Bruno Scaillet
email: bruno.scaillet@cnrs-orleans.fr

Francois Holtz
email: f.holtz@mineralogie.uni-hannover.de

Michel Pichavant
email: pichavan@cnrs-orleans.fr

Experimental Constraints on the Formation of Silicic Magmas

Keywords: granite, rhyolite, phase equilibria, water, redox state, metaluminous, peraluminous, peralkaline, viscosity

INTRODUCTION

Silicic magmas (SiO 2 > 65 wt%) may originate from either partial melting of crustal material or protracted crystallization of parental basaltic (mafi c) magmas. Hence, modern experiments have tackled the origin of natural silicic rocks by either establishing phase equilibria of natural granites/ rhyolites to understand magma storage and differentiation conditions (e.g. [START_REF] Scaillet | Experimental crystallisation of leucogranite magmas[END_REF][START_REF] Clemens | Assembly of a zoned volcanic magma chamber from multiple magma batches: the Cerberean Cauldron, Marysville Igneous Complex, Australia[END_REF] or by performing partial melting experiments on their putative source rocks (e.g. Patiño [START_REF] Douce | Experimental constraints on Himalayan anatexis[END_REF][START_REF] Sisson | Voluminous granitic magmas from common basaltic sources[END_REF]. Such experiments have offered a range of P-T-H 2 O-fO 2 conditions thought to be present during magma production or storage, and these are summarized below. Comparing studies performed either on plutonic or on volcanic rocks allows us to address the question of whether there is, in fact, a plutonic-volcanic connection.

Classifi cation of silicic rocks, whether extrusive or intrusive, has been the subject of countless studies and has been mainly used to constrain the origin (mantle vs. crustal sources) or geodynamic settings of felsic melts. Granitic magmas are widely classifi ed as S-(sedimentary protolith) or I-(igneous protolith) type (e.g. [START_REF] Chappell | Two contrasting granite types[END_REF]. A further category is the A-type, which corresponds to alkali-rich granites. In this article, we summarize experimental studies bearing on the origin of silicic magmas and employ the compositional parameter A/CNK, i.e. molar Al/(2Ca + Na + K), which is used to defi ne magmas/silicic rocks that are either peraluminous (A/CNK > 1), metaluminous (1.1 > A/CNK > 1 and A/NK > 1), or peralkaline (A/NK < 1). The A/ CNK ratio fundamentally refl ects the fact that, in addition to quartz, felsic rocks are made of feldspar, typically having 60 wt% feldspar and 30 wt% quartz, in which Al is stoichiometrically balanced by the Na, K and Ca cations. As we will show, A/CNK exerts a strong control on the nature of rockforming minerals other than the quartzo-feldspathic component.

We fi rst present a brief historical perspective, as well as the current state of knowledge, concerning the modes of production of silicic magmas. We then discuss the available experimental constraints that seem to govern the emplacement conditions of peraluminous, metaluminous and peralkaline silicic magmas.

ORIGINS

Progress in our understanding of the origin of granite (petrogenesis) via the experimental approach has been marked by several major technical and conceptual milestones. [START_REF] Tuttle | Origin of granite in the light of experimental studies in the system NaAlSi 3 O 8 -KAlSi 3 O 8 -SiO 2 -H 2 O[END_REF] laid the foundations for an impressive number of subsequent studies and provided the fi rst quantitative evaluation of P-T-H 2 O conditions of granite production. Following this seminal work, which was limited to low pressures (<5 kb), the magmatic origin of granites, sensu lato, was widely accepted. The advent of the modern piston-cylinder apparatus in 1960 represents a second milestone, one that allowed the systematic exploration of the phase equilibria to upper-mantle pressures (e.g. [START_REF] Stern | Phase relationships of I-type granite with H 2 O to 35 kilobars: the Dinkey Lakes biotite-granite from the Sierra Nevada Batholith[END_REF], demonstrating that magmas with more than 60-65 wt% SiO 2 and less than 4-5 wt% MgO, i.e. granites sensu lato, cannot be produced by direct mantle melting. The origin of granite must lie either in the crystal fractionation of mafi c magmas or in the partial melting of crustal rocks with mafi c, silicic or Al-rich compositions (e.g. amphibolites, gneisses, schists). High-pressure experiments have also shown that the Archean tonalitetrondhjemite-granite (TTG) association requires partial melting of basaltic lithologies in equilibrium with garnet at pressures of 10-30 kb.

Silicic magma production by crystallization of mafi c magmas has been achieved in various laboratory studies, which have shown that, regardless of the detail of bulk compositions, rhyolitic derivatives require at least 80 wt% crystallization of basalt magma, whereas the production of andesite-dacite liquids requires 40-60 wt% crystallization (e.g. [START_REF] Pichavant | Source and H 2 O content of high-MgO magmas in island arc settings: an experimental study of a primitive calc-alkaline basalt from St. Vincent, Lesser Antilles arc[END_REF][START_REF] Berndt | An experimental investigation of the infl uence of water and oxygen fugacity on differentiation of MORB at 200 MPa[END_REF][START_REF] Sisson | Voluminous granitic magmas from common basaltic sources[END_REF] with higher oxygen fugacities, fO 2 , promoting higher SiO 2 (e.g. [START_REF] Berndt | An experimental investigation of the infl uence of water and oxygen fugacity on differentiation of MORB at 200 MPa[END_REF].

Because of the compositional and mineralogical diversity of crustal lithologies, the origin of silicic melts by partial melting of the crust has also been the subject of numerous studies. These have shown that fl uid-absent partial melting of crustal rocks produces melts with compositions similar to natural granites up to temperatures approaching 1,000 °C [START_REF] Montel | Partial melting of metagreywackes, Part II. Compositions of minerals and melts[END_REF]. Such studies also provide quantitative data for the parameterization of melt productivity with intensive variables such as temperature (e.g. 10 wt% melt at 800 °C and 20 wt% at 900 °C for an amphibolite). Dehydration (i.e. fl uid-absent) melting of the continental crust without mantle input is a viable process in continental collision zones, such as the Himalayas; but in many geotectonic settings, crustal melting seems to be fundamentally driven by basaltic magmatism [START_REF] Hildreth | Gradients in silicic magma chambers: implications for lithospheric magmatism[END_REF]. In this case, fl uid-absent melting would imply either that the intruding basaltic magmas are volatile-poor or that their contribution is limited to heat supply. In subduction zone settings, however, studies have shown that arc basalts, even primitive ones, can be quite H 2 O-rich (e.g. [START_REF] Pichavant | Source and H 2 O content of high-MgO magmas in island arc settings: an experimental study of a primitive calc-alkaline basalt from St. Vincent, Lesser Antilles arc[END_REF]. Hence, intrusion of arc basaltic magma at the crust-mantle interface or in the lower crust -a process widely believed to be the main source of silicic magmatism and crust production [START_REF] Hildreth | Gradients in silicic magma chambers: implications for lithospheric magmatism[END_REF][START_REF] Annen | The genesis of intermediate and silicic magmas in deep crustal hot zones[END_REF]) -must produce, at least locally, H 2 O-rich environments during basalt crystallization. The fate of such H 2 O-rich fl uid in the lower crust of active arc settings is unclear, but it opens up the possibility of fl uid-present conditions during melting of the base of the crust.

Lastly, silicic magma petrogenesis probably also involves mixing, in particular for explaining crystal-rich magmas with intermediate compositions, such as andesite. Although andesitic liquids do erupt in various volcanic centers (e.g. [START_REF] Ownby | Origin of andesite in the deep crust and eruption rates in the Tancítaro-Nueva Italia region of the central Mexican arc[END_REF], petrological and geochemical observations have shown that intermediate rocks occurring in arc settings result from mixing/mingling between mafi c and felsic magmas as well, in particular when end-members are broadly in equal proportions and iso-viscous (e.g. [START_REF] Laumonier | On the conditions of magma mixing and its bearing on andesite production in the crust[END_REF].

EVOLUTION AND MAGMA STORAGE

Phase equilibrium experiments carried out directly on magmatic rocks provide quantitative constraints on the evolution and storage conditions of felsic magmas. Below, we use selected examples to illustrate the main differences between the phases (minerals) that crystallize in peraluminous, metaluminous or peralkaline silicic magmas. The experimentally determined phase diagrams presented here were all derived under fl uid-present conditions, but at various water activities. In each diagram (FIGS. 1, 2 AND 3), the water activity is directly related to the water content of the melt, which is reported either in the x-axis or as isopleths. The maximum water content that can be reached at water-saturated conditions (i.e. a water activity of 1) depends on pressure and is marked by the near-vertical curves, limiting the phase diagrams on the right side in FIGURES 1, 2 and 3. The left-most boundary in each phase diagram is the solidus curve.

Peraluminous Silicic Magmas

Representative compositions used in these phase-relation experiments are listed in TABLE 1. Peraluminous silicic rocks occur in three general types of geological environment: fi rst, in continental areas that have a thick crust, the result of continental collisional tectonics as has occurred in the Himalayas or in the Hercynian belt across Europe; second, in areas of active oceanic subduction beneath overthickened continental crust, such as in the Peruvian Andes; third in post-orogenic settings, such as in the Devonian terranes of eastern Australia. Minerals typifying the peraluminous character of felsic rocks include cordierite, garnet, muscovite, tourmaline, hercynite, and the aluminosilicates of andalusite or sillimanite. In reduced felsic and iron-rich (>1.5 wt% FeO tot ) magmas and at pressures above 4-5 kbar, garnet crystallizes at near-liquidus conditions; the same magmatic conditions restrict cordierite formation to nearsolidus conditions (Clemens and Birch 2012) (FIG. 1B). In contrast, near-liquidus cordierite only occurs at or below 2 kb (FIG. 1C). In felsic leucogranites (e.g. iron-poor with FeO tot < 1.5 wt%), Mn-rich garnet (spessartine) occurs only in late-stage derivatives; this contrasts with higher temperature almandine-type garnet occurring in more mafi c peraluminous granites. In felsic end-member leucogranites of S-type affi nity, muscovite is the diagnostic phase of a strongly peraluminous magma, but magmatic muscovite is only expected at pressures higher than 3.5 kbar. Muscovite is also a late-crystallizing mineral (FIG. 1A) except when fO 2

Metaluminous Silicic Magmas

The dominant type of silicic magma found in subduction zone settings is metaluminous, but this category also occurs in anorogenic zones and hot-spots. Compared to peraluminous and peralkaline varieties, the SiO 2 content of common metaluminous silicic rocks goes down to values as low as 60 wt%: these are andesites and dacites, which are of so-called intermediate compositions and which dominate in arc settings. When hydrous, the mafi c mineralogy of andesites and dacites is dominated by biotite and by calcic amphibole (hornblende). These magmas are typically considered to have originated from igneous sources, either via fractional crystallization of mafi c magmas or by partial melting of older, crustal metaluminous intrusive during which biotite and amphibole breakdown takes place. Mixing processes may also act at any stage during magma evolution. The range of temperatures of metaluminous magmas is broadly similar to that of peraluminous ones, though temperatures of 1,000 °C or higher have been recorded. This is, in part, related to the greater compositional range covered (i.e. greater mafi c character) and to the local remelting of dehydrated crust.

The [START_REF] Tuttle | Origin of granite in the light of experimental studies in the system NaAlSi 3 O 8 -KAlSi 3 O 8 -SiO 2 -H 2 O[END_REF] work primarily applies to evolved metaluminous magmas. Phase equilibria at H 2 O-saturation in the system quartz-albite-orthoclase have shown that the minimum composition, or eutectic, trends toward more sodic compositions with increasing pressure [START_REF] Luth | The granite system at pressures of 4 to 10 kilobars[END_REF]). The experimental constraints observed at H 2 O-saturation in this system have been used to infer P-T conditions for the emplacement of relatively felsic granites in the crust, and, more recently, of magma ascent to the surface from shallow reservoirs [START_REF] Blundy | Petrologic reconstruction of magmatic system variables and processes[END_REF]. However, the quantitative application of experimental results obtained in this synthetic system to natural cases is hampered by the incomplete understanding of the effect of small amounts of Ca on the haplogranite phase relationships. Similarly, investigation of the role of CO 2 [START_REF] Holtz | Effects of H 2 O on liquidus phase relations in the haplogranite system at 2 and 5 kbar[END_REF]) has shown that a decrease in H 2 O melt at constant total pressure displaces the minimum (eutectic) toward more potassic melts at constant normative quartz content. This effect is not yet fully accounted for in current thermodynamic models.

The compositions of representative natural metaluminous silicic magmas used in experiments are listed in TABLE 1, and representative phase relationships are shown in FIGURE 2. The results obtained on ferroan metaluminous granites outcropping in anorogenic settings show that they have 4-5 wt% H 2 O melt at temperatures up to 950 °C for the more mafi c varieties (e.g. [START_REF] Clemens | Origin of an A-type granite: experimental constraints[END_REF];

FIGURE 1 Isobaric T-H 2 O melt
phase relationships of peraluminous silicic magmas (NNO-1 means an fO 2 one log unit below the NNO solid buffer). (A) Fe-poor leucogranite from the High Himalayas (composition 4 in TABLE 1; [START_REF] Scaillet | Experimental crystallisation of leucogranite magmas[END_REF]. (B) and (C) Fe-rich granite from SE Australia [START_REF] Clemens | Assembly of a zoned volcanic magma chamber from multiple magma batches: the Cerberean Cauldron, Marysville Igneous Complex, Australia[END_REF]composition 2 in TABLE 1). In (B) and (C), the H 2 O melt is shown as isopleths labeled as 2, 3, 4 and 5. The black near-vertical curve at high H 2 O melt in (A) is the water solubility curve. The black curve on the left of all three diagrams is the solidus curve. In these and all subsequent phase diagrams (see FIGS. 2 and 3), a fl uid phase composed of H 2 O and CO 2 coexists with the melt and solid phases. The solidus temperature, as well as H 2 O melt , depend on the proportion of H 2 O and CO 2 in the fl uid phase. Phase abbreviations are Af (alkali feldspar), Bt (biotite), Crd (cordierite), Grt (garnet), Hc (hercynite), Ms (muscovite), Opx (orthopyroxene), Pl (plagioclase), Qz (quartz).

Ms

Peraluminous silicic magmas

SiO 2 =73 wt%, FeO tot =0.9 wt% SiO 2 =69.8 wt%, FeO tot =4.2 wt% SiO 2 =69.8 wt%, FeO tot =4.2 wt%

A B C

Dall 'Agnol et al. 1999;[START_REF] Klimm | Fractionation vs. magma mixing in the Wangrah Suite A-type granites, Lachlan Fold Belt, Australia: experimental constraints[END_REF]. The comparison of phase equilibria and petrologic observations provides a constraint on the pressure of magma emplacement to be around 1-3 kbar, with redox states in the range of fO 2 that corresponds to the fayalite-magnetite-quartz (FMQ) and Ni-NiO (NNO) buffers. Most metaluminous magmas, notably the more mafi c (i.e. intermediate) ones -with H 2 O melt >4 wt%; compare FIGURES 2A and 2B -contain hornblende at pressures higher than 1 kbar. Hornblende is, however, not stable in the most felsic (i.e. Ca-poor) metaluminous granites, these normally being the most K-rich [START_REF] Klimm | Fractionation vs. magma mixing in the Wangrah Suite A-type granites, Lachlan Fold Belt, Australia: experimental constraints[END_REF]) and having biotite as the dominant hydrous mineral. The most fractionated examples of A-type metaluminous magmas have concentrations of F reaching or exceeding 1 wt%, something also observed in peraluminous rhyolites. Phase equilibria of these particular metaluminous magmas indicate emplacement temperatures in the range 675-720 °C and a H 2 O melt of 4-5 wt% [START_REF] Webster | Phase equilibria of a Be, U and F-enriched vitrophyre from Spor Mountain, Utah[END_REF]. The low liquidus temperatures are due to the near-eutectic compositions and to the fl uxing effect of F on silicate systems.

Although metaluminous rhyolites are not as abundant as intermediate magmas (dacite/ andesite or granodiorite) in arc settings, they sometimes erupt as single entities or as a part of a zoned eruption (e.g. [START_REF] Castro | Rapid ascent of rhyolitic magma at Chaitén volcano, Chile[END_REF], and when this happens, they display the same phase assemblages as anorogenic granites. The available phase relationships for metaluminous rhyolites point to pre-eruptive temperatures of around 800-850 °C, with H 2 O melt >4 wt%, storage pressures of 1.5-2 kbar, and fO 2 somewhat higher than anorogenic equivalents (from NNO up to 1.6 log units above it, or NNO+1.6). Except for the redox state, these conditions are essentially identical to those inferred for anorogenic granites.

Metaluminous rhyolites may also occur as the products of large-volume eruptions in hot spot settings. Amphibole is very often absent from such rhyolites, which instead contain pyroxenes in addition to fayalite. Detailed phase equilibria by [START_REF] Almeev | High-temperature, low-H 2 O silicic magmas of the Yellowstone hotspot: an experimental study of rhyolite from the Bruneau-Jarbidge Eruptive Center, Central Snake River Plain, USA[END_REF] revealed that such felsic magmas may be dry and hot, with inferred H 2 O melt <1.5 wt%, temperatures approaching 1,000 °C, and storage pressure of 2-4 kbar. This is the sole experimentally documented instance of a dry and hot rhyolitic system; it is, therefore, not known whether it is representative of most hot spots. The dry and hot conditions may refl ect melting of a (locally?) previously dehydrated crust. It is worth noting that the redox state of hot spot rhyolites lies close to the lower end of terrestrial values (i.e. fO 2 one log unit below FMQ, or FMQ-1), though it is not as reduced as for peralkaline rhyolites.

A number of phase equilibrium studies have been performed on the more mafi c silicic magmas (dacites/andesites) dominantly erupted in subduction zones to constrain their pre-eruptive conditions and petrogenesis (e.g. [START_REF] Rutherford | The May 1, 1980, eruption of Mount St. Helens: 1. Melt compositions and experimental phase equilibria[END_REF][START_REF] Costa | Petrological and experimental constraints on pre-eruption conditions of Holocene dacite from volcan San Pedro (36°S, Chilean Andes) and the importance of sulphur in silicic subduction-related magmas[END_REF]. For these silicic rocks, hornblende is generally the main hydrous phase, having an upper thermal stability of about 850-900 °C depending on composition (FIGS. (NNO and FMQ are reference solid fO 2 buffers: NNO+1 means an fO 2 one log unit above NNO; NNO-FMQ means an fO 2 between those two buffers). (A) Fe-rich granite from Australia [START_REF] Clemens | Origin of an A-type granite: experimental constraints[END_REF]composition 7 in TABLE 1). (B) Fe-rich granite from NE Brazil [START_REF] Dall'agnol | An experimental study of a lower Proterozoic A-type granite from the Eastern Amazonian Craton, Brazil[END_REF]composition 6 in TABLE 1). (C) and (D) Fe-poor granites from Australia [START_REF] Klimm | Fractionation vs. magma mixing in the Wangrah Suite A-type granites, Lachlan Fold Belt, Australia: experimental constraints[END_REF]compositions 12 and 13 in TABLE 1, respectively). Dashed lines on Brazilian granite (B) show the effect of increasing fO 2 up to NNO+2 on mineral stabilities. (E) Andesite from Mt. St. Helens [START_REF] Rutherford | The May 1, 1980, eruption of Mount St. Helens: 1. Melt compositions and experimental phase equilibria[END_REF]composition 10 in TABLE 1). (F) Dacite from San Pedro volcano (Costa et al. 2003;composition 11 in TABLE 1). Dotted lines on the dacite phase diagram give the melt fraction in wt%. Phase abbreviations are as in FIGURE 1 plus Cpx (clinopyroxene), Fe-Ti (Fe-Ti oxides), Hbl (hornblende), Ilm (ilmenite). SiO 2 =72.1 wt%, FeO tot =3.7 wt% SiO 2 =75.7 wt%, FeO tot =1.7 wt% SiO 2 =73.6 wt%, FeO tot =3 wt% SiO 2 =77.6 wt%, FeO tot =1.1 wt% SiO 2 =63.8 wt%, FeO tot =3.9 wt% SiO 2 =66.3 wt%, FeO tot =3.9 wt%

Cpx

A B C F E D

all silicic magma compositions. In iron-rich granites, low fO 2 (at or below FMQ) depresses the thermal stability of amphibole and expands that of orthopyroxene (FIG. 2B). Because fO 2 affects the stability fi elds of mafi c minerals and the melt structure (Fe 2+ /Fe 3+ ratio), the stability fi elds of framework silicates, in particular that of plagioclase, also depend on fO 2 , being somewhat depressed at low fO 2 [START_REF] Dall'agnol | An experimental study of a lower Proterozoic A-type granite from the Eastern Amazonian Craton, Brazil[END_REF]). This feature is also documented in basalt melting experiments [START_REF] Sisson | Voluminous granitic magmas from common basaltic sources[END_REF]. Lastly, the effect of sulfur on phase equilibria has been explored in some detail (e.g. [START_REF] Costa | Petrological and experimental constraints on pre-eruption conditions of Holocene dacite from volcan San Pedro (36°S, Chilean Andes) and the importance of sulphur in silicic subduction-related magmas[END_REF]). One of the most signifi cant fi ndings is that, under moderately oxidizing conditions (around NNO+1), biotite thermal stability is increased by elevated f S 2 , whilst that of hornblende shows the opposite trend, possibly as a result of Ca-S complexation in the melt at high fO 2 . As for fO 2 , however, there are not suffi cient data to establish quantitative and general trends related to changes of fS 2 . Systematic investigation of the role of sulfur on phase equilibria, under controlled fO 2 and f S 2 , clearly represents an important avenue for future research.

Peralkaline Silicic Magmas

Peralkaline magmas occur mostly in rift zones, back arc settings or hot spot environments and are typically associated with basalts of transitional affi nity: ones that have alkali contents between those of mid-ocean ridge and alkali basalts. Together, peralkaline magmas and transitional basalts form strongly bimodal volcanic provinces.

The phase equilibria of peralkaline silicic melts were fi rst investigated in synthetic systems. Petrologic evidence shows that most, if not all, peralkaline silicic magmas are quite reduced (NNO-1 or below; e.g. [START_REF] Scaillet | Phase relations of peralkaline silicic magmas and petrogenetic implications[END_REF]. The origin of the peralkaline character has long been a matter of debate and is still unresolved: No experimental study has produced a peralkaline silicic liquid by partial melting of a continental protolith. This in itself provides clear evidence that peralkaline silicic rocks result from processes involving differentiation from mantle magmas, consistent with fi eld evidence and geochemical signatures.

Representative compositions of peralkaline silicic rocks that have been investigated experimentally are listed in TABLE 1, with the corresponding isobaric phase relationships shown in FIGURE 3. One of the key features of such magmas is their relatively low liquidus temperatures, despite having elevated bulk iron contents (compared to metaluminous systems) which vary between 2 wt% for incipiently peralkaline (A/ CNK = 0.9, or = 0.95) up to more than 7 wt% for the most peralkaline (A/CNK = 0.49, or A/NK = 0.59) rhyolites. The phase assemblage is dominated by the crystallization of alkali feldspar, the magma being too Ca-poor for plagioclase to be stable. In peralkaline rhyolites with higher Ca concentrations, which are the less peralkaline of a given series, the calcic silicate phase is Fe-rich clinopyroxene. In the less calcic and more peralkaline systems, amphibole of the sodic-calcic (riebeckite-arfvedsonite) end-members crystallizes. In contrast to calcic amphiboles from metaluminous systems (hornblende), the thermal stability of sodic amphibole increases with decreasing H 2 O melt because of F-OH substitution. The F-rich character allows sodic amphiboles to be more stable at lower pressures (e.g. during ascent and surface outfl ow) than their calcic equivalent in metaluminous magmas. Amphibole occurrence as a nearliquidus mineral in peralkaline silicic rocks (i.e. crystalpoor volcanic rocks) indicates H 2 O-rich conditions and temperatures below 750 °C. Higher fO 2 promotes aegirine crystallization at the expense of amphibole. However, aegirine may also appear at low fO 2 but at lower temperature than amphibole (FIG. 3C).

Pre-eruptive conditions derived from experimental data indicate invariably water-rich conditions, with H 2 O melt >4 wt%, temperatures below 800 °C and even down to <700 °C, and redox state at or below NNO-1. The pressure of magma storage or crystallization is inferred to be low, around 1 kbar, in agreement with geological/volcanological inferences. Clearly, there is no evidence that peralkaline rhyolitic magmas are drier than other silicic magmas. In contrast, their redox state, be it inferred from phase equilibria or mineral barometry in quenched volcanic rocks, lies at the low end of the redox range displayed by felsic terrestrial magmas.

CONCLUSIONS AND PERSPECTIVES

The constraints on magmatic water content from phase equilibria indicate that the vast majority of silicic melts contain several wt% H 2 O in solution very early in their evolution (e.g. [START_REF] Whitney | The origin of granite: the role and source of water in the evolution of granitic magmas[END_REF]). This is interpreted as occurring at their production site, with temperature and H 2 O being roughly inversely correlated [START_REF] Andújar | Relationships between pre-eruptive conditions and eruptive styles of phonolite-trachyte magmas[END_REF]. Altogether, silicic magma compositions often refl ect their source, including the source's redox state. Magmas originating from metasediments are peraluminous and reduced, with fO 2 possibly refl ecting the graphitesaturated character of many sedimentary protoliths. Silicic magmas formed by partial melting of igneous sources are, on average, more oxidized, though some may be quite reduced. However, the common assumption that water-rich magmas are more oxidized than water-poor magmas is not supported by experiment. This is perhaps best illustrated by FIGURE 3 Phase relationships of peralkaline silicic magmas (NNO-1.6 and NNO-2 mean an fO 2 1.6 or 2 log units below the NNO buffer, respectively). (A) and (B) Moderately peralkaline magma (comendite) from Kenya [START_REF] Scaillet | Phase relations of peralkaline silicic magmas and petrogenetic implications[END_REF]compositions 14 and 15 in TABLE 1, respectively). Horizontal dashed line in (A) is the H 2 O-saturated solidus of the haplogranite system. (C) Strongly peralkaline magma (pantellerite) from Kenya [START_REF] Scaillet | Experimental constraints on pre-eruption conditions of pantelleritic magmas: evidence from the Eburru complex, Kenya Rift[END_REF]composition 17 in TABLE 1). Phase abbreviations are as in FIGURES 1 and 2, plus Aeg (aegirine), Arfd (arfvedsonite), Fay (fayalite), Fl (fl uorite), Hd (hedenbergite), Ox (oxides), Richt (richterite) SiO 2 =75.2 wt%, FeO tot =1.8 wt% SiO 2 =74.1 wt%, FeO tot =3.9 wt% SiO 2 =71.2 wt%, FeO tot =6.9 wt%

Arfd

A B C

the existence of reduced but H 2 O-rich peralkaline rhyolites.

There is, thus, a decoupling between magma redox state and degree of hydration.

In terms of phase equilibria, the fundamental distinction between S-and I-type silicic magmas appears to be still valid more than 40 years after its defi nition [START_REF] Chappell | Two contrasting granite types[END_REF]. The usefulness of the A-type categorydefi ned to label granites that are not only rich in alkalis but also anhydrous and that outcrop in anorogenic settings -is less obvious (e.g. [START_REF] Clemens | Origin of an A-type granite: experimental constraints[END_REF]): for example, there is no clear distinction in their alkali/alumina ratio. Besides the fact that A-type magmas are not systematically drier than other types, experimentally produced metaluminous A-types are signifi cantly different from A-types that lead to peralkaline melts, the latter producing some of the coldest magmas erupted on Earth (660 °C), while the former may yield some of the hottest silicic magmas (1,000 °C). Another difference between the metaluminous and peralkaline A-types is that metaluminous A-type systems often derive from the partial melting of older, continental crust igneous sources. In this respect metaluminous A-types differ little in terms of phase equilibria from I-types. In sharp contrast, peralkaline silicic magmas derive from the fractionation of basaltic parents either by protracted crystal fractionation or by small degrees of partial melting. These peralkaline magmas have little to no interaction with continental crust because any signifi cant contribution of (Al-rich) crustal material will inevitably counteract the peralkalinity.

Although considerable progress has been made over the last two decades in constraining the P-T-X conditions of silicic magma production and evolution, the detailed investigation of the role of volatiles other than H 2 O (i.e. S, F, Cl, CO 2 and others) still needs to be carried out so as to better model the conditions of silicic magma storage. Careful and systematic evaluation of the role of additional components to the haplogranite system, such as Ca and Fe, should also be pursued in order to provide accurate compositional datasets to go with thermodynamic modeling approaches.

A

  rich history of experimental petrology has revealed the paths by which silicic igneous rocks follow mineral-melt equilibria during differentiation. Subdividing these rocks by 'molar Al versus Ca + Na + K' illustrates fi rst-order differences in mineralogy and gives insight into formation mechanisms. Peraluminous magmas, formed by partial melting of sediments, largely owe their attributes and compositions to melting reactions in the protoliths, whereas most metaluminous felsic magmas record both continental and mantle inputs. Peralkaline rhyolites are mainly derived from either protracted crystallization or small degrees of partial melting of basalt, with only a marginal crustal contribution. Most silicic magmas hold 3-7 wt% H 2 O melt , which is inversely correlated with pre-eruptive temperature (700 °C to >950 °C) but unrelated to their reduced/oxidized state.

TABLE 1

 1 COMPOSITIONS USED IN PHASE EQUILIBRIUM EXPERIMENTS ON PERALUMINOUS(1-5), METALUMINOUS (6-13), AND PERALKALINE (14-17) FELSIC ROCKS. Sources listed below.

	Felsic Rock		Peraluminous					Metaluminous					Peralkaline
	Composition (wt%)	1	2	3	4	5	6	7	8	9	1 0	1 1	1 2	1 3	1 4	1 5	1 6	1 7
	SiO 2	75.77	69.83	70.46	73.04	72.94	72.1	73.6	70.77	73.74	63.83	66.30	75.65	77.56	75.2	72.64	74.17	71.25
	TiO2	0.11	0.65	0.69	0.13	0.06	0.8	0.34	0.65	0.46	0.61	0.52	0.17	0.1	0.17	0.18	0.17	0.3
	Al2O3	13.54	14.75	14.92	15.32	15.57	13.4	12.44	13.22	11.96	18.18	16.24	13.04	12.39	12.11	10.3	10.89	8.03
	FeOtot	1.69	4.21	3.51	0.89	0.76	3.7	3	3.98	4	3.97	3.90	1.71	1.13	1.81	4	3.98	6.93
	MnO	0.01	0.05	-	0.01	0.01	0.07	0.08	0.06	0.01	0.07	0.10	0.06	0.06	0.04	0.06	0.06	0.21
	MgO	0.31	1.5	1.54	0.2	0.14	0.7	0.27	0.62	0.24	1 .72	1.71	0.19	0.04	0.07	0.04	0	0.01
	CaO	0.65	2.76	1.92	0.85	0.57	2.2	1.24	2.08	1.13	5.77	4.05	0.96	0.51	0.44	0.1	0.29	0.33
	Na2O	2.64	2.45	2.5	3.85	4.56	3.8	3.53	2.96	2.22	4.96	4.21	3.4	3.45	4.59	5.68	5.81	6.54
	K2O	5.27	3.79	4.53	4.96	4.14	3.4	4.23	5.41	5.93	1.31	2.76	4.8	4.76	4.73	4.35	4.68	4.6
	P2O5	-	-	-	0.14	0.19	0.3	0.07	0.11	0.08	-	0.16	0.05	0.01	-	-	-	-
	A/CNK	1.21	1.12	1.19	1.16	1.20	0.96	0.98	0.91	0.99	0.91	0.94	1.04	1.05	0.90	0.72	0.72	0.49

SOURCES

: 1, 2 (Clemens and Birch 2012); 3 (Clemens and Wall 1981); 4, 5

[START_REF] Scaillet | Experimental crystallisation of leucogranite magmas[END_REF]

; 6 (Dall'Agnol et al. 1999); 7

[START_REF] Clemens | Origin of an A-type granite: experimental constraints[END_REF]

); 8, 9

[START_REF] Almeev | High-temperature, low-H 2 O silicic magmas of the Yellowstone hotspot: an experimental study of rhyolite from the Bruneau-Jarbidge Eruptive Center, Central Snake River Plain, USA[END_REF] 10 (Rutherford et al. 1985)

; 11

[START_REF] Costa | Petrological and experimental constraints on pre-eruption conditions of Holocene dacite from volcan San Pedro (36°S, Chilean Andes) and the importance of sulphur in silicic subduction-related magmas[END_REF]

); 12, 13

[START_REF] Klimm | Fractionation vs. magma mixing in the Wangrah Suite A-type granites, Lachlan Fold Belt, Australia: experimental constraints[END_REF]

; 14, 15, 16 (Scaillet and Macdonald 2001); 17 (Scaillet and Macdonald 2006) (Patiño Douce and Harris 1998

). These temperature-H 2 O constraints are essentially identical to those based on phase equilibria experiments carried out on the granite itself

[START_REF] Scaillet | Experimental crystallisation of leucogranite magmas[END_REF]

. The production of more mafi c peraluminous magmas (i.e. compositions 2 and 3 in TABLE 1) requires higher temperatures, which should involve biotite breaking down in the source region to form orthopyroxene and/or garnet in the residue. The available data indicate that felsic volcanic and plutonic peraluminous rocks share common P-T-H 2 O-fO 2 conditions. As for other silicic categories, there is no experimental basis to support the claim that rhyolitic melts crystallizing at depth to form plutonic magmas are drier, and, hence, more viscous and less mobile than melts from volcanic systems with equivalent whole-rock compositions.

  majority of studied cases, a storage pressure around 2 kbar seems to be the rule. At 2 kbar, pyroxenes and plagioclase are the liquidus silicate minerals (FIGS. 2E, 2F). Oxides, either magnetite or ilmenite or both, generally belong to this assemblage: as a rule of thumb, magnetite is present alone (as oxide) at fO 2 above NNO+1 whereas ilmenite is the single oxide at NNO-1 or below. The lack of amphibole in volcanic rocks, however, does not necessarily imply a dry magma or crystallization at shallow pressures.

	It may
	simply refl ect that the temperature is too high to crystallize
	amphibole, possibly as a result of sustained mafi c magma
	infl ux which buffers the reservoir temperature above
	the thermal stability of hornblende. Pre-eruptive T-H 2 O
	conditions of intermediate (dacite to andesite) arc magmas
	retrieved from phase equilibria vary from 760 to 950 °C
	and from 4 to 7 wt% H 2 O melt, respectively. Corresponding
	redox states fall in the NNO-NNO+1.7 range.
	It is worth stressing that the phase equilibria of metalumi-
	nous silicic magmas depend signifi cantly not only on P,
	T and H 2 O but also on redox state, though there are not
	enough detailed data to fully appreciate how fO 2 affects
	FIGURE 2 Phase relationships of metaluminous silicic magmas

2E, 2F)

. When such magma is stored at pressures below 1.5 kbar, or when H 2 O melt is lower than ~4 wt%, hornblende is replaced by pyroxenes. However, in the vast

ACKNOWLEDGMENTS

We thank T. Sisson and R. Lange for their extensive and helpful reviews. The editorial guidance, as well as constructive comments by A. Glazner and C. Lundstrom, is also greatly appreciated. The authors thank the CNRS/ University of Orléans and the German Research Foundation for the continuous support over the last three decades, which helped maintain experimental and analytical facilities at Orléans and Hannover at the requested levels.


H Helbling

A Benabou

A Van Gorp²

A Tounzi

M El

W Boughanmi

D Laloy

Effect of Industrial Impregnation Process on the Magnetic Properties of Electrical Steels

Keywords: Magnetic Properties, Iron Losses, Manufacturing Process, Impregnation Process

This paper deals with the experimental investigation of the effect of impregnation process on the normal magnetization curve and iron losses of electrical steels. To address this issue, several laminated toroidal magnetic circuits have been designed to characterize the magnetic properties with the flux metric method. The first configuration considers magnetic circuits wrapped with adhesive tape so that the dielectric resin will be deposited only on the outer surface of the magnetic circuit. In the second configuration, the magnetic circuits are unwrapped, which will allow the resin to diffuse within the inter-laminar spaces of the magnetic circuit. The obtained experimental results show significant effects on the magnetic properties in both cases. However, depending on the considered configuration, the resin diffusion also has an influence on the changes in magnetic properties.

Introduction

The magnetic circuits of electrical machines play a significant role in the efficiency of the energy conversion process and also on the machine performances. Therefore, to be able to increase the energy efficiency of these machines, it is relevant to consider the magnetic core properties within the context of their operating conditions as well as their manufacturing processes. In this latter case, the impact of manufacturing processes on the magnetic properties of electrical steels may be significant. In the literature, the most commonly studied processes are the cutting, welding, pressing or shrink-fitting [START_REF] Bali | Modeling the effect of cutting on the magnetic properties of electrical steel sheets[END_REF][START_REF] Bourchas | Influence of cutting and welding on magnetic properties of electrical steels[END_REF][START_REF] Schoppa | Influence of welding and sticking of laminations on the magnetic properties of non-oriented electrical steels[END_REF][START_REF] Yamazaki | Loss analysis of induction motors by considering shrink fitting of stator housings[END_REF][START_REF] Helbling | Effect on magnetic properties of inhomogeneous compressive stress in thickness direction of an electrical steel stack[END_REF] of laminations or magnetic cores. However, for some specific industrial applications such as large alternators, the magnetic circuits are impregnated, under vacuum pressure followed by a heat treatment, with a dielectric resin. This impregnation process is realized once the magnetic circuits are built and wound. Its objectives are mainly to ensure the thermal properties, electrical insulation, mechanical withstand capability and also to reduce the vibrations of the electrical machine during operation [START_REF] Ayat | Estimation of Equivalent Thermal Conductivity for Impregnated Electrical Windings Formed from Profiled Rectangular Conductors[END_REF], [START_REF] Singal | The effect of windings, frame and impregnation upon the resonant frequencies and vibrational behavior of an electrical machine stator[END_REF]. Preliminary considerations indicate that the resin will shrink around the magnetic circuit when cooled down after the heat treatment, thus requiring investigating its effect on the magnetic circuit properties. However, no study was conducted on the effect of this specific process on the magnetic properties.

In that context, the presented work investigates the effect of an industrial impregnation process on the normal magnetization curve and iron losses of electrical steel. Particularly, this paper makes a first link between the effects of an impregnation process on the magnetic properties and the diffusion of the resin within the magnetic core. To address this issue, several laminated toroidal magnetic circuits have been designed to characterize the magnetic properties before and after undergoing an industrial impregnation process. The magnetic measurements are performed with standard equipment based on the flux metric method.

This work presents several highlights. To our best knowledge, the proposed study constitutes the first investigation concerning the effect of impregnation process on the magnetic properties. The study shows a link between the level of resin diffusion within the magnetic circuit, the resin thermal contraction and the modifications of magnetic properties. Finally, the obtained experimental results, which have been consolidated by a repeatability analyzis, are analyzed and discussed relying in particular on thermo-mechanical simulations.

The paper is structured as follows. The second section describes the adopted methodology, including the presentation of the industrial impregnation process, the design of the studied samples, the magnetic measurement method and the experimental protocol that was followed. Then, results related to the effect of impregnation process on the iron losses and the normal magnetization curves are given. Moreover, thanks to thermo-mechanical finite element simulations, these effects are linked to the thermal retraction of the resin on the magnetic circuit. Finally, the main conclusions of the study and future work are presented.

Methodology and experimental protocol

The studied industrial impregnation process

Usually, large electrical machines, once the magnetic circuits are built and wound, are impregnated with a dielectric resin that is polymerized under heat treatment. As mentioned in the introduction, the aims of this process are mainly to ensure thermal properties, electrical insulation and reduction of the machine vibrations during operation. In this study, the considered industrial impregnation process involves two cycles as presented in Figure 1. Each cycle includes a vacuum pressure impregnation phase followed by a heat treatment phase. The impregnation phase consists in placing the machine in a tank which is subjected to a defined level of vacuum and applying the resin. The following heating phase consists in placing the impregnated machine in an oven under a temperature T 1 for duration d 1 (respectively T 2 and d 2 for the second cycle). During these operations, the conductive areas are protected by a coating.

Methodology

The methodology of this work is as follows. First, four laminated toroidal magnetic circuits have been prepared for a characterization with the flux metric method. Two configurations are considered: the first one with two cores wrapped by a non-porous adhesive tape and the second one with two non-wrapped cores. In the first configuration, the nonporous adhesive tape will not allow the resin to diffuse within the magnetic circuits, which means that the resin is deposited only on the outer surface of the circuit. Without any tape, the resin will diffuse within the inter-laminar spaces of the magnetic circuit. All the magnetic cores are impregnated using the same process. Finally, the impregnated cores are characterized, including a repeatability analyzis concerning the impregnation process and the magnetic measurement method. A simplified schematic diagram of the methodology is presented in Figure 2.

Design of the magnetic cores

All toroidal magnetic circuits come from the same coil of fully processed non-oriented electrical steel of grade M400-65A. This grade is commonly used for large electrical machines. Moreover, the toroidal magnetic circuits have been cut at the same time by wire electrical discharge machining (WEDM) to ensure a limited impact of the cutting method on the magnetic properties [START_REF] Manescu Paltanea | Energy loss analysis and magnetic properties of non-oriented electrical steel cut through different technologies[END_REF]. The inner and outer radii of the toroids are 86 mm and 100 mm respectively, and their height is 13 mm with 20 stacked strips of 0.65mm thickness. The technical characteristics of the non-porous adhesive tape are given in Table 1. The maximum operation temperature of the non-porous adhesive tape is higher than the temperatures involved by the impregnation process. Regarding the dielectric resin, this latter is an epoxy based resin that is conventionally used for industrial impregnation processes.

As illustration, a ring core with the non-porous tape is shown after being impregnated in Figure 3. 1 -Technical characteristics of the non-porous tape

Magnetic Measurement

Magnetic measurements are performed on the MPG200D equipment from Brockhaus in accordance with the standard IEC 60404-4 [START_REF]International Standard IEC 60404-4. Magnetic Materials -Part 4: Methods of Measurements of d.c. Magnetic Properties of Iron Steel[END_REF]. The repeatability of the measurements with the ring core tester equipment is less than 0.1%.

We consider the configuration before the impregnation process as the reference case. The corresponding iron losses and normal magnetization curves are given in Figure 4 for all samples (N°1 to 4). The iron losses under sinusoidal magnetic flux density of 1.5T (peak) and 50Hz are approximately 3.75 W/kg, which fulfils the requirements of the studied M400-65A electrical steel grade. It also means that the sample cutting did not affect significantly the material properties regarding the small width (7mm) of the magnetic circuit. toroidal samples before the impregnation process

Experimental protocol

The experimental protocol is as follows. First, the magnetic circuits are characterized before being impregnated. To reduce the risk of winding degradation and to avoid short circuits with the magnetic core, a first adhesive tape is wrapped on each ring core before putting the secondary winding. This latter is also wrapped by a second adhesive tape layer before placing the primary winding.

After this step, the circuits are separated into two groups: the first is composed of magnetic circuits which are unwound and unwrapped, leaving only the lamination stack. For the second group, neither the adhesive tape nor the winding are removed. The magnetic circuits of both groups are then impregnated. For the first group, the resin will be directly in contact with the magnetic cores and will diffuse within the inter-laminar spaces. Whereas, for the second group, due to use of a non-porous adhesive tape, the resin will remain on the outer surface of the magnetic cores.

The employed non-porous adhesive tape can withstand the temperatures T 1 and T 2 (see Figure 1) during the heat treatment phase of the impregnation process. Both groups undergo the full impregnation process and the magnetic cores of the first group are wound and wrapped again. Finally, the magnetic properties of all impregnated circuits are characterized to investigate the influence of the impregnation process. Measurements are carried out under sinusoidal magnetic flux density varying from 0.05T to 1.6T at given frequencies of 5Hz, 50Hz and 300Hz.

A first analyzis of the measurements shows that the error induced by the reproducibility of measurements is negligible compared to the effect of the impregnation process on the magnetic properties. In the most unfavorable case, the reproducibility is twenty times smaller than the variation observed following the impregnation process. Therefore, in the next section, and for more convenience, we will present the results for a single sample from each group.

Results and discussion

Normal magnetization curves

First, results concerning the normal magnetization curves are given at 50Hz in Figure 5 and Figure 6. We observe that, with or without tape, the studied industrial impregnation process leads to the degradation of the normal magnetization curves. To emphasize this degradation, the relative increase of the magnetic field, to reach a given magnetic flux density, is calculated by considering the samples before the impregnation process as being the reference. For each induction level and each impregnation process, the variation ΔH=H 1 -H 0 , as illustrated in Figure 5, is determined; where H 0 and H 1 are the magnetic fields before and after impregnation respectively. The obtained relative differences ΔH/H 0 are presented in Figure 7 for the frequencies 5Hz, 50Hz and 300Hz. These results show a degradation for low induction levels (linear part <1T) and in the knee region (between 1T and 1.4T), with a more significant effect when the resin diffuses within the cores (without tape). However, the orders of magnitude of the degradation are relatively close between both configurations, especially in the knee region.

Figure 5 -Normal magnetization curves at 50Hz, before and after the impregnation process, for the magnetic circuit without tape (diffusion of the resin within the core)

Figure 6 -Normal magnetization curves at 50Hz, before and after the impregnation process, for the magnetic circuit with tape (only surface diffusion of the resin)

We also observe in Figure 5 that the saturation levels of the normal magnetization curves before and after impregnation show a slight discrepancy whereas they are expected to be the same, regardless of the impregnation process. Indeed, the saturation depends mainly on the composition of the magnetic material, which has not been modified in the process. The observed discrepancy in the saturation region of Figure 5 can be explained by a more significant impact of the impregnation process even in the high excitation field region. To address this issue, magnetic measurements were carried out to 1.75T (H ≈ 12 000A/m) and reported in Figure 7. The relative difference ΔH/H 0 tends to zero, meaning that the saturation level is indeed the same, even for the case without tape. In addition to previous observations, in Figure 8, the relative difference on the magnetic field is summarized for frequencies 5 Hz, 50 Hz and 300 Hz. It appears that the level of degradation decreases when the frequency increases. This observation can be explained by the required magnetic field H=H hyst +H dyn to magnetize the material in the dynamic regime. Indeed, with increasing frequency and to reach a given induction level, the dynamic field H dyn becomes more predominant with regard to the static field H hyst . This suggests that the static field contribution is the one mostly affected by the impregnation process, a result that is corroborated with the loss behavior detailed in next section.

Previous results show clearly that the impregnation process degrades the magnetic properties on the whole range of the magnetization process of the material. Also, these observations indicate that the way the resin diffuses, or not, within the magnetic core, has a more or less significant influence on the magnetic properties. Indeed, as each core was subjected to the same impregnation process, the only difference is the ability of the resin to diffuse either only on the outer surface or within the magnetic circuit. 2 -Experimental values, before and after impregnation process, of the required magnetic field to reach induction levels of 0.5T, 1T and 1.5T

Iron losses

Another sensitive indicator of the process influence on the magnetic properties is given by the iron losses. The impact of the impregnation process on these losses is shown in Figure 9 and Figure 10 for both considered configurations. As for the normal magnetization curve, the effect on power losses is given by the ratio ΔP/P 0 , where P 0 represents the losses before the impregnation process and ΔP represents the difference on power losses, before and after the impregnation process. These results show that the impregnation process leads to a significant increase of the iron losses.

In Figure 10, a zoom of Figure 9 is given for induction levels above 0.4T, which are more relevant magnetization regions for energy conversion devices. The increase of iron losses is about two times greater when the resin diffuses within the magnetic circuit, compared to the case where the resin is deposited only on the surface. This result shows that the impact on the magnetic properties depends on the way in which the resin diffuses within the magnetic circuit.

Moreover, the lower the frequency is, the more the total iron losses increase. This observation strongly suggests that, among the three loss contributions (hysteresis, classical and excess losses [START_REF] Bertotti | General properties of power losses in soft ferromagnetic material[END_REF]), the hysteresis loss contribution is the one mostly affected by the impregnation process. In order to confirm this assumption, the evolution of the hysteresis losses must be extracted from the measurements. Therefore, to determine the hysteresis loss contribution, several measurements were made at the following frequencies: 5, 20, 50, 150, 200 and 300Hz. Then, the specific energy (total power losses divided by the frequency) is extrapolated to zero frequency for each level of induction in order to determine the static (hysteresis) contribution of the losses. Finally, and similarly to previous analyzes, the relative difference of the hysteresis losses ΔP Hyst /P Hyst0 is calculated and given in Figure 11.

According to Figure 10 and Figure 11, it appears that the effect of the impregnation process on the hysteresis losses is significant and very close to that observed on the total iron losses. These results confirm that the hysteresis losses are the most impacted by the impregnation process.

Figure 9 -Relative difference on iron losses, due to impregnation process with (left) and without (right) tape, for 5Hz, 50Hz and 300Hz

Figure 10 -Relative difference on iron losses, due to impregnation process with (left) and without (right) tape, for average and high induction levels and for 5Hz, 50Hz and 300Hz

Figure 11 -Relative difference on hysteresis losses, due to impregnation process with and without tape, for all induction levels (left) and for average and high induction levels (right)

Finally, we give in Table 3 the power losses values for 0.5, 1 and 1.5T before and after the impregnation process. 3-Experimental values of the iron losses before and after impregnation process for induction levels of 0.5T, 1T and 1.5T

Discussion

To further analyze all previous results, one has to first consider the resin mechanical properties. According to the literature, the coefficient of thermal expansion of an epoxy resin is about four times greater than that of steel. After the heat treatment of the impregnation process, the magnetic circuit and the resin will cool down at the same time, which means that the resin will shrink much more than the steel because of its higher coefficient of thermal expansion. Thus, a mechanical stress will be induced on the magnetic circuit. To estimate this mechanical stress, a thermo-mechanical Finite Element (FE) study is performed with the software Abaqus [START_REF] Abaqus | ABAQUS Documentation[END_REF]. The case of study corresponds to a magnetic circuit (having the same size as those used for the experimental measurements) surrounded by one millimeter of resin thickness. The FE simulation is a coupled temperature-displacement problem, with an initial temperature equivalent to T 2 and a final temperature corresponding to 23°C. The mechanical and thermal characteristics used for the FE simulations are given in Table 4. The studied geometry has an axial symmetry around (see Figure 12), thus we have considered one fourth of the device with the planes and as boundary conditions. Also, the studied device has a plane of symmetry parallel to that allows representing only half of the device along the height. A zero displacement condition is imposed on this symmetry plane. The results in Figure 13 show the mechanical stresses along the magnetic flux direction, denoted (Figure 13-a), orthogonal to the flux direction, denoted (Figure 13b), and along the height of the magnetic circuit, denoted (Figure 13-c). In Figure 13-a, we observe that the stress along the flux direction is quite homogeneous within the magnetic circuit with a compressive stress around -15MPa. Still, Figure 13-b shows that in the plane of the laminations the stress, in the direction orthogonal to the flux direction, is near zero at the center of the magnetic core and progressively increases to a compressive value of -15MPa (light blue) or -30MPa (dark blue). Along the height direction (Figure 13-c), the compressive stress is relatively homogeneous and its value is about -10MPa. Thus, considering the three directions, the magnetic core is exclusively subjected to compressive stress. It is well established in the literature [START_REF] Shirkoohi | Effects of stress on magnetostrictive properties of low silicon non-oriented electrical steel[END_REF][START_REF] Baghel | An alternative approach to model mechanical stress effects on magnetic hysteresis in electrical steels using complex permeability[END_REF][START_REF] Miyagi | Influence of compressive stress on magnetic properties of laminated electrical steel sheets[END_REF][START_REF] Aydin | Effect of multi-axial stress on iron losses of electrical steel sheets[END_REF] that mechanical stress influences the magnetic behavior. Indeed, when considering the magnetic field in the same direction as the applied stress, a tensile stress can lead to slight magnetic improvements for low stress levels before deteriorating the magnetic behavior above a threshold. Regarding the compressive stress, this one leads to a continuous degradation effect that is, at the same stress level, more pronounced than the effect of the tensile stress [START_REF] Shirkoohi | Effects of stress on magnetostrictive properties of low silicon non-oriented electrical steel[END_REF][START_REF] Baghel | An alternative approach to model mechanical stress effects on magnetic hysteresis in electrical steels using complex permeability[END_REF][START_REF] Miyagi | Influence of compressive stress on magnetic properties of laminated electrical steel sheets[END_REF]. In the present study, the compressive stress levels, as suggested by the thermo-mechanical FE simulations, are indeed a source of degradation for the magnetic properties, as also observed in the literature for compressive stresses applied in the lamination plane [START_REF] Aydin | Effect of multi-axial stress on iron losses of electrical steel sheets[END_REF].

Unit

One must also note that the study has been carried out on ring-shaped magnetic cores whereas the effect of impregnation process is expected to be strongly related to the geometry of the magnetic circuit. Indeed, the way the resin will diffuse, and consequently its impact on the magnetic properties, is directly linked to the geometry of the core.

Conclusions

The presented study deals with a first investigation of the effect of an industrial impregnation process on the magnetic properties of a lamination stack. In particular, the changes in magnetic properties have been related to the way the resin diffuses within the magnetic circuit. For this, two groups of magnetic cores have been studied: a first group with ring cores that are wrapped by a non-porous adhesive tape, implying that the resin will only be distributed on the outer surface and a second group without tape, implying that the resin will diffuse within the magnetic core. Experimental results show that in both cases the impregnation process has a significant impact on the magnetic properties. In particular, they show that the more the resin diffuses within the magnetic circuit, the more the magnetic properties are deteriorated. Finally, the results of this study demonstrate the interest of investigating the impact of an impregnation process on magnetic properties of laminated magnetic cores.

One must note that the level of impact in the presented results is valid for the studied geometries, namely magnetic circuits of small sizes. Indeed, for larger magnetic circuits, in particular in the case of electrical machines, it is necessary to investigate whether and how the resin will diffuse over the entire magnetic circuit. However, this first investigation that shows the effect of the impregnation process on magnetic properties has many perspectives. In particular, the effect of impregnation can be accounted for in magnetic models of materials (loss model and normal magnetization curve). These models are required to further analyze the effect of impregnation process on electrical machine performances. Finally, studies need to be carried out in order to investigate to what extent the resin diffuses within the magnetic circuit, especially by investigating the diffusion process between the laminations. This way, the effect of resin diffusion process in magnetic cores with larger dimensions, such as those of high power electrical machines, can be accurately predicted.

Figure 1 -

 1 Figure 1 -Schematic diagram of the studied impregnation process

Figure 2 -

 2 Figure 2 -Schematic diagram of the used methodology

Figure 3 -

 3 Figure 3 -Impregnated magnetic circuit with the non-porous adhesive tape Support type Polyester Adhesive type Silicone Total thickness (support + adhesive) 63μm Maximum temperature 204°C Elongation at break 100%Table 1 -Technical characteristics of the non-porous tape

Figure 4 -

 4 Figure 4 -Iron losses (left) and normal magnetization curves (right) at 50Hz in the case of all toroidal samples before the impregnation process

Figure 7 -Figure 8 -

 78 Figure 7 -Relative difference on magnetic field, due to the impregnation process with and without adhesive tape, at 50Hz

4 -Figure 12 -

 412 Figure 12 -View of the magnetic circuit (black) and the resin (grey) -Perspective view (left) and top view (right)

Figure 13 -

 13 Figure 13 -Induced stress in the cross section due to the thermal contraction of the resinflux direction (a), orthogonal to the flux direction (b) and along the height of the lamination stack (c)

Table 2

 2

	for the induction levels 0.5, 1 and 1.5T
		0.5T	1T	1.5T
	Sample with non-porous tape
	Magnetic field before Impregnation Process (A/m)	67	142	1650
	Magnetic field after Impregnation Process (A/m)	75	168	1659
	Sample without tape
	Magnetic field before Impregnation Process (A/m)	65	142	1650
	Magnetic field after Impregnation Process (A/m)	80	172	1790
	Table