[END_REF] . Backward electron emission is measured using a Lanex screen, protected by a 13 µm thick Al-foil, which detects electrons with energies > 150 keV. The Lanex screen was calibrated prior to the experiment using a 3-MeV RF accelerator. The absolute charge is estimated from the electron energy spectrum obtained from the PIC simulations described below, combined with the known spectral response of the Lanex screen. The resulting uncertainty, of the order of 50%, is mainly due to the fact that the exact shape of the energy spectra was not measured. The angular electron distribution in the backward direction is recorded for -3 • < θ < 75 • and -15 • < φ < 15 • where θ and φ are the angles with respect to target normal respectively in the incidence and transverse planes.

Figures 2(a)-2(f) show the measured electron signal as a function of the delay between the prepulse and the main pulse for 5 different laser pulse durations. We first find a strong electron emission for short delays (∆t < 20 ps), corresponding to a sharp plasma-vacuum interface. This emission, detected for every pulse duration, is optimal for a delay ∆t ≈ 9 ps, i.e. L < λ 0 /5. In this regime, the push-pull mechanism mentioned in the introduction is responsible for the ejection of electrons from the plasma [START_REF] Thévenet | On the physics of electron ejection from laser-irradiated overdense plasmas[END_REF][START_REF] Thévenet | Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator[END_REF][START_REF] Bocoum | Anticorrelated emission of high harmonics and fast electron beams from plasma mirrors[END_REF] . A typical electron angular distribution in this case is displayed in Fig. 2(g), showing a broad divergence angle of ≈ 50 • .

As the delay is further increased, the detected charge drops (10 ps < ∆t < 30 ps), and then rises again for longer delays (∆t > 50 ps). This time however, electrons are only emitted when few-cycle pulses (≤10 fs) are used. Note that chirping a few-cycle pulse to increase its duration results in a similar decline of the electron signal, as can be seen in Fig. 3. This is thus a very distinct physical regime, in which the gradient length is much larger (L > λ 0 ) and the duration of the laser pulse plays a major role. In this case, the obtained electron beams have more charge and a narrower divergence angle of ≈ 25 • as is visible in Fig. 2(h). The electrons are emitted near the specular direction, with a slight shift towards the normal direction. The detected signal is very stable over a wide range of delays (50 ps< ∆t <200 ps), indicating that the electron ejection mechanism is not highly sensitive to the exact shape of the plasma density profile. Contrary to the emission of electrons for short delays (∆t < 20 ps) which is strongly correlated with high-harmonics generation 25 , we measure no significant high-harmonics signal at these longer delays (∆t > 30 ps).

III. PIC SIMULATIONS

To understand the origin of this new electron emission process, we turn to 2D Particle-In-Cell (PIC) simulations using the code WARP 48,49 coupled to the high performance PIC-SAR library [50][START_REF] Vincenti | Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference maxwell solver[END_REF][START_REF] Vincenti | An efficient and portable simd algorithm for charge/current deposition in particle-in-cell codes[END_REF][START_REF] Vincenti | Ultrahigh-order maxwell solver with extreme scalability for electromagnetic pic simulations of plasmas[END_REF] . We use the same laser parameters as in the experiments (more details are given in the Supplementary Material). A moving window is started after the interaction in order to follow the accelerated electrons far from the plasma. We took great care in providing a realistic description of the plasma density gradient. First, the plasma is initially partially ionized (up to Si 4+ and O 2+ ) in order to model ionization by the prepulse. The initial ionization states are estimated from the prepulse peak intensity (∼ 10 15 W/cm 2 ) and the intensity thresholds for barrier-suppression ionization [START_REF] Gibbon | Short pulse laser interactions with matter[END_REF] in silicon and oxygen. Further ionization by the main pulse is also taken into account in the simulations. Second, the plasma density profile is obtained by performing hydrodynamic 1D simulations with the code ESTHER [START_REF] Colombier | Optimized energy coupling at ultrafast laser-irradiated metal surfaces by tailoring intensity envelopes: Consequences for material removal from al samples[END_REF] . Figure 4 shows the resulting profiles for 4 different values of the delay between the prepulse and the main pulse. Note that the density profiles are not always exponential in Fig. 4, contrary to results from models assuming isothermal expansion. The gradient appears to have an exponential shape only for short delays (i.e. for sharp plasmavacuum interfaces) but not for longer delays. The isothermal hypothesis, used to estimate the gradient scale length in the previously mentioned interferometric measurements [START_REF] Bocoum | Spatial-domain interferometer for measuring plasma mirror expansion[END_REF] , likely fails due to radiation and convection losses on these longer timescales. In our case, the electron beam appears for long delays ∆t and we therefore use the density profiles shown in Fig. 4 as inputs for the PIC simulations.

Snapshots from two different PIC simulations are shown in Fig. 5. Both simulations use the plasma density profile obtained with a delay ∆t = 80 ps (i.e. the red curve in Fig. 4), a value for which the electron beam is detected in the ex- periments. The pulse duration is either 5 fs or 24 fs, resulting in peak intensities of 10 19 W/cm 2 (a 0 = 2.15) and 2.1 × 10 18 W/cm 2 (a 0 = 0.98) respectively.

The first striking feature is the formation of high amplitude plasma waves in the wake of the 5-fs pulse. Their wavefront is bent by the density gradient, akin to the plasma waves generated by Brunel electrons in the coherent wake emission mechanism of high-harmonic generation [START_REF] Thaury | High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms[END_REF] . Even though these wakefields appear in the whole region where the 5-fs pulse propagates, inside which the density ranges from n c /1000 to n c cos 2 θ i ∼ 0.3n c 56 , they are completely absent in the 24-fs pulse simulation. This can be easily explained by the fact that wakefield excitation is optimal at the resonance condition, i.e. when the pulse duration is on the order of half the plasma wavelength 10 : τ λ p /2c. This gives a resonant density of n c /14 for 5-fs pulses, versus n c /300 for 24-fs pulses, explaining why large wakefields appear for the few-cycle pulse only (see also Supplementary Material). Some electrons, represented in green in Fig. 5, are trapped and accelerated by the plasma waves' strong electric fields, that reach up to 1 TV/m. The angular and energy distribu- tion of these LWFA electrons is shown in the green curves of Fig. 6(a) and Fig. 6(c) respectively. Their energy spectrum extends to ≈ 2.5 MeV and their total ejected charge is ≈ 7 pC/ µm. These electrons are emitted in the same direction as the electrons detected at long delays in experiments (see the red curve in Fig. 6(a)). Moreover, as in experiments, these electrons only appear for few-cycle pulses. We therefore conclude that the electron beam detected at long delays in experiments originates from LWFA. We may notice that the angular distribution of these electrons is significantly narrower in the simulation than in experiments. This is likely due to space charge effects during the propagation of the electron beam to the detector, which we expect to be important for a sub-MeV beam with tens of pC of charge. The electrons are indeed only propagated for tens of microns in the simulation while the Lanex screen is located ≈ 10 cm away from the target in experiments.

In the simulations, the LWFA electrons come from the Lshell of silicon. They have high binding energies (from ≈ 150 eV to ≈ 500 eV) and can therefore only be ionized by the huge electric fields inside the main laser pulse. The fact that only electrons ionized in the center of the pulse are accelerated suggests that injection by ionization, a well-known mechanism in underdense plasmas [START_REF] Mcguffey | Ionization induced trapping in a laser wakefield accelerator[END_REF][START_REF] Pak | Injection and trapping of tunnel-ionized electrons into laser-produced wakes[END_REF] , is responsible for trapping the electrons into the wakefields. Taking field ionization into account is therefore needed to properly describe the injection of electrons into the plasma waves and more generally to correctly model laser interactions with overdense plasmas when the plasma scale length is large.

Another family of electrons, shown in yellow in Fig. 5 and labelled "reflection electrons", is ejected from the plasma in the simulations. These electrons are accelerated at the reflection point of the laser, where the density is n c cos 2 θ i . Their angular and energy distributions are displayed in the yellow curves of Fig. 6. This family of electrons, which appears for both 5-fs and 24-fs pulses and has a very large angular divergence spreading across all directions, is not detected in experiments. This fact shows that our 2D PIC simulations do not accurately reproduce the ratio between the two populations. This second family of electrons would likely be attenuated in more accurate but more costly 3D simulations. However, this is not a major concern because the simulations explain the main experimental observations, i.e. a well-defined beam of LWFA electrons that appears only for extremely short pulse duration.

It is also worth noting that the same qualitative results are found when the simulations are performed with an exponential density profile with L = 3λ 0 , thus confirming our previous observation that the electron ejection mechanism is not highly sensitive to the exact shape of the plasma density profile. Another interesting point is that a similar trend can be found when the intensities are interchanged in the simulations (i.e. when the 5-fs simulation is carried out with a peak intensity of 2.1 × 10 18 W/cm 2 , while the 24-fs simulation is performed with a 1 × 10 19 W/cm 2 peak intensity). In this case, even though the laser pulse energy is 25 times lower in the 5-fs simulation, a very small number of electrons remain laser wakefield accelerated while there is still no plasma wave formation in the 24-fs simulation (see Supplementary Material). These simulations show a clear effect of pulse duration and confirm that the emergence of the electron beam is not simply due to the increase in intensity when reducing the pulse duration.

IV. PLASMA WAVE FORMATION AND ELECTRON ACCELERATION IN A TRANSVERSE GRADIENT

A unique feature of this acceleration regime is that the electrons are not emitted in the same direction as the driving laser pulse, as is usually the case with LWFA, even with similar laser parameters and plasma densities [START_REF] Guénot | Relativistic electron beams driven by khz single-cycle light pulses[END_REF][START_REF] Gustas | High-charge relativistic electron bunches from a khz laser-plasma accelerator[END_REF] . This is because the wakefields' wavefronts are rotated by the density gradient. To explain this rotation, we use a simple heuristic model based on the following assumptions: (i) the plasma wave is initiated at the temporal center of the laser pulse. This is formally equivalent to an infinitely short driving pulse and is reasonable if the pulse duration is much shorter than a plasma period. (ii) The plasma wave is longitudinal, i.e. the electrons forming it oscillate in the direction of laser propagation. This assumption is equivalent to an infinitely wide (1D) driving laser pulse and is valid when the laser transverse size is larger than a plasma wavelength. (iii) The center of the laser pulse travels at c, neglecting the decrease in group velocity. (iv) The phase of the plasma wave varies at each point at the local plasma frequency. This is valid if the gradient scale length is much larger than the plasma wavelength [START_REF] Thaury | High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms[END_REF] . With these assumptions, the phase ϕ of the plasma wave is:

ϕ(x, z,t) = ω p (x)(t -t 0 (x, z)) (1)
Here, ω p is the local plasma frequency and t 0 = (z sin θ ix cos θ i )/c is the time at which the temporal center of the laser pulse excites the plasma wave. Plasma wavefronts obtained using Eq. ( 1) in an exponential density gradient are shown in Fig. 7. Even though this simple model is not perfectly valid for the considered experimental case, it can qualitatively reproduce the shape of the plasma waves. Physically, the rotation of the wavefronts can be explained by the density gradient seen by the laser, i.e. the fact that one side of the laser pulse excites a plasma wave with a higher frequency than the other. A given phase will therefore be reached quicker in the region of higher frequency, which results in rotated wavefronts.

We can also use this model to qualitatively explain the measured angular distribution. Let us consider an electron moving with an angle θ e with respect to the x-axis at a position where the wavefront of the plasma wave makes an angle θ w with respect to the z-axis (see Fig. 7(b)). We first note that since the plasma frequency only depends on x, the phase velocity of the plasma waves in the z-direction is (v ϕ ) z = c/ sin θ i . We can then, using the law of sines, calculate the phase velocity along the direction of electron motion:

(v ϕ ) θ e = sin θ w cos(θ e -θ w ) sin θ i c (2)
If the electron is trapped in the wakefield, its velocity is mainly colinear with the electric field of the plasma waves, i.e. perpendicular to the wavefronts. In this case, we have θ e ≈ θ w and Eq. ( 2) is simplified to:

(v ϕ ) θ e = sin θ e sin θ i c (3)
Trapping of electrons by the plasma wave is only possible if the phase velocity of the wakefield is lower than c, meaning in our case that electrons can only be emitted when θ e < θ i . Furthermore, electron acceleration to relativistic energies is efficient when the phase velocity is close to c. Equation (3) therefore indicates that the electrons should be emitted close to the specular direction with a slight shift towards the normal direction, in good agreement with experiments and simulations. Electrons directed closer to the grazing direction (θ e > θ i ) cannot be trapped as the phase velocity of the plasma waves in their direction is greater than c while electrons emitted close to the normal direction cannot reach high energies as they would quickly dephase from the plasma waves.

V. CONCLUSION

In conclusion, we detect an electron beam that only appears for few-cycle pulses and large plasma scale lengths. Particle-In-Cell simulations successfully explain the experimental results: the detected electrons are injected by ionization into wakefields formed behind the pulse. These plasma waves can only be efficiently excited by few-cycle pulses at these nearcritical densities, explaining why this new electron emission mechanism is only observed with extremely short pulses. A singular trait of this acceleration regime is that, due to the rotation of the wakefields induced by the density gradient, the electron beam is not emitted in the same direction as the driving laser pulse. This work offers a better understanding of the interaction between ultraintense laser pulses and solid targets and confirms that extremely short pulse durations and controlled plasma conditions provide access to new acceleration regimes.

VI. SUPPLEMENTARY MATERIAL

Supplementary material consists of 6 sections. In the first section, we present the experimental results obtained when reducing the main laser pulse intensity. In the second section, we provide detailed explanations regarding how fewcycle laser pulses are modeled in our Particle-In-Cell simulations. In the third section, we give more informations concerning the numerical parameters of the Particle-In-Cell simulations presented in the main text. In the fourth section, we present simulations performed with the other pulse durations studied experimentally. In the fifth section, we present more exhaustively the simulations with interchanged intensities that are mentioned in the main text. In the sixth section, we estimate the amplitude of the plasma waves generated in our experiments using the 1D nonlinear theory of wakefield generation.

VII.

FIG. 2 .

 2 FIG. 2. (a)-(e)Electron angular distribution integrated over the φ angle as a function of the delay between the prepulse and the main pulse for respective pulse durations of 24, 10, 7.5, 5 and 3.5 fs. (f) Total ejected charge as a function of the delay between prepulse and main pulse. (g), (h) Typical electron angular distribution obtained with 5-fs pulses respectively in the short (∆t = 9 ps) and long (∆t = 140 ps) plasma scale length regimes. The gradient scale lengths given in the top axis are obtained from interferometric measurements[START_REF] Bocoum | Spatial-domain interferometer for measuring plasma mirror expansion[END_REF] . The white lines in (a)-(e) represent the prepulse leads corresponding to the ticks in (f). The red lines and dots mark the specular direction.

FIG. 3 .FIG. 4 .

 34 FIG.3. Total detected charge as a function of pulse duration for a delay ∆t = 90 ps between the prepulse and the main pulse. The pulse duration is tuned here by chirping positively (red points) or negatively (blue points) the 3.5-fs driving laser.

FIG. 5 .

 5 FIG. 5. Laser magnetic field and electron density from PIC simulations with a large plasma scale length (∆t = 80 ps) and a pulse duration of (a)-(c) 5 fs or (d)-(f) 24 fs. The green and yellow dots show a sample of ejected electrons. T 0 is the laser optical oscillation period and B 0 = E 0 /c with E 0 defined earlier. See also videos for a more comprehensive view of the simulations.

FIG. 6 .

 6 FIG. 6. (a),(b) Angular and (c),(d) energy distribution of the two families of electrons that are ejected in the (a),(c) 5 fs and (b),(d) 24 fs simulation. The distributions are obtained at the end of the simulation, long after the interaction. The red dashed curve in (a) shows for comparison the experimental angular distribution integrated along the φ angle obtained with a 5 fs pulse and an 80 ps prepulse lead, in arbitrary units.

FIG. 7 .

 7 FIG.7. Wavefronts (darker lines) obtained using Eq. (1) during the propagation of a laser pulse (represented in blue and red) in a plasma with an exponential density profile (L = 3λ 0 ). Two consecutive wavefronts are separated by a phase of 2π.

ACKNOWLEDGMENTS

We would like to thank H. Vincenti for his help and expertise with PIC simulations and for insightful discussions. This work was funded by the European Research Council under Contract No. 306708 (ERC Starting Grant No. FEMTOELEC), the Région Île-de-France (under Contract No. SESAME-2012-ATTOLITE), the Agence Nationale pour la Recherche (under Contracts No. ANR-11-EQPX-005-ATTOLAB and No. ANR-14-CE32-0011-03), the Extreme Light Infrastructure-Hungary Non-Profit Ltd (under Contract No. NLO3.6LOA) and the LabEx PALM (ANR-10-LABX-0039). This work was granted access to the HPC resources of CINES under the allocation A0020506057 made by GENCI.