Emilie Cardona

Jérôme Bugeon

Emilien Segret

Julien Bobe

VisEgg: A ROBUST PHENOTYPING TOOL TO ASSESS RAINBOW TROUT EGG FEATURES AND VIABILITY

Keywords:

Assessing female fish reproductive success requires a thorough evaluation of egg characteristics, including egg number, size and variability as well as egg developmental potential through the monitoring of embryo survival after fertilization. While embryonic success relies, at least in part, on paternal contribution, some parameters are strictly related to egg characteristics, one of the main ones being the viability of the egg when released into the water at spawning. It is however not necessarily possible, at least in salmonid fish that lay non-transparent eggs, to separate the different causes of egg/embryo failure.

In this context, our aim was i) to develop a simple and rapid system to capture images of rainbow trout eggs combined with computerized processing of these images to perform a fully automatic individual characterization of egg features including number and size ii) to estimate unfertilized egg viability through the monitoring of the percentage of eggs that will not survive to water hydration.

To evaluate the VisEgg system, unfertilized eggs (approximatively 400 eggs per batch) originating from 105 different females were hydrated in water. After 24h, a picture of the eggs was obtained using a dedicated shooting system consisting of a light source and a digital single-lens reflex (SLR)

camera. An image processing algorithm was developed to allow the automatic detection and separation of the eggs and to perform automatic measurements of egg number and individual egg size. The presence of white egg was used as an indirect measure of egg integrity, the "whitening" being the result of water entry into the egg through the vitelline membrane. These white eggs were therefore considered as non-viable, as a result of their lack of physical integrity.

Fertilization assays were performed in parallel using a subsample of the same egg batch. Embryonic development was monitored and hatching rate was calculated. A significant correlation between white egg percentage after hydration and hatching rate was observed (Spearman coefficient =-0.557,

Introduction

The control of egg quality (i.e. the ability of the egg to be fertilized and subsequently develop into a normal embryo) is of major importance for many, if not all, aquaculture fish species [START_REF] Migaud | Gamete quality and broodstock management in temperate fish[END_REF]. A regular supply of high quality eggs is mandatory for rainbow trout hatcheries sustainability [START_REF] Bromage | Broodstock management, fecundity, egg quality and the timing of egg production in the rainbow trout (Oncorhynchus mykiss)[END_REF]. Given the high cost of broodstock rearing, large variations in the quantity or quality of gametes can significantly impact the competitiveness and sustainability of fish farms and aquaculture companies [START_REF] Bromage | Broodstock management, fecundity, egg quality and the timing of egg production in the rainbow trout (Oncorhynchus mykiss)[END_REF][START_REF] Bobe | Egg quality in fishU: Present and future challenges[END_REF]. Hence, controlling egg quality is a major issue in aquaculture with important economic consequences.

Teleost eggs consist of an inner ooplasm comprising vitellus (or yolk) surrounded by the vitelline membrane also known as plasma membrane. The outer membrane called the chorion is a thick layer with a single micropyle. Spermatozoa must pass across the micropyle to penetrate the egg and allow fertilization [START_REF] Kuchnow | Ultrastructure of the chorion and its micropyle apparatus in the mature Fundulus heteroclitus (Walbaum) ovum[END_REF]. Teleost eggs are soft in the ovary and when the egg is freshly stripped from the female, the chorion is limp and the egg is flaccid, egg is not really round. A thin space between the chorion and the vitelline membrane exists and corresponds to the perivitelline space. When eggs are transferred into water, a contractile activity of the yolk mass occurs as a result of subsequent discharge of the cortical vesicle contents in the perivitelline space [START_REF] Kobayashy | Electron microscopic observation of the breakdown of cortical vesicles in the chum salmon egg[END_REF].

Colloid substances, with water taking up property, are thus discharged into the perivitelline space.

Water is osmotically drawn through the fine pores of the chorion into the perivitelline space. This process creates a turgid pressure in the egg and the chorion is stretched until a steady state between internal and external environment is achieved, resulting in the hardening of the chorion [START_REF] Alderdice | Osmotic and Ionic Regulation in Teleost Eggs and Larvae[END_REF]. The stage of equilibrium is reached in about 20 minutes. This phenomenon is called egg water hardening process and egg from rainbow trout absorbs approximatively 20% of its initial volume in water [START_REF] Yamamoto | Physiology of fertilization in fish eggs[END_REF][START_REF] Blaxter | Development: eggs and larvae[END_REF][START_REF] Lahnsteiner | Physiological and biochemical parameters for egg quality determination in lake trout , Salmo trutta lacustris[END_REF]. The vitelline membrane is the only significant barrier to the diffusion of water and ions between the vitellus and the external medium.

When eggs are of good quality, the vitelline membrane is highly impermeable to water and electrolytes and it is not easy to cause a rupture of the membrane [START_REF] Gray | The osmotic properties of the eggs of the trout (Salmo fario)[END_REF]. Inversely, when eggs are of bad quality, the vitelline membrane is weakened and the water pressure is sufficient to break it. The vitellus is rich in vitellogenin and protein, specifically in globulin. Globulins and vitellogenins are soluble due to the salts contained in the vitellus. But when the membrane breaks, the water enters and salts are diluted resulting in the precipitation of globulins [START_REF] Gray | The osmotic properties of the eggs of the trout (Salmo fario)[END_REF][START_REF] Van Heerden | Effect of excreta, blood and vitellus contamination on fertilisation success of Oncorhynchus mykiss[END_REF] and vitellogenins [START_REF] Engelmann | The native vitellogenin of the cockroach Leucophaea maderae[END_REF][START_REF] Fremont | Biochemical analysis of vitellogenin from rainbow trout (Salmo gairdneri): fatty acid composition of phospholipids[END_REF]. In this case, egg turns white. The presence of white egg was thus interpreted as an indirect measure of vitelline membrane integrity, the "whitening" reflecting the result of water entry into the ooplasm. These white eggs were thus considered as non-viable.

Improvement of female reproductive traits (egg diameter, absolute fecundity, number of viable eggs) through changes in their rearing conditions (feed, temperature, light cycle, etc.) or genetic selection implies an ability to measure the quality of the spawn in a very large number of individuals. The assessment of fish breeding performance requires, in particular, a precise evaluation of the number of spawned eggs but also information on the egg ability to be fertilized and subsequently develop into a viable embryo. Prior to fertilization, it is extremely difficult to estimate differences between good and bad quality eggs in rainbow trout, despite the fact that the characterization of predictive estimators or egg quality markers would have major applications for research and industry [START_REF] Migaud | Gamete quality and broodstock management in temperate fish[END_REF]. For the above reasons, enabling a comprehensive evaluation of egg quality before fertilization is highly desirable in aquaculture. Moreover, during fertilization and incubation, poor egg quality can lead to several problems including insufficient egg hydration, lack of fertilization, developmental arrests, embryonic mortalities and deformities [START_REF] Brooks | Egg quality in fishU: what makes a good eggU?[END_REF][START_REF] Bobe | Egg and sperm quality in fish[END_REF][START_REF] Migaud | Gamete quality and broodstock management in temperate fish[END_REF]. Given the wide variety of the problems observed, it is usually very difficult to determine the causes of embryonic/developmental failure.

In the present study, an automatic phenotyping system based on image analysis was developed to characterize different egg features (number, size) and the occurrence of non-viable eggs in order to separate this cause from other events that may occur later during fertilization or embryonic development. The phenotype measured here is based on the egg ability, specifically the vitelline membrane capacity, to resist to water pressure during hydration process. This method is complementary, yet much more rapid, of a full evaluation of developmental success that is performed on fertilized eggs to separate the origin of egg quality defects (viable eggs vs. non-viable eggs that do not allow developmental success).

Material & methods

Ethical statements

Experimentations were conducted in the INRA PEIMA experimental facility (Sizun, France -Agreement number B29-277-02). All fish were reared and handled in strict accordance with French and European policies and guidelines of the INRA PEIMA Institutional Animal Care and Use Ethical Committee, which specifically approved this study. Fish were monitored daily during the experiment.

If any clinical symptoms (i.e. morphological abnormality, restlessness or uncoordinated movements) were observed, fish were sedated by immersion in MS-222 solution at a concentration of 50mg.L -1 and then euthanized by immersion in a MS-222 solution at a concentration of 400mg.L -1 (anesthetic overdose) during 3 minutes.

Broodstock breeding and experimental design

Female rainbow trout from an autumn-spawning strain were held under natural photoperiod until their first reproduction (2 years) in INRA PEIMA experimental facility. After spawning, fish were transferred into 6 outdoor 2m 3 tanks (initial weight: 1693 ± 306g). Females were fed a commercial trout broodstock diet (Le Gouessant, Lamballe, France) for a period of five months. During this fivemonth period, an artificial photoperiod regime was applied to obtain a second reproduction during summer: a 2.5-month long photoperiod (20 hours light, 4 hours dark from December to March, 2017) followed by a 2.5-month short photoperiod (8 hours light, 16h hours dark from March to June, 2017).

Water temperature during experiment ranged from 6 to 12°C.

Sample acquisition

During spawning season (June 21 th to August 3 rd , 2017), females were checked for ovulation once a week by applying a manual pressure onto the abdomen. When ovulation was detected, fish were given an intraperitoneal injection of an antibiotic (vetrimoxin) to prevent Flavobacterium infection.

Two days after the detection of ovulation, mature females were manually stripped. Eggs were weighted and two samples were taken for fertilization assays and for VisEgg phenotyping analysis. A total of 105 spawns were analyzed individually.

Fertilization assays

For each spawn (i.e. each female, n=105), approximately 400 eggs were fertilized with a pool of sperm collected from males fed ad libitum on a commercial diet and embryonic success was monitored. Fifteen microliters of a pool of semen obtained from five males presenting the highest sperm motility were used, and 15 ml of Actifish solution (sperm motility activating saline solution, IMV technologies, L'Aigle, France) were added onto the eggs. Five minutes later, the sperm motility activating solution was drained and egg batches were transferred into individual incubators in a recirculated water unit. Water temperature (12.0-12.6°C) was monitored daily. Dead eggs and embryos were periodically manually counted and removed. Survival at eyeing, hatching and completion of yolk-sac resorption (YSR) were monitored and were calculated as a percentage of the initial number of eggs used for fertilization. The occurrence of noticeable morphological malformations (spinal cord torsion, head or caudal fin malformations, etc.) at YSR was also recorded.

Phenotyping analysis

For VisEgg phenotyping, unfertilized eggs (20 to 25 grams corresponding to approximatively 400 eggs) were stored in 100 ml container and then water from the incubation system was added to hydrate the eggs (80mL). After a 24-hour hydration at 4°C, a picture of the egg sample was taken using a dedicated commercially available shooting system. This system consisted in a light tablet and a digital SLR camera (canon EOS 1000D, resolution: 10.1 M pixels) (Figure 1). Eggs were rinsed with water and delicately poured into a petri dish (diameter=14cm). The image calibration was performed with an image of 1 euro coin with a known area to calculate the pixel size. The petri dish was then placed on the light tablet. It was verified that the eggs were not superimposed and a picture was taken. An image processing algorithm was developed and coded using a Visual Basic for Applications (VBA) macro with Visilog 7.3 software (Thermo Scientific). This software allows the automatic detection and separation of the eggs in order to make fully automatic measurements of egg number and specific measurement for each egg (size, shape, color, white egg occurrence). The total number of ovulated eggs per females could be back calculated using the number of measured eggs and the total weight of the spawn. The workflow of the VisEgg macro-command is presented in Figure 2. All details and relevant information about the VisEgg image analysis workflow are available here: https://github.com/LpgpImage/VisEgg/wiki.

Statistical analysis

Statistical analysis of the data was carried out using the R software. Percentage data were transformed using an arcsine transformation before analysis. Simple linear regressions were performed to test the correlation between survival rates at different stages. Multiple linear regressions (MLR) were performed to test the correlation between different egg quality parameters measured with VisEgg (i.e. egg diameter, variability of egg diameter and white egg percentage) and hatching rate. MLR was simplified to the minimal adequate model by stepwise removing of nonsignificant elements. The adequacy of the final linear regression has been assessed by making residual plots to check the normality. This showed that nothing was amiss; the analysis was thus validated. Spearman coefficients were calculated.

For statistical analysis performed to compare the two calculating methods of hatching rate (see Figure 5), the normality of data distribution and homogeneity of variance were checked. These conditions were not respected; a Kruskall-Wallis test was used followed by Dunn test's post hoc analysis.

Results & discussion

Automatic assessment of egg features

Evaluating the reproductive performance traits requires counting the eggs and monitoring developmental success. This time-consuming task, performed manually in hatcheries, is particularly tedious. In most cases eggs are weighed and not counted, as the weight is easier to determine. Furthermore, measuring the mean weight of a spawn does not provide information on individual variability within each spawn, which is also an indicator of spawn quality. Using the VisEgg automatic phenotyping tool presented here, we were able to observe differences that would have been overlooked using more simple approaches.

The total egg number is indicator of reproductive performance variability between females as illustrated in Figure 3 for two different females: total egg number can be similar despite a different weight of the spawn. When only the total weight of the spawn is used, the size of the eggs remains unknown. Using VisEgg, it is now possible to measure a large number of eggs very easily. In this study, a very large number of eggs (n=52,000 eggs originating from 105 spawns) were automatically individually measured. This significantly increased the accuracy of the measurement. Using VisEgg we were able to measure individual egg size of all sampled eggs and therefore to estimate intra-spawn variability (i.e. individual egg variability) and inter-spawn variability (i.e. individual female variability).

The distribution of egg diameter obtained with 105 spawns individually analyzed showed values ranging from 3.8 to 5.2 mm with a mean of 4.6 mm. The distribution of the coefficient of variation of egg diameter for all spawns ranged from 2.2 to 9.2% with a mean of 4.6%. These values show a high variability between the spawns analyzed in this study that could not have been observed with a standard technique.

Egg size remains an interesting parameter to measure. Although the possible benefit effect of egg size on egg survival and alevins is still debated, especially under aquaculture conditions [START_REF] Bobe | Egg and sperm quality in fish[END_REF][START_REF] Bromage | Broodstock management, fecundity, egg quality and the timing of egg production in the rainbow trout (Oncorhynchus mykiss)[END_REF][START_REF] Campbell | Stress Reduces the Quality of Gametes Produced by Rainbow Trout[END_REF][START_REF] Jastrebski | Egg size variation in lake trout: phenotype-habitat correlations show an effect of rearing environment[END_REF][START_REF] Migaud | Gamete quality and broodstock management in temperate fish[END_REF]Springate and Bromage, 1985b), it is established that larger eggs produced larger alevins [START_REF] Springate | Effects of egg size on early growth and survival in rainbow trout (Salmo gairdneri richardson)[END_REF] with substantial fitness advantages over small alevins [START_REF] Heath | Rapid evolution of egg size in captive salmon[END_REF]. While egg size is very often measured in studies on fish reproductive performance, it is unusual to observe egg size variability in intra spawn as a measured parameter. This is certainly due to the difficulty of assessing this parameter. Female rainbow trout (Oncorhynchus mykiss) is a groupsynchronous species which produces a single spawn each year where all oocytes develop and ovulate at the same time [START_REF] Lubzens | Oogenesis in teleosts: How fish eggs are formed[END_REF]. In normal conditions, eggs from a single spawn are of homogeneous size; the presence of large egg size variability in intra-spawn for salmonid can be the consequences of a disruption of the physiological processes underlying oogenesis [START_REF] Jastrebski | Egg size variation in lake trout: phenotype-habitat correlations show an effect of rearing environment[END_REF]. The measurement of this parameter therefore appears to be relevant for rainbow trout reproduction studies.

Thus, VisEgg is a convenient and reliable tool to obtain accurate individuals measures, as egg size and variability.

Assessment of egg viability regardless of fertilization and subsequent developmental success

Unfertilized eggs rather than fertilized eggs were used to evaluate our phenotyping tool because hardening process is independent of fertilization [START_REF] Lahnsteiner | Physiological and biochemical parameters for egg quality determination in lake trout , Salmo trutta lacustris[END_REF]. Two distinct phenotypes can be observed after the hydration process. Either the egg hydrates normally and grows slightly or the egg turns white. This phenotype is easily observable on images (Figure 3D). Moreover, VisEgg can separate normal (i.e. viable) eggs from white (i.e. non-viable) eggs and then calculate the percentage of white egg for each analyzed egg batch (Figure 3C).

In this study, multiple linear regression was performed to test the correlation between hatching rate and the different parameters measured with VisEgg (i.e. egg diameter, variability of egg diameter and white egg percentage). Finally, only white egg percentage was significantly correlated with hatching rate. Here, egg size and variability appear to have no link with egg quality and alevins survival (Spearman coefficient=0.39 and -0.30, respectively for egg diameter and variability of egg diameter). Linear regression between white egg percentage and hatching rate shows a significant negative correlation (p-value=2.6 x10 -10 ; Spearman coefficient=-0.56).

It should be noted that we observed highly significant correlations between surviving rates at eyeing and hatching as well as between surviving rates at hatching and yolk-sac resorption (p-value= <2 x10 - 16 , Spearman coefficient=-0.99 for both correlations). Surviving rates at eyeing and YSR are therefore also significantly correlated with the percentage of non-viable eggs (p-value=9.9 x10 -11 , Spearman coefficient=-0.58 and p-value=4.7 x10 -10 , Spearman coefficient=-0.55 for eyeing and YSR, respectively).

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which this version posted May 5, 2020. ; https://doi.org/10.1101/2020.04.21.052472 doi: bioRxiv preprint

The negative correlation between white egg percentage and developmental success was expected because non-viable eggs will not allow successful embryonic development. In addition, the modest coefficient of correlation can be explained by the composite nature of survival rate that includes the capacity of egg to survive in water (i.e. egg viability), to be fertilized and to develop into an embryo (or to die at different times during development). Figure 4 illustrates the successive different origins of egg/embryo failure between spawning and yolk-sac resorption. The graph shows means values obtained using the 105 different spawns analyzed in the present study.

Figure 5A shows the hatching rate calculated using all eggs (in blue) or only on viable eggs (in red), the batches being ranked based on the overall hatching rate (blue dots). The blue and red dots do not follow exactly the same pattern due to differences in the origins of egg/embryo failure up to hatching, with major differences between the two groups for some individuals. In some cases, when the red and blue dots are far apart, there is a high incidence of egg viability on the overall developmental success. In contrast, when the red and blue dots overlap (or are close) there is a low incidence of egg viability on the overall developmental success. Figure 5 (A&B) shows that a high incidence of egg viability is observed for a significant number of females. It should be noted that the importance of egg viability is highly variable as illustrated by significant differences between red and blue dots that can be observed regardless of the overall development success with the exception of high quality spawns (> 80% hatching rate; Figure 5B). In 15.2% of the cases, there is more than 10% of difference between red and blue dots. The percentage of batches over 10% variation between the two calculating methods of hatching rate can reach 50% of the batches for hatching rates ranging from 21 to 40%. While it is not necessarily easy to decipher the causes of egg/embryo failure up to hatching, VisEgg offers the possibility to quantify the percentage of viable eggs. As just an example, four particular cases are shown in figure 6 to illustrate the different causes that can lead to a similar developmental success. Fish A and Fish B present low and equivalent hatching rates (23.0% and 24.3%, respectively). However, Fish A exhibits a high incidence of egg viability (39.6%) on the overall developmental success whereas Fish B exhibits a low incidence of egg viability (0.2%) on the overall developmental success. Similarly, Fish C and Fish D exhibit high hatching rates (65.2% and 69.2%, respectively) but for different reasons: Fish C exhibits a high incidence of egg viability (22.1%) on the overall developmental success whereas Fish D exhibits a low incidence of egg viability (1.1%). These two examples clearly illustrate that similar developmental success (either low or high) can be observed even though the phenotype, and most likely the biological underlying cause, is completely different. The VisEgg tool offers the possibility to separate and quantify the incidence of non-viable eggs on the overall developmental success rather than loosing this information when only developmental success is monitored. This approach is thus complementary of a full evaluation of developmental success that is performed on fertilized eggs to separate the origin of egg quality defects (viable eggs vs. non-viable eggs that do not allow developmental success).

Conclusion

In summary, VisEgg is a convenient, fast, automatic and reliable tool to obtain individual measures of trout eggs. It can be used to assess not only egg size and number but also to assess unfertilized egg viability before fertilization. VisEgg is the first automatic phenotyping tool for egg viability, a key component of egg quality. This tool, developed in rainbow trout, is now being used routinely on trout eggs but it could be adapted to the eggs of other species such as sturgeon. In the future, VisEgg will be adapted to measure other egg characteristics such as color, shape (eccentricity value) and over ripening eggs. Fertilized eggs and survival at eyeing, hatching and YSR are expressed as a percentage of the initial number of eggs used for fertilization. Non-malformed alevins with full completion of yolk-sac resorption are considered as viable alevins. Alevins with noticeable morphological malformations (spinal cord torsion, head or caudal fin malformations, etc.) and dead alevins between hatching and resorption are considered as non-viable alevins (*non-viable or malformed alevins). Supplementary Table 1: Table presenting raw data for all 105 spawns used for the construction of

Figures & Tables

Figure

  Figure 1: The VisEgg system equipment and setup.

1 :

 1 Figure 1: The VisEgg system equipment and setup.

Figure 2 :

 2 Figure 2: The VisEgg workflow.

Figure 3 :

 3 Figure 3: Images of trout eggs as processed by VisEgg. (A) Initial image obtained with VisEgg system equipment presented in Figure 1; (B) Image as processed by VisEgg for an automatic detection and separation of the eggs in order to make fully automatic measurements of egg number and size; (C) Image as processed by VisEgg for an automatic detection of white eggs and normal eggs (white eggs and normal eggs are represented in red and blue color, respectively); (D) Pictures with macro objective illustrating normal and white eggs after hydration.

Figure 4 :

 4 Figure 4: Different causes and relative importance of egg quality defects calculated using VisEgg and embryonic monitoring. Data represent the average percentage values calculated from 105 egg batches followed individually. Viable and non-viable eggs data were obtained with VisEgg system.

Figure 5 :

 5 Figure 5: (A) Hatching rate calculated on number of all eggs (blue) or on only viable eggs (red); (B) Percentage of batches with ≥10% variation between the two calculating methods of hatching rate. Statistical differences were evaluated by Kruskal-Wallis test followed by Dunn test post hoc analysis. Different causes of egg quality defects for FISH A, B, C and D were represented in figure 6.

Figure 6 :

 6 Figure 6: Different causes of egg quality defects that can occur between spawning and yolk-sac resorption in four fish displayed on figure 5. See legend from figure 4 for details on calculation methods.

Figure

  Figure 4 and 5.

Acknowledges

We thank François Guivarc'h for animal care and all the people of PEIMA and LPGP for their help during reproduction season.


El Hadji

Ndongo Diaw

Séverine Le

Gilbert Teyssèdre

Eddy Aubert

M E N Diaw

Current Measurements in High Performance Polymers Used in Aeronautic Cables

Keywords: HVDC aeronautic cables, polymers, PTFE, Polyimide, current measurement

This article presents experimental characterisation of PI (polyimide, Kapton-FN) and PTFE (polytetrafluoroethylene), two polymers used as insulators in aeronautic cables. Current measurements are performed for different electric fields and temperatures, and the current behaviour is analysed with the help of a conductivity law. We then discuss the conductivity law and its optimized parameters.

INTRODUCTION

THE actual main challenge in aeronautic applications is to propose a more electrical aircraft. This (r)evolution is driven by two aspects: An economic one: the use of electrical energy instead of pneumatic or hydraulic energy decreases the weight of an aircraft, which in turn will decrease the fuel consumption 1 . Moreover, electrical energy requires less maintenance compared to hydraulic and pneumatic energies. An ecological aspect: there is a trend to use new and hybrid energies such as hydrogen fuel cells, solar… in order to reduce the ecological footprint.

Three types of energy sources are actually in use in an aircraft to operate auxiliary functions [START_REF] Madonna | Electrical power generation in aircraft: Review, challenges, and opportunities[END_REF]: electric (for navigation instruments, actuator controls, etc), pneumatic (for anti-icing and de-icing system as an example), and hydraulic (for actuation system, flight controls, landing gears and thrust reversers).

The perspective of a more electrical aircraft implies a necessary increase of the embedded power to replace hydroelectric and pneumatic energy by electric energy. DC network seems a potential candidate and has advantages over AC: the transmitted power is higher for the same cable dimension, and presents fewer losses. Low voltage DC (<28 V) has been used for long in the civil aeronautics. This last decade has seen the development of aircrafts (A350, B787) with more embedded electric energy for passenger's comfort but also in avionics (bleedless air regulation, engine start or even brakes controllers [START_REF] Sarlioglu | More electric aircraft: Review, challenges, and opportunities for commercial transport aircraft[END_REF]).

This increase in power level pushes the actual systems to their limits. This is particularly the case for DC cables transmitting the electricity through the aircraft, with environmental constraints that are pressure, temperature, and electrical stress, depending on the area where the cable is located. There are no specific HVDC cables in aeronautics, as it is the case for terrestrial HVDC. The actual cables used for AC and for 270 V DC are the ones that are thought to be used for HVDC (i.e. >540 VDC). In the future, the prospects will be oriented to further increase this voltage level up to 3 kV DC based on existing technologies. Hence, there is a need to understand the dielectric behaviour of the insulating materials constitutive of the aeronautic cables.

DC network presents an advantage over AC in that partial discharge phenomena, which are a real concern for increasing the service voltage in aerospace field [START_REF] Xin | A Study of partial discharge in high voltage DC distribution systems for hybrid electric aircraft[END_REF], are in principle much less active. But, contrary to AC regime, dominated by the capacitive field, under DC, the electric field distribution is driven by the electrical conductivity of the materials. The latter varies in a much more substantial way as a function of temperature, electric field, or material than permittivity. As a result, the field distribution is much more difficult to anticipate.

Looking at the literature on HVDC cables for the submarine or terrestrial transmission of electricity, where polyethylene (PE) is the main insulating material, the electrical conductivity is strongly dependent upon electric field (non-linear behaviour) and temperature. Moreover, many works [START_REF] Montanari | The electrical degradation threshold ofpolyethylene investigated by space charge and conductioncurrent measurements[END_REF] have revealed the accumulation of space charge in the insulator, leading to local strengthening of the electric field compared to the geometric field. The same kind of conclusion is encountered in the literature for materials such as polyimide (PI) or polytetrafluoroethylene (PTFE) [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], that are materials also used as insulation in domains such as microelectronics or space applications.

The aim of the present work is to characterize the behaviour of two materials used as insulators in the actual aeronautic cables, and analyse it using well known equations of the literature [START_REF] Dissado | Electrical Degradation and Breakdown in Polymers[END_REF]. To do so, different experimental protocols have been used to get the widest range of electric fields and temperatures. A conductivity law is then proposed and is discussed as regards known injection/conduction processes.

METHODS

INVESTIGATED MATERIALS

Most of aeronautic cables are made of a combination of PI and of fluorinated polymers such as PTFE, providing the insulation respectively with high thermal and electrical insulation properties [START_REF] Hondred | Electrothermal lifetime prediction of polyimide wire insulation with application to aircraft[END_REF][START_REF] Huang | Morphological evolution of polytetrafluoroethylene in extreme temperature conditions for aerospace applications[END_REF] and resistance to arc tracking and fire propagation. Figure 1 shows an example of cross-section of a cable used for power transmission in aircraft. It consists of metal strands and different layers of insulation (inner layer: PI of 60 µm and outer layer: PTFE of 200 µm thickness) wrapped around the conductor, of rough diameter about 3.70 mm. The exact insulation thickness depends on the number of tapes, which is not the same all over the circumference.

PI samples used in the present study were provided in the form of films of thickness ranging from 30 up to 36 µm. The size of each sample is approximately 4x4 cm². The type of PI used is a Kapton® FN, which is a Kapton® HN type covered on both sides by FEP (fluorinated ethylene propylene) polymer layers [START_REF] Mckeen | Polyimides[END_REF], having a thickness of ≈2.5 µm each. This FEP layer allows having a good adhesion between PI and PTFE during cable manufacturing.

PTFE samples used were also provided in the form of films of thickness ranging from 72 up to 77 µm. The size of each sample is approximately 4x4 cm². As-received PTFE samples are not sintered, unlike PTFE on real aeronautic cables, which has been thermally treated during cable manufacturing. Sintering was performed in the laboratory for all PTFE samples in an oven at 360°C for 5 to 10 min in order to obtain samples representative of materials in operation.

DSC MEASUREMENTS

Differential Scanning Calorimetry (DSC) was performed on PTFE samples to verify that the thermal treatment (sintering) achieved at lab scale provides a material with the same structural properties as the PTFE used for aeronautic cables, with sintering realized during cable production. This is also to verify if the sintering conditions have an impact on the physical properties of PTFE. Sintering does not change the structure of PI, so DSC measurements are not proposed for PI in the present paper. Information such as the melting, crystallization and glass transition temperatures of the sample can be determined. Measurements were achieved using a TA DSC 2010 CE differential scanning calorimeter, using samples having a weight of 8 mg. For each measurement, two temperature scans are performed, the first to erase the "thermal history" of the sample and the second to provide information on the thermal transitions. For this study, temperature ranges from -50 °C to 400 °C for a temperature ramp of 10 °C/min with a return to 20 °C. The degradation temperature of PTFE is 420 °C, so upper temperature is limited to 400 °C in our study.

CURRENT MEASUREMENTS

Current measurements were realized on PI and PTFE samples, metallized on both sides with 50 nm-thick gold layer of diameter 20 mm, deposited by cold plasma sputtering. A silicon ribbon is added at the periphery of the electrodes to avoid electric field enhancement due to edge phenomena, possibly leading to breakdown. PI or PTFE samples are sandwiched between two plane parallel brass electrodes, and measurements are performed under air at atmospheric pressure. The current is recorded through a Keithley 617 ammeter with a 2 s dwelling time. Investigated materials have a really low conductivity and questions of noise level was addressed. A low ripple 35 kV DC supply from Fug GbmH was used as voltage source. The lowest detectable current above noise was estimated to 0.2 pA in the environment used.

Two different protocols have been applied on each material. The first protocol consists in applying, at a constant temperature, cycles of 3 hours of polarization and 3 hours of depolarization (voltage set to zero) for electric fields ranging from 4 up to 160 kV/mm for PTFE, and from 1 up to 120 kV/mm for PI. The difference of maximum applied electric field is due to the dielectric breakdown strength of each material. This protocol (cf. Figure 2a as an example for PTFE), performed on an automatized set-up, has been applied for temperatures of 20, 50, and 90 °C. A new sample is used for each temperature.

The second protocol has been used to characterize each material at higher temperatures, on a non-automatized set-up. The protocol, presented on Figure 2b has been applied for temperatures ranging from 100 up to 200°C, and for a low (20 kV/mm) and a high applied electric field, being 100 kV/mm for PI and 140 kV/mm for PTFE. It is to note that for this protocol also, the depolarization cycle consists in applying a zero voltage at the electrode, i.e. the sample is not shortcircuited. A new sample is used for each electric field value. It is difficult in practice to obtain the steady state current in highly insulating materials. For example, Ghorbani et al. showed that the DC current in polyethylene under constant field at moderate temperature could evolve for months [START_REF] Ghorbani | Long-term conductivity decrease of polyethylene and polypropylene insulation materials[END_REF]. Stressing for long time may involve space charge build-up and field redistribution in a way that it is not clear of which field the obtained current is representative. Here, time under voltage application has been set arbitrarily to three hours, which is almost the longest time intervals published in the literature for PI [START_REF] Sharma | Electrical conduction in Kapton polyimide film at high electric fields[END_REF][START_REF] Sessler | Electrical-conduction in polyimide films[END_REF].

EXPERIMENTAL RESULTS

DSC ON PTFE

Figure 3 presents the DSC thermograms obtained from a PTFE sintered at lab scale, and a PTFE taken from a real cable, for the second temperature scan. The peaks representing the different thermal transitions for each sample appear at the same temperatures. When the sample is heated, the first characteristic temperatures are observed at 18.14°C and at 31.4°C and correspond to crystalline PTFE transitions, between triclinic and hexagonal crystalline systems [START_REF] Khanna | The melting temperature of polytetrafluoroethylene[END_REF]. The melting temperature of the sample is 324.4 °C and characterizes the disappearance of the crystalline phase of PTFE [START_REF] Khanna | The melting temperature of polytetrafluoroethylene[END_REF]. At this temperature, PTFE turns into a viscous liquid.

During cooling, a peak of crystallization is observed at a temperature of 313.7 °C, for all samples. From Figure 3, the sintered material at lab scale and the cable material have the same thermal transitions, and the same melting temperature. DSC also allows calculating the crystallinity of the material, by integrating the area under the curve. The crystallinity of a lab sintered material is of the order of 33% (mean of three measurements), while the one of the PTFE from cable is 33.5%. The difference is within experimental error. It is to note that several sintering durations have been tested (from 5 to 8 min), giving the same thermal characteristics as the one presented in Figure 3 for a lab sintered PTFE, and the same thermal transitions. The degree of crystallinity and the different thermal transitions are also consistent with data found in the literature [START_REF] Khanna | The melting temperature of polytetrafluoroethylene[END_REF]. The sintering performed in the lab allows obtaining PTFE sample having the same physical properties than the one encountered directly on an aeronautic cable. A second behaviour is observed for higher temperatures (140 and 180°C on Figure 4). For these temperatures, the current density is higher than for lower temperatures. It also presents two slopes: a first slope at short time, with a slow decrease of the current density, while at longer times, the slope is larger. For these high temperatures, the current does not tend to stabilize, even after 3 hours of applied voltage.

CURRENT MEASUREMENTS ON PI

These differences in the current transient behaviour at different temperatures are certainly linked to different dominant processes. Current vs. time curves have been analysed in the literature, for HVDC terrestrial cable materials [START_REF] Steven | Conductivity measurements and space charge inference in polymeric-insulated HVDC model cables[END_REF]. Polarization processes, linked to polar species, have been proposed as the dominant process at low temperatures, as conduction and/or injection processes do not contribute significantly to the current. At higher temperatures, polar contribution to current dominate at short times, but rapidly conduction becomes the dominant process. The same kind of hypotheses could hold in the case of PI, as PI is a polar material. Comparing polarization currents to depolarization currents (not presented here) strengthens the hypothesis that conduction processes are dominant for electric fields above 40 kV/mm at 20°C. It is however difficult in the present case to decipher if conduction arises from ionic of electronic species, as it has been proposed in the literature that ions may be present and participate to conduction [START_REF] Sharma | Electrical conduction in Kapton polyimide film at high electric fields[END_REF]. Many hypotheses have been proposed in the literature to interpret DC current behaviour in PI, ranging from dipolar processes, to interface processes (injection), or to volume processes (Poole-Frenkel, ionic conduction….) [START_REF] Sharma | Electrical conduction in Kapton polyimide film at high electric fields[END_REF][START_REF] Segui | Electrical conductivity of poly (amide-imide) films[END_REF][START_REF] Sessler | Electrical-conduction in polyimide films[END_REF]. However, these studies have been performed on different types of PI for different experimental protocols of voltage application, and most importantly various times under voltage application, ranging from 300 s to some hours. Our purpose here is only to highlight that for all temperatures, for relatively low to high electric fields, the current is thought to be dominated by conduction processes.

To strengthen this hypothesis, the current density has been plotted as a function of electric field for low temperatures (20, 50 and 90°C) and is presented in Figure 5. Each current value is the mean of the currents over the last 2 minutes of the 3 h recording time at each voltage step. The feature current/electric field shows two regions separated by a threshold situated at 40 kV/mm. For electric fields lower than 40 kV/mm, there is a slow increase of current, with a calculated slope in a log-log plot around 1. PI is thought to have an ohmic behaviour for fields below 40 kV/mm [START_REF] Motyl | On the electrical conduction in polyimide[END_REF]. For electric fields higher than 40 kV/mm, the slope is over 3 (3.36). Considering the Space Charge Limited Current (SCLC) theory [START_REF] Dissado | Electrical Degradation and Breakdown in Polymers[END_REF], the second slope is not linked either to a space charge limited region (slope normally equal to 2) or a trap filled limited region. However, depending on the physical processes at play (injection, transport of electronic, ionic species, trapping…), values of the slopes can differ from the theory. For all measured field values, there is no difference of conductivity value for temperatures in the range 20-90 °C, i.e. conductivity is not evidently temperature dependent for temperatures below 90 °C. The threshold in electric field appears at about 40 kV/mm in all cases.

To evaluate the dependence of conductivity on temperature, the current density has been measured as a function of temperature up to 200 °C for two electric fields (Figure 6), choosing a low electric field (20 kV/mm), in the first region of Figure 5, and a higher electric field (100 kV/mm), in the second region of Figure 5. At 20 kV/mm, for temperatures below 120°C, the current seems constant. Above this temperature value, the current tends to increase. At 100 kV/mm, the threshold in temperature is observed at around 100°C. In the literature, several reports are available on the behaviour of PI under thermo-electrical stress [START_REF] Motyl | On the electrical conduction in polyimide[END_REF][START_REF] Sharma | Electrical conduction in Kapton polyimide film at high electric fields[END_REF][START_REF] Segui | Electrical conductivity of poly (amide-imide) films[END_REF][START_REF] Sessler | Electrical-conduction in polyimide films[END_REF], but the materials and experimental protocol differ from the ones used the present study. Motyl et al [START_REF] Motyl | On the electrical conduction in polyimide[END_REF] reported on a threshold in current-field characteristic for all temperatures; this threshold value decreases when the temperature increases, to reach 40 kV/mm at 160°C. A threshold in temperature is reported at 110°C for a field of 100 kV/mm, moved to 160°C under 20 kV/mm. The behaviour of this material is not far from Kapton-FN used in the present study, regarding the temperature threshold, but differs slightly when looking at the electric field threshold.

CURRENT MEASUREMENTS ON PTFE SAMPLES

The same kind of measurement has been performed for PTFE samples using the same two protocols.

Figure 7 shows current transients as a function of time for various electric fields applied on PTFE sample at a fixed temperature (20°C). Current trend is decreasing and shows two different zones: one of sharp decrease and another in which current decreases more slowly and does not seem to stabilize at long times. This slope break depends on electric field as it appears earlier when the applied electric field is increased. At longer times, the current seems to stabilize only for the highest electric field after 3 hours of polarization. Nevertheless, the higher the value of the electric field, the more the current seems to be moving towards a stationary value.

Figure 8 presents the current density versus electric field obtained for different temperatures on PTFE samples. Current density increases according to the electric field. A threshold in field appears at 100 kV/mm, i.e. at a higher value than the one observed for PI. The first slope (below 100 kV/mm) is also 1, i.e. PTFE has an ohmic behaviour up to relatively high applied electric fields, while the second slope is steeper, of the order of 5.8. For the tested temperatures, ranging from 20 to 90°C, the current seems temperature independent. Current has also been measured for temperature values above 90°C, for two applied electric fields only, to investigate the impact of temperature on electrical conductivity. Figure 9 shows current density as a function of temperature for each applied electric field (20 kV/mm and 140 kV/mm in the case of PTFE).

At 20 kV/mm, the current varies slightly with temperature. It is however difficult to discriminate if these variations are due to the measurement error, or if there is a real increase of the current for temperatures above 150°C. For an applied field of 140 kV/mm, it becomes clear that two regions appear, separated by a threshold at around 90°C.

In the literature, the electrical properties of PTFE were particularly investigated with current measurements, although it is not clear if the material under study is the same PTFE as the one measured in this paper. As an example, for PTFE samples of 130 µm thickness metallized with silver electrodes, Sussi et al [START_REF] Sussi | Electrical conduction currents in polytetrafluoroethylene[END_REF] measured the current as a function of electric fields, for fields up to 25 kV/mm and temperatures ranging from 40 up to 200°C. They observed three different regions in the J-E behaviour, with an ohmic regime measured below an applied field value of 2 kV/mm. These data are far from our experimental values.

PTFE samples of 50 µm thickness, metallized with aluminium electrodes and placed in an oil bath, have also been characterized using current measurement at high electric fields (10 up to 400 kV/mm) and low temperatures (up to 40°C) [START_REF] Lee | Nonlinear conduction properties of polytetrafluoroethylene film[END_REF]. The J-E characteristic obtained with these measurements shows four regions. At 20°C, the electric field thresholds [START_REF] Lee | Nonlinear conduction properties of polytetrafluoroethylene film[END_REF] are located at 20 kV/mm, 100 kV/mm and 200 kV/mm. For electric field below 20 kV/mm the conduction current is ohmic. The second region is assigned to Poole-Frenkel effect. For an electric field between 100 and 200 kV/mm, the current is attributed to Schottky effect and region 4 seems to be tunnelling current (Fowler-Nordheim effect) [START_REF] Lee | Nonlinear conduction properties of polytetrafluoroethylene film[END_REF]. These different threshold values decrease with the increase in temperature. According to our results, there is only one threshold, appearing at 100 kV/mm at 20°C as an example. It may correspond to the second threshold reported in reference [START_REF] Lee | Nonlinear conduction properties of polytetrafluoroethylene film[END_REF]. This different behaviour can be due to the fact that the nature of PTFE or the measurement conditions are not similar to ours. It is however difficult to find studies in the literature that report on the current at the same time at high fields and high temperatures, in the same experimental conditions (gold electrodes).

ELECTRICAL CONDUCTIVITY LAW FOR MATERIALS

A large number of equations can be found in the literature to describe the dependence of conductivity versus field and temperature of dielectric materials. Experimental data have clearly pointed out conductivity processes at high electric fields/ high temperatures, for both materials. As it is difficult to segregate injection-controlled processes from bulk-limited conduction processes, injection processes such as Fowler-Nordheim or Schottky have been applied to our experimental data. Although these equations could fit the current-field characteristic for a specific temperature, the difference increases when the temperature increases. Hence, the current density behaviour cannot be approximated using charge injection equations. Conductivity laws have been applied to the experimental data, and among them one can cite [START_REF] Morshuis | Calculation and measurement of space charge in MV-size extruded cables systems under load conditions[END_REF][START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]:

𝜎(𝑇, 𝐸) = 𝐶 𝑒𝑥𝑝 - 𝐸 𝑘 𝑇 𝑠𝑖𝑛ℎ(𝐷(𝑇)𝐸) 𝐸 (1)
𝜎(𝑇, 𝐸) = 𝐶 𝑒𝑥𝑝 - 𝐸 𝑘 𝑇 𝑠𝑖𝑛ℎ(𝐷(𝑇)𝐸) 𝐸 (2)
𝜎(𝑇, 𝐸) = 𝜎 𝐸 𝐸 𝑒𝑥𝑝 𝛽(𝑇 -𝑇 ) ( 3
)
where T is the temperature, kB the Boltzmann's constant, E the electric field, Ea an activation energy, D(T) a temperaturedependent parameter, γ a constant, Eref the reference electric field, σref the reference electrical conductivity, Tref the reference temperature. Equation ( 1) is directly linked to a physical process (hopping mechanism [START_REF] Steven | Conductivity measurements and space charge inference in polymeric-insulated HVDC model cables[END_REF]). Equation ( 2) is derived from Equation (1), while Equation ( 3) is with less obvious link with physical processes at play in the dielectric. Figure 10a) presents the above equations applied to current density vs. electric field for PI at a temperature of 50°C. Parameters used for the different equations are presented in Table 1. Equation (3) clearly differs from experimental data at low fields, while equation ( 2) correctly fits the experiment. This is an expected result as regards the non-linear behaviour (log-log scale) of the experimental current density as a function of electric field. Figure 10b) presents the current density vs. reciprocal temperature for the different equations under study, for PI. On the contrary of Figure 10a), for Figure 10b) equation ( 3), with an exponential associated to the temperature, seems to better fit the experimental data for a specific electric field (100 kV/mm). None of these equations correctly fits our experimental data, for PI. The same is also true for PTFE (not shown here). Hence, another equation is proposed to fit electrical conductivity for PI and PTFE:

𝜎(𝑇, 𝐸) = 𝐴 1 + 𝑒𝑥𝑝 𝐵(𝑇 -𝑇 ) (1 + ( 𝐸 𝐸 ) ) (4)
The parameters of Equation ( 4), A, B, T0, E0 and α, are constants, and detailed in Table 1 for each material. Figure 10a presents the comparison of model/experimental current densities for PI as a function of electric field for a temperature of 50°C. With Equation ( 4) and parameters from Table 1, simulation results are consistent compared to experiment over the range of electric fields under study. This holds for temperatures ranging from 20 up to 90°C. It is also the case for current density as a function of temperature (1000/T) for an electric field (100 kV/mm), as equation ( 4) is the one that better reproduce the experimental data on Figure 10b). The same holds for a lower electric field. For PTFE, experimental and fitted data are compared in Figure 11a as a function of applied fields for a low temperature, and in Figure 11b as a function of temperature for low and high electric fields. At low temperature (Figure 11a), the variation of conductivity with electric field is well reproduced. The agreement between model and experimental data at higher temperature for fixed electric fields (Figure 11b) is fairly consistent for a high electric field, but not for 20 kV/mm, where the conductivity is almost constant. For this electric field, the fit is consistent for low temperatures, but diverges from experimental data when the temperature increases to reach a conductivity that is a decade higher than the experimental one.

One must question about the validity of the model as well as the experiments for the difficulty in identifying a model for PTFE. Regarding experiments, obtained currents are larger than the detection limits of the set-ups (cf. case of PI), therefore it seems not the limiting factor. The second possibility is material modification during experiments due to thermal conditioning. Humidity variation, morphological evolution are possible reasons. This seems unlikely here as PTFE is hydrophobic material, and sintering was applied before measurements, meaning that stabilization of the structure has occurred. The last potential reason is, as discussed previously, the necessary limitation in time of the measurements and therefore the possibility that different processes are dominant at different time scales, depending on the temperature. This makes the link with questioning about the model. Equation ( 4) that is used to fit experimental current density is composed of two parts. The first part describes temperaturedependence of electrical conductivity. The function that has been used does not include a thermal activation energy with Arrhenius law but accounts for a temperature threshold and temperature dependence of conductivity beyond the threshold. The function for the electric field dependence is defined by a power law in field above a given threshold, consistently with previous expressions and following the classical way of interpreting current-field characteristics. The chosen expression assumes that there is no simple /dominant process governing the macroscopic conduction, amongst those found in the literature with different formulas reflecting Schottky emission, Poole-Frenkel or other mechanisms. It globally fits all experimental data.

As such, Equation (4) decouples temperature and field effects. It means that a temperature dependent field threshold for nonlinear conduction for example, as was reported elsewhere for other materials [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF] cannot be reproduced unless parameters of the equation become temperature dependent. At present data on PI or PTFE are not enough documented for introducing such effect.

Looking at the parameters of Table 1, A is a constant that describes the initial electrical conductivity value when field is very low and temperature is low. T0 defines the threshold at which conductivity begins to increase with temperature and B the rate of increase of conductivity beyond this threshold. At the level of electric field dependence of conductivity, E0 defines the field threshold for non-linear conductivity and α reflects the rate of change of conductivity beyond this field. At the temperature or field threshold, the conductivity becomes twice as the one at low field/low temperature. This provides an easy way to compare the characteristics of different materials. The dielectric permittivity is lower (i.e. more favourable for electrical insulation purpose) in PTFE (r = 2.1 [START_REF] Li | Dielectric properties of aged polymers and nanocomposites[END_REF]) compared to PI (r = 3.4 [START_REF] Mckeen | Polyimides[END_REF]). The temperature threshold is lower (80°C) for PI compared to PTFE (106.7°C), which reflects the difficulty in establishing a clear temperature dependence of conductivity for PTFE. Regarding the field threshold, it is substantially higher for PTFE (130 kV/mm) compared to PI (60 kV/mm). Therefore, although the low field / low temperature conductivity is about twice in PTFE compared to PI, the former seems to have better DC insulation performances. A further criterion regarding performances is the breakdown strength. It is well known that values are extremely dependent on the insulation thickness, on sample area and on test methodology [START_REF] Diaham | Dielectric breakdown of polyimide films: Area thickness and temperature dependence[END_REF]. DC breakdown strength beyond 600 kV/mm has been reported both for PI and PTFE for films thicknesses in the range 5 to 25 µm [START_REF] Min | Thickness-dependent DC electrical breakdown of polyimide modulated by charge transport and molecular displacement[END_REF][START_REF] Kerwien | Large area DC dielectric breakdown voltage measurement of BOPP and PTFE thin films[END_REF], indicating high performances for both materials. However, there is no available parallel study on breakdown strength and its temperature dependence realized in similar conditions. Such analysis would be interesting in parallel to conductivity measurements since thermal breakdown is one of the possible breakdown process [START_REF] Nagao | Dielectric breakdown of polyimide film in high temperature region[END_REF] aside spacecharge induced breakdown [START_REF] Li | Space charge modulated electrical breakdown[END_REF].

CONCLUSIONS

Current measurements have been performed for PI and PTFE materials, both used as insulation in HVDC aeronautic cables, in order to characterize their behaviour as regards electric field and temperature. The current/field characteristics show a threshold in field at around 40 kV/mm for PI and at 100 kV/mm for PTFE, for relatively low temperatures up to 90°C. According to the results on PI, the threshold in temperature is at around 160°C and 110°C respectively for 20 kV/mm and 100 kV/mm. From these experimental data, a conductivity law has been found to better fit the experimental characteristics of both materials. Although PTFE shows no variation of conductivity at low fields over the range of tested temperatures, there is a threshold in temperature for higher fields. These experimental data need to be strengthened for a larger number of electric field values for the tested range of temperatures. The conductivity law will also serve as an input in a macroscopic model to simulate the electric field distribution and interfacial charge accumulation in real cable geometries to understand the electric field behaviour in aeronautic cables under thermoelectric stress.

Figure 1 .

 1 Figure 1. Example of cross-section of an aeronautic cable (DR8). The inner black layer is taped polyimide insulation, 60 µm thick; the outer layer is taped PTFE, 200 µm thick. The rough diameter of the conductor is 3.70 mm.

Figure 4

 4 Figure 4 presents normalized current densities (i.e. apparent transient conductivity) as a function of time for different applied electric fields and temperatures on PI films. For each electric field (20 and 100 kV/mm), two behaviours are observed. The first one is relevant to relatively low temperatures where the current density presents two regions: a fast decrease at short times, and a second region at longer times where the decrease of the current is slower. This behaviour is clearly observed for temperatures below 120°C, although only 50 and 90°C data are presented on Figure 4. For this first behaviour, when the temperature increases (from 50 to 90°C) the change in slope appears earlier in time. Comparing the data for a specific temperature, the current density increases when the electric field increases.A second behaviour is observed for higher temperatures (140 and 180°C on Figure4). For these temperatures, the current density is higher than for lower temperatures. It also presents two slopes: a first slope at short time, with a slow decrease of the current density, while at longer times, the slope is larger. For these high temperatures, the current does not tend to stabilize, even after 3 hours of applied voltage.These differences in the current transient behaviour at different temperatures are certainly linked to different dominant processes. Current vs. time curves have been analysed in the literature, for HVDC terrestrial cable materials[START_REF] Steven | Conductivity measurements and space charge inference in polymeric-insulated HVDC model cables[END_REF]. Polarization processes, linked to polar species, have been

Figure 2 .

 2 Experimental protocols used for current measurements on PI and PTFE. a) protocol n°1 consisting of cycles of polarization/depolarization of 3 hours for PTFE, for low temperatures (20 up to 90°C; b) protocol n°2 consisting in applying a voltage at temperatures above 90°C.

Figure 3 .

 3 Figure 3. DSC results for PTFE samples.

Figure 4 .

 4 Figure 4. Normalized current densities as a function of time for different electric fields and temperatures on a 36 µm thick PI film.

Figure 6 .

 6 Figure 6. Current density versus temperature for two applied fields (20 kV/mm and 100 kV/mm) for PI.

Figure 8 .

 8 Figure 8. J-E for different temperatures (20, 50, 70 and 90°C) for PTFE.Figure 5. Current density versus electric field for different values of temperature (20, 50 and 90°C) for PI.

Figure 5 .

 5 Figure 8. J-E for different temperatures (20, 50, 70 and 90°C) for PTFE.Figure 5. Current density versus electric field for different values of temperature (20, 50 and 90°C) for PI.

Figure 9 .

 9 Figure 9. Current density versus temperature for different electric field (20 kV/mm and 140 kV/mm) on PTFE.

Figure 7 .

 7 Figure 7. Charging current as function of time for different electric fields at 20°C on PTFE.

  a) Current-field characteristic b) Current-temperature characteristic Figure 11. Fitted and experimental current density for PTFE.

Table 1 .

 1 Parameters for electrical conductivity laws.

	Equations	Parameters	PI	PTFE
		A (S/m)	2.3×10 -16	4.5×10 -16
		To (°C)	80.5	106.7
	Equation (4)	B (°C -1 )	0.04	0.04
		Eo (kV/mm)	60	130
		α	3.49	6.97
		σref (S/m)	8.92×10 -18	2.71×10 -18
		Tref (°C)	22.3	22
	Equation (3)	Eref (kV/mm)	18.2	79.2
		β	0.04	0.022
		ν	2.5	5.7
		C	0.14	22.5
		D (m/V)	3.68×10 -8	3.3×10 -8
	Equation (2)	Ea (eV)	0.71	0.41
		γ	-0.51	-0.58