C Djaou

C Villeneuve-Faure

L Boudou

K Makasheva

G Teyssedre

Thermally induced effects on the injection and retention of electrical charges in SiO 2 layers containing silver nanoparticles

Introduction

Under electrical stress, dielectric materials can accumulate electrical charges. This may even lead to a breakdown, i.e. to a system failure [START_REF] Witvrouw | Materials issues in the processing, the operation and the reliability of MEMS[END_REF][START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation[END_REF] . To prevent the harmful consequences of this phenomenon, charge trapping by metallic, silver nanoparticles (AgNPs) has been considered [START_REF] Milliere | Efficient barrier for charge injection in polyethylene by silver nanoparticles/plasma polymer stack[END_REF] . Even though the space charge build-up mitigation was demonstrated, the underlying mechanisms remain poorly described. To identify the AgNPs influence, their response needs to be probed at relevant scale, i.e. at the nanoscale. Thus, our overall objective is to determine the impact of AgNPs on the charge injection and retention in thin dielectric layers. The considered structures consist of nanostructured thin SiO 2 layers; a bare SiO 2 layer and two SiO 2 layers containing a 2D-plan of AgNPs of 20 nm of size, located at 7 nm and 21 nm from the free surface. The structuration of the dielectric layers is achieved in a hybrid plasma process [START_REF] Makasheva | Dielectric engineering of nanostructured layers to control the transport of injected charges in thin dielectrics[END_REF] . A Bruker multimode 8 apparatus, equipped with a controlled environment cell, is used to probe the surface potential in Amplitude Modulation Kelvin Probe Force Microscopy (AM-KPFM) with 50 nm lift. Charge injection and surface potential measurements are performed using a PtIr-coated Si AFM tip. The injection and KPFM measurement are done at temperatures varying from 20°C to 140°C with a step of 30°C.

Results and Discussion

First of all, one can notice that both carriers, electrons and holes, present the same behavior for charge distribution (lateral spreading and increase of the amount of injected charge with the applied bias) and decay dynamics. As far as the injection is concerned, the AgNPs close to the free surface (i.e. at 7 nm), induce an increase of the amount of injected charge mainly due to enhanced lateral spreading compared to the bare SiO 2 or to the layer with AgNPs embedded far from the surface (i.e. at 20 nm). The temperature increase influences in different ways the charging process. Indeed, for the bare SiO 2 or for the SiO 2 layer with AgNPs far from the surface, the lateral spreading and the amount of injected charge increase in the temperature range from 20°C to 80°C and then decrease for higher temperatures. When the AgNPs are embedded close to the free surface, the lateral spreading and the amount of charges increase slowly with the temperature in the whole range. For each temperature the bare SiO 2 layer presents good charge retention with a constant lateral spreading and a slow release of the charge with time. For the nanostructured layers the charge decay presents different behavior. The lateral charge spreading is increased while the amount of charge is decreased with time. The evolution is faster when the AgNPs are situated close to surface. It means that the charge decay follows a volume-type mechanism for the bare SiO 2 and a coupled lateral and volume-type mechanism in presence of AgNPs.

Conclusions

It is found in this work that during charge injection at low temperature, the AgNPs located close to the surface act as charge traps. For temperatures higher than 80°C, the amount of injected charge is higher for the bare SiO 2 or for the SiO 2 layer with AgNPs situated far from the surface. The temperature increase induces more important charge decay when the AgNPs are embedded close to surface.

Acknowledgements

Research supported by the program IDEX ATS 2015 of the Université de Toulouse under project SEPHIR (2016-066-CIF-D-DRVD).


N Sainlot

I Vlastélic

F Nauret

S Moune

F Aguilera

Sr-Pb isotopes signature of Lascar volcano (Chile): Insight into contamination of arc magmas ascending through a thick continental crust

In the Central Volcanic Zone of the Andean cordillera (CVZ), thickening of the continental crust 30 Ma ago led to the production of increasingly differentiated magmas. Better constrain on the interactions between ascending magmas and the thick continental crust are needed to understand the contamination processes and their implications on the geochemical diversity of arc magmas.

Lascar volcano figures among the most active Quaternary volcano of the CVZ and yet geochemical studies on its volcanic products remain scarce. We lead major-, trace elements and Pb-Sr isotopes measurements on 10 Lascar samples representative of the different petrologic types (andesitic to dacitic) in order to better characterize the Pb-Sr isotopic signature and diversity of Lascar magmas yet defined based on only 8 samples. 206 Pb/ 204 Pb (18.770-18.823), 207 Pb/ 204 Pb (15.636-15.655), 208 Pb/ 204 Pb (38.711-38.809) and 87

Sr/ 86 Sr isotope ratios (0.705731-0.706564) show small variations within the previously defined isotopic field of Lascar. In Pb-Sr or Pb-Pb isotope space, the data points show a triangular distribution that requires the contribution of at least three end-member components at the source of Lascar magmas. We built up a two-stage three-components assimilation and fractional crystallization model (AFC) that reproduces the entire diversity of Lascar magmas.

It allows us to geochemically constrain the three end-member components compositions : (BA) a common mantellic source with low 87 Sr/ 86 Sr (<0.70575), low 206 Pb/ 204 Pb (<18.768), 207 Pb/ 204 Pb (<15.637) and 208 Pb/ 204 Pb (<38.711) (EB) a lower crust and/or slab component radiogenic in Sr ( 87 Sr/ 86 Sr >0.70656) and in Pb ( 206 Pb/ 204 Pb >18.82 ; 207 Pb/ 204 Pb > 15.647 ; 208 Pb/ 204 Pb > 38.79), (C) a felsic upper continental crust (> 65.1 wt% of SiO2) with similar Sr-Pb isotope composition as EB ( 87 Sr/ 86 Sr > 0.70643; 206 Pb/ 204 Pb >18.823 ; 207 Pb/ 204 Pb >15.655 ; 208 Pb/ 204 Pb > 38.809). Both BA and EB components occur in lavas with <57 wt.% SiO2.

This model predicts that Lascar magmas assimilated ≤ 30 % of lower crust and ≤ 29 % of upper crust. Our conclusions are in good agreement with the CVZ literature that reports the contribution of three ubiquitous end-member components at the source of CVZ magmas, with similar natures and origins.

Introduction

Earth mantle and crust constantly interact and exchange materials through different processes.

Cyclic production and recycling of the oceanic lithosphere is one of those main processes, and is accountable for the formation of volcanic arcs in subduction settings. Andean subduction has been particularly studied for the diversity of its magmatism, geodynamics and geochemistry [START_REF] James | The Combined Use of Oxygen and Radiogenic Isotopes as Indicators of Crustal Contamination[END_REF]Wörner et al., 2005;[START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF][START_REF] Nauret | The Genetic Relationship between Andesites and Dacites at Tungurahua Volcano, Ecuador[END_REF]. The geochemical variability of magmas in subduction context has been ascribed to the heterogeneity of the mantellic source (Francallanci et al., 1989;[START_REF] Wendt | Geochemistry of Lavas from the Garrett Transform Fault: Insights into Mantle Heterogeneity beneath the Eastern Pacific[END_REF][START_REF] Hochstaedter | Accros-arc geochemical trends in the Izu-Bonin arc: Constraints on source composition and mantle melting[END_REF][START_REF] Hofmann | Sampling Mantle Heterogeneity through Oceanic Basalts: Isotopes and Trace Elements[END_REF], the variable input of melts and fluids derived from the slab and melt extraction from distinct mantle lithologies (Spiegelman&Kelemen, 2003 ;[START_REF] Rawson | Compositional Variability in Mafic Arc Magmas over Short Spatial and Temporal Scales: Evidence for the Signature of Mantle Reactive Melt Channels[END_REF].

Crustal contamination and fractional crystallization processes (AFC) are further liable for magma differentiation and diversity. In the Andean cordillera that spreads on 7000 km, the Central Volcanic Zone (CVZ) segment is well suited for studying continental subductionrelated magmatism and magma-crust interactions. Indeed, CVZ magmas are characterized by overall enriched geochemical signatures (radiogenic in Sr, Pb, Nd, and LREE/HREE fractionation) [START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF] in comparison to the depleted MORB mantle. Subducted sediments, sub-continental tectonic erosion [START_REF] Stern | Role of subduction erosion in the generation of Andean magmas[END_REF][START_REF] Kay | Episodic arc migration, crustal thickening, subduction erosion, and magmatism in the south-central Andes[END_REF] or the enriched subcontinental lithosphere (Rogers&Hawkesworth, 1989;[START_REF] Davidson | The source of central Andean magmas; Some considerations[END_REF], all may participate to the enriched signature of Andean magmas but are not considered as the main factors controlling CVZ magma geochemical signature [START_REF] Kay | Magma source variations for mid-late Tertiary magmatic rocks associated with a shallowing subduction zone and a thickening crust in the central Andes (28 to 33°S)[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF].

In fact, the particular geochemical signature of Central Andean magmas is shown to be mostly the result of the interaction of mantle-derived magmas with a composite crust that grows importantly since 30 Ma (Harmon&Barreiro, 1984;Hildreth&Moorbath, 1988;[START_REF] Davidson | The source of central Andean magmas; Some considerations[END_REF][START_REF] Kay | Magma source variations for mid-late Tertiary magmatic rocks associated with a shallowing subduction zone and a thickening crust in the central Andes (28 to 33°S)[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF][START_REF] Kay | Magma sources and tectonic setting of Central Andean andesites (25.5-28°S) related to crustal thickening, forearc subduction erosion and delamination[END_REF]. The Central Andean composite crust is nowadays the thickest of the Andean cordillera, reaching more than 75km [START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF]. It is admitted that intermediate to silica-rich magmas emitted in the CVZ are the result of physica-chemical processes such as crustal assimilation coupled with fractional crystallization (AFC) and melting processes (Davidson et al., 1990). These processes are known to operate from the melting zone where primitive mafic magmas are produced, up to different levels of the continental crust where magmas are stored and then extracted (Bachmann&Bergantz, 2008;[START_REF] Freymuth | The Origin and Crust/Mantle Mass Balance of Central Andean Ignimbrite Magmatism Constrained by Oxygen and Strontium Isotopes and Erupted Volumes[END_REF]. Differentiated magma emissions occur more often in arc context in comparison to other geodynamical context (hotspots, ocean ridge) and are taken responsible for arc stratovolcanoes unpredictable activity alternating long dormancy periods and violent explosive eruption (Denlinger&Hoblitt, 1999).

Lascar volcano (Chile) has been the concern of previous geochemical studies (Harmon&Barreiro, 1984;[START_REF] Hilton | Helium Isotope Characteristics of Andean Geothermal Fluids and Lavas[END_REF][START_REF] Déruelle | Petrology of Pumices of April 1993 Eruption of Lascar (Atacama, Chile)[END_REF][START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF]Risarcher&Alonso, 2001;[START_REF] Rosner | Slab-Derived Boron Isotope Signatures in Arc Volcanic Rocks from the Central Andes and Evidence for Boron Isotope Fractionation during Progressive Slab Dehydration: Slab-derived boron isotope signatures[END_REF][START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF][START_REF] Tassi | The Magmaticand Hydrothermal-Dominated Fumarolic System at the Active Crater of Lascar Volcano, Northern Chile[END_REF][START_REF] Menard | Gas and Aerosol Emissions from Lascar Volcano (Northern Chile): Insights into the Origin of Gases and Their Links with the Volcanic Activity[END_REF]. Particularly, it has been shown that Lascar magmas interact with buried gypsum from paleosalars underlying the Andean Cordillera and outcropping in the Cordillera del Sal, West of Lascar volcano (Risarcher&Alonso, 2001). These interactions between magmas and continental crust components lead us to investigate Lascar magma geochemistry and its possible interaction with the thick continental crust.

Our study aims at understanding the andesitic and dacitic magmas relationship in a volcanic arc context, during the whole period of activity of Lascar volcano from 26.5 ky to the last major eruption in 1993, and the processes that could account for the large heterogeneity of andesites.

Major and trace elements contents as well as Sr-Pb isotopic compositions of Lascar magmas lead us to conclude that at least two different mafic, presumably deep sources, are responsible for the large range of andesitic compositions. Moreover, the contamination of these mafic andesitic magmas by the upper local basement, via AFC, appears to be the main process that governs dacitic magma formation in the shallow levels of the crust. These dacitic magma bodies are mobilized during the large eruption events (vulcanian to plinian). Extensive continental crust/magma interaction inevitably tends to wipe off mantellic signature in emitted magmas.

Geological context

Lascar is a stratovolcano located in northern Chile (23°22' S/67°44'W/5590m), Est of Salar de Atacama in the Antofagasta area, on the western margin of the Andean altiplano (Fig. 1) and results from the Nazca plate subduction (<60 Ma) under the South-American one (7-9 cm/y, 25° (Dorbath&Paul, 1996). Considered as the most active volcano of northern Chilean Andes, Lascar figures among the 44 potentially active edifices of the CVZ that extends from Northern Chile to North-West of Argentina, South-West of Bolivia and Southern Peru (De [START_REF] Silva | Volcanoes of the Central Andes[END_REF][START_REF] Stern | Active Andean Volcanism: Its Geologic and Tectonic Settings[END_REF] and among the 56 volcanoes of Chile with proved (dated or observed) historical eruptions (Global Volcanism Program).

Lascar volcano composite stratocone is elongated on a WSW-ENE axis [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF] and include two distinct edifices: the active east one and the dormant west one. Indeed, during stage I of Lascar stratocone formation (<43 ka), the active zone was constrained in the eastern cone and Lascar had a mafic andesitic activity. It shifted during stage II to the west with a global silicic andesitic to dacitic activity of lava dome building and ignimbrite formation (Soncor ignimbrite at 26,45 ka). Stage III of activity consisted in developing the western stratocone over Soncor event, and culminated with Tumbres event (9,2 ka) characterized by andesitic scoria flows and crater collapses. Finally, the active zone shifted to the east during stage IV of andesitic activity, which consisted in building the three summit nested craters aligned on a E-W axis and observable nowadays (Richter et al., 2018) (crater A, B andC from W to E (Zeeuwvan Dalfsen et al., 2017)). Crater A is the seat of the current activity. Significant morphological and structural changes of the active crater occurred during the historical period [START_REF] Matthews | The 1984 to 1996 Cyclic Activity of Lascar Volcano, Northern Chile: Cycles of Dome Growth, Dome Subsidence, Degassing and Explosive Eruptions[END_REF]) such as apparition of arcuate fractures along the crater rims, E-W faults crossing along the active crater since 1993 eruption [START_REF] Pavez | Insight into ground deformation at Lascar volcano (Chile) from SAR interferometry, photogrammetry and GPS data : Implications on volcano dynamics and future space monitoring[END_REF], small-scale subsidence and asymmetric horizontal displacements of all summit craters [START_REF] Richter | Constraints on the geomorphological evolution of the nested summit craters of Lascar volcano from high spatio-temporal resolution TerraSAR-X interferometry[END_REF]. However, the current locus of activity remains quite stable through time.

Lascar has been active for the past 220 ky and emitted about 30-40 km 3 of magma [START_REF] Gardeweg | Evolution of Lascar Volcano, Northern Chile[END_REF]. It lies on Devonian to early Carboniferous sandstones (Lila formation), Permian volcanic rocks and granites (Cas formation) and Permo-Trias volcanic products (Peine Strata et Cerro Negro Strata) [START_REF] Gardeweg | Evolution of Lascar Volcano, Northern Chile[END_REF]. Occurrence of coated gypsum on volcanic ash samples at Lascar revealed the presence of Tertiary gypsum deposits of the Cordillera de la Sal formations at depth (Risarcher & Alonso, 2001).

Geochemical studies on Lascar volcano are scarce in spite of its regular volcanic activity with 27 eruptions reported between 1848 and 2007, the nearly continuous passive degassing of the active crater and its active hydrothermal system. It emits calk-alkali products with composition ranging from basaltic-andesitic to dacitic. Eruption products are mainly two-pyroxene andesites and dacites with few hornblende dacites found in the Soncor flow products. Plagioclase phenocrysts are dominant in the mineral assemblage of Lascar eruptive products followed by orthopyroxene, augite, magnetite, ilmenite as well as minor hornblende, quartz and olivine [START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF]. Among the 162 samples previously studied (Pichler et al., 1968;Siegers et al., 1969;Deruelle et al., 1982;[START_REF] Hilton | Helium Isotope Characteristics of Andean Geothermal Fluids and Lavas[END_REF][START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF][START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF][START_REF] Rosner | Slab-Derived Boron Isotope Signatures in Arc Volcanic Rocks from the Central Andes and Evidence for Boron Isotope Fractionation during Progressive Slab Dehydration: Slab-derived boron isotope signatures[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF][START_REF] Menard | Gas and Aerosol Emissions from Lascar Volcano (Northern Chile): Insights into the Origin of Gases and Their Links with the Volcanic Activity[END_REF]Grockes et al., 2016), 107 are identified as andesites, 40 as dacites and 2 as rhyodacites gathering lavas, pumices and scorias. Petro-geochemical evidences suggest that Lascar magmas are generated by combined processes of plagioclase-and pyroxene-dominated fractional crystallization, periodic magma mixing and crustal contamination [START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF]. Lascar magmatic system at depth is composed of a 6km-depth open-system reservoir regularly fed with mafic magma injections leading to a complex zoned magma chamber [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF].

Since 1984, Lascar displays a cyclic activity [START_REF] Mather | Characterization and Evolution of Tropospheric Plumes from Lascar and Villarrica Volcanoes, Chile[END_REF] with repetition of dome formation, subsidence, crater collapse, magmatic system suppression and vulcanian to plinian explosion (September 1986, Febuary 1990, April 1993) [START_REF] Matthews | The 1984 to 1996 Cyclic Activity of Lascar Volcano, Northern Chile: Cycles of Dome Growth, Dome Subsidence, Degassing and Explosive Eruptions[END_REF] with eruptive column reaching 25 km high. The last major eruption of Lascar volcano (VEI 4), the 19 th -20 th of April in 1993, emitted more than 0,1 km 3 of volcanic products [START_REF] Gardeweg | Evolution of Lascar Volcano, Northern Chile[END_REF][START_REF] Tassi | The Magmaticand Hydrothermal-Dominated Fumarolic System at the Active Crater of Lascar Volcano, Northern Chile[END_REF]. Few months before this plinian eruption, degassing pathway obstructed and overpressure was released through minor explosions in the active crater. The last eruption occurred the 4 th of April, in 2013 (Sernageomin). Small-scale phreatic explosions occurred at Lascar in 2015 [START_REF] Gaete | Seismic activity during the 2013-2015 intereruptive phase at Lascar volcano, Chile[END_REF].

Samples and analytical methods

Samples include 10 volcanic rocks that encompass a large diversity of Lascar products in terms of rock type (lava, scoria, and pumice), composition (andesitic to dacitic), and age (Soncor eruption 26.45ky; Tumbre eruption 9.2ky; 1993 eruption) (Supplementary material, Fig. 2).

Analysis were all carried at Laboratoire Magmas et Volcans, Clermont-Ferrand, with 7 new samples (6 andesites and 1 dacite) characterized for major-, trace-and Pb-Sr isotopic compositions and 3 andesitic samples from (Menard, PhD, 2014;unpublished) analyzed for Pb isotopes. In the literature, 162 samples are analyzed in terms of major-and trace element compositions whereas the Pb and Sr isotopic composition has only been measured on 8 and 17 samples only, respectively. Gathering Lascar data (this study + literature data), Lascar database is composed of 113 andesites and 41 dacites. The 10 new Pb-Sr isotopic data double the existing Pb-Sr isotope database on Lascar eruptive products.

Samples were sawn, crushed using a BB 250 XL Retsch jaw crusher and reduced into a micrometric (<80 µm) homogeneous powder in an agate bowl using a planetary mill (PM 100 Retsch). Both jaw crusher and agate bowl were pre-contaminated with each Lascar sample prior to the crushing and pulverizing steps. Major elements concentrations were measured with ICP-AES after dissolution of 100 mg of each sample by alkaline fusion. In order to quantify the amount of interstitial water H2O + , rock powders are weighted before and after exposition at 110°C during 2 hours. H2O -is estimated following the same methodology after another 1 hour of exposition at 1000°C, which allows quantifying the total amount of structural water. Major oxide normalization takes into account this volatile content. Trace element concentrations and Sr-Pb isotopic composition are measured on the same dissolution: 100 mg of each sample was dissolved in concentrated HNO3 and HF acids (ratio 1:3). After evaporation, the fluoride residue was reduced by repeated additions and evaporations of a few drops of 7M HNO3. Stock solutions were prepared adding 3x10 ml of 7M HNO3. Daughter solutions were prepared by taking 2.4g from the stock solution. These new solutions were evaporated at 75°C, and the dry residue was dissolved in 30 ml 0,5M HNO3 and homogenized during 12h at 60°C. Trace elements concentrations are obtained by ICP-MS (Agilent 7500) measurements on daughter solutions. Repeated analysis of synthetic multi-element standard CMS (Inorganic Venture) and rocks standards BE-N, JA-1 and BCR-2 are used to evaluate the accuracy and the reproducibility of major and trace elements measurements. Internal reproducibility (2σ) is 5% for most elements. External reproducibility (repeated analysis of standards) is better than 10% for most elements, except for some chalcophile and siderophile elements. The difference between JA-1 and BCR-2 standards measured values and references values (GeoRem, 2019) is within the external error.

Pb and Sr were isolated from stock solutions following the protocol described by [START_REF] Pin | Rapid, Simultaneous Separation of Sr, Pb, and Nd by Extraction Chromatography Prior to Isotope Ratios Determination by TIMS and MC-ICP-MS[END_REF], and their isotopic compositions were performed on MC-ICP-MS (Neptune +) and Thermal Ionization Mass Spectrometry (TIMS, Triton, ThermoScientific), respectively. Pb isotopic compositions are corrected for mass fractionation by adding a solution of the NIST SRM 997 Tl standard to the samples before analyses. Measurements are normalized to the recommended values of the international NBS 981 standard (Todt et al., 1996). Total procedural blanks contain less than 0.1 ng of Pb (<0.05% of the total amount of Pb loaded on the column).

Sr isotopic compositions were carried in static mode on single Re filaments. Sr isotopic data were normalized to the recommended value of the NIST 987 standard ( 87 Sr/ 86 Sr = 0.710245).

Results

Major elements

Major elements concentrations of Lascar bulk rocks are reported in Supplementary Materials.

Lascar eruptive products define a calk-alkaline series with SiO2 content between 57.6 wt% and 65.1 wt% (Fig. 3) with 9 andesites and 1 dacites. Most major elements (2.0 wt% <MgO<5.0 wt%; 3.3 wt% <CaO< 7.4 wt%; 14.2 wt% <Al2O3< 17.1 wt%) are negatively correlated to the silica content except Na2O and K2O (Fig. 2). These trends reveal the fractionation of olivines, clinopyroxenes, Fe-Ti oxides and plagioclases [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF]. Major elements contents measured in our samples span nearly the entire compositionnal field of Lascar volcano reported in literature .

Trace elements

Trace elements concentrations are reported in Supplementary Materials. Trace elements concentrations diagram of Lascar bulk rocks normalized to primitive mantle (Fig. 4) is consistent with literature data from the CVZ. It shows typical arc-related patterns mostly defined by high content in large ion lithophile elements (Cs, Rb, Ba) and U, Th, Pb with concentrations that reach more than 100 times those of the primitive mantle (Sun&McDonough, 1995). High field strength elements display negative anomalies (Nb (7-11 ppm); Ti (3765-5240 ppm)). These elements remain enriched with content 5 to 10 times primitive mantle values.

Heavy rare earth elements (HREE)-and middle rare earth elements (MREE) content are depleted relative to light rare earth elements (LREE) content. We observe an increase of the (La/Sm)N ratio (from 2.8 to 3.7) with the increase of the silica content (Fig. 5). Inversely, (Dy/Yb)N ratio (MREE/HREE) slightly decreases with silica content (1.30 to 1.13), which has been related to the fractionation of amphibole during magma differentiation [START_REF] Davidson | Amphibole "Sponge" in Arc Crust?[END_REF]. In La/Yb vs. Sm/Yb diagram (Fig. 6a), a vertical trend reveals amphibole fractionation as MREE and HREE do not fractionate from each other during amphibole fractionation (D MREE Amph ~ D HREE Amph). Differently, La content increases (D LREE Amph < D HREE Amph) as amphibole crystallizes (Tiepolo et al., 2007).

Compatible elements contents (V, Cr, Sr) decrease with the silica content (178 to 78 ppm, 106 to 30 ppm and 728 to 334 ppm, respectively) following plagioclase, pyroxene and amphibole crystallization [START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF] and is in good agreement with literature data (12<V<335; 0.2<Cr<264; 139<Sr<1939) (Fig. 5). Sr content of Lascar bulk rocks reveal (1) a flat trend with increasing silica content and (2) a second trend toward Sr-rich content while increasing the differentiation index (samples from [START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF]Fig. 5). The Sr-rich trend gathers only andesitic magmas (SiO2 < 63 wt%). Incompatible elements (Th, Ba) contents increase with differentiation (5 to 14 ppm and 344 to 543 ppm, respectively while remaining within the range of literature values (4<Th<24 ppm and 218<Ba<1871 ppm). We observe a geochemical heterogeneity of the andesitic terms (between 56 and 63 wt% SiO2) (Fig. 5). Incompatible trace element ratios Th/La, Ba/U and Rb/Th vary from 0.25 to 0.58, from 115 to 259 and from 8.08 to 9.60 respectively, in good agreement with literature values (0.21<Th/La<1.00 ; 66<Ba/U<631 and 1.45<Rb/Th<15.84). Th/La ratio positively correlates with silica content while Ba/U and Rb/Th ratios display a negative correlation with silica content. Both Th/La and Ba/U ratios evolutions with differentiation partly reveal the fractionation of amphibole [START_REF] Nauret | The Genetic Relationship between Andesites and Dacites at Tungurahua Volcano, Ecuador[END_REF]. Because amphibole is rarely a phenocryst phase of Lascar magmas, amphibole may fractionate at depth [START_REF] Davidson | Amphibole "Sponge" in Arc Crust?[END_REF].

Pb-Sr isotopes

Pb-Sr isotopic compositions of Lascar eruptive products are reported [START_REF] Harmon | Regional O-, Sr-, and Pb-Isotope Relationships in Late Cenozoic Calc-Alkaline Lavas of the Andean Cordillera[END_REF][START_REF] Hilton | Helium Isotope Characteristics of Andean Geothermal Fluids and Lavas[END_REF][START_REF] Déruelle | Petrology of Pumices of April 1993 Eruption of Lascar (Atacama, Chile)[END_REF][START_REF] Rosner | Slab-Derived Boron Isotope Signatures in Arc Volcanic Rocks from the Central Andes and Evidence for Boron Isotope Fractionation during Progressive Slab Dehydration: Slab-derived boron isotope signatures[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF] . The 207 Pb/ 204 Pb ratios of andesites cover the entire range of variation of Lascar magmas, from 15.62 to 15.66. Increasing the differentiation index, dacites display more homogeneous 207 Pb/ 204 Pb between 15.650 and 15.655. 206 Pb/ 204 Pb ratios of Lascar eruptive products are positively correlated to 207 Pb/ 204 Pb and 208 Pb/ 204 Pb (Fig. 7). In this figure, we report the compositions of the subducted component (i.e. Nazca plate, Unruh&Tatsumoto, 1974), the local basement (Upper continentale crust composed of the Quepe Strata and the Cordon de Lila, [START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF], the average composition of the lower continental crust [START_REF] Weber | Crustal Make-up of the Northern Andes: Evidence Based on Deep Crustal Xenolith Suites, Mercaderes, SW Colombia[END_REF] we observe a triangular shape, which results from the geochemical heterogeneity of the andesitic terms (Fig. 8). This ternary distribution cannot be explained by a simple binary mixing process [START_REF] Schiano | Simple Mixing as the Major Control of the Evolution of Volcanic Suites in the Ecuadorian Andes[END_REF] but could result from a more complex process involving at least three end-member components at the source of Lascar magmas [START_REF] Keay | A Three-Component Sr-Nd Isotopic Mixing Model for Granitoid Genesis, Lachlan Fold Belt, Eastern Australia[END_REF].

Discussion

Three ubiquitous end-members at the source of CVZ magmas

Several isotope spaces, including 207 Pb/ 204 Pb (and 208 Pb/ 204 Pb) vs. 206 Pb/ 204 Pb space and 87 Sr/ 86 Sr vs. 206 Pb/ 204 Pb (Fig. 9) show a triangular dispersion of quaternary magmas emitted in the CVZ (data compilation by [START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF], including Lascar data. This triangular distribution is also observable at Lascar scale (Fig. 7&8). Such a distribution is a robust evidence for the presence of three ubiquitous end-members at the source of all CVZ magmas (Harmon&Barreiro, 1984;Godoy et al., 2014;[START_REF] Freymuth | The Origin and Crust/Mantle Mass Balance of Central Andean Ignimbrite Magmatism Constrained by Oxygen and Strontium Isotopes and Erupted Volumes[END_REF]Blum-Oeste&Wörner, 2016). Among them, Blum-Oeste&Wörner (2016) identified two mafic end-members formed by deep processes; a typical basaltic andesite here referred as BA component, and an enriched basalt here referred as EB component. This overall andesite geochemical heterogeneity in arc magmas may be explained by the chemical variability of the mantle source, the recurrent recycling of slab components [START_REF] Mcculloch | Geochemical and Geodynamical Constraints on Subduction Zone Magmatism[END_REF][START_REF] Plank | The Chemical Composition of Subducting Sediment and its Consequences for the Crust and Mantle[END_REF][START_REF] Elliott | Tracers of the Slab[END_REF]Turner and Langmuir, 2015b) and the complex interaction between melt and peridotite in melt extraction channels [START_REF] Cann | A Review of Melt Migration Processes in the Adiabatically Upwelling Mantle beneath Oceanic Spreading Ridges[END_REF][START_REF] Rawson | Compositional Variability in Mafic Arc Magmas over Short Spatial and Temporal Scales: Evidence for the Signature of Mantle Reactive Melt Channels[END_REF]. However, at the CVZ scale, the geochemical diversity of low-silica magmas is often explained by ; (1) lower crust contamination (Harmon&Barreiro, 1984;Hildreth&Moorbath, 1988;Davidson et al., 1990;Vatin-Pérignon et al., 1991;Godoy et al., 2014). Magmas interaction with the lower continental crust at depth is recorded by trace elements (Davidson et al., 1990;Davidson et al., 1998;Godoy et al., 2014), He (Hilton et al., 1982), O, Pb and Sr isotopes (Harmon&Barreiro, 1984;Godoy et al., 2014;[START_REF] Freymuth | The Origin and Crust/Mantle Mass Balance of Central Andean Ignimbrite Magmatism Constrained by Oxygen and Strontium Isotopes and Erupted Volumes[END_REF]. Geochemical data on CVZ magmas converge toward a common interpretation; typical mantellic arc magmas ascent from their melting zone to the lower crustal zone where they are stored, differentiate and assimilate country rocks in deep "MASH zones" (Melting, Assimilation, Storage, Homogeneization (Hildreth&Moorbath, 1988;[START_REF] Wörner | The Nevados de Payachata Volcanic Region (18°S/69°W, N. Chile)[END_REF][START_REF] Wörner | Largeand Fine-Scale Geochemical Variations Along the Andean Arc of Northern Chile (17.5°-22°S)[END_REF][START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF]Godoy et al., 2014[START_REF] Freymuth | The Origin and Crust/Mantle Mass Balance of Central Andean Ignimbrite Magmatism Constrained by Oxygen and Strontium Isotopes and Erupted Volumes[END_REF]. (2) The chemical variability of the mantle source swollen by the recurrent recycling of slab components and sediments [START_REF] Mcculloch | Geochemical and Geodynamical Constraints on Subduction Zone Magmatism[END_REF]Vatin-Pérignon et al., 1991;[START_REF] Plank | The Chemical Composition of Subducting Sediment and its Consequences for the Crust and Mantle[END_REF][START_REF] Kay | Tertiary to recent transcient shallow subduction zones in the central and southern[END_REF][START_REF] Elliott | Tracers of the Slab[END_REF][START_REF] Goss | Andean Adakite-like High-Mg Andesites on the Northern Margin of the Chilean-Pampean Flat-Slab (27-28•5°S) Associated with Frontal Arc Migration and Fore-Arc Subduction Erosion[END_REF]Turner and Langmuir, 2015b). However, [START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF] argued that the hyperaridity of the western Andean slope since the late Oligocene/Miocene [START_REF] Rech | Neogene Climate Change and Uplift in the Atacama Desert, Chile[END_REF][START_REF] Hartley | Neogene Climate Change and Uplift in the Atacama Desert, Chile: Comment[END_REF], the presence of the Coastal Cordillera that prevents sedimentary transport into the ocean [START_REF] Allmendinger | Trench-Parallel Shortening in the Northern Chilean Forearc: Tectonic and Climatic Implications[END_REF] and the absence of accretion prism (von [START_REF] Huene | Subduction Erosion along the North Chile Margin[END_REF], all argue against the presence of significant amounts of sediments in the subduction zone to enrich Andean magmas. Thus, lower-to mid crustal contamination of mantellic magmas through deep mash zones storage likely explains the geochemical heterogeneity of low-silica lavas.

At Lascar, the basic composition of the Andean lower crust (Godoy et al., 2014) supports the hypothesis that temporary storage/assimilation of mantle derived magmas within the lower crust might shift the geochemical trend toward low-silica and radiogenic (Pb-Sr) compositions.

In fact, this hypothesis is supported by petrologic and petrographic analysis of Lascar Piedras Grande andesite which is interpreted to form by remobilization and melting of an igneous protolith following the new injection of hydrous mafic magma [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF]. This latter is thought to have evolved in the lower crust by high-pressure fractionation and lower crust assimilation [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF].

Finally, the evolution towards silica-rich compositions (RD, Blum-Oeste&Wörner, 2016) is ascribed to shallow differentiation by assimilation of the upper continental crust (AFC) [START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF]Blum-Oeste&Wörner, 2016;[START_REF] Nauret | The Genetic Relationship between Andesites and Dacites at Tungurahua Volcano, Ecuador[END_REF]. Indeed, magmas assimilation of the upper crust by AFC processes is prone to increase the silica content of magma by differentiation as well as their Sr-Pb isotopic composition. The chemical and isotopic diversity of high-silica arc magmas at the CVZ scale is explained by the local heterogeneity of the Andean upper continental crust [START_REF] Wörner | Andean Cenozoic Volcanic Centers Reflect Basement Isotopic Domains[END_REF][START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF].

At least 2 mafic end-members at the source of Lascar magmas

Three ubiquitous end-members have been identified at the source of all CVZ magmas. At a smaller scale, the study of Lascar lavas allow us to constrain how the 3 end-members interplay within the plumbing system of one of the most active stratovolcanoes of the CVZ.

At Lascar, we observe a strong geochemical heterogeneity of the less differentiated terms (basaltic andesites and andesites). The mineral assemblage [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF] of Lascar andesites (Plagioclase + Clinopyroxene + Orthopyroxene + Amphibole + Oxide + Biotite with minor apatite and olivine) is not able to efficiently fractionate incompatible elements (i.e, Rb, Th) as their partition coefficient is <<1. Thus, the large range of variation of incompatible elements ratios (Fig. 5) in the less differentiated magmas (<63 wt% SiO2) cannot result from fractional crystallization in a closed system [START_REF] Davidson | The Origin and Evolution of Magmas from the San Pedro-Pellado Volcanic Complex, S. Chile: Multicomponent Sources and Open System Evolution[END_REF]. This heterogeneity of andesite terms is ascribed to the heterogeneity of mafic end-members at the source of andesite magmas.

Moreover, the two flat-( 1) and increasing-( 2) trends in Sr vs. SiO2 diagram (and Ba vs. SiO2) (Fig. 5) could not respond to a simple fractional crystallization process as Sr content commonly decreases with fractional crystallization. The absence of Eu positive anomaly (Eu/Eu* ratio >1) precludes plagioclase accumulation as being the cause of these high Sr values and the overall Sr variability at SiO2 < 63 wt%. This is consistent with the study of [START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF] that estimated a low extent of crystallization (≤11.5%) of predominantly plagioclases and pyroxenes in Lascar magmas. Other processes have to be considered to explain these trace elements variabilities in low-silica magmas. Samples which exhibit strong Sr (up to 1716 ppm) and Ba (up to 1676 ppm) enrichments also display low Ni and Cr contents (<65 and <168 ppm, respectively), high Sr/Y ratio (from 84 to 697) and LILE/HFSE ratios with (Ba/Nb)N up to 18,4. These geochemical characteristics are typical of the common EB end-member at the source of CVZ magmas (Bloom-Oeste&Wörner, 2016). Thus, Lascar magmas may have interact with the EB pole, providing an explanation to Lascar andesite heterogeneity. This idea is supported by the Pb-Sr isotopic heterogeneity of Lascar andesites (Fig. 7), which is a strong clue for the existence of this deep source heterogeneity underneath Lascar volcano.

Another hypothesis is based on the petrographic analysis of Lascar products, which allows the identification of three processes occurring in the plumbing system of Lascar volcano; (a) fractional crystallization (b) assimilation of the country rock and (c) magma mixing between a felsic and a mafic end-member [START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF][START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF]. The latest is notably suggested following the observation of zoned plagioclases and pyroxenes, disequilibrium textures and the occurrence of mafic inclusions. Mixing process could be liable for the low-silica magmas heterogeneity as new mafic injections in a dacitic reservoir are prone to trigger eruption by rapid magma mixing (Spark et al., 1977;[START_REF] Murphy | The role of magma mixing in triggering the current eruption at the Soufriere Hills Volcano, Montserrat, West Indies[END_REF]Snyder et al., 1999) with little fractional crystallization of plagioclase and/or limited assimilation of the country-rock. The flat Sr trend (1) could finally reflects a small extent of plagioclase fractionation balanced by an input of Sr from a Sr-rich country-rock formation (AFC).

Evidence for crustal contamination of Lascar dacite

Several observations reported in literature provide clues in favor of crustal assimilation/mixing processes being responsible for the geochemical diversity of Lascar magmas. First, Risarcher&Alonso (2001) found large amounts (an estimation of 700,000 tons) of soluble CaSO4 coated on ash grains emitted during the three days of the 1993 plinian eruption. This has been attributed to the massive recycling of buried Cenozoic evaporates underneath Lascar volcano, accounting for the interaction between magmas and the upper crustal basement of Lascar volcano. In a similar way, calcsilicates xenoliths occur in at least five eruptive products emitted by Lascar volcano, namely the andesitic-dacitic Piedras Grandes block and ash flow, the andesitic-dacitic Soncor flow, the dacitic Capricorn lava flow, the andesitic Tumbres scoria flow and the deposits of the andesitic 1993 short-lived plinian eruption [START_REF] Matthews | Active Skarn Formation beneath Lascar Volcano, Northern Chile: A Petrographic and Geochemical Study of Xenoliths in Eruption Products[END_REF].

Xenoliths compositions strongly suggest that the protholith corresponds to the Upper Cretaceous Yacoraite formation that crops out in NW Argentina. This formation is composed of diverse carbonate-calcareous-dolomitic lithology but also contains shales and sandstones.

Moreover, petrological studies on Lascar eruptive products [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF] suggest that the hydrous mafic magmas underwent deep-fractionation processes at high pressure (lower crust level) and evolved by lower crust assimilation processes.

Furthermore, the dataset on Lascar volcano supports the idea that crustal contamination plays a key role in dacites formation. Indeed, the decrease of highly incompatible trace elements ratios (Fig. 5), such as Rb/Th (from 14.47 to 5.21) with the increase of the silica content could not respond to a simple process of crystallization [START_REF] Davidson | The Origin and Evolution of Magmas from the San Pedro-Pellado Volcanic Complex, S. Chile: Multicomponent Sources and Open System Evolution[END_REF]. Indeed, as incompatible elements do not fractionates during fractional crystallization, this Rb/Th decrease requires the input of a genetically unrelated component with low Rb/Th ratio. A Th-rich crustal component would be a possible candidate responsible for this evolution. The evolution of Lascar magma towards radiogenic Pb and Sr composition is consistent with assimilation of the shallow radiogenic crust.

Finally, Lascar data defines a linear trend in the 1/V vs. Rb/V diagram (Fig. 6b), which is used to distinguish which processes between partial melting, fractional crystallization and mixing, are responsible for the evolution of magmas compositions [START_REF] Schiano | Simple Mixing as the Major Control of the Evolution of Volcanic Suites in the Ecuadorian Andes[END_REF]. In this diagram, the linear trend reveals a binary mixing process [START_REF] Langmuir | A General Mixing Equation with Applications to Icelandic Basalts[END_REF] at the origin of Lascar magmas heterogeneity. Inversely, a curved distribution would have reflected a crystallization process. The linear trend formed by andesites and dacites bulk rocks from Lascar reveals mixing process as the main co-genetic link between low-silica and high-silica magmas.

However, petrological and geochemical evidences clearly suggest that amphibole crystallization plays a major role. Both mixing and crystallization processes must be taken into account for the formation of dacitic magmas. This is in good agreement with Blum-Oeste&Wörner (2016) who showed that crustal melting and mixing with evolved magmas derived from the mantle wedge (BA) are the most likely processes to generate the RD endmember at CVZ scale. Thus, we propose that assimilation fractional crystallization (AFC) is the main process controlling Lascar magmas compositions. Though crustal mixing in MASH zones at lower crust depth (30-50 km) is likely to be responsible for the formation of the RD end-member at CVZ scale, Lascar magmas compositions do not tend exactly toward the common RD end-member (Blum-Oeste&Wörner, 2016). Indeed, the slight difference between the RD end-member and its local equivalent below Lascar volcano is thought to reflect smallscale heterogeneity of the CVZ basement and/or a shallow origin of the ubiquitous RD endmember. At Lascar scale, RD is now called C to emphasize on that difference.

AFC models i.

Constrains on BA and EB end-members

In order to test the hypothesis of interaction between these three end-members (BA, EB, C) at the source of Lascar magmas, and estimate the amount of crust assimilated by Lascar volcanic products, we built up a 2-stages 3-components AFC model [START_REF] Depaolo | Trace Element and Isotopic Effects of Combined Wallrock Assimilation and Fractional Crystallization[END_REF]. First, the geochemical and Pb-Sr isotopic composition of the two end-members common in all CVZ magmas (BA, EB) and the local crustal component specific to Lascar (C) have to be defined. ii.

2-stages 3-components AFC model

We Estimated results represent minima of the assimilation extent at Lascar as samples analyzed for Pb and Sr isotopes do not correspond to Lascar samples with extreme major and trace elements contents. This model takes into account the mineralogical assemblage [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF], the composition of the most primitive end-members (BA and EB), the composition of the crustal contaminant (C), the assimilation rate r defined by the mass ratio between assimilated and crystallized material, and the magma mass ratio F between the initial magma and the contaminated one. Because the upper crustal material around Lascar is highly heterogeneous, we tested several potential contaminant C ; a Northern Chile Paleocene intrusion [START_REF] Haschke | Repeated Crustal Thickening and Recycling during the Andean Orogeny in North Chile (21°-26°S): Recycling of newly underplated mafic crust[END_REF], a Paleozoic gneiss from the Salar de Antofalla (Lucassen et al., 2001;[START_REF] Siebel | Geochemistry and Isotope Systematics of Smallto Medium-Volume Neogene-Quaternary Ignimbrites in the Southern Central Andes: Evidence for Derivation from Andesitic Magma Sources[END_REF], a Northern Chile Paleozoic gneiss (Loewy et al., 2004), Cordon de Lila Proterozoic gneiss [START_REF] Bock | Tracing Crustal Evolution in the Southern Central Andes from Late Precambrian to Permian with Geochemical and Nd and Pb Isotope Data[END_REF] and an Ordovician Antofalla intrusion [START_REF] Lucassen | Lead Evolution of the Pre-Mesozoic Crust in the Central Andes (18-27°): Progressive Homogenisation of Pb[END_REF].

Distribution coefficients have been calculated using the partition coefficients of reference [START_REF] Ewart | Mineralogy and geochemistry of the younger volcanic islands of Tonga, S.W. Pacific[END_REF]Ewart&Griffin, 1994;Bacon&Druitt, 1998) and a mineralogical assemblage of 23.2% Plagioclase + 1.2% Clinopyroxene + 0.9% Orthopyroxene + 0.6% Olivine + 0,1% Hornblende with 74.0% of matrix inferred by [START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF] based on the mineralogical composition of lavas from Lascar (LAS451a, LAS451b, LAS61, LAS62).

In order to reproduce the andesite geochemical variability (trend n°1), our model indicates that with F parameter ranging between 0.05 and 0.45, r should vary between 0,02 and 0.32. Lascar magmas would have assimilated between 1 and 30% of the lower crust in order to produce the observe andesite geochemical variability.

It is known that crustal contamination is not uniform and is ruled by the composition, the structure and the thermal conditions of the local crustal basement through which magmas ascent [START_REF] Godoy | Srand Nd-Isotope Variations along the Pleistocene San Pedro -Linzor Volcanic Chain, N. Chile: Tracking the Influence of the Upper Crustal Altiplano-Puna Magma Body[END_REF]. Among local upper crustal components, the Paleozoic gneiss from Salar de Antofalla displays the closest compositions to the C pole and would be a potential contaminant of Lascar magmas. Moreover, Cordon de Lila gneiss intrusion that has already been described as Lascar basement [START_REF] Gardeweg | Evolution of Lascar Volcano, Northern Chile[END_REF] shows Pb isotopic compositions similar to the composition estimated for the contaminant and is prone to be the upper crustal component. Inversely, we notice that northern Chile Paleocene intrusion [START_REF] Haschke | Repeated Crustal Thickening and Recycling during the Andean Orogeny in North Chile (21°-26°S): Recycling of newly underplated mafic crust[END_REF] as well as the Ordovician intrusion from Antofalla domain [START_REF] Lucassen | Lead Evolution of the Pre-Mesozoic Crust in the Central Andes (18-27°): Progressive Homogenisation of Pb[END_REF] are not potential contaminants. Besides, studies on Lascar's neighbor San-Pedro-Linzor volcanic chain in northern Chile showed major contamination of the magmas by the Altiplano-Puna Magma Body (APMB), a large batholith settled in the upper crust [START_REF] Godoy | Srand Nd-Isotope Variations along the Pleistocene San Pedro -Linzor Volcanic Chain, N. Chile: Tracking the Influence of the Upper Crustal Altiplano-Puna Magma Body[END_REF]. They identify that Lascar volcano lies outside the APMB, which explains why Lascar magmas are mostly preserved from the APMB contamination (<10% vol.). The absence of strong connection between Lascar magmatic system and the APMB is also pointed out by the mean of magnetotelluric measurements along profiles south of Lascar, crossing the Salar de Atacama, the volcanic arc and the western border of APMB (Diaz et al., 2012). Thus, we do not consider APMB as a potential contaminant of Lascar magmas. In spite of the few data on Lascar basement and its geochemical heterogeneity, Cordon de Lila is prone to be the main contaminant of Lascar magmas. Nonetheless, Cordon de Lila Pb-Sr database is scarce and heterogeneous and cannot explain the full isotopic range of Lascar magmas, suggesting that either the entire geochemical heterogeneity of Cordon de Lila has not been sampled or another lithology is responsible for the contamination of Lascar magmas.

A generic composition of the contaminant is estimated by iteration in order to best-fit data dispersion during the 2 nd step of the AFC model. respectively. These estimations are in good agreement with the geochemical signatures previously suggested for this end-member and are, based on the new and published data, the most robust constrains on the contaminant of Lascar magmas. With F parameter ranging between 0.05 and 0.45, and r varying between 0.1 and 0.3, magmas would have assimilated between 6 and 29% of this generic upper crustal end-member. It is noteworthy that these ranges of values are obtained by running the model in all Pb-Sr isotopic spaces.

Finally, the presence of Yacoraite xenoliths in Lascar volcanic products is a strong clue for the involvement of this calcsilicate formation in the contamination of Lascar magmas. However, no Pb-Sr isotopic measurements are available for these xenoliths to better constrain the role of this potential upper crustal contaminant C. In such situation, we used trace elements (Nd, Ba, Rb, Sr and Pb) to model the AFC evolution of EB-BA hybrid magmas considering assimilation of Yacoraite calcsilicates (referred to as C'). LA-143 sample from Lascar [START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF] is used as a starting material and the sample 92/212 from Yacoraite formation (Marquillas et al., 2011) plays the role of Lascar magmas contaminant. We tested two AFC models using

Conclusions

Major-trace element concentrations and high precision Pb-Sr isotopes measurements are reported for 10 new rock samples from Lascar volcano, extending the yet limited database available for this edifice. New and published data allow us to draw several conclusions regarding magma contamination bellow Lascar and the Central Volcanic Zone (CVZ):

(1) Lascar magmas display typical arc calcalkaline series compositions from basaltic andesites to dacites. As for several arc volcanoes, Lascar magmas shows a large geochemical diversity of its low-silica (<60 wt% SiO2) products.

( (4) This study on Lascar and those done at the scale of the CVZ reach converging interpretations regarding the origin of the ubiquitous end-members: BA the mantle wedge, EB an enriched component (lower continental crust and/or the slab), C the local upper continental crust.

Figure captions

Figure 1 Location map of Lascar volcano in the Central volcanic zone in the Antofalla domain, Northern Chile, modified from [START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF][START_REF] Menard | Gas and Aerosol Emissions from Lascar Volcano (Northern Chile): Insights into the Origin of Gases and Their Links with the Volcanic Activity[END_REF] Figure 2 Geological map from Lascar modified from [START_REF] Gardeweg | Evolution of Lascar Volcano, Northern Chile[END_REF]. Localization of Lascar samples is shown.

Figure 3 K2O, MgO, CaO and Al2O3 vs. SiO2 diagram for Lascar bulk rock samples. Literature data sources : (Siegers et al., 1969;Deruelle et al., 1982;[START_REF] Harmon | Regional O-, Sr-, and Pb-Isotope Relationships in Late Cenozoic Calc-Alkaline Lavas of the Andean Cordillera[END_REF][START_REF] Hilton | Helium Isotope Characteristics of Andean Geothermal Fluids and Lavas[END_REF][START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF][START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF][START_REF] Rosner | Slab-Derived Boron Isotope Signatures in Arc Volcanic Rocks from the Central Andes and Evidence for Boron Isotope Fractionation during Progressive Slab Dehydration: Slab-derived boron isotope signatures[END_REF][START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF]Grockes et al., 2016). High K, medium K and low K fields are defined after [START_REF] Peccerillo | Geochemistry of Eocene calc-alkaline volcanic rocks from the Kastamonu area, northern Turkey[END_REF]. Same symbols as in Fig. 6.

Figure 4 Primitive mantle-normalized trace element diagram (normalized values after [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF]) for Lascar bulk rock samples.

Figure 5 Trace element concentration (V, Ba, Sr, Th) and trace element ratios (Ba/U, Th/La, (La/Sm)N, Rb/Th vs. SiO2 for Lascar bulk rock samples.

Figure 6 a) La/Yb vs. Sm/Yb plot showing Lascar data. A vertical trend is accountable for amphibole fractionation (Tiepolo et al., 2007). b) 1/V vs. Rb/V diagram for Lascar bulk rocks. The linear trend highlight a binary mixing process [START_REF] Schiano | Simple Mixing as the Major Control of the Evolution of Volcanic Suites in the Ecuadorian Andes[END_REF]. Literature data sources : (Siegers et al., 1969;Deruelle et al., 1982;[START_REF] Harmon | Regional O-, Sr-, and Pb-Isotope Relationships in Late Cenozoic Calc-Alkaline Lavas of the Andean Cordillera[END_REF][START_REF] Hilton | Helium Isotope Characteristics of Andean Geothermal Fluids and Lavas[END_REF][START_REF] Matthews | Lascar volcano, Northern Chile; Evidence for Steady-State Disequilibrium[END_REF][START_REF] Matthews | The Piedras Grandes-Soncor Eruptions, Lascar Volcano, Chile; Evolution of a Zoned Magma Chamber in the Central Andean Upper Crust[END_REF][START_REF] Rosner | Slab-Derived Boron Isotope Signatures in Arc Volcanic Rocks from the Central Andes and Evidence for Boron Isotope Fractionation during Progressive Slab Dehydration: Slab-derived boron isotope signatures[END_REF][START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF][START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF]Grockes et al., 2016).

Figure 7 (a) replenishment/rate of assimilation) parameters that account for the concentration variations of several elements. A common set of (r, β, ρ) corresponds to potential solutions for a set of selected elements and plots in the 3D space as the intersection of the (r, β, ρ) surfaces of each element (c). These parameters are calculated for each element according to [START_REF] Aitcheson | Quantification of crustal contamination in open magmatic systems[END_REF] based on input parameters Ca, the element concentration in the assimilant, Cm 0 the element concentration in the original magma, Cm the element concentration in the contaminated magma and, D the bulk partition coefficient of the original magma fractionating mineral assemblage. The ranges of variation (min/max) of r, F (mass of magma remaining), and β are set before running calculations as well as the zero threshold value. The zero threshold value corresponds to the allowed difference between all ρ values of the selected set of elements and should not exceed 10 -2 .We run the model for Sr, Rb, Ba, Pb and Cr, beginning with ranges of variations of r, F and β fixed between 0 and 3 and the zero threshold at 10 -2 . In the r-β-ρ space, the surfaces of solutions obtained for each elements are sub-parallel and do not intersect a single point, meaning that no common solution exists for the considered set of elements. If one decreases the zero threshold values and r, F, β ranges of variation, then model results converge toward a rate of assimilation of 0 (red line on Fig. 11d).

  then tested a two-stages three-components AFC model in the206 Pb/ 204 Pb -207 Pb/ 204 Pb -208 Pb/ 204 Pb isotope space (Fig.10). The solutions of the model were calculated using the analytic equations from De Paolo(1981). The model includes a first binary BA-EB contamination step followed by a 2 nd assimilation step between the hybrid BA-EB component and C. The two stages (BA-EB and BAEB-C) are thought to occur successively given the nature of the selected end-members. Indeed, magma ascension through the crust implies a first reaction of the magma with the lower crust (EB, MASH zones) and subsequently, the interaction of this hybrid magma with the upper part of the crust (C) before erupting at earth surface. AFC models are verified in all the dimensions of the considered spaces ( 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, 208 Pb/ 204 Pb, 87 Sr/ 86 Sr).

1 )

 1 AFC equations from De Paolo (1981) (Fig. 11 a&b) and 2) AFC3D software (Guzman et al., 2014) (Fig. 11 c&d). To first order, results of the calculations show that Yacoraite could act as an assimilant at Lascar. The AFC trend toward Yacoraite overlaps a large range of Lascar magmas geochemical diversity (Fig. 11a&b) with ranges of variation of r and F parameters (0.1-0.3 and 0.20-0.45, respectively) consistent with previous estimations. Nonetheless, results with AFC3D software show that no common set of (r, β, ρ) is found for the considered elements, meaning that each element yields a different extent of assimilation. The inconsistency between the two models results from the fact that De Paolo (1981)'s model yields different results depending on which element is considered. It shows that the assumptions of the AFC model (e.g. constant D, same composition of primitive magma and contaminant for all samples) are too simple to account for the complexity of natural AFC processes.

Figure 11 Probing

 11 Figure 11

  Figure 1

  Figure3

  Figure 9

Figure 11

 11 Figure10

  Table 4. 206 Pb/ 204 Pb ratios range between 18.77 and 18.82, 207 Pb/ 204 Pb ratios between 15.64 and 15.65 and 208 Pb/ 204 Pb ratios between 38.71 and 38.80. 87 Sr/ 86 Sr isotope ratio range between 0.705731 and 0.706564. Our data are consistent with the literature data on Lascar volcano with 18.740< 206 Pb/ 204 Pb<18.840; 15.620< 207 Pb/ 204 Pb<15.659; 38.660< 208 Pb/ 204 Pb<38.842 and 0.70560< 87 Sr/ 86 Sr<0.70719

  and the DMM (Depleted MORB Mantle, Rehkamper & Hofmann 1997). Lascar bulk rocks plot in the field of the local basement composition, in the center of a triangle formed by the DMM, the radiogenic upper crust and a third pole less radiogenic in Pb. Using different geochemical parameters ( 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, 208 Pb/ 204 Pb, 87 Sr/ 86 Sr, SiO2),

  38.809) and displays the highest Th content (up to 14.2 ppm). However, the absence of isotopic measurements on primitive melt inclusions from Lascar and local lower crust does not allow us to further constrain geochemical signature of BA and EB end-members. Thus, we estimated generic BA, EB compositions at CVZ scale which are defined at the extremity of the triangular

	shaped distribution gathering all the CVZ quaternary eruptive products (Fig.9) : BA: 206 Pb/ 204 Pb
	= 16.61; [Pb] = 11ppm and 87 Sr/ 86 Sr = 0.7040; [Sr] = 100ppm; EB: 206 Pb/ 204 Pb = 17.70; [Pb] =
	30ppm and 87 Sr/ 86 Sr = 0.7080; [Sr] = 200ppm.
	At Lascar scale, we can isotopically constrain these three end-members; (BA) a typical
	mantellic arc magma with low 87 Sr/ 86 Sr (<0.70575), low 206 Pb/ 204 Pb (<18.768), 207 Pb/ 204 Pb
	(<15.637) and 208 Pb/ 204 Pb (<38.711) and (EB) a mafic component presumably derived from the
	lower crust, radiogenic in Sr (>0.706564) and in Pb (>18.82 ; > 15.647 ; > 38.79) with higher

Th concentration than component A. These two compositions are best preserved in lavas with <57wt% SiO2. The third pole (C) corresponds to the local basement (> 65.1 wt% of SiO2), which is similarly radiogenic in Sr and Pb as component EB

(> 0.70643; >18.823; >15.655; >

  The generic contaminant composition displays 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, 208 Pb/ 204 Pb and 87 Sr/ 86 Sr values of19.12, 15.73, 39.20 and 0.7080,

  ) Combined geochemical parameters (SiO2 content, incompatible trace element ratios, 87 Sr/ 86 Sr, 206 Pb/ 204 Pb, 207 Pb/ 204 Pb and 208 Pb/ 204 Pb) and AFC modeling indicate that at least three end-members are involved at the source of Lascar magmas. These three sources likely have the same origin as the three ubiquitous components identified at the regional scale of the CVZ. The geochemical signature of the upper crustal contaminant slightly varies from place to place due to the upper crust heterogeneity.

	(3) Two-stages three-components AFC model reproduces the entire dispersion range of
	Lascar bulk rocks and allows us to better constrain end-members geochemical
	composition: (BA) a common mantellic source with low 87 Sr/ 86 Sr (<0.70575), low
	206 Pb/ 204 Pb (<18.768), 207 Pb/ 204 Pb (<15.637) and 208 Pb/ 204 Pb (<38.711), (EB) a deep-
	mafic source radiogenic in Sr (>0.706564) and in Pb (>18.82 ; > 15.647 ; > 38.79), (C)
	the local upper crust (> 65.1 wt% of SiO2) with similar Sr-Pb isotope composition as
	EB (> 0.70643; >18.823 ; >15.655 ; > 38.809).

  207 Pb/204 Pb and (b)208 Pb/ 204 Pb vs.206 Pb/204 Pb diagram of Lascar bulk rocks. The isotopic fields are shown for the lower continental crust (LCC,[START_REF] Weber | Crustal Make-up of the Northern Andes: Evidence Based on Deep Crustal Xenolith Suites, Mercaderes, SW Colombia[END_REF], the upper continental crust (UCC,[START_REF] Mamani | Composition and Structural Control of Crustal Domains in the Central Andes: Crustal domains in the Central Andes[END_REF], the Nazca plate(Unruh & Tatsumoto, 1974), and the depleted MORB mantle(Rehkamper & Hofmann 1997). North Hemisphere Reference line (NHRL) is from(Hart et al., 1984). A, B and C are the components required to explain andesites heterogeneity. More details and references in the main text. Sr and 207 Pb/ 204 Pb vs. 206 Pb/ 204 Pb for Lascar bulk rocks and eruptive products from CVZ DePaolo et al., 1981) is presented in 207 Pb/ 204 Pb, 208 Pb/ 204 Pb and 87 Sr/ 86 Sr vs. 206 Pb/ 204 Pb spaces with black lines for Lascar bulk rocks. BA, EB,

	Figure 8
	(a) 87 Sr/ 86 Sr vs. 206 Pb/ 204 Pb diagram and (b) 207 Pb/ 204 Pb vs. SiO2 wt% diagram of Lascar bulk
	rocks. Suggested end-members (A, B, C) are required to explain the triangular distribution due
	to andesites heterogeneity. Origin of A, B, C is detailed in the text.
	Figure 9
	87 Sr/ 86 Figure 10
	(a) 2-stages 3-components AFC model (

quaternary volcanoes (compilation from

[START_REF] Mamani | Geochemical Variations in Igneous Rocks of the Central Andean Orocline (13°S to 18°S): Tracing Crustal Thickening and Magma Generation through Time and Space[END_REF]

). CVZ volcanoes are grouped according to crustal domains. Three end-members (BA, EB, C) are required to explain the triangular distribution at CVZ scale. Origin of BA, EB, C is discussed in the main text. and C are the three end-members required to model the whole geochemical dispersion of Lascar dataset. Trend (1) corresponds to AFC modelling between BA and EB end-members considering EB as the lower crust. Trend (2) corresponds to AFC modelling between diverse BA-EB mixing products and C, the upper crust. Two potential local upper crustal contaminants (Cordon de Lila and Salar de Antofalla) are considered in the second stage of the AFC modelling. Both contaminants cannot account for the 207 Pb/ 204 Pb values of Lascar bulk rocks.

Acknowledgements

D. Auclair, A. Gannoun, J.L. Piro contributed to data acquisition. We thank S. Guzman and an anonymous reviewer for their constructive comments, and P. Samaniego for his useful remarks and for handling the manuscript. This work benefited from the financial support from the Institut de Recherche pour le Développement (ECOS-sud project no. C11U01, P.I. O. Roche), the French Government Laboratory of Excellence initiative n°ANR-10-LABX-0006, the Région Auvergne and the European Regional Development Funds. This is Laboratory of Excellence ClerVolc contribution number 397.

Supplementary Material

Table S1: Geochemical database (major-, trace elements and Pb-Sr isotopic compositions) gathering published and new data on Lascar volcano eruptive products (GERM database; Menard, PhD, 2014; This study).


E N Diaw

S Le Roy

G Teyssèdre

E Aubert

Electric Field and Current Conduction Modelling in Bi-layers Insulations HVDC Aeronautic Cables

Keywords: HVDC aeronautic cables, cables insulations, current measurement, macroscopic models, field inversion, interfacial charge

For decades, electrical energy network in aircrafts was based on relatively low voltage (mainly 115V ac and 28V dc), providing the power to the different energy functions of the aircraft. Great strides have been made in the new aircraft generations, notably the A380 and the Boeing 787, with an increase of the aircraft size, and with the input of electrical energy in replacement of certain hydraulic or pneumatic actuations. Today, there is a tendency to replace HVAC network with HVDC (+/-270 V dc, 540 V dc and higher in the future) network in order to benefit from these many advantages. This increase of the electrical energy pushes the transmission cables to their limits and leads to questions about the impact of these new constraints on the aeronautic cables insulation. This article presents a macroscopic model and comparison between simulation results and measurements made on bi-layer materials used in actual aeronautic cable insulation. The electric field distribution within materials and kinetic of interfacial charges build-up are analyzed.

I. INTRODUCTION

Electrical energy occupies a minority place since the beginning of the history of aeronautics and until recently compared with the mechanical, pneumatic and hydraulic energies, which are mainly run. With the increase of the size of planes and the related needs in embedded power, aeronautic electrical networks experience permanent progress and today, electrical energy takes a more and more important part, to the detriment of other energies vectors with new architectures [START_REF] Madonna | Electrical power generation in aircraft: Review, challenges, and opportunities[END_REF][START_REF] Sarlioglu | More electric aircraft: Review, challenges, and opportunities for commercial transport aircraft[END_REF]. This transition to the more electric aircraft is not without consequences and thus requires the control of new technologies to meet the requirements of the high electrical power.

Studies show that, in energy transmission in terrestrial HVDC networks [START_REF] Montanari | The electrical degradation threshold of polyethylene investigated by space charge and conduction current measurements[END_REF], cables insulation materials can accumulate space charge, and macroscopic models are used to predict electric field distribution [START_REF] Morshuis | Calculation and measurement of space charge in MV size extruded cables systems under load conditions[END_REF][START_REF] Jeroense | Electric fields in HVDC paper-insulated cables[END_REF]. In fact, with HVDC systems, electric field is driven by electrical conductivity, which is usually dependent on temperature and electric field, even for materials used in aeronautic domain [START_REF] Motyl | On the electrical conduction in polyimide[END_REF][START_REF] Sussi | Electrical conduction currents in polytetrafluoroethylene[END_REF][START_REF] Lee | Nonlinear conduction properties of polytetrafluoroethylene film[END_REF]. In the perspective of more electric aircraft, insulating materials behaviour has been investigated by performing experimental characterization on two materials used as insulation in aeronautic cables: Polytetrafluoroethylene and Polyimide (PTFE) and Kapton FN [START_REF] Diaw | Current measurements on insulating materials used in aeronautic HVDC cables[END_REF]. Measurements have also been performed on bilayer materials PTFE/PI, to achieve a more realistic characterization. Macroscopic modelling based on electrical conductivity function of temperature and electric field was used to predict the electric field distribution considering different geometries.

II. EXPERIMENTAL METHODS AND MACROSCOPIC MODEL

A. Current measurements

PTFE and PI (polyimide, Kapton FN) film samples used for current measurements are metallized on both sides with 50 nm-thick gold layer of 20 mm diameter. Kapton FN samples have a thickness ranging from 30 up to 36 μm. Kapton FN contains a FEP layer (fluorinated ethylene propylene) on each face. PTFE films are 72 to 77 µm-thick.

Current measurements results were obtained on bi-layer samples (PI/PTFE) at 50°C for electric fields ranging from 1 to 120 kV/mm for 3 hours of polarization and 3 hours of depolarization. These experimental data will be used to validate simulation results on bi-layer samples for different geometries.

B. Macroscopic models

In the literature, macroscopic models are proposed to determine electric field distribution in cables [START_REF] Morshuis | Calculation and measurement of space charge in MV size extruded cables systems under load conditions[END_REF][START_REF] Jeroense | Electric fields in HVDC paper-insulated cables[END_REF]. Modelling is performed using COMSOL Multiphysics® software. Model resolution is performed using the three equations below

(1) (2) (3)
Here J is the current density, Je an external current density, ρ is the net charge density, V is the applied voltage and E is the electric field. The main input of this model is the electrical conductivity, which varies upon temperature and electric field.

Current measurements have already been performed on Kapton and PTFE samples separately [START_REF] Diaw | Current measurements on insulating materials used in aeronautic HVDC cables[END_REF] to deduce an electrical conductivity law as a function of field and temperature for each material [START_REF] Diaw | Current measurements on insulating materials used in aeronautic HVDC cables[END_REF][START_REF] Diaw | Current Measurements in High Performance Polymers used in Aeronautic Cables[END_REF]. This conductivity is of the form, for both materials: [START_REF] Morshuis | Calculation and measurement of space charge in MV size extruded cables systems under load conditions[END_REF] where T is the temperature in °C and E the electric field in V/m. A, C, T 0 , E 0 and α, are constants, presented in Table 1 for Kapton and PTFE respectively. Permittivity is considered as constant for both materials (3.4 for Kapton and 2.1 for PTFE). Two types of simulations have been performed: -A plane parallel sandwich geometry: a PTFE of thickness 76.2µm is set on top of a Kapton sample of thickness 31µm. The voltage is applied on the Kapton, while the PTFE is grounded. The simulation is in one dimension, the origin (y=0) is set on the Kapton side. For these simulations, the temperature is supposed constant. The simulation results are given at steady-state.

-A cable geometry inspired by a DR16 cable (Fig. 1). DR16 cable consists in a 1.45 mm diameter conductor. PI insulation is 41 µm thick and PTFE insulation is 185 µm thick. This model represents the real geometry of DR16 cable, taking account the cylindrical bi-layer insulation and the metal strands. Voltage is applied on the metal strands. We suppose that the outer layer of the cable is grounded. Real characteristics of air gaps like the nature of gas, its electrical conductivity and dependencies are not modelled. The model is resolved in non-isotherm conditions, the power being injected in the conductor. Temperature modelling is based on the time dependent heat transfer equation, of the form: [START_REF] Jeroense | Electric fields in HVDC paper-insulated cables[END_REF] where C p is the heat capacity at constant pressure, ρ p is the material density, k is the thermal conductivity and Q is the heat generated from the conductor by Joule effect, which is: [START_REF] Motyl | On the electrical conduction in polyimide[END_REF] where I is the current in the conductor, ρ cu is the temperaturedependent resistivity of copper and A is the cross section area of the conductor. The boundary condition is set to be convective heat flux at the outer layer of the cable with ambient air temperature of 20°C. A. Model Results on plane-parallel Bi-layer sample Fig. 2 shows a comparison between experimental current densities and simulated ones on a plane-parallel sandwich of Kapton/PTFE, for mean applied electric fields ranging from 1 to 120 kV/mm at 50°C and 160°C. Comparisons are also proposed for a single mean electric field (60 kV/mm) at different temperatures (140 and 200°C). At 50°C and for electric fields below 60 kV/mm, simulated current density is close to the measured one. Beyond 60 kV/mm, the model and measurements diverge. At this temperature, this difference may be because the bi-layer model does not really represent the real system, as the bilayer behavior of Kapton film is not detailed. It is also possible that for relatively high fields, the variation in electrical conductivity alone is not sufficient to predict the behaviour of the bi-layer insolation, and that other physical mechanisms come into play. For the other experimental data (different electric fields at 160°C and different temperatures at an electric field of 60 kV/mm), the simulated results are close to the experimental ones.

With the macroscopic model, it is possible to obtain the electric field distribution across the Kapton/PTFE sandwich, which is more difficult to obtain experimentally. Fig. 3 presents the electric field distribution across the sandwich for different mean applied fields at 50°C. For mean electric fields below 60 kV/mm, the electric field is higher in the Kapton compared to PTFE. The electric field distribution in each material is not only dependent of the permittivity variation. The electrical conductivity value has a dominant impact. Previous current measurements on one material alone show that at 50°C, PTFE is less conductive than Kapton for electric fields below 60 kV/mm, and becomes more conductive above that field. The inversion of higher electric field from Kapton to PTFE is directly linked to this variation in relative value of electrical conductivity.

The electric field inversion is also observed when the temperature increases. Fig. 4 shows the simulation results for a mean applied field of 40 kV/mm for temperatures of 50 and 90°C. As previously, this inversion is explained by the fact that beyond a certain temperature value, PI becomes more conductive than PTFE.

Current transient can also be compared to simulation results. Fig. 6 shows an example of measured and simulated current transient for a mean field of 60 kV/mm, at 50°C. A nearly constant current is observed in the simulation as opposed to the measured current density. This different behavior may be explained by the fact that the conductivity equation has been developed considering that after 3 hours of polarization; the current achieved the steady state. From what is observed in Fig. 5, this is clearly not the case, and experimentally, other processes not linked to conduction (polarization as an example) certainly play a non-negligible role. The simulated results are relatively correct when the time considered in long (above 1000s).

with [START_REF] Lee | Nonlinear conduction properties of polytetrafluoroethylene film[END_REF] The sign of the interfacial charge and its dependence in time depends on the variation of the electrical conductivity of the two materials which is driven by electric field and temperature. Fig. 6 present the calculated interfacial charge as a function of time for different mean electric fields at 50°C. For electric fields below 80 kV/mm, the interfacial charge is negative. A steady state is reached for times above 1.10 5 s for applied fields below 80 kV/mm, well above the experimental 3hours of voltage application. The larger the field applied, the faster the charge stabilizes. For fields ranging from 1 to 40 kV/mm, the steady state interfacial charge increase. After 40 kV/mm, the interfacial charge decreases and becomes positive for fields above 80 kV/mm. B. Model Results on a bi-layer cable geometry Simulations have been performed for a bi-layer cable geometry, on the basis of DR 16 real aeronautic cable. In this configuration, the electric field within the cable radius is nonhomogenous. Moreover, local electric field intensification takes place in air gaps at the interface between metal strands and Kapton. This also has an impact on the electric field inside the Kapton and PTFE insulations. Fig. 7 presents the electric field distribution within the cable calculated for an applied voltage of 1 kV on the conductor with a current intensity of 15 A, which corresponds to an average field of 3.88 kV/mm and a temperature of 40°C on the conductor.

Electric field within PI is closed to 10 kV/mm. This value is higher than the applied field on the conductor and can be explained by the fact that, at the contact with a metal strand, a local electric field intensification affects the one found in Kapton insulation. Within PTFE, calculated electric field is close to 2.8 kV/mm and is lower than the one in Kapton. In all cases, the calculated electric field in each material is lower than the material dielectric breakdown. It is to note that the electric field calculated in the air gaps is relatively high compared to the breakdown field in air, as no attempt has been made to simulate the conductivity variation in air with temperature and electric field. The actual simulated results in Kapton and PTFE are certainly overestimated. It will be important in the future to be able to take into account the true nature of the gas between the metal strands and the variation in its electrical conductivity as a function of electric field, temperature and pressure.

No experimental measurements are available on DR16 cables to compare the simulated current values issued from the macroscopic model to experimental ones. Experimental current measurements were performed on a DR8 cable (same as DR16 with 3.85 mm diameter conductor. PI insulation is 50 µm thick PI and PTFE insulation is 200 µm thick) for temperatures ranging from 30°C to 90°C with mean electric fields from 1 kV/mm to 20 kV/mm. Fig. 8 shows a comparison between experimental current densities and simulated ones on DR8 model cable at 50°C. AT this temperature and field range, a good correlation is observed between simulation and measurements also on cable geometry. However, it will be interesting to perform current measurements on DR8 cable for fields higher than 20 kV/mm as the threshold in field is clearly above this value for both materials. A macroscopic model is proposed to predict the electric field distribution in plane parallel bi-layer Kapton/PTFE samples and in real aeronautic cable geometry with multilayers insulation. Depending on the applied voltage on the conductor, or on the temperature value, the maximal electric field can be localized either in the PI layer or in the PTFE layer. This behavior is directly linked to the interfacial charge, that can be positive or negative depending on the experimental conditions (voltage and temperature). In real cables, the same behavior takes place, i.e. an inversion on the maximal electric field from Kapton to PTFE with temperature and/ or filed. Care will be taken in the future in the modelling of air gaps, that has been observed as having a non negligible impact on the electric field distribution inside both insulations.

Fig. 1 .

 1 Fig. 1. DR16 cable (a) and cylindrical geometry cable model (b) III. RESULTS

Fig. 2 .

 2 Fig. 2. Experimental results on current density vs electric field in bilayer with 3h charging time compared to steady state current from model.

Fig. 3 .

 3 Fig. 3. Electric field distribution in a PI/PTFE bi-layer model calculated at 50°C. Legend shows average electric fields

Fig. 4 .Fig. 5 .

 45 Fig. 4. Electric field inversion on bi-layer model. Average field of 40 kV/mm

Fig. 6 .

 6 Fig. 6. Time-dependent interfacial charge for a PI/PTFE bi-layer model at 50°C

Fig. 7 .

 7 Fig. 7. Electric field map on DR16 cable model

Fig. 8 .

 8 Fig. 8. Comparison between measurements and simulation on DR8 cable IV. CONCLUSIONS

TABLE 1 :

 1 PARAMETERS FOR ELECTRICAL CONDUCTIVITY LAW.

	Parameters	PI	PTFE
	A (S/m)	2.3×10 -16	4.5×10 -16
	To (°C)	80.5	106.7
	C (°C -1 )	0.04	0.04