Thomas Dépret
email: thomas.depret@lgp.cnrs.fr

Hervé Piégay

Violaine Dugué

Lise Vaudor

Jean-Baptiste Faure

Jérôme Le Coz

Benoît Camenen

Estimating and restoring bedload transport through a run-of-river reservoir

Weirs or run-of-river dams can disrupt bedload transfer with negative ecological effects downstream due to sediment starvation. The way and the degree to which bedload is trapped is nevertheless not straightforward and few studies have examined this topic. This study focuses on a 13km-long reservoir of the Rhône River, France, created by a diversion dam equipped with bottom gates.

Our main objective was to determine the degree of alteration of the bedload transfer downstream and to identify to which extent the implementation of Ecomorphogenic Flow (EmF), defined as environmental flow whose objective is specifically to increase bedload transfer through the reservoir to promote downstream habitat diversity, could increase bed mobility. The results show that the potential for morphological adjustments in the reservoir was already low before dam completion (1968) in response to a substantial decrease in coarse sediment supply, but that this potential was progressively reduced due to the impoundment. However, the bedload transfer continuity has been at least partially maintained since dam completion. According to numerical simulations, only particles smaller than medium gravels ( 14 mm) could be exported downstream of the dam for relatively rare discharge (50-years return-interval flood). Implementation of EmF could neatly improve the bedload transfer since it would allow to strongly increase the competence: for a 2-years and a 50-years return-interval floods, the maximum particle size exportable downstream is respectively 9 and 4 times larger than for normal functioning of the reservoir operating.

Introduction

The effects of large dams on river morphology and sediment transport have been widely studied and are therefore relatively well known. Since they modify the upstream hydraulic condition in the impounded sections by lowering the energy slope, dams interrupt bedload transport and sometimes suspended load, inducing a progressive filling of the reservoirs [START_REF] Kondolf | Sustainable sediment management in reservoirs and regulated rivers: Experiences from five continents[END_REF][START_REF] Morris | Sedimentation engineering: Processes, measurements, modeling, and practice[END_REF]. Whereas at their entrance, coarse sediment deposits form a prograding delta with grain size decreasing with downstream distance, reservoirs are mainly filled by fine and more homogenous silty deposits that can be settled by turbidity currents [START_REF] Kostic | Progradational sand-mud deltas in lakes and reservoirs. Part 1. Theory and numerical modeling[END_REF][START_REF] Lajczak | Modelling the long-term course of non-flushed reservoir sedimentation and estimating the life of dams[END_REF][START_REF] Morris | Reservoir sedimentation handbook: Design and management of dams, reservoirs, and watersheds for sustainable use[END_REF][START_REF] Snyder | Estimating accumulation rates and physical properties of sediment behind a dam: Englebright Lake, Yuba River, northern California[END_REF]. Downstream of dams, the effects of flow and sediment regime alteration is highly variable, depending on the pre-dam context (sediment size and supply, competence and capacity of the river, flow regime) and on the intensity and nature of the perturbations [START_REF] Williams | Downstream effects of dams on alluvial rivers[END_REF][START_REF] Brandt | Classification of geomorphological effects downstream of dams[END_REF]Petts andGurnell, 2005, 2013;[START_REF] Schmidt | Metrics for assessing the downstream effects of dams[END_REF][START_REF] Curtis | Temporal and spatial scales of geomorphic adjustments to reduced competency following flow regulation in bedloaddominated systems[END_REF][START_REF] Dade | Sediment transport constraints on river response to regulation[END_REF][START_REF] Grant | The Geomorphic response of gravel-bed rivers to dams: Perspectives and prospect[END_REF]. Most of the time, dams cause a geomorphic simplification [START_REF] Graf | Downstream hydrologic and geomorphic effects of large dams on American rivers[END_REF], generally induced by bed incision, a decrease in lateral mobility and bed armouring [START_REF] Rollet | Assessment of consequences of sediment deficit on a gravel river bed downstream of dams in restoration perspectives: Application of multicriteria, hierarchical and spatially explicit diagnosis[END_REF]. Together with the modification of the flow regime, geomorphic simplification results in a loss in aquatic and riparian ecological diversity [START_REF] Lobrera | Effects of flow regulation on river bed dynamics and invertebrate communities in a Mediterranean river[END_REF][START_REF] Nilsson | Alterations of Riparian Ecosystems Caused by River Regulation[END_REF][START_REF] Rolls | Environmental and ecological effects of flow alteration in surface Water ecosystems[END_REF][START_REF] Rosenberg | Global-scale environmental effects of hydrological alterations: Introduction[END_REF].

Until very recently, less attention has been paid to the impacts of run-of-river dams (Csiki andRhoads, 2010, 2014;[START_REF] Ibisate | Channel response to multiple damming in a meandering river, middle and lower Aragon River (Spain)[END_REF], despite their widespread presence. Yet, particularly because of their potential cumulative effects, series of run-of-river dams can also modify hydrological and sediment dynamics, as well as ecological functions [START_REF] Dessaix | Changes of the macroinvertebrate communities in the dammed and by-passed sections of the French upper Rhône after regulation[END_REF][START_REF] Kibler | Cumulative biophysical impact of small and large hydropower development in Nu River, China[END_REF][START_REF] Anderson | The impacts of 'run-of-river' hydropower on the physical and ecological condition of rivers[END_REF]Fencl et al., 2015). The term "run-of-river dam" still suffers from a lack of a clear definition, and other words such as "weir", "low-head dam", "overflow dam" or "small dam" are usually employed to define similar kinds of structures (Csiki andRhoads, 2010, 2014;Fencl et al., 2015). Here, we will retain the definition given by [START_REF] Csiki | Hydraulic and geomorphological effects of run-of-river dams[END_REF], namely a "structure that extends across the width of a stream or river channel, has no mechanism inhibiting discharge of water over the dam, and is of a height that generally does not exceed the elevation of the channel banks upstream -i.e., water stored upstream at base flow is contained within the river channel width of a stream or river channel". [START_REF] Costigan | Rapid response of a sand-dominated river to installation and removal of a temporary run-of-the-river dam[END_REF] note that 97% of dams in the United States are run-ofriver dams. In France, the ROE (Référentiel des Obstacles à l'Ecoulement), a large national database listing most of the transverse engineering structures impeding flow, identifies more than 57,400 weirs (May 2014 inventory), namely 81% of the total number of dams. Concerning their influence on bedload, two main questions systematically arise. First, how much is the sediment transport altered? Second, in case of partial or total interruption, what solutions could be applied to enhance or restore the sediment transfer through the reservoir? In some countries of the European Union, this concern has been integrated into the national legislative frame following the Water Framework Directive. In France for example, authorities must now guarantee "sufficient transport" maintaining or restoring the morphological and ecological structures and functions of rivers [START_REF] Malavoi | Eléments de connaissance pour la gestion du transport solide en rivière[END_REF].

All other conditions being equal, the intensity of a run-of-river dam's influence on the morphodynamics and coarse sediment transport in impounded reaches is mainly controlled by the presence or absence of bottom gates. In absence of such gates or when they are maintained closed, and at least in an initial stage, all or most of the bedload can be trapped in the reservoir [START_REF] Kibler | Learning from dam removal monitoring: Challenges to selecting experimental design and establishing significance of outcomes[END_REF][START_REF] Pearson | Bedload transport over run-of-river dams, Delaware[END_REF] and the grain size of coarse deposits tends to show a decreasing downstream pattern [START_REF] Sindelar | Effects of weir height and reservoir widening on sediment continuity at run-of-river hydropower plants in gravel bed rivers[END_REF]. Depending on dam height, bed hydraulic characteristics before impoundment, grain size and sediment yield, bedload transfer can nevertheless be preserved or restored, at least for medium-term periods. For example, [START_REF] Csiki | Influence of four run-of-river dams on channel morphology and sediment characteristics in Illinois[END_REF] documented the case of four run-of-river dams showing an absence of a statistically significant difference in the percentage of sand or gravel in the bed material between upstream and downstream portions of dams, indicating no coarse sediment accumulation in the reservoir and a probable preservation of the bedload transfer continuity. [START_REF] Pearson | Bedload transport over run-of-river dams, Delaware[END_REF] demonstrated that partial reservoir filling can be sufficient to reestablish sediment transfer if a gently sloping ramp is formed just upstream of the dam.

If the bedload transfer is disrupted too much, and if there are no possibilities to control water level or discharge, dam removal is the only option for restoring continuity [START_REF] Bednarek | Undamming Rivers: A review of the ecological impacts of dam removal[END_REF][START_REF] Magilligan | River restoration by dam removal: Enhancing connectivity at watershed scales[END_REF].

The presence of bottom gates should theoretically reduce the dam's influence on bedload, and so should maintain, at least partially, sediment transfer. This is, for example, the case of the Jons dam on the Rhône River (France), where opening the gates for a discharge slightly lower than the annual flood allows the entire bedload to pass (Petit et al., 1996). If needed, the sediment transfer can be enhanced through flushing and/or sluicing operations whose effects can be reinforced using different strategies, implying a modification of the functioning of the plant associated with the dam, or construction of engineering works along the reservoir, such as training walls [START_REF] Bieri | Modeling of sediment management for the Lavey run-of-river HPP in Switzerland[END_REF][START_REF] Bizzi | On the control of riverbed incision induced by run-of-river power plant[END_REF][START_REF] Isaac | Sediment management studies of a run-of-the river hydroelectric project using numerical and physical model simulations[END_REF][START_REF] Sindelar | Effects of weir height and reservoir widening on sediment continuity at run-of-river hydropower plants in gravel bed rivers[END_REF].

When bedload transfer aims at being restored for ecological considerations, water releases can be implemented as part of environmental flows [START_REF] Poff | Beyond the natural flow regime? Broadening the hydro-ecological foundation to meet environmental flows challenges in a non-stationary world[END_REF][START_REF] Poff | Evolution of environmental flows assessment science, principles, and methodologies[END_REF][START_REF] Poff | Ecological responses to altered flow regimes: a literature review to inform the science and management of environmental flows[END_REF], defined in the Brisbane declaration (2007) as "the quantity, timing, and quality of the water flows required to sustain freshwater and estuarine ecosystems and the human livelihoods and wellbeing that depend on them" (http://www.watercentre.org/news/declaration). If the objective of such operation is specifically to increase bedload transfer to promote downstream habitat diversity, we suggest using the term "Ecomorphogenic Flows" (EmF). An increase in bedload transport is supposed to promote local sediment storage such as bars which should create topographic and grain size variability that will provide a variety of habitats for organisms [START_REF] Gaeuman | Mitigating downstream effects of dams[END_REF][START_REF] Yarnell | The influence of relative sediment supply on riverine habitat heterogeneity[END_REF], a higher range of hydraulic patterns and an improved connectivity between benthic and hyporheic compartments. While such process-based restoration is highly attractive, especially because of its expected long-lasting and sustainable effects [START_REF] Beechie | Process-based principles for restoring river ecosystems[END_REF], it can nevertheless be difficult to implement depending on the context because of the frequent need for trade-off with other water uses such as navigation, electricity production and irrigation. An alternative to this solution can be coarse sediment augmentation downstream of dams [START_REF] Arnaud | Monitoring gravel augmentation in a large regulated river and implications for process-based restoration[END_REF][START_REF] Gaeuman | Mitigating downstream effects of dams[END_REF][START_REF] Rheinheimer | Tools for sediment management in rivers[END_REF].

The main objectives of this paper are to provide answers to the following questions. How much can a river bed readjust in a run-of river reservoir following dam completion? What are the current conditions of bed-material load entrainment in the reservoir? What is the degree of bedload transfer downstream of the reservoir? Could bedload mobilization be improved for mitigating downstream ecological impacts? What are the consequences of these issues for bedload management and restoration? We focus on a case study, the Bourg-lès-Valence reach (Figure 1), which can serve as a reference frame for the coarse sediment management of most of the other reservoirs of the Rhône River (France) and more broadly of rivers influenced by run-of-river dams and presenting a strong and long-standing bedload deficit.

Study site

Rhône River context

Coming from the Swiss Alps, the Rhône River flows over 812 km draining a catchment area of 98,500 km² (512 km long, with 90,500 km² in France, cf. Figure 1; [START_REF] Olivier | The Rhône river basin[END_REF][START_REF] Bravard | Discontinuities in braided patterns: The River Rhône from Geneva to the Camargue delta before river training[END_REF]. The runoff at its outlet accounts for one-sixth of the total runoff into the Mediterranean Sea (Fruget and Dessaix, 2003).

During the second half of the 20 th century, the Rhône River underwent an important phase of taming with the construction of 16 artificial canals parallel to the river course [START_REF] Stroffek | La logique de réhabilitation physique appliquée à un grand fleuve : le Rhône[END_REF][START_REF] Olivier | The Rhône river basin[END_REF][START_REF] Bravard | Historical development and integrated management of the Rhône River foodplain, from the Alps to the Camargue delta, France[END_REF]. These canals were built to convey most of the annual runoff to hydropower plants, improve commercial navigation and increase irrigation (Stroffek et al., Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019Environment, 654 ( ) 1146Environment, 654 ( -1157Environment, 654 ( 1996;;[START_REF] Olivier | The Rhône river basin[END_REF][START_REF] Bravard | Historical development and integrated management of the Rhône River foodplain, from the Alps to the Camargue delta, France[END_REF]. Since then, the discharge in bypassed reaches is residual (until 2014, between 1/3 and 1/322 of the average discharge), except during floods when discharge is higher than the power plants capacity. The Rhône River is thus composed of a quasicontinuous series of reservoirs and bypassed reaches. Located at the upstream end of the bypassed reaches, diversion dams (run-of-river dams with diversion according to the classification of [START_REF] Mcmanamay | Classification of US hydropower dams by their modes of operation[END_REF] are equipped with bottom gates that are opened during high flows, theoretically allowing the transport of coarse sediments. While bedload continuity remains possible, dams have modified the condition of bedload transport through the reservoirs to an unknown extent.

Further, bedload could actually be null due to the low frequency for which critical shear stresses are exceeded. The coarse sediment yield has indeed decreased since the second half of the 19 th century due to the channelization of the riverbed associated with bank protections downstream of Lyon (lateral dykes, weirs, groynes, cross-beams) [START_REF] Bravard | Le Rhône[END_REF][START_REF] Bravard | Historical development and integrated management of the Rhône River foodplain, from the Alps to the Camargue delta, France[END_REF][START_REF] Poinsart | Effets des aménagements fluviaux sur les débits liquides et solides[END_REF][START_REF] Poinsart | Histoire de l'endiguement du Rhône à l'aval de Lyon (XIXe siècle). Actes du colloques "Le fleuve et ses métamorphoses[END_REF], preventing any sediment supply by lateral erosion. It is also affected by a reduction in sediment supply from the tributaries [START_REF] Astrade | Detailed chronology of mid-altitude fluvial system response to changing climate and societies at the end of the Little Ice Age (Southwestern Alps and Cévennes, France)[END_REF][START_REF] Bravard | Les réponses des systèmes fluviaux à une réduction des flux d'eau et de sédiments sous l'effet du reboisement en montagne[END_REF][START_REF] Bravard | Principles of engineering geomorphology for managing channel erosion and bedload transport, examples from French rivers[END_REF][START_REF] Bravard | La disparition du tressage fluvial dans les Alpes françaises sous l'effet de l'aménagement des cours d'eau (19-20ème siècle)[END_REF][START_REF] Lefort | Incidence des aménagements hydro-électriques sur la morphologie des tronçons court-circuités de la Durance et du Verdon[END_REF][START_REF] Liébault | Assessment of bedload delivery from tributaries: The Drôme River case, France[END_REF]Liébault et al., , 2002;;Liébault and Piégay, 2002;[START_REF] Rollet | Assessment of consequences of sediment deficit on a gravel river bed downstream of dams in restoration perspectives: Application of multicriteria, hierarchical and spatially explicit diagnosis[END_REF][START_REF] Warner | Gross channel changes along the Durance River, Southern France, over the last 100 years using cartographic data[END_REF]. Due to channel incision, sediment winnowing and sediment supply control, bedload is very low on most of the river course and the bed is armoured [START_REF] Cortier | Causes et conséquences du blocage actuel de la dynamique fluviale et du transit sédimentaire du Rhône[END_REF]. Nevertheless, respective impacts of each main taming phase on bedload transport still need to be quantified and we do not know precisely if the bed is still able to adjust vertically, since this dimension is the only one in which morphological changes can occur. To counter the adverse effects of these two main taming phases, a large restoration project was initiated in the 1990s (Lamouroux et al., 2015) to improve main channel and former channel ecological diversity in bypassed reaches. In a first step the minimal flow was increased and abandoned channels were rejuvenated by dredging. More recently, a new strategy has emerged, more focused on process-based restoration with riprap removal to reactivate bedload transport and shifting riverscape mosaics, raising

especially the question of the potential for bedload transfer through impounded reaches.

Bourg-lès-Valence reach

The study reach is located in the middle section of the Rhône River, just upstream of its confluence with the Isère River, one of its most important tributaries (e.g., catchment size : 11,900 km 2 ; mean annual flow at the Beaumont-Monteux gauging station: 329 m 3 s -1 ) (Figure 1). In the same way as the whole Rhône river course downstream of Lyon, the Rhône in this section was constricted from the mid-19th century to the first part of the 20th century with engineering works, built in three steps.

Dikes in the floodplain were first erected, from 1810 to 1865. Submersible dykes appeared then from 1862 to 1897. Finally, transverse structures as groynes and cros-beams were constructed between 1880 and 1908 (source: 1922 bathymetric map).

Material and Methods

We adopted a methodological strategy combining geomorphic and hydraulic approaches. First, we characterized the morphological evolution of the study reach since the end of the 19 th century by comparing longitudinal profiles of the thalweg. Second, we assessed if the bedload transfer continuity is still at least partially preserved by establishing sediment budgets in the reservoir and in the upstream section of the bypassed reach. Finally, using a 1D hydraulic model, we estimated the current condition of bed mobility by determining the competence of the river along the reservoir as well as the maximum grain size exportable downstream.

Bed vertical adjustment following channelization and impoundment

The adjustment intensity following channelization (which occurred between 1862 and 1908) and impoundment (1968) was determined by comparing longitudinal profiles of the thalweg from different dates every 500 m [START_REF] Parrot | Analyse spatio-temporelle de la morphologie du chenal du Rhône du Léman à la Méditerranée[END_REF] between kp 90.00 and kp 99.00. The vertical evolution during the first decades following channelization is not documented. Bathymetry was surveyed in 1897 and between 1969 and 2009. For the earliest date, data were extracted from old bathymetric maps on which thalweg elevation is indicated at least every 100 m and isolines with a resolution ranging from 0.20 m to 0.50 m are drawn. If information relative to the accuracy of these survey are unfortunately not available, it seems reasonable to assume that is was lower than their resolution. For the 1969-2009 period, data come from surveys conducted by the CNR.

Continuity of sediment transfer downstream the reservoir

First, we computed a sediment budget in the reservoir between 1969, one year after the commissioning of the hydropower plant, and 2011 (Figure 1 and Figure 2). The study reach encompasses most of the reservoir until the dam (kp 90.90-99.20). Then, we computed a sediment budget for the 1992-2013 period along the upstream section of the bypassed reach, from the dam to the Isere confluence (kp 99.90-103.10). A recent inventory of authorized extractions indicates that gravel was here intensively mined until 1992, with a removal of 1,409,000 m 3 (+56,000 m 3 possibly mined) [START_REF] Coeur | Etude historique des prélèvements de sédiments dans le Rhône[END_REF]. Extractions lowered sharply the bed and created three successive deep in-channel pits (with a maximum deepening of 8 m, 11 m and 4.5 m from upstream to downstream) in which we assume that most, or even all, of the bedload possibly passing the dam is trapped. It should thus allow to estimate the bedload volume transported from the reservoir since 1992, if any.

Data

Bathymetric data were supplied by the CNR. They consist of points along cross sections 100 m apart (Table 1). The mean point spacing along cross sections varies between 4.1 and 6.5 m. Data were collected using a plumb line, a single-beam or a multi-beam sounder. The maximum measurement error, given by the CNR, is respectively estimated between 0.1 and 0.4 m depending on date.

Method

Sediment budget were obtained applying the method of [START_REF] Guertault | Long term evolution of a dam reservoir subjected to regular flushing events[END_REF] by computing area evolution along each cross section for successive dates and by longitudinally interpolating evolution area considering it as representative of changes that occurred between the mid-distance to the upstream cross section and the mid-distance to the downstream cross section. The budget is associated with a total error, composed of two terms: a measurement error and an interpolation error. It was computed applying the method developed by [START_REF] Arnaud | Monitoring gravel augmentation in a large regulated river and implications for process-based restoration[END_REF]. The measurement error was nevertheless determined as follows and not from repeated measurement of the same points at different dates where no change was assumed, as done for example by Brasington et al. (2000) or Gaeuman (2014): assuming a Gaussian distribution of the measurement error and approximating that the maximum error is equal to three times the standard deviation (σ), we estimated the measurement error ( ) as the maximum error divided by 3.

Maximum grain size transported downstream of the reservoir: current functioning and optimization scenarios

Using a 1D hydraulic model implemented along the Rhône River from the Lake Geneva outlet to the delta [START_REF] Dugué | How big of an effect do small dams have? Using geomorphological footprints to quantify spatial impact of low-head dams and identify patterns of across-dam Variation[END_REF], we estimated for five different flood discharges the competence along the reservoir as well as the maximal grain size exportable downstream the dam. It was done for the current functioning of the reservoir but also for EmF scenarios aiming at maximizing the bedload transfer downstream of the reservoir (Table 2). For these optimisation scenarios, we increased the velocity in the reservoir by steepening the water slope along its whole course and/or we increased the discharge as much as possible in the bypassed section of the reservoir (Table 1). To this end, several combinations were tested by modifying at least one of the three following parameters that allow controlling the water elevation and the discharge in the different reaches of the facility: the maximum water elevation authorized in the bypassed section of the reservoir, the distribution of the discharge between the bypassed section and the headrace canal and the opening degree of the hydropower plant Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157

gates. We finally retained two scenarios. The first one is characterised by a lowering of the maximum authorized water surface elevation at kp 98.30 (i.e. at the diversion), from 117.1 m for normal functioning to 114 m. For a 50 years return-interval flood, it decreases the waterfall height at the la Roche-de-Glun dam from 4.4 m for normal functioning to 0.7 m. The second scenario i) lowers the water surface elevation at kp 99.35 (i.e. at the Roche-de-Glun dam), from 116.8-117 m for normal functioning to 114 m, ii) derives most of the total discharge in the bypassed channel (keeping a residual flow of 100 m 3 s -1 in the headrace canal), iii) closes the gates of the power plant..

Modelling parameters and simulated discharges

Running in "steady state" mode, the model was built with topo-bathymetric cross sections 100 m apart acquired by the CNR from 2004 to 2007. Inputs of tributaries were taken into account by assigning them a constant discharge equal to their mean annual discharge (Doux = 8.6 m³ s -1 ; Isère = 329 m³ s -1 ). The five simulated discharge values were chosen within a range from frequent to rare floods. They correspond to a return-interval (RI) at the Ternay gauging station equal to 2 (3,200 m 3 s - 1 ), 5 (3,900 m 3 s -1 ), 10 (4,300 m 3 s -1 ), 20 (4,700 m 3 s -1 ) and 50 (5,200

m 3 s -1 ) years (Q 2 , Q 5 , Q 10 , Q 20
and Q 50 respectively). The model predicts surface elevation and section-averaged velocity from which were computed local shear stress and competence at each node of each of the cross sections of the model.

Competence along the reservoir

For each simulated discharge and for each node of the model along each cross section, we determined the maximum sediment size that can be mobilized. In absence of any information regarding the bed state and structure, we provided two estimations of the competence, obtained with a critical Shields number of 0.03 and 0.06. The first one corresponds to a loose structure of the bed Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019Environment, 654 ( ) 1146Environment, 654 ( -1157 between samples (see Figure 1 for location of the samples), we had to use an estimate on most of cross sections. Two values were computed for each cross section. The first one (hereafter G1) was obtained by the linear interpolation between two consecutive samplings. For the second one (hereafter G2), the grain size at the location of each sample was used on a distance equal to half the distance to the next or the following sample.

Results

Bed readjustment following channelization and impoundment

The comparison of the thalweg elevation from 1897 to 2009 clearly shows that most of the geomorphic changes along the study reach occurred following the first taming phase of the Rhône River , characterized by the channelization and the disconnection of its multi-thread bed channels (Figure 3). The incision induced by the channelization is probably underestimated since the first decades following it are not documented. Between 1897 and 1969, a large and widespread incision occurred, with a mean value of -1.67 m (σ = 0.95 m), equivalent to -0.021 m y -1 . From 1969 to 2009, the bed stabilized downstream of kp 94.00, with a mean vertical evolution of -0.066 m (σ = 0.14 m), equivalent to -0.0005 m y -1 . Along this section, the incision rate is 33 times lower than that of the 1897-1969 period. Upstream of kp 92.50, incision continued with a mean value of -1.64 m (σ = 1.1 m), equivalent to -0.042 m y -1 . The incision occurred mainly before 1986. The section between kp 92.50 and kp 93.50 underwent aggradation, very likely resulting from sediment reinjections (silt and/or sand) that occurred from 1984 to 2009 (five campaigns in 1984, 1997, 2000, 2001 and 2009). Figure 5 -Insight of morphological evolution of the reservoir in its downstream bypassed section.

Sediment budget in the bypassed reach since 1992

More evidence of the preservation of the bedload transfer continuity is given by the morphological evolution downstream of the dam, along the upstream section of the bypassed channel (from the dam to the confluence with the Isère canal). Here the sediment budget between 1992 and 2013 is positive, with a value of 5,800 m 3 y -1 (± 600) (Figure 4 and Figure 6). It means that at least such volume were transported each year from the reservoir for this period. An important part of these sediments were deposited along the short upstream pit (kp 100.30-100.60) (Figure 4 and Figure 6). Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157 Figure 6 -Morphological evolution of the bypassed section downstream of the dam and upstream of the Isère confluence.

Maximum grain size exportable from the reservoir

Current functioning

For the whole reservoir length, and whatever the simulated discharge or the grain size considered, the maximum competence along each cross section decreases downstream, showing the clear longitudinal influence of the dam on bedload transport (Figure 7). Furthermore, the lowest value of the maximal competence is systematically located at kp 99.10. For a Q 2 , only very fine gravels (according to classification of [START_REF] Blott | GRADISTAT: A grain size distribution and statistics package for the analysis of unconsolidated sediments[END_REF], at best, could be exported from the reservoir (2 mm at kp 99.10 for a critical Shields number of 0.03 and for grain size G2) (Figure 7). For a Q 50 , the size increases to 14 mm, which belongs to medium gravel class (kp 99.10 for a critical Shields number of 0.03 and for grain size G2).

EmF conditions

The effect of EmF is evident since the trend towards a downstream decrease of the competence observed in conditions of normal functioning tends to ease, even to disappear, at least up to kp 97.00 (Figure 7). The attenuation of the trend is stronger for scenario 1 than for scenario 2 (Figure 7). For scenario 1, the stronger the discharge is, the stronger the attenuation is. Conversely, for scenario 2, the attenuation decreases when the discharge increases.

Upstream of the diversion, the best gain in maximum competence compared to normal functioning is obtained for scenario 1. Downstream of the diversion, scenario 2 would be the most efficient for all the simulated discharges except Q 50 , for which the maximum competence is slightly higher for scenario 1 (Figure 7 and Figure 8). Moreover, the difference along this section between both scenarios is little by little reduced when the discharge increases: while for scenario 1 the competence rises systematically, for scenario 2 it reaches a maximum for a Q 5 and then drops slightly (Figure 7 and Figure 8). Furthermore, the maximum competence for scenario 1 at Q 50 and scenario 2 at Q 5 are almost the same.

For scenario 1, the lowest value of the maximal competence in the whole reservoir is located at kp 99.30 whatever the grain size, except for a Q 50 with grain size G2 where it is located at kp 98.20, just upstream the diversion (Figure 7). Furthermore, it increases with discharge. For scenario 2, the lowest value of the maximal competence is systematically located at kp 98.20 (Figure 7). It increases until Q 5

and then drops very slightly or remains almost constant.

Until a Q 5 , the maximal sediment size that could be exported from the reservoir is obtained with scenario 2 (Figure 7). For a Q 2 , it is equal to 18 mm (kp 98.20 for a critical Shields number of 0.03 and for grain size G2), representing a nine fold increase compared to the normal functioning (2 mm). From Q 10 , the maximal sediment size that could be exported from the reservoir is obtained with scenario 1 (Figure 7). For a Q 50 , it is equal to 56 mm at the best (kp 98.20 for a critical Shields number of 0.03 and for grain size G2), which is a fourfold increase compared to the normal functioning (14 mm).

Figure 8 -Box plots of the maximum competence for each of the 11 cross sections located along the bypassed section of the reservoir depending on the choice of the Shields parameter and GSD. other reservoirs, it means that for the coarse fraction of the bedload, each Rhône River reach composed of the succession of a bypassed section and its downstream reservoir should be considered as almost independent of the surrounding ones. Depending on the grain size, bedload management should therefore be considered at different spatial scales: very schematically, the reach scale for sizes from fine gravels to boulders and the scale of the river corridor for very fine gravels and coarse sands.

Discussion

Bedload transfer in the reservoir

Anticipating what could become the reinjected sediments therefore requires determining their grain size as well as the longitudinal gradient of the competence from the restored bypassed reach to the dam of the downstream reservoir.

So that habitat improvement can be beneficial at the largest spatial and temporal scales, promotion of re-erosion or sediment augmentation must be done ideally on long bypassed reaches, with injection in their upstream section. Nevertheless, because a large part of the bedload, if not all of it, should not pass reservoirs, it could have potential future counter-effects that need to be considered (mainly limitation for navigation and flood hazard aggravation). To make the existing human constraints and the maximization of ecological benefits compatible, process-based solutions can then be implemented jointly with gardening.

A more complex and elaborate way to manage bedload and to increase sediment transfer from restored bypassed reaches would be the implementation of EmF using different configurations depending on the discharge and the longitudinal location of dams in bypassed sections. For dams located at diversions, and whatever the discharge, EmF similar to scenario 1 presented here (no modification of the discharge distribution between the bypassed channel and the headrace canal) should be preferred. For dams located downstream of the diversion, as for our study case, scenario 2

(almost no diversion of discharge in the headrace canal) seems more appropriate for relatively frequent discharges (up to a maximum Q 5 -Q 10 ). This strategy should obviously be adjusted according to the maximum grain size for which restoration of the continuity is planned. Broadly, these lessons regarding the principles of bedload management learned from the present case study could be generalized to similar rivers influenced by run-of-river dams presenting a strong and long-standing bedload deficit and for which sediment replenishment is carried out.

Conclusion

This study aimed at estimating the potential for morphological adjustment of a run-of-river dam impoundment, in which sediment augmentation was carried out, and for bedload transfer downstream.

Most of the geomorphic changes occurred before dam completion (1969) due to a decrease in coarse sediment supply that occurred during the preceding 100 years because of channelization of the river and less sediment delivery from tributaries. Since the reservoir's creation, changes are minor but the bedload transfer is still maintained. Nevertheless, only particles up to medium-coarse gravels, at best, can be exported downstream of the dam (2-3 mm for a Q 2 and 14-23 mm for a Q 50 ), which is less than Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157

the bed D 50 on most of the reservoir. Implementation of Ecomorphogenic Flows, here defined as environmental flows whose objective is specifically to increase bedload transfer through the reservoir to promote downstream habitat diversity, could improve the situation since the maximum grain size exportable from the reservoir would increase strongly (a ninefold increase for a Q 2 , and around a fourfold increase for discharges from a Q 5 to a Q 50 ).

Beyond the imperative need for trade-offs with other water uses if such a measure were implemented, bedload management must be considered at the scale of the entire river corridor in order to precisely localize and quantify the possible sources of sediment supply as well the conditions of bedload transfer (competence and capacity). This characterization of the longitudinal bedload patterns, as developed in [START_REF] Vazquez-Tarrio | Present-day bed load transport capacities along the Rhône River following a century and half of human modifications[END_REF], can identify where a coarse sediment reinjection (by gravel augmentation or by promoting lateral erosion through riprap removal) could be the most sustainable and thus the most efficient. Finally, the use of an integrated and interdisciplinary methodological approach (sediment budget, 1D model, surface-subsurface grain-size determination)

appears especially relevant since it increases the robustness of the results and potentially reduces uncertainty.

Figure 1 -

 1 Figure 1 -Location of the study reach in France (A), the Rhône basin (B) (1: Ternay gauging station, 2: Beaumont-Monteux gauging station, 3: Valence gauging station), details of the local context (C), and description of the methodological combination used to characterize bed mobility in the study reservoir (D). Pb affichage echelle à résoudre

Figure 2 -

 2 Figure 2 -Daily discharge in the study reach between 1968 and 2013 (corresponding to the daily discharge at the Valence gauging station just downstream of the Isère confluence from which we substrated the daily Isère discharge at the Beaumont-Monteux gauging station just upstream of the confluence, see Figure 1 for location) and sediment budget computation periods .

Figure 3 -Figure 4 -

 34 Figure 3 -Thalweg elevation every 500 m along the reservoir from 1897 to 2009. Pb affichage ligne à résoudre

  Figure 7 -Longitudinal distribution of the maximum competence for the different GSD and discharges.

  Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157

  Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157The study reach encompasses most of the reservoir of the Bourg-lès-Valence power plant facility and extends over 9.8 km from kp 90.00 (acronym for kilometric point, which indicates the kilometric distance from Lyon, with negative values upstream and positive downstream), 400 m upstream of the confluence with the Doux River to kp 99.35, where the dam is located. The mean river width is 306 m (range, 161-431 m) and the mean annual discharge is 1067 m 3 s -1 . It was computed for the 1956-2013 period from the daily Rhône discharge at the Valence gauging station just downstream of the Isère confluence from which we subtracted the daily Isère discharge at the Beaumont-Monteux gauging station located just upstream of the confluence). , T., Piégay, H.,Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157

	Dépret

  Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157

Table 1 -

 1 Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157 Dates of bathymetric surveys and data characteristics.

	Survey date	Reach	Device	Measurement error (m)	Mean number of points per cross section	Mean space between points (m)
	1969	Reservoir Plumb line	0.4	41.7	6.5
	1992	Bypassed Single-beam	0.2	24.1	8.4
	2011	Reservoir Multi-beam	0.1	46.3	5.9
	2013	Bypassed Multi-beam	0.1	49.4	4.1

Table 2 -

 2 Synthesis of the three scenarios tested with the 1D hydraulic model (Qr = Discharge in the reservoir).

	Reservoir operating scenario	Water elevation (m)	Discharge at the headrace canal entrance (m 3 s -1 )	Discharge in the bypassed channel (m 3 s -1 )	Power plant gates
	Normal functioning	117.1 at kp 98.3 116.8-117 at kp 99.35	2,000	Qr -2,000	Opened
	EmF1	114 at kp 98.3	2,000	Qr -2,000	Opened
	EmF2	114 at kp 99.35	100	Qr -100	Closed

  Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157

Acknowledgments

This study was conducted within the Rhône Sediment Observatory (OSR), a multi-partner research program funded through the Plan Rhône by the European Regional Development Fund (ERDF), Agence de l'eau RMC, CNR, EDF and three regional councils (Auvergne-Rhône-Alpes, PACA and Occitanie).

surface, theoretically characterizing a high mobilization frequency of the bed material. The second one corresponds to a high degree of bed compaction, theoretically characterizing a low mobilization frequency of the bed material. The computation steps were the following.

We first computed the section-averaged total shear stress from the 1D model: Eq. 4 where is the water density (1000 kg m -3 ), is the gravitational acceleration in m s -2 , is the hydraulic radius in m, and is the energy slope in m m -1 .

The section-averaged effective bed shear stress was then computed from the Meyer-Peter and Müller equation ( 1948):

where is the total Strickler coefficient in m 1/3 s -1 , and the skin Strickler coefficient (grain resistance) in m 1/3 s -1 was computed from the following equation:

where is the size of bed material in millimetres for which 90% of the number of sediment clasts have a smaller size.

Then, we estimated for each node i of the model the local effective bed shear stress assuming a simple bed shear stress distribution based on the water depth, and assuming a homogeneous roughness throughout the river section [START_REF] Camenen | Assessment of methods used in 1D models for computing bed-load transport in a large river: the Danube River in Slovakia[END_REF]:

where is the water height in metres at node I of the cross section, and the section-averaged water depth.

The competence at each node i was finally determined as follows:

Eq. 8 where is the competence in i, in metres, is the critical Shields number and is the sediment density (2650 kg m -3 ).

Surface 90 th grain size percentile (D 90 ) used in equation ( 6) was obtained from three volumetric samples taken in 2012 along the reservoir by [START_REF] Parrot | Analyse spatio-temporelle de la morphologie du chenal du Rhône du Léman à la Méditerranée[END_REF]. Because grain size remains unknown The slight modifications that have occurred since the dam construction in 1968 (Figure 3) indicate that the bed was almost totally adjusted to the conditions imposed by its previous channelization and by the bedload supply decrease from tributaries and/or that the impoundment has inhibited the possibilities for further adjustment. If the second factor played a role, we should expect a decrease through time in the intensity of geomorphic changes in case of similar flood intensity and duration.

The comparison of degraded volumes between the two periods dominated by channel degradation since 1969 (1969-1986 and 1999-2004) shows such a decrease despite comparable hydrological conditions: for 1969-1986 and 1999-2004, there were respectively 15 and 10 days with discharge higher than the 10-year RI discharge, which is the limit below which no significant changes in the reservoir, especially degradation, could occur; and for each of both periods, one flood with a RI at least equal to 35 years and at least one flood with a 10-year RI were counted [START_REF] Dépret | Mesures et modélisations du fonctionnement hydrosédimentaire du secteur de Bourg-lès-Valence -Final synthesis report[END_REF].

Furthermore, while degraded volumes for 1969-1986 were distributed quite linearly along the reservoir, those for 1999-2004 diminished more and more downstream [START_REF] Dépret | Mesures et modélisations du fonctionnement hydrosédimentaire du secteur de Bourg-lès-Valence -Final synthesis report[END_REF]. This

indicates that the study reach had still some potential for morphological changes at the time of dam completion, even if most of the readjustments following channelization were probably already realized, and that such potential was progressively reduced due to the impoundment.

Sediment budget downstream of the dam since 1992 indicates a bedload volume coming from the reservoir at least equal to 5,800 m 3 y -1 (± 600). This value is 3.6 time higher than that given by [START_REF] Cortier | Causes et conséquences du blocage actuel de la dynamique fluviale et du transit sédimentaire du Rhône[END_REF] (1,600 m 3 y -1 ) and 19.7 times lower than their estimation of the annual bedload before impoundment and channelization (114,000 m 3 ). The situation could be greatly improved by implementations of EmF since compared to a normal functioning of reservoir operating, the maximum grain size that could be exported from the impoundment would increase from 2 cm to 18 cm for a Q 2 and from 14 cm to 56 cm for a Q 50 .

Implications for coarse sediment management in rivers influenced by run-of-river dams

On some of the bypassed reaches of the Rhône River, riprap removal, implying an increase of the sediment supply to the river [START_REF] Bravard | Historical development and integrated management of the Rhône River foodplain, from the Alps to the Camargue delta, France[END_REF], has been recently designed. The main goals of these process-based restoration actions are to reactivate bedload transport and promote a shifting riverscape mosaic to improve aquatic and riparian habitats. It raises the operational and scientific questions of the degree of bedload transfer through a bypassed reach to its immediate downstream reservoir, and then to the next bypassed reach. This will condition the spatial scale at which the management of these sediment reinjections should be designed.

The present study shows that according to the most optimistic estimations, and in the absence of EmF, the maximum grain size that could be exported from the reservoir would be smaller than coarse gravels (according to the classification of [START_REF] Blott | GRADISTAT: A grain size distribution and statistics package for the analysis of unconsolidated sediments[END_REF]. It corresponds at the best to very fine gravels (2 mm) for a Q 2 and to medium gravels for a Q 50 (14 mm). In case of similar competence in Dépret, T., Piégay, H., Dugué, V., Vaudor, L., Noirot, B., Faure, J.-B., Cassel, M., Le Coz, J., Camenen, B. Estimating and restoring bedload transport through a run-of-river reservoir, Science of the Total Environment, 654 (2019) 1146-1157


Sad Rafik

Paul Lachat

Nadia Bennani

Veronika Rehn-Sonigo

Towards a Distributed Inference Detection System in a Multi-Database Context

The omnipresence of services offered by diverse applications leads customers to share more and more personal data, among which some are sensitive. Dishonest entities perform inference attacks by querying non-sensitive data in order to deduce the stored sensitive data. Detecting those attacks is still an open problem in a setting where a dishonest entity has access to distinct data controllers' databases containing data collected from the same customer. This problem has been addressed considering a centralized detection system. However, this approach is limited because of this centralized nature where the system protects the customers' privacy at the expense of the data controllers' privacy. Hence, we propose in this article the description of a distributed architecture to detect inference attacks in a multi-database context, while preserving the privacy of both the applications and the customers.

Introduction

Nowadays, individuals are used to share both non-sensitive and, more carefully, sensitive personal data with distinct applications, in order to benefit from a multitude of services. The data controllers are collecting, storing, and sharing a part of this information with external entities based on the individuals' consent [START_REF] Gerl | LPL, Towards a GDPR-Compliant Privacy Language: Formal Definition and Usage[END_REF]. Hence, access control systems are leveraged in order to protect the sensitive data against unauthorized direct access. Yet, dishonest entities perform inference attacks on sensitive data by querying non-sensitive data, for which they have an authorized access, to deduce the sensitive data stored in the databases [START_REF] Farkas | The Inference Problem: A Survey[END_REF]. Inference detection systems (InfDSs) have been proposed in the literature with the aim of protecting a single personal database against inference attacks [START_REF] Chen | Protection of Database Security via Collaborative Inference Detection[END_REF]; [START_REF] Guarnieri | Securing Databases from Probabilistic Inference[END_REF]; [START_REF] Toland | The Inference Problem: Maintaining Maximal Availability in the Presence of Database Updates[END_REF]; [START_REF] Chang | A Study of Inference Problems in Distributed Databases[END_REF]. However, this issue is still open in a setting where a dishonest entity has access to databases managed by distinct controllers containing data collected from the same customers.

To illustrate this threat, let us consider an example in which a customer creates an account on two distinct applications: Train and Flight allow to buy train and plane tickets, respectively. At each account creation, the customer is invited to share some of their personal data (e.g., name, age, sex, and so on). Locally, the services protect the customers' privacy thanks to both an access control system and an InfDS. While respecting the consent of customers, the services share the non-sensitive data with authorized entities. In this setting, when a dishonest but authorized entity tries to gather a subset of non-sensitive data related to a targeted customer in a single application, the InfDS of this application will detect and prevent any queries leading to an inference attack. However, by leveraging the fact that the targeted customer has subscribed to the two services, and that the two services are asking for a common subset of personal data, the dishonest entity queries a subset of non-sensitive data from each application so that an inference attack becomes possible once combining the two subsets of personal data. In this case, the inference attack is not detected locally by the InfDSs since the queried subsets are not harmful when considered separately. This example illustrates the threat of inference attacks exploiting the distributed dependency strategy (DDS) [START_REF] Woodall | A Systematic Literature Review of Inference Strategies[END_REF].

In order to cope with this kind of inference attacks an InfDS must: (i) keep track of the information that each entity obtains from all the collaborating applications; (ii) be able to identify the semantic similarities between differently formatted data managed by distinct applications. This observation has motivated a previous work by Lachat et al. [START_REF] Lachat | Towards an Inference Detection System Against Multi-database Attacks[END_REF] to address this problem by making the applications collaborate with a centralized InfDS. The work presented in [START_REF] Lachat | Towards an Inference Detection System Against Multi-database Attacks[END_REF] is based on the two knowledge representations proposed by Chen et al. [START_REF] Chen | Protection of Database Security via Collaborative Inference Detection[END_REF]: the Semantic Inference Model (SIM) which represents the probabilistic dependencies of a database at schema level, and the Semantic Instance Graph (SIG) which reflects the dependencies expressed by the SIM at instance level. We proposed the Global Instance Graph (GIG) which is composed of all the SIGs of the collaborating applications, extended with a new kind of links (i.e., the semantic links) representing semantic similarities between attributes of distinct databases. In order to build the GIG, the centralized detection system requires to have access to the schema of every database in order to identify the similarities, as well as to the instances from distinct databases in order to incorporate those similarities in between the SIGs.

The solution lacks privacy for both individuals' data and databases schema shared with the centralized InfDS, which discourages the applications to collaborate with such a system. Therefore, to increase the acceptance of such a detection system, it should be able to detect inference attacks without centralizing and having access to the schema and the instances in clear. Hence, a distributed InfDS must satisfy the following requirements in this multi-database context: (i) The GIG has to be build in a distributed way preventing any schema and data disclosure. (ii) The knowledge that an entity obtains by issuing a query has to be propagated to all the collaborating applications to correctly keep track of the queried information, while limiting the impact on the query answer time. Thus, such a system will provide the required warranties in order to increase the motivation of applications to participate.

The main contribution of this paper is the proposition of a first solution towards the distributed detection of inference attacks, which protects both customers' and applications' privacy based on Chen et al. solution.

This paper is organized as follows: Section 2 presents the limitation of inference detection systems w.r.t the described issue. Section 3 presents the SIM and the SIG, the two models on which is based Chen et al. solution. Section 4 describes our solution for the distributed detection of inference attacks. Section 5 presents the conclusion and the future research directions.

Related works

In this section, we review the related work in the field of inference detection and raise their limitations to overcome the issues listed in Section 1. Most of the proposed solutions focus on inference attacks on a single database.

Chen et al. [START_REF] Chen | Protection of Database Security via Collaborative Inference Detection[END_REF] and Guarnieri et al. [START_REF] Guarnieri | Securing Databases from Probabilistic Inference[END_REF] propose to tackle inference attacks by building a model which represents probabilistic inference channels. Guarnieri et al. propose a system where one module acts as a policy decision point whereas the other checks inference attempts. The two solutions address inference attack detection with the assumption of protecting a single static personal database. The solution of Guarnieri et al. works under the assumption that only closed queries are issued to the database.

The system presented by Toland et al. [START_REF] Toland | The Inference Problem: Maintaining Maximal Availability in the Presence of Database Updates[END_REF] models the Functional Dependencies (FDs) within a database to compute the disclosed knowledge each time a query is issued. In their work the FDs are limited to logical dependencies. This work is the only one that considers database updates (i.e., tuple updates, deletion or insertion), by storing the most recent updates in the query history log. This solution however focuses on protecting a single personal database.

Similarly to Chen et al., Chang et al. [CM03] propose a mechanism which reasons on the probabilistic dependencies among attributes, but for a distributed personal database. The authors are focusing on a distributed database, the solution is not suitable to model the semantic similarities between databases owned by distinct applications, thus having different schemas. Lachat et al. [START_REF] Lachat | Towards an Inference Detection System Against Multi-database Attacks[END_REF] extend the work of Chen et al. in order to detect inference attacks exploiting multi-database inference channels using data linkage techniques. While Lachat et al. is the only work which, to the best of our knowledge, focuses on protecting multiple databases, it leads to the limits described in Section 1.

Detection in presence of a single database

The contribution presented in this article relies on two models proposed by Chen et al. [START_REF] Chen | Protection of Database Security via Collaborative Inference Detection[END_REF]. In this section, we provide a short description of the Semantic Inference Model (SIM) and the Semantic Instance Graph (SIG). The SIM represents existing probabilistic dependencies at the schema level. This model is based on the Probabilistic Relational Model (PRM), which itself relies on Bayesian networks. According to [START_REF] Getoor | Learning Probabilistic Relational Models[END_REF], the PRM "[...] allows the properties of an object to depend probabilistically both on other properties of that object and on properties of related objects". This model is composed of a skeleton and parameters. The skeleton describes the direct influences between parents attributes and some child attribute (i.e., a DAG). The parameters define the Conditional Probability Distribution (CPD) between a child attribute and its parents. The CPDs represent the probabilistic distribution of a given snapshot of the stored data. Chen et al. define three kinds of links for the SIM: (i) dependency link: which corresponds to an edge in the skeleton of the PRM, (ii) schema link: which models relationships between primary keys and foreign keys, and (iii) semantic link: which represents an influence between attributes which can be manually specified based on domain knowledge for instance. In order to reason on queries selecting specific instances of the database, the dependencies of the SIM must be instantiated at the instance-level. This results in a SIG where the nodes of the graph represent an instance attribute value. To detect inference attacks based on the SIG, the system administrator must first define which attribute are considered as sensitive in the SIM as well as defining for each of them an inference threshold. Each queried parent attributes will modify the percentage of confidence an entity has concerning the sensitive child attribute. Hence, when a new query is issued to the protected database, the detection system applies an evidence on each of the selected nodes in the SIG. Then, the system checks whether the probability of a sensitive attribute becomes greater than its defined inference threshold.

In the following we develop an example, extracted from [START_REF] Chen | Protection of Database Security via Collaborative Inference Detection[END_REF], based on the SIM and SIG depicted by Figure 1 in order to illustrate how the solution of Chen et al. [START_REF] Chen | Protection of Database Security via Collaborative Inference Detection[END_REF] works. Here, a subset of the SIG makes references to three distinct instances: LAX, R1, and C5 which correspond to an airport, a runway, and an aircraft, respectively. Each attribute is prefixed with the name of its related instance to avoid any ambiguity. In this illustration, the sensitive attribute is TAKEOFF_LANDING_CAPACITY (TLC) with an inference threshold equal to 70%. Assuming that an entity knows, e.g., via a previous query, that C5 is able to land on R1 from LAX and that she has queried C5_MIN_LAND_DIST (= long) and C5_MIN_RUNWAY_WIDTH (= wide), then the entity is able to infer the value of TLC with a confidence of 58.3%. If she succeeds to query LAX_PARKING_SQ_FT (= large), she would be able to infer that TCL is equal to large with a percentage of confidence of 71.5%. Since it is above the defined inference threshold, an inference attack is detected for this last query. Therefore, this solution is limited to detecting attacks that issue queries to the protected database only, and not from external sources, e.g., from collaborating data controllers.

Distributed detection of inference attacks

In the following, we propose a solution to the problem of distributively detecting inference attacks leveraging the DDS. As a first step, we define two generic assumptions. We assume that: (i) The applications are collaborating in order to protect the privacy of their customers. (ii) The authorized entities use a single identity when they interact with the applications (i.e., there is no collusion between entities).

As depicted in Figure 2a, the collaborating applications are uniquely identified and form a peer-to-peer (P2P) network to share information for the distributed detection ❶. Each application creates and manages locally its own SIM ❸ and its own SIG ❹, and is able to locally detect inferences thanks to the local InfDS (see Figure 2b). Hence, upon receiving the query of an authorized entity, an application performs two actions: (i) ■ It checks locally if the selected attribute leads or not to an inference on its own database. (ii) ✱ It informs the other applications about the queried information, via the P2P network, in order to let them keep track of the knowledge obtained by the entity and to detect inference attacks leveraging the DDS.

This second action requires that each application knows what the semantic similarities are that exist between its own database and the databases of the other applications. Consequently, the applications must cooperate to build a distributed GIG while protecting their own privacy and the privacy of their customers.

Distributed computation of the GIG

The applications must compute the GIG without relying on a centralized system, but instead they exchange, via the P2P network, the required information to build the GIG. Now, the risk is to leak private information to the other collaborating applications. Hence, the required information must be shared while providing privacy guarantees to the applications. Thus, the following privacy requirements must be met when building the distributed GIG:

1. In the distributed context, the schema information which appears in a SIM must be shared with other applications to be able to compute the similarity links. However, this information must be protected (e.g., encrypted, hashed, etc.) so that another application cannot access the name of an attribute, while still being able to perform a schema matching technique.

2. In order to compute the semantic similarities between SIGs, the applications must identify which instances in distinct databases are related to the same real world customers [START_REF] Lachat | Towards an Inference Detection System Against Multi-database Attacks[END_REF]. The instances shared among applications must be encoded in a way which enables the computation of a similarity score between instances of distinct databases, while preventing other applications to retrieve attribute values of an instance.

3. If one of the collaborating applications becomes malicious, by design the solution must limit the information that is obtained about other applications. When an application receives information from the P2P network, it should not be able to know from which application it originates. Hence, both the schema and the instances must be protected using techniques to avoid disclosing this identity.

For the first requirement, we assume that at the start of the collaboration, each application has access to a common semantic repository (e.g., using a generic resource such as Wikidata [START_REF] Erxleben | Introducing Wikidata to the Linked Data Web[END_REF]) and maps each of its SIM nodes to a semantic term from the semantic resource ❷. The usage of such resource enables the data controllers to share information about their database schema, without having to share the schema by itself. They can choose to provide precise semantic terms to improve the accuracy of the identified semantic similarity links, or more generic terms to reduce the schema information indirectly leaked to the other DCs. The issues related to the requirements 2 and 3 are not tackled in this article.

Based on those requirements, we replicate the two stages described in Section 1 to compute the GIG. First, in addition to the local SIM and SIG, each application has a SIM table, ❺ in Figure 2b, with three columns: (i) the unique identifier of a node (i.e., an attribute) in the local SIM (ii) the semantic term associated to this attribute (c.f., requirement 1) (iii) one or multiple encrypted SIM node identifiers, which have the same semantic term in other collaborating applications. Those identifiers are stored in an encrypted way to prevent the application from identifying the origin and the name of the attribute. Figure 3 shows an example where two SIMs are connected, since two attributes are semantically similar in the two distinct databases. The SIM table enables applications to keep track of those links between the SIMs of collaborating applications. Following the same idea, each application has a SIG table ❻ with three columns: (i) the unique identifier of a node (i.e., the attribute of an instance) in the local SIG (ii) the identifier of the related attribute in the local SIM (iii) one or multiple encrypted (c.f., requirement 1) SIG node identifiers, related to a similar instance in the other collaborating applications. Thus, the SIG table allows the collaborating applications to have a distributed representation of the GIG by keeping track of the similarity links between the SIGs. Note that the way the SIM and the SIG tables are filled in thanks to some protocols among application is an ongoing work and will not be presented in this paper.

Local detection & Propagation of the queried information

As described above, once receiving a query issued by an authorized entity e, the local InfDS performs the detection in two phases. First, it uses its local SIG to check if there is an inference attack on its own database. If so, then the application prevents the attack by denying the query. Otherwise, it shares the information about the queried data with the other collaborating applications, in order to let them keep track of the knowledge obtained by the entity. The local InfDS sends on the P2P network a message containing the protected identifier of the queried node in its local SIG, as well as the entity's identifier. As soon as this message is received, each application checks that the protected identifier of the node appears in its SIG table. If so, it updates its local SIG, indicating that this entity e has queried this information from one of the collaborating applications. Otherwise, it means the application does not have a similarity link with the queried node, hence it ignores the message.

In case an entity issues at the same time multiple queries to distinct applications, it can lead to an unintended disclosure. For instance, if each application first checks locally for an inference, they each conclude that the received query does not lead to an inference and thus answer it. To prevent this threat, the distributed detection system implements a token distribution. In this way, when an entity e queries a data from the database of one of the collaborating applications p, p takes the token of the entity e and releases it once the distributed detection is finished. Hence, any further query by the same entity could not be answered in the mean time. Note that a more intelligent token management system with smaller granularity could be studied to assign tokens only if the data asked in parallel could be a threat on a data at a participating application.

The distributed detection is performed following one of the three strategies listed below:

(i) It starts by propagating the queried information to the network ✱. (a) If another collaborating application says that this information leads to an inference, then the initial application concludes to not answer the query, in order to avoid the attack. (b) If no inference is detected, the application checks if the query leads to an inference for its local SIG ■.

(ii) It first performs locally the detection ■, propagates the information to the network ✱, then concludes if it can safely answer the query.

(iii) It first performs locally the detection ■, concludes based on the result if it can safely answer the query, and propagates the information to the network ✱.

In the two first choices, the initial application ensures that the query does not lead to an inference, both for itself and for others. However, it increases the query answer time, since it waits for the answer of each other application. In the last choice the application prioritizes the decrease of the query answer time, while still allowing other applications to keep track of the queried knowledge, although the disclosure risk still exists.

A first implementation of the proposed distributed system is currently in progress. The communication via a peer-to-peer network is based on the p2pnetwork library1 . The local detection of inferences is implemented based on the pyAgrum library [START_REF] Gaspard Ducamp | aGrUM/pyAgrum : a toolbox to build models and algorithms for Probabilistic Graphical Models in Python[END_REF] to leverage the Bayesian network data structure (to represent the SIM & the SIG), as well as algorithms to apply evidences and to propagate probabilities.

Conclusion

In this paper, we have highlighted the lack of solutions aiming at distributively detecting inference attacks in a multi-database context, in order to protect both the privacy of applications and the privacy of its customers. We have provided an overview of a distributed architecture in which the detection is performed by the collaborating applications. As a future work, we plan to formalize the three proposed protocols. We plan to finish the ongoing prototype to demonstrate the feasibility of our approach on a case study. Finally, we plan to evaluate and compare the different distributed detection strategies listed in Section 4.2.

Figure 1 :

 1 Figure 1: Example of a SIM and a SIG. Partial reproduction of Fig.1 in [LRB20].

  Architecture of an application in the network.

Figure 2 :Figure 3 :

 23 Figure 2: Distributed architecture enabling the collaboration of applications in order to detect inference attacks using the DDS.

https://github.com/macsnoeren/python-p2p-network


Christian Vetter

Remo Giust

Luca Furfaro

Cyril Billet

Luc Froehly

Francois Courvoisier
email: francois.courvoisier@femto-st.fr

High aspect ratio structuring of glass with ultrafast Bessel beams

Controlling the formation of high aspect ratio void channels inside glass is important for applications like the high-speed dicing of glass. Here, we investigate void formation using ultrafast Bessel beams in the single shot illumination regime. We characterize the morphology of the damages as a function of pulse energy, pulse duration and position of the beam inside fused silica, Corning Eagle XG and Corning Gorilla glass. While a large set of parameters allow for void formation inside fused silica, the operating window is much more restricted for Eagle XG and Gorilla glass. The transient formation of a molten layer around voids enables us interpreting the evolution of the morphology with pulse energy and duration.

Introduction

Cutting and drilling glass is an important technological problem, particularly when the width over which the material has to be modified is much smaller than the length of the modification. This is high aspect ratio structuring. In this context, ultrafast laser processing has been very attractive because the infrared wavelength and the very high intensity of the pulses enable energy deposition in three dimensions, including inside the bulk of glass [START_REF] Sugioka | Ultrafast lasers-reliable tools for advanced materials processing[END_REF] . The laser-induced micro/nano-structures can be index modifications, nanogratings or even voids [START_REF] Gattass | Femtosecond laser micromachining in transparent materials[END_REF] . These modifications can be combined with chemical etching, which led to a number of advances in the field of photonics, microfluidics chips, mechanics [START_REF] Malinauskas | Ultrafast laser processing of materials: from science to industry[END_REF][START_REF] Sugioka | Progress in ultrafast laser processing and future prospects[END_REF] .

Because point by point scanning is relatively slow, a number of techniques have been developed to improve the overall speed for the micro-structuring. In addition, elongated voids cannot be formed by scanning, since a nano-void produced by a first pulse would be erased by the microexplosion produced by the second pulse next to it [START_REF] Watanabe | Motion of bubble in solid by femtosecond laser pulses[END_REF] . Bessel beams have revealed to be excellent candidates to control the formation of high aspect ratio elongated structures inside transparent materials [START_REF] Bhuyan | High aspect ratio nanochannel machining using single shot femtosecond bessel beams[END_REF][START_REF] Courvoisier | Ultrafast laser micro-nano structuring of transparent materials with high aspect ratio[END_REF] . Bessel beams are formed by a conical super-position of plane waves, where the central hot spot maintains its diameter over the whole length of the interference region [START_REF] Durnin | Diffraction-free beams[END_REF][START_REF] Duocastella | Bessel and annular beams for materials processing[END_REF] . Importantly, when the focusing angle of the Bessel beam is sufficiently high, the conical flow of energy crosses the high intensity region only in the central hot spot. This drastically reduces the influence of the Kerr effect, so that longitudinally-invariant structures can be processed within dielectrics [START_REF] Polesana | Filamentation in kerr media from pulsed bessel beams[END_REF][START_REF] Garzillo | Optimization of laser energy deposition for single-shot high aspect-ratio microstructuring of thick BK7 glass[END_REF][START_REF] Lamperti | Invited article: Filamentary deposition of laser energy in glasses with bessel beams[END_REF] .

Laser structuring with high aspect ratio is particularly useful in the context of stealth dicing, a concept in which a series of pulses under high-speed translation of the sample is used to create an entire modification plane [START_REF] Kumagai | Advanced dicing technology for semiconductor waferstealth dicing[END_REF] . A mechanical, chemical or thermal stress is then used to cleave the glass along the modified plane. The main benefit of this approach is that cutting is possible at very high speed (typically 10 cm to 1 m per second). Filamentation, i.e., ultrafast pulse self-channeling in glass, was first used for stealth dicing purposes [START_REF] Hosseini | Method of material processing by laser filamentation[END_REF][START_REF] Butkus | Rapid cutting and drilling of transparent materials via femtosecond laser filamentation[END_REF] . Bessel beams offer in addition the possibility to control very easily the onset of the material 1 damage by simple geometrical considerations since nonlinear effects are reduced. They were used to cut glass and sapphire [START_REF] Bhuyan | High-speed laser-assisted cutting of strong transparent materials using picosecond bessel beams[END_REF][START_REF] Mishchik | Improved laser glass cutting by spatio-temporal control of energy deposition using bursts of femtosecond pulses[END_REF][START_REF] Jenne | High-quality tailored-edge cleaving using aberration-corrected bessel-like beams[END_REF][START_REF] Dudutis | In-depth comparison of conventional glass cutting technologies with laser-based methods by volumetric scribing using bessel beam and rear-side machining[END_REF][START_REF] Li | Stealth dicing of sapphire sheets with low surface roughness, zero kerf width, debris/crackfree and zero taper using a femtosecond bessel beam[END_REF] . Since beam length and focusing angle can be independently adjusted, it is also possible to produce very long Bessel beams with the same angle that allows for cutting thick glass. This however requires high pulse energies since the energy is spread over the entire focal line of the beam [START_REF] Mitra | Millijoule femtosecond micro-bessel beams for ultra-high aspect ratio machining[END_REF] . With millijoule energy, Bessel beams were used to cleave glass up to 1 cm thick [START_REF] Meyer | Extremely high-aspect-ratio ultrafast bessel beam generation and stealth dicing of multi-millimeter thick glass[END_REF][START_REF] Feuer | Single-pass laser separation of 8 mm thick glass with a millijoule picosecond pulsed gaussian-bessel beam[END_REF] . Recently, breaking the symmetry of the Bessel beam was used to improve the precision and ability of guiding fractures [START_REF] Meyer | Single-shot ultrafast laser processing of high-aspect-ratio nanochannels using elliptical bessel beams[END_REF][START_REF] Meyer | Submicron-quality cleaving of glass with elliptical ultrafast Bessel beams[END_REF][START_REF] Jenne | Facilitated glass separation by asymmetric bessel-like beams[END_REF][START_REF] Flamm | Structured light for ultrafast laser micro-and nanoprocessing[END_REF] . Controlling the formation of voids with ultrafast laser pulses is key to improve the stealth dicing of glass.

Here, we show that, depending on the material, voids do not form for the same parameters. We compare three glass types: fused silica, Corning Eagle XG and Corning Gorilla glass. We investigate the regimes in which various structures are produced using single shot Bessel beams depending on pulse energy, pulse duration and position in the sample. We have observed that these three parameters control the formation of various types of structures inside glass. Future development of applications such as laser cutting should therefore operate in the right parameter window.

Materials and Methods

Our experimental setup (see Figure 1) is composed of a chirped Pulse amplified (CPA) Ti-Sapphire laser source, at 800 nm central wavelength and of a reflective axicon (Cailabs) associated to a telescopic arrangement to magnify the cone angle [START_REF] Boucher | Generation of high conical angle bessel-gauss beams with reflective axicons[END_REF] . The laser pulses can be stretched from 100 fs to 3ps using the grating compressor of the amplifier. The experimental characterization of the beam is shown in Figure 2. The Bessel beam has a cone angle of 19.5 • in air, which corresponds to a central spot diameter of 0.9 µm Full Width at Half Maximum (FWHM). The Bessel beam length is ∼ 220 µm FWHM. One can notice the high degree of circular symmetry of the Bessel beam. All samples were 700 µm thick. After processing, the laser-modified regions were characterized by scanning the sample with white light, brightfield illumination, in an optical microscope arrangement with a numerical aperture of 0.8 and aberration-correction. Stitching the microscope images provided high resolution images of the whole high aspect ratio structure. Figure 3 shows the result of single shot illumination in fused silica at a pulse-energy of 52 µJ, for increasing pulse durations. A periodic background pattern can be observed and simply arises from the illumination inhomogeneity associated to the stitching operation.

Results

Microstructure types In Figure 3, at a pulse duration of 125 fs, only a line of faint index change is observable. In the cases of 250 and 500 fs, high aspect ratio voids are observed, they are characterized by black marks. We readily see that the void structure is shorter than the Bessel beam length. The void is present only in the moderate intensity region while in the highest intensity region, the void structure has almost vanished. From 1000 fs, the black mark is split around its center into small dots: these are void bubbles (see scanning electron microscopy image in Fig. 4 of reference [START_REF] Velpula | Spatio-temporal dynamics in nondiffractive bessel ultrafast laser nanoscale volume structuring[END_REF] ). This process is called bubbling hereafter.

Faint bubbling appears here in the central region of the Bessel beam and is slightly stronger for the case of 2000 fs. Importantly, the morphology of the material transformation can vary along the beam. An example is shown in Figure 4 where we report the results for the interaction of a 3 ps Bessel beam in Gorilla glass for different focusing positions inside the sample. In this example, the material modification undergoes minor variations with the position. We can observe three sections with different morphologies from left to right: i) a void with faint bubbling in the relatively low intensity region of the Bessel beam (onset), ii) a wide index modification in the highest intensity segment of the Bessel beam, and iii) a void. The central panel allows us to understand the ordering of the material modification type with increasing intensity: index modification on a small diameter (central lobe), void formation, structure with more or less randomly distributed bubbles, wide index index modification on a diameter much larger than the beam central lobe. The wide modification is developed longitudinally step-wise, suggesting a threshold-based mechanism. It has erased all structures like void or bubbles. Note that the bubbles appear elliptical because we compressed the horizontal axis scale by a factor 5.

We have further explored in a parametric study, the evolution of the laser-induced structures as a function of pulse energy, pulse duration, and beam position. We have summarized our results in Figure 5 for three positions of the Bessel beam inside the fused silica sample. In Figure 5(a), the beam is positioned at the center of the sample such that none of the entrance and exit surfaces are damaged. We classified the modifications in 5 groups, ranging from no damage to strong bubbling. We note that we did not make a separate class for the wide index modification such as the one shown in Figure 4, because those modifications are conventionally useless for applications. Also, they often occur alongside voids, which we are more interested in. For the drilling and cutting of glass applications, the narrow index modifications and nice voids, shown respectively as gray and green markers, are the most interesting features. When bubbling occurred on a substantial section of the beam, the structure was classified as bubbling.

In Figure 5(a), we see that the relatively large range of parameters allow for inducing nice voids in fused silica, similarly as in reference [START_REF] Bhuyan | Single-shot high aspect ratio bulk nanostructuring of fused silica using chirp-controlled ultrafast laser bessel beams[END_REF] . Higher energies and longer pulse durations tend to create bubbling. When the pulse duration is increased, the energy required to open a void is reduced, but bubbling also arises earlier. The energy range over which nice voids can be opened is reduced at longer pulse durations. In Figure 5(b), the beam crosses the entrance side. In this case, the shortest pulse durations provide conditions where voids can be opened on a larger range of parameters. The presence of the interface increases the ability of void opening after energy deposition, as was already noticed in a former reference [START_REF] Bhuyan | High aspect ratio nanochannel machining using single shot femtosecond bessel beams[END_REF] . In Figure 5(c), the beam crosses the exit interface. In this case, the short pulse durations induce voids with very small diameters. A much larger range of energies and pulse durations enable void formation. In almost all the cases tested here, nice voids could be produced. We hypothesize that our results can be understood by the following: the presence of the interface allows the phenomenon of ablation cooling [START_REF] Kerse | Ablation-cooled material removal with ultrafast bursts of pulses[END_REF] where a fraction of the energy deposited inside the material can be evacuated via the open channel at the surface. This allows for a fast quenching of the material relaxation which increases the capability of "freezing" a void before the compressed melt part surrounding the void can close it. In the case where the beam crosses the entrance surface (Fig. 5(b)), the dynamics of plasma formation is slightly different from the two other cases because a dense plasma can form on the surface which can then shield light preventing void formation in the very first micrometres from the surface. This could prevent the effect of the ablation cooling described above.

Other glasses In Figure 6, we show the results for Eagle XG glass (Fig. 6(a)) and Gorilla glass (Fig. 6(b)) when the beam is enclosed within the sample, as in Figure 5(a). For these two materials, the situation highly differs from the case of fused silica. Overall it is much more difficult to create voids particularly for short pulses, where no modification is apparent below a threshold pulse duration of 1 ps.

The operating window for void formation is restricted to a small energy range before bubbling sets in. This window is even smaller in the case of Gorilla glass. We remark that for most of the pulse durations in Gorilla glass, above the energy for the bubbling regime, only faint structures are found, whereas this phenomenon occurs in Eagle XG only for 1.5 ps and never in fused silica. It could be attributed to a slower relaxation in Gorilla glass than in the other media.

We attribute the differences between the different glasses in terms of void opening to the difference in softening point. Indeed, it exceeds 1500 • for fused silica while it is only of 971 • for Eagle XG and 853 • for Gorilla glass. Therefore, assuming a similar profile of laser-deposited energy, the molten region is wider in the case of Eagle XG and Gorilla glass than in the case of fused silica. This would lead to a faster quenching of the relaxation in fused silica, with stronger gradients, in contrast with the other two glasses.

In Eagle XG and Gorilla glass, beam positioning close to the entrance and exit surfaces yield to similar tendencies as in the case of fused silica. While no major differences could be observed with Figure 6 when the beam crosses the entrance surface, we have observed a much larger operating window for void opening when the beam crosses the exit surface for both glass types.

Large heat-affected zone for picosecond pulses Figure 7 shows the result of a 3 ps laser shot in Eagle XG. One can notice that the heat affected zone is very wide, typically above 8 µm in diameter. Importantly, in this regime, the bubbles are not aligned: it seems that they have randomly moved from the optical axis during the relaxation stage. This well supports the interpretation of a large molten layer around the void at large pulse energies and duration.

Conclusion

We have observed that void formation in transparent glasses strongly depends on energy and pulse duration. In fused silica, voids can be formed for a relatively large set of parameters. By increasing pulse energy and pulse duration, the high aspect ratio void channel splits into bubbles with a diameter of approximately 1 µm. This structure can even vanish for higher energies. In Eagle XG and Gorilla glass, only very long pulse durations could yield void formation, but for a very limited energy range. For a pulse duration of 2 ps and 16 µJ pulse energy, a void can be formed in all three materials, with a length of 150±10 µm in Eagle XG, of 170±10 µm in fused silica and the highest length is for Gorilla glass with 230±10 µm. For all materials, we remark that void formation is possible over a larger range of energies when the beam crosses the exit surface.

We interpret the evolution of the morphology of the damages induced by ultrashort Bessel beams in these glasses in the following way. For sufficiently high energies, a void can form inside glass, either after a micro-explosion [START_REF] Juodkazis | Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures[END_REF][START_REF] Beuton | Numerical studies of dielectric material modifications by a femtosecond bessel-gauss laser beam[END_REF] or by cavitation inside a molten zone [START_REF] Bhuyan | Ultrafast laser nanostructuring in bulk silica, a "slow" microexplosion[END_REF] . We infer that this void can be transiently surrounded by a molten layer, whose thickness depends on the glass type and pulse duration. The longest pulse durations and the highest energies tend to increase the thickness of the molten layer. A low softening point, such as in the case of Eagle XG and Gorilla also increase the molten layer. Thicker molten layers increase the occurrence of bubbling or are even closing the void. We understand the formation of bubbles as a re-distribution of the material during the cooling stage, by splitting or even fully closing the void transiently formed. We interpret the role of the exit surface as a cooling agent. The evacuation of a fraction of the hot material via the void channel produced at the center of the Bessel beam, allows for quenching the relaxation and maintains the void structure even for parameters where the void would be partially or totally re-closed by the molten material around it. Recent results on double pulse illumination let us anticipate that double pulse could partially reduce the amount of the molten layer, and increase the temperature contrast between the optical axis and the surrounding lobes [START_REF] Del Hoyo | Nanoscale confinement of energy deposition in glass by double ultrafast bessel pulses[END_REF] .

Figure 1 :

 1 Figure 1: Experimental setup. The ultrafast laser beam is shaped by a reflective axicon (Cailabs). It is then demagnified by a telescopic arrangement in a 2f-2f configuration. The laser-written structures are observed using an incoherent white light source.

Figure 2 :

 2 Figure 2: Characterization of the experimental Bessel beam. (left) Longitudinal cross-cut of the fluence distribution as a function of the relative propagation distance in air. Please note the aspect ratio of the axes. (right) Cross-section of the fluence distribution at the center of the beam.

Figure 3 :

 3 Figure 3: Microscope images of damages produced in fused silica glass for several pulse durations, for the same beam position inside the sample and for a constant single shot energy of 52 µJ. Please note the image aspect ratios (left insets show 1:1 zooms of the panels to their right). The beam propagates from left to right.

Figure 4 :

 4 Figure 4: Brightfield microscopy images of damages produced in Gorilla glass with 3 ps pulse duration at a constant energy of 52 µJ as in Fig. 4. The position of the beam in the sample was varied from top to bottom. Please note the image aspect ratios (left insets show 1:1 zooms of the panels to their right).

Figure 5 :

 5 Figure 5: Morphology of the single shot-induced damage in fused silica as a function of pulse energy and pulse duration. This is performed for a Bessel beam position: (a) at the center of the sample, (b) crossing the entrance surface, (c) crossing the exit surface.

Figure 6 :

 6 Figure 6: Morphology of the single shot-induced damage in (a) Eagle XG and (b) Gorilla glass as a function of pulse energy and pulse duration. The beam is centered inside the sample.

Figure 7 :

 7 Figure 7: Strong bubbling in Eagle XG glass. The pulse duration is 3 ps, pulse energy 141 µJ. Please note the image aspect ratio. The bottom inset shows a 1:1 zoom of the marked area in the panel above.

These results shed light on the formation of high aspect ratio void channels inside different glasses. We believe they will impact on future technologies for ultrafast laser material processing of glass.

Acknowledgments

We gratefully acknowledge the technical support of E. Dordor.

Funding

This research was funded by Corning Incorporated, Region Franche-Comte council and Agence Nationale de la Recherche ( EQUIPEX+ SMARTLIGHT platform ANR-21-ESRE-0040), I-SITE BFC project (contract ANR-15-IDEX-0003), and the EIPHI Graduate School ANR-17-EURE-0002.

Conflicts of interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript.


Laetitia Martinerie

Eric Pussard

Laurence Foix-L'hélias

François M Petit

Claudine Cosson

Pascal Boileau

Marc Lombès

Physiological partial aldosterone resistance in human newborns

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