T T N Vu

L Berquez

G Teyssèdre

Space charge measurement by electroacoustic method: impact of acoustic properties of materials on the response for different geometries

Keywords: Pulse electroacoustic method, deconvolution, acoustic properties, dielectrics, space charges

The pulsed electro-acoustic method (PEA) allows dynamic measurements of space charge density distribution with good temporal resolution and is suitable for both flat samples (a few hundred micrometers thickness) and coaxial cable samples. The response obtained by the technique is tributary to the electromechanical properties of the materials through which acoustic waves propagate. Hence, when dealing with multilayer dielectrics, the acoustic properties of individual layers are to be taken into account. Also, the acoustic attenuation and dispersion phenomena, especially when dealing with relatively thick samples, affect the space charge resolution at positions far away from the sensor. Therefore, application of a calibration procedure on experimental signals is necessary to recover space charge density profile from PEA raw signals and to provide real results on charge density both on its temporal and spatial dependence. We illustrate here in different samples configurations, spanning from flat samples, multi-layer and cable geometry, how the calibration is achieved and how the acoustic properties of materials impart the response.

Introduction

The need for knowledge about space charge formation and accumulation mechanisms in insulating materials led to the development in past decades of new measurement techniques giving access to spatial distribution of charge density -and thus of electric field. The low mobility of carriers in polymeric insulators allows non-destructive spatially resolved measurement of charge density. These non-destructive techniques, with spatial resolution, include three families according to the nature of perturbation introduced to probe charges [START_REF] Miz Tani | Space charge measurement techniques and space charge in polyethylene[END_REF][START_REF] Ditchi | Non-destructive methods for space charge distribution measurements: what a e the diffe ences?[END_REF]: methods based on thermal perturbation of various shape (Thermal Pulse, Light Intensity Modulation Method, Thermal Step), acoustic wave (Piezoelectrically Induced Pressure Wave, Laser Induced Pressure Pulse) and electric field pulse in pulsed electro-acoustic method (PEA). These three groups of non-destructive techniques are based on the same principle in which a non-homogeneous perturbation of the electrostatic state (elastic forces in case of PEA) is introduced by an external stimulus [START_REF] Notingher | An insight into space charge measurements[END_REF].

In the group of thermal methods, diffusion of heat is used to modify the equilibrium of charges through permittivity variation and volume expansion and thus induce an electrical response. Acoustic methods use deformation produced by propagation of pressure waves to modify the electrostatic equilibrium and to induce an electrical signal. Finally, the electro-acoustic method relies on an excitation by electric field pulses; the electrostatic force produced by interaction with the charges generates a mechanical response. Various techniques currently make it possible to establish charge density distribution in polymer insulators; however, depending on the technique used, each type of measurement technique has advantages and drawbacks.

The PEA method was developed in 1985 by Japanese researchers (T. Maeno, T. Takada and their collaborators [START_REF] Takada | Meas ement of elect ic fields at a dielectric/electrode interface using an acoustic t ansd ce techniq e[END_REF], [START_REF] Maeno | Meas ement of spatial charge distribution in thick dielectrics using the pulsed electroacoustic method[END_REF]). The method consists of applying electric field pulses (of the order of 1 kV/mm) of very short duration (of the order of one nanosecond) through a sample. The production of a Coulomb type force induces a transient elementary displacement of the charge cloud around its equilibrium position. Then, two acoustic waves, of amplitude proportional to the quantity of charges, are generated. One is in extension; the other in compression and they propagate in opposite directions.

One of these pressure waves is detected by means of a piezoelectric sensor (lower electrode) which converts the acoustic signal into an electrical signal. The electrical signal is amplified before being recorded using a digital oscilloscope. Adequate signal processing then makes it possible to recover the space charge density profile.

The PEA method has the advantage of being able to perform measurements in the presence of external voltage (DC or AC). It is therefore perfectly suited to study the mechanisms of injection and transport of charges in the insulation of high voltage cables [START_REF] Hoz | Di ect obse ation of time-dependent space charge profiles in XLPE cable under high electric fields[END_REF].

In the case of conventional PEA method, for flat specimen, the sample is placed between two electrodes (Figure 1). The upper electrode is made of a semiconducting material, i.e. a polymer doped with carbon black particles having acoustic properties approaching those of the polymeric sample such as to minimize wave reflections at the interface with the sample. This electrode is connected to the high voltage power supply and the pulse generator. The lower aluminium electrode is connected to ground. A piezoelectric sensor, usually Poly (Vinylidene Fluoride) -PVDF, with some attempts of using Lithium Niobate material with higher thermal withstanding [START_REF] Kitajima | Measurement of space charge distribution at high temperature using the pulsed electro-acoustic (PEA) method[END_REF], is placed under the lower electrode and converts the acoustic wave into an electrical signal. Finally, under the piezoelectric sensor is placed an acoustic absorber usually made of poly(methyl methacrylate) -PMMA intended to produce only a positive reflection, which allows to remove a pole in the sensor response.

The principle of the PEA technique for cables (coaxial geometry) is similar to that of the conventional PEA method. However, the space charge recovery technique for PEA cable needs to take into account cylindrical geometry, along with the attenuation and the dispersion of the acoustic waves when the insulation is relatively thick.

Sensor response

According to the scheme given in Figure 1, acoustic waves generated by a sheet of charges propagate in opposite directions, one of them being directed towards the piezoelectric sensor. We designate by p Al (t) the pressure wave reaching the interface between the Al ground electrode and the piezoelectric sensor. We consider first how the acoustic waves are converted into an electrical signal.

A. Piezoelectric sensor response

When entering in the PVDF, the acoustic wave generates at point z' (z'=-x + d Al , cf. Figure 1) a polarization P P (z') proportional to the mechanical stress. Therefore, the voltage at PVDF bounds in open circuit conditions is given by [START_REF] Bernstein | nalysis of the electrically stimulated acoustic-wave method for observing space charge in semiinsulating films[END_REF]: [START_REF] Miz Tani | Space charge measurement techniques and space charge in polyethylene[END_REF] where g 33 is the piezoelectric coefficient,  Piezo the sensor dielectric permittivity and L T its thickness.

The pressure inside the sensor is related to that at its entrance by: Absorber (PMMA)

-d Al Piezoelectric sensor (PVDF) Lower electrode (Aluminium)
Surface charges

Volume charges

Surface charges

+ + + + + + + + + + + (d)

----------------(0)

+ + + + (z) Sample V DC & V pulse Upper electrode (SC) p Al (t) 0 x d d DC Position L T z' 0 L T 0 (2)
where T Al-PVDF is the transmission coefficient of acoustic wave at Al/PVDF interface and  Piezo is the sound velocity. Writing:

(3) we obtain: [START_REF] Takada | Meas ement of elect ic fields at a dielectric/electrode interface using an acoustic t ansd ce techniq e[END_REF] This can be written as the convolution between the transfer function of the piezoelectric sensor h(t) and pressure entering in the sensor p Al (t). If the response of the piezoelectric sensor is homogeneous along its thickness, h(t) can be considered as a rectangular window function : V i (t) is given, with a coefficient, by a convolution equation: [START_REF] Maeno | Meas ement of spatial charge distribution in thick dielectrics using the pulsed electroacoustic method[END_REF] with [START_REF] Hoz | Di ect obse ation of time-dependent space charge profiles in XLPE cable under high electric fields[END_REF] Expression [START_REF] Maeno | Meas ement of spatial charge distribution in thick dielectrics using the pulsed electroacoustic method[END_REF] allows qualitative analysis of the effect of the piezoelectric sensor thickness on signal V i (t). To simplify our analysis, the pulse is assumed of a rectangular type.

B. Transducer response (Piezoelectric sensor + Amplifier)

One face of the piezo sensor is connected to a broadband amplifier having an input impedance R E of 50Ω. The transducer can be modelled by the RC circuit of Figure 2 [START_REF] Bernstein | nalysis of the electrically stimulated acoustic-wave method for observing space charge in semiinsulating films[END_REF].

The impulse response of the circuit (high-pass) is given by: [START_REF] Kitajima | Measurement of space charge distribution at high temperature using the pulsed electro-acoustic (PEA) method[END_REF] where  e = R E .C 0 , C 0 is the effective capacity of the transducer. u(t) is a step function. Therefore, the response V S (t) at the output of the amplifier is: The transducer produces a voltage by integrating stress across its thickness (cf. Eq. 5) which is then detected through the high-pass filter [START_REF] Bernstein | nalysis of the electrically stimulated acoustic-wave method for observing space charge in semiinsulating films[END_REF]. The frequency response of the transducer depends on the transit time and the time constant . Depending of these two time constants, the transducer could have different responses. A flat response can be obtained if In this case the piezoelectric sensor is thicker than the acoustic signal and is connected to a low impedance amplifier. As a result, the output will be proportional to the acoustic signal and the time domain signal will trace the charge distribution. For a piezoelectric sensor sandwiched between a delay line and an absorber, the signal components near are amplified and the lower frequency components are attenuated. Moreover, this resonant configuration introduces a damped oscillation on the signal.

(8)

PEA method and deconvolution techniques for flat samples

A. Classic PEA device

The experimental setup used for space charge measurements on flat samples is shown in Figure 3. The PEA cell is placed in an oven allowing measurements under controlled temperature in the range between 0°C and 70°C. This cell, provided by TechImp, Italy, is well suited for measuring space charge in flat samples with thicknesses between 200 and 500 μm. A pulse generator delivers the stimuli necessary for measurement and synchronizes the PEA signals. The maximum amplitude of the pulses is 2 kV and maximum repetition frequency is 50 kHz. The pulses width at half maximum is of the order of 5 ns. The high voltage is supplied by a DC voltage generator provided with polarity reversal module. In addition, the DC high voltage generator can be controlled from a PC via a GPIB bus offering the possibility of programming long-term protocols. A digital storage oscilloscope (DSO) with a 2 GHz bandwidth allows measuring signals from PEA up to 1 GS/s. Thus, very fast signals can be captured with a very acceptable temporal resolution. The DSO exhibits high processing speed offering the possibility of averaging a large number of raw signals in a relatively short time improving the signal-to-noise ratio (SNR). The data is then recorded and processed by means of a computer to recover space charge profiles from deconvolution techniques.

B. Deconvolution technique for flat samples

For a homogeneous insulator, the signal from the piezoelectric sensor in time domain v PEA (t) is given by convolution of the various transfer functions [START_REF] Visso Anadin | Maté ia x de câble à isolation synthétiq e po des applications a t anspo t d'éne ie HVDC[END_REF], [START_REF] Thomas | Space charge dynamic in polyethylene: from DC to AC stress[END_REF]: [START_REF] Visso Anadin | Maté ia x de câble à isolation synthétiq e po des applications a t anspo t d'éne ie HVDC[END_REF] where B is a constant; h(t) and g(t) are respectively the transfer function of the transducer and impulse response of sensor defined previously; d Al and v Al are respectively the thickness and velocity of sound in aluminium which constitutes the lower electrode of PEA cell.

The function r(t) = (t.v s ) = (z) represents the space charge density profile along the insulation thickness with v s the sound velocity in the sample.

The simplest method for charge recovery consists in using spectral division between the measured signal and a calibration signal obtained from a known source of charges, as described below. In the frequency domain, the relationship between signal and charge profile is simplified. Indeed, the Fourier transform of v PEA (t) gives: [START_REF] Thomas | Space charge dynamic in polyethylene: from DC to AC stress[END_REF] where S(f) is the transfer function of the whole system [START_REF] Takada | Characteristics of space charge formed in a laminated LDPE/EVA dielectric under DC stress[END_REF] This transfer function can be derived from a signal calibration V PEA1 (f) produced by capacitive charge ( 1 ) formed at lower electrode (connected to ground) when a DC voltage U ref is applied through a sample of thickness d: [START_REF] Li | Space charge characteristics of LDPE nanocomposite/LDPE insulation system[END_REF] with [START_REF] Xu | Interfacial characteristics of space charge in multi-layer LDPE[END_REF] We can deduce R(f) : [START_REF] Iddrissu | The Impact of interfaces and space charge formation on breakdown strength of epoxy resin[END_REF] Moreover, by neglecting the attenuation phenomenon of elastic waves, the space charge profile is given by the real part of inverse Fourier transform of R(f): [START_REF] Morshuis | Dielectric interfaces in DC constructions: Space charge and polarization phenomena[END_REF] The signal processing is performed through Matlab software. The in-built functions are used to calculate direct and inverse Fourier transforms of PEA signals. Since PEA signals have limited frequency bandwidth, the division between the spectrum of signal and that of the reference systematically leads to amplification of high frequency noise. A Gaussian (low-pass) filter is then used after spectral division to eliminate high frequency noise. Note also that the choice of the bandwidth for the Gaussian filter is of great importance with regard to the spatial resolution of charge profile. A synoptic of the signal conditioning for deconvolution method is sketched on Figure 4.

C. Deconvolution technique in the case of bilayer materials

Multilayer specimen can be interesting to investigate, first for fundamental purpose in an attempt to distinguish charges injected at the electrodes from those generated in the volume [START_REF] Takada | Characteristics of space charge formed in a laminated LDPE/EVA dielectric under DC stress[END_REF], also to investigate the impact of material modification as with nanocomposites [START_REF] Li | Space charge characteristics of LDPE nanocomposite/LDPE insulation system[END_REF]. Space charge was reported in layered films of the same material pointing to specific features at the surface of the film [START_REF] Xu | Interfacial characteristics of space charge in multi-layer LDPE[END_REF][START_REF] Iddrissu | The Impact of interfaces and space charge formation on breakdown strength of epoxy resin[END_REF]. There are also practical reasons to investigate dielectric stacks with materials of different nature, as with joints in cables [START_REF] Morshuis | Dielectric interfaces in DC constructions: Space charge and polarization phenomena[END_REF], or when oil and solid insulations are associated paper-oil insulations [START_REF] Huang | Effect of interface on space charge behavior in Multi-layer Oil-Paper insulation[END_REF]. Complex dynamic features are revealed when switching from capacitive to resistive field grading and with interfacial charge development. The case of oil-solid insulation is especially tricky as the time constant for Maxwell interface charge can be relatively short and the acoustic impedance mismatch is relatively high [START_REF] Beyer | Space charge phenomena in laminated HVDC insulation[END_REF]. We illustrate here the case of association of materials for cable joints, with cross-linked polyethylene -XLPE and rubber material. We assume that the two materials are tightly associated as when crosslinked altogether, layer 1 is rubber -EPDM (ethylene-propylene-diene monomer) and layer 2 is XLPE, cf. Figure 5. For space charge measurement, the voltage is applied on the EPDM as shown in the figure. XLPE is to the ground electrode.

Due to discontinuities on the permittivity and acoustic parameters, in particular the speed of sound, special attention must be paid to the processing of raw PEA signals for space charge recovery in case of dielectric bilayer structures. The specificities to consider are among the following:

-calibration aspect owing to the fact that the influence charge evolves with time due to Maxwell interface polarisation;

-changes in sound velocity and impact on charge profile; -reflection of acoustic waves at the interface due to acoustic impedance mismatch;

-acoustic response due to field step at the interface. In the PEA method, the surface charge density used for calibration is first calculated by applying

Gaussian theorem and boundary conditions on electric potential. It is assumed as a first approximation that the field distribution is capacitive and that the interface charge due to difference in conductivity between the two materials can be neglected during the calibration procedure. This assumption is verified a posteriori by considering the time constant necessary to establish interface charge compared to the polarization time of less than 1 min in calibration procedure. Under these conditions, the expression of capacitive charge located at the ground electrode in case of bilayers is given by: (

where  1 ,  2 , d 1 and d 2 are respectively the permittivity and the thicknesses of insulating layers 1 and 2.

U is the applied voltage.

b) The acoustic impedance match Acoustic waves can be reflected at the interface between the two materials due to acoustic impedance mismatch. In the facts, acoustic reflections are more often accounted for at the interface with the electrodes where the mismatch is larger rather than between dielectrics [START_REF] Mier-Escurra | A calibration method for acoustic space charge measurements using multilayer samples[END_REF]. This is supported by the fact that the acoustic impedance of polymers does not vary substantially from one material to another [START_REF] Maeno | Calibration of the pulsed electroacoustic method for measuring space charge density[END_REF]. For this reason, semi-conductive layers with acoustic impedance similar that of a tested insulation are used as top electrode in the PEA cell. In detail, the transmission coefficient from material 1 to material 2 obtained from conservation of stress is defined as [START_REF] Bernstein | nalysis of the electrically stimulated acoustic-wave method for observing space charge in semiinsulating films[END_REF]:

(17) (2) XLPE (1) EPDM + V
where Za is the specific acoustic impedance defined as the product between sound velocity and specific density. With data given in Table 1, T 12 exceeds 99% which means that the matching is excellent in this case. Note that depending on the relative values of impedance, the amplitude of the waves can be decreased or increased when crossing the interface.

V PEA (f) and H setup (f) are respectively calculated by the Fourier transform of temporal signals v PEA (t) and h setup (t). v s (x) is the velocity profile of sound in bilayer sample (v s1 and v s2 in materials 1 and 2 respectively). Position x and time t are linked by the relationship: x = v s (x)*t. As shown in Figure 6, a simple homothetic variation on time (t) of profile (t), obtained by deconvolution of PEA raw signals, makes it possible to obtain the space charge profile as a function of position (x) [START_REF] Vu | Correlating conductivity and space charge measurements in multi-dielectrics under various electrical and thermal stresses[END_REF].

d) Response due to permittivity gradient

Holé et al. [START_REF] Holé | nfl ence of di e ent elect ic fields on space-cha e dist ib tion meas ements by elastic methods[END_REF] used the general expression for the force density in a dielectric under field with 4 contributions related to the variation of the dielectric constant, to the effect of electrostriction, and to the presence of charges and of permanent dipole densities in an electric field. Whereas in a homogeneous material the contributions can be greatly simplified, it is not the case with stacked dielectrics and more generally inhomogeneous materials. In 1D and supposing that there is no permanent polarization (as could be with ferroelectrics), the force density (per unit volume) is expressed as: Under a pulse field , neglecting second order terms, the transient force can be expressed as: [START_REF] Holé | nfl ence of di e ent elect ic fields on space-cha e dist ib tion meas ements by elastic methods[END_REF] where α is the electrostriction coefficient and represents the static field. The Equation [START_REF] Holé | nfl ence of di e ent elect ic fields on space-cha e dist ib tion meas ements by elastic methods[END_REF] shows that in presence of a field gradient, a transient force is generated (second term) due to the electrostriction effect. The permittivity gradient existing at the interface between two dielectrics also leads to a transient pressure. Under applied DC stress, the pressure, obtained by integration along the x-direction defined by Figure 1, is of the form [START_REF] Bodega | Space cha e meas ements on m ltidielect ics by means of the p lsed elect oaco stic method[END_REF]: [START_REF] Bodega | Space cha e meas ements on m ltidielect ics by means of the p lsed elect oaco stic method[END_REF] where D is the electric displacement (homogeneous across the interface in absence of interface charges). So the pressure generated at the interface should appear as a fraction of the capacitive charge.

Bodega et al. [START_REF] Bodega | Space cha e meas ements on m ltidielect ics by means of the p lsed elect oaco stic method[END_REF] concluded on the fact that generally, when a multi-dielectric is tested, the detected acoustic signal does not correspond to the space charge distribution. The reasons are on the one hand the presence of an acoustic response with distributed permittivity, even in the absence of interfacial charge, cf. Eq. 22. The other aspect is linked to the fact that the detected acoustic signal does not correspond to the pressure distribution if the layers of the multi-dielectric have different acoustic properties. A second consequence of acoustic mismatching is overlapping of reflected waves with the waves representing the pressure distribution inside the multi-dielectric.

C. Example of results for stacked dielectrics

Let us consider now an example of results obtained with the XLPE/EPDM structure. Figure 7 shows a mapping of space charge profiles in material XLPE (a) and bilayer XLPE/EPDM (b) at 40 0 C under various applied electric fields obtained by deconvolution of raw PEA signals. The specific procedures adopted here to treat the rough data concern the accurate estimation of the interface charge in the calibration step (Eq. 15) and the correction for the sound velocity gradient. In case of multilayer dielectric, much more charges are detected, one of the reasons being the presence of the interface. The analysis of the charge build and charge decay, considering amount, sign, and kinetic is proposed elsewhere [START_REF] Vu | Correlating conductivity and space charge measurements in multi-dielectrics under various electrical and thermal stresses[END_REF][START_REF] Vu | Maxwell-Wagner effect in multi-layered dielectrics: interfacial charge measurement and modelling[END_REF]. A pretty good agreement was obtained between results obtained by conductivity measurements and space charge build-up, i.e. independent experiments, and modelling with accounting for Maxwell-Wagner interface charge process. Regarding specific acoustic phenomena linked to the multilayer nature, the fact that the acoustic impedance of the two materials is the same avoids having spurious reflections. The permittivity on its own side is different from one material to the other, see Table 1. However, even though there is such contrast, we did not observe in an evident way a specific signal due the permittivity gradient. In absence of interface charge, the acoustic signal due to permittivity gradient should produce an apparent charge of the same sign as the capacitive charge on the higher permittivity material [START_REF] Bodega | Space cha e meas ements on m ltidielect ics by means of the p lsed elect oaco stic method[END_REF] i.e.

EPDM. This was not observed in the present results. The detected signal is fully consistent with Maxwell-Wagner interface polarization and even the change in sign of the interface with increasing field could be explained by the behaviour of nonlinear conductivity in the two materials. There can be two reasons for the absence of acoustic response: i/ it can be quickly overlapped by the interface polarization, or the permittivity values given here for a frequency of 50Hz are not the same at the DC limit or a frequency of the voltage pulses.

PEA method for model cable

A. PEA-cable device

The first PEA system for space charge measurement in a cable appeared in the 1990s [START_REF] Yas Da | Meas ement of charge distributions in coaxial cable using the pulsed electroacoustic method[END_REF], [START_REF] Hoz | Space cha e dist ib tion meas ement in a lon size XL cable sin the p lsed elect oaco stic method[END_REF], [START_REF] Takada | lsed elect o-acoustic method for measurement of space charge distribution in powe cables nde both DC and C elect ic fields[END_REF]. The initial device was equipped with a curved electrode system (fixed radius of curvature) and was therefore adapted to a single type of cable. Difficulties arise naturally when one wants to make measurements on cables with different radius. To overcome this limitation, a flat-electrode PEA system now replaces the original device [START_REF] F G. Chen | Space charge measurement in power cables using a modified PEA system[END_REF] and the PEA method is considered one of the most efficient techniques for measuring space charge in high voltage model cables [START_REF] Takada | Space charge measurements as a diagnostic tool for power cables[END_REF]. An example of PEA cable mounting developed by TechImp, Italy, is shown in Figure 8. The cable is attached to the PEA sensor cell by mounting bracket to adjust cable clamping, thus ensuring good acoustic contact between outer semiconductor of the cable and aluminium electrode of measurement cell. The pulsed voltage is injected at the measurement zone via outer semiconductor of cable by a pulse generator of 5kV maximum amplitude, 30ns width and 10 kHz of repetition rate. The outer semiconductor is removed over a 5 cm length between the measurement point and the region where pulses are applied. In this way, the cable itself is used as a decoupling capacitor. To ensure that pulsed voltage at measuring point is high enough, the length of outer SC at point of application of the pulse is kept larger compared to that at the measuring point. A 100 kV high-voltage generator supplies the DC voltage, which is applied at conductor via a Rogovsky electrode. This type of electrode is used to avoid any field intensification.

For measurements at different temperatures, the cable is heated by an alternating current flowing in the cable core with control through a current transformer. In this way, a thermal gradient appears within the insulation since the cable surface is in contact with ambient air. The temperature at the surface of the cable is measured using a thermocouple. The current flowing in the cable is measured using an ammeter clamp. Knowledge of these two quantities and of the cable geometry enables to estimate cable core temperature.

B. Deconvolution in coaxial geometry

Recall that PEA method relies on detection of electrostatic forces generated by the interaction between internal charges and external electric pulse [START_REF] Maeno | Hi h-resolution PEA charge distribution measurement system[END_REF]. The propagation of acoustic waves towards the piezoelectric sensor is affected mainly by attenuation and dispersion. These phenomena are even more important when the insulating layer is relatively thick, for example in case of medium voltage cable samples (MV cable). In addition, the generation and propagation of acoustic waves are affected by the geometry of the cable [START_REF] Chon | Calib ation of the pulsed electroacoustic technique in the presence of trapped cha e[END_REF]. Due to the divergence of electric field in coaxial geometry, the contribution to PEA signals of electrostriction force resulting from variation of permittivity induced by mechanical deformation of the polymer, during acoustic wave generation must be taken into account [START_REF] Holé | nfl ence of di e ent elect ic fields on space-cha e dist ib tion meas ements by elastic methods[END_REF]. Following the same development as above for flat specimen, for a homogeneous material, in cylindrical geometry, the transient force density generated by the interaction of the static DC field and the electric pulse field at the radius r can be expressed as follows [START_REF] Visso Anadin | Decon ol tion techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF]:

The first term represents the response due to the space-charge induced field distortion (without space charge, the divergence of the field is null) and the second one is the electrostriction contribution, stating that the strain due to the non-homogeneity of electrical stress induces a variation on the relative permittivity which generates an elastic force.

Hence, the deconvolution method used for cable requires correction of attenuation, dispersion, and electrostriction as well as the PEA instrument response (sensor + voltage pulse) for recovering space charge profiles from PEA raw signals. The flowchart of deconvolution technique used for PEA-cable rough data is presented in Figure 9. The different steps are detailed in the following.

The deconvolution requires an accurate description of the whole system which is composed by the measuring instrument and the tested cable. The calibration procedure is used to establish the transfer function of the system. This step consists of acquiring raw signal from capacitive charges generated by application of DC voltage (U cal ). The PEA signal detected at the piezoelectric sensor v PEA (t) is

given by the following expression [START_REF] Visso Anadin | Decon ol tion techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF]:

t h set p t m . t m . t (24)
where r I and r E are the inner and outer radius of cable. h setup (t) and g(r,t) are respectively the transfer function of instrument and cable through which is taken into account the propagation of acoustic waves in the polymer material. m(r) is an intermediate variable depending on the cable radius (r) and the applied electric field E DC (r) [START_REF] Visso Anadin | Decon ol tion techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF]. Notably, it contains the term related to electrostriction. The PEA calibration signal consists of two parts due to the responses of capacitive charges at the external v PEA1 (t) and internal electrodes v PEA2 (t) (Fig. 9). g(r E ,t) is the Dirac function of time at the position r E . Consequently, the first part of PEA signal, v PEA1 (t), makes it possible to derive the instrument transfer function h setup (t) [START_REF] Visso Anadin | Decon ol tion techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF]: The second part of PEA calibration signal in Equation ( 24) is generated by the capacitive charges located at the internal electrode (cable core) and therefore contains information related to the acoustic wave propagation (in particular attenuation coefficient and phase velocity). In the frequency domain, V PEA2 (f) is given by the expression below: [START_REF] Takada | lsed elect o-acoustic method for measurement of space charge distribution in powe cables nde both DC and C elect ic fields[END_REF] where H setup (f) and G(r,f) are the Fourier transform of h setup (t) and g(r,t). G(r,f) is the transfer function of the cable through which is taken into account attenuation effects (f) and dispersion c(f) of the acoustic waves in the cable. The frequency spectra of attenuation coefficient and phase velocity can be deduced from the spectrum of the two parts of calibration signal. This procedure for determination of ultrasonic attenuation and phase velocity in solid dielectrics was initially introduced by Ditchi et al.

[32]:

where d = r E -r I and  is the phase of the spectrum of the PEA signal.

The global transfer function H syst (f) of the system is obtained by multiplying the transfer function of the cable G(r,f) and that of the instrument H setup (r, f). Thus, any PEA signal can be modelled in the frequency domain by equation 29:

The intermediate function m(r) is calculated by the inverse Fourier transform of the ratio between the signal V PEA (f) and the transfer function of the system H syst (f). The electric field profile E(r) and the space charge density profile (r) are derived from m(r).

C. Example of results for MV cable

Figure 10 presents a map of space charge density (a) and of electric field profiles (b) obtained at different times on a MV cable with -40kV applied for 3h to the cable conductor. Then the voltage was removed for 30min before increasing the voltage to -80kV. In Fig. 10b, after 200 s at -40 kV, since the material is free of charge, the field distribution is similar to the Laplacian field (for which the field value is -12.5 kV/mm at the inner electrode and -6.5 kV/mm at the outer electrode). Then, due to the negative homocharges build-up (see Figure 10a, blue zone at cathode) the field decreases at the cathode and practically vanishes after 3 hours of polarization and increases in the bulk reaching a maximum value of about 12.5 kV/mm at r=8 mm.

Due to the presence of negative charges at the beginning of polarization under -80 kV, the electric field shape is similar to that at the end of polarization step under -40 kV and the maximum enhancement is found at 8 mm. At the end of the second polarization step, the maximum electric stress is located at the outer electrode due to heterocharge build-up. The field at the outer radius is estimated to about 22 kV/mm, which corresponds to the value of the geometrical field at the inner electrode for an applied voltage of -80 kV.

D. Impact of acoustic properties of materials

From calibration taken on XLPE-insulated MV cables, the frequency dependence of acoustic properties given in Figure 11 were obtained [START_REF] Visso Anadin | Decon ol tion techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF] using the Nearly Local Kramers-Kronig (NLKK) approximation. Using a pulse width of typically 30ns, a sensor of 25µm thickness, and outer semicon thickness of 500µm (which can contribute to broaden the response), the acoustic response associated with the calibration signal is typically in the frequency range from 1 to 10 MHz for a MV cable.

Figure 11 shows that the higher the frequency the stronger the attenuation. For insulation thickness of 4.5mm the attenuation factor is typically of 20% at 1MHz and over 93% at 9MHz. Because of this feature, the pulse shape must be adapted to the thickness of sample to be probed, as a compromise between spatial resolution and damping of the acoustic signal. The linear variation of the attenuation coefficient vs. frequency is consistent with literature reports on acoustic properties of various polymers [33] [34], though from a mathematical point of view, it brings some inconsistency in the application of the Kramers-Kroning relations and the relation of attenuation and dispersion [START_REF] Waters | Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion[END_REF]. The al e of α of abo t 600m -1 at 10MHz appearing in Figure 10 is in full agreement with those reported earlier for polyethylene ( [START_REF] Hartmann | Ultrasonic hysteresis absorption in polymers[END_REF], [START_REF] Adachi | High frequency ultrasonic studies of polyethylene[END_REF]). This linear dependence, called hysteresis absorption, has been explained by the freezing of the polymer in one of its many local energy minima [START_REF] Hartmann | Ultrasonic hysteresis absorption in polymers[END_REF]. Relaxation processes bring contributions in the form of deviation from the linear dependence [START_REF] Hartmann | Ultrasonic hysteresis absorption in polymers[END_REF], [START_REF] Adachi | High frequency ultrasonic studies of polyethylene[END_REF], especially at high frequencies (>10MHz). This means that the absorption depends on the free volume, and for crystalline polymers, on the degree of crystallinity. The attenuation changes substantially from one mate ial to anothe examples bein α ≈150m -1 at 10MHz fo MM amo pho s and ≈800m -1 PEO with 80% crystallinity. The absorption increases with the crystalline fraction and a second effect for crystalline polymers is the scattering of waves by crystalline regions as observed for high crystalline materials like poly(tetrafluoroethylene) for example. Hartman and Jarzynski [START_REF] Hartmann | Ultrasonic hysteresis absorption in polymers[END_REF] proposed an expression of following the form for the volume and velocity dependence of the absorption, which also accounts for the temperature variation: [START_REF] Chon | Calib ation of the pulsed electroacoustic technique in the presence of trapped cha e[END_REF] where a and b are constant for a given polymer. V is the volume of the polymer and v the sound velocity. The above considerations on materials acoustic properties have two consequences in practical implementation of the PEA method. First, the temperature dependence of acoustic properties should be analysed when measurements are achieved under temperature gradient. In a temperature span of 20°C, according to literature data on PE [START_REF] Adachi | High frequency ultrasonic studies of polyethylene[END_REF], the velocity decreases by about 10%. So a correction similar to that achieved for bilayers should be achieved in the time to position transformation. The temperature dependence of the attenuation does not vary in a monotonous way vs. temperature: the variation is primarily dependent on the thermal expansion coefficient variations and on relaxation features in the investigated temperature range [START_REF] Adachi | High frequency ultrasonic studies of polyethylene[END_REF]. Xia et al. [START_REF] Wang | Recovery Algorithm for Space Charge Waveform in Coaxial Cable under Temperature Gradient[END_REF] amended the system transfer function by adding quadratic approximation to the dispersion coefficients for calibration in coaxial geometry under temperature gradient.

Second, from the attenuation of acoustic waves, one can immediately anticipate the limitation in spatial resolution linked to materials behavior. With increasing the frequency (i.e. using shorter voltage pulses to improve the resolution), the attenuation increases substantially, meaning that measurements under higher resolution must go with thinner samples. By doing so, resolution of 1 to 2 µm could be reached on thin sample (50 µm) provided sensor thickness and pulse waveform were modified accordingly [START_REF] Galloy | High-resolution pulsed electro-acoustic (HR PEA) measurement of space charge in outer space dielectric materials[END_REF][START_REF] Kumaoka | Development of space charge measurement system with high positional resolution using pulsed electro acoustic method[END_REF].

Conclusion

In this work, the principle of deconvolution techniques for the PEA method in case of three different kinds of sample (flat, bilayer materials and geometric cables) has been described. PEA signal from the calibration procedure is used to build the system transfer function by deriving the frequencydependent attenuation coefficient and the phase velocity. Application of these deconvolution techniques enables to observe space charge and stress distribution after few hours of polarization in material with different geometry and further to study mechanisms at the origin of charge build-up in such samples. The deformation of acoustic waves when travelling across the material can be relatively well accounted for, along with the dependence of their magnitude upon the perturbation pulse field in case of divergent geometry. However, the acoustic signal produced by indirect effects of charges, such as the electrostrictive forces due to non-homogeneous electric field is not easy to recover and to discriminate from the total signal since the actual field distribution should be known.

Acknowledgment

We are grateful to B Vissouvanadin for his advises and provision of figures for the manuscript.

Figure 1 :

 1 Figure 1: Principle and main elements of a PEA test cell

Figure 2 :

 2 Figure 2: Transducer equivalent circuit [8]

Figure 3 :

 3 Figure 3: Schematics of the PEA test bench for flat specimen. Adapted from [10].

Figure 4 :

 4 Figure 4: Block diagram of signal processing

Figure 5 :

 5 Figure 5: Bi-layer materials EPDM/XLPE

( 20 )Figure 6 :

 206 Figure 6: Determination of space charge profile versus position from space charge profile versus time from deconvolution of PEA raw signals in dielectric bilayers.

Figure 7 :

 7 Figure 7: Mapping of space charge profiles in XLPE material (a) and bilayer XLPE/EPDM (b) at 40 °C under different applied electric field. The color bar represents the scale for charge density in C/m 3 . In a): applied fields were 10, 20, 30 and 40kV/mm followed by polarity reversal. In b): average fields were from 2 to 30kV/mm [20].

Figure 8 :

 8 Figure 8: Sketch of PEA cable test rig [9]

Figure 9 :

 9 Figure 9: Synoptic of deconvolution method on PEA cable

Figure 10 :

 10 Figure 10: Map of space charge density (a) and electric field distribution profiles (b) in a medium voltage cable stressed under -40 kV and -80 kV at room temperature and different times. The colour bar represents the scale for charge density in C/m 3 .

Figure 11 :

 11 Figure 11: Frequency dependence of the attenuation coefficient (a) and sound velocity (b) from XLPE obtained from PEA calibration on a MV cable. Line (c) represents the attenuation of acoustic wave across a 4.5mm thick insulation.

Thi

  Thu Nga Vu was born in 1981 in Hanoi, Vietnam. She received the Master's degree in 2007 from the Hanoi University of Science and Technology, in Vietnam. She received the Ph.D. degree in electrical engineering from the University of Toulouse, France, in 2014 for a research work on space phenomena in polymeric insulating materials intended for HVDC cable application at the Laboratory of Plasma and Energy Conversion -Laplace in Toulouse, France. She has been working since 2004 as a researcher and lecturer at the Electric Power University in Hanoi, Vietnam. Laurent Berquez was born in Abbeville, France, in 1970. He received the M.Sc. degree in acoustics in 1994, and the Ph.D. degree in 1998 from the Toulouse University. He is full professor at the Toulouse University and works on multidimensional mapping of polarization and space-charge distributions in thin dielectric polymers at the Laboratory of Plasma and Energy Conversion -Laplace in Toulouse. He is heading a research team working on the reliability of dielectrics in electrical equipment. Gilbert Teyssedre was born in 1966 in Rodez, France. He received his Engineer degree in materials physics and Masters in solid state physics in 1989 at the National Institute for Applied Science (INSA). Then he joined the Solid State Physics Lab in Toulouse and obtained the Ph.D. degree in 1993 for work on ferroelectric polymers. He joined the CNRS in 1995 and has been working since then at the Laplace in Toulouse. His research activities concern luminescence techniques in insulating polymers with focus on chemical and physical structure, degradation phenomena, space charge and transport properties. He is currently Senior Researcher at CNRS in a team working on the reliability of dielectrics in electrical equipment.

Table 1 . Dielectric and acoustic properties of tested materials (for density, standard values given)

 1

	Material	Relative permittivity  r	Sound velocity (m/s)	Density	Acoustic impedance Za (kg/m²/s)
	EPDM	2.9	1800	1.10	1980
	XLPE	2.3	2100	0.93	1950

c) The velocity difference for charge recovery According to the expression (

16

), the space charge distribution at the origin of raw signals v PEA (t) is given by:


N Belkahla

N Saidi-Amroun

G Teyssedre

L Berquez

S Mouaci

M Saidi

Space charge and conduction measurements in gammairradiated polyethylene terephthalate

Keywords: Space charge, LIMM, gamma irradiation, PET

We report on the impact of irradiation on the dielectric properties of Poly(Ethylene Terephthalate)(PET).Thin films of PET were irradiated in air at room temperature by means of a 60 Co gamma source at a dose rate of approximately 31 Gy/min. Total doses of 30 kGy and 150 kGy were adopted in this work. The space charge profiles and residual electric field of virgin material and material exposed to these representative doses, obtained after 30 min of depolarization following field application in the range 40-200 kV/mm, have been examined by Laser-Intensity Modulation Method (LIMM). The dependence of space charge density with electric field values and irradiation dose is analysed. Under high DC voltages and after irradiation, the space charge stored in PET tends to be less than in reference PET. The charging and discharging currents tend to increase with the irradiation, considering both the transient contribution to the current and the conductivity contribution. Space charge and conduction measurements exhibit good agreement in the fact that higher conductivity would prevent charge accumulation.

I. INTRODUCTION

Owing to their excellent properties, polymeric materials have a great potential in many important applications with severe service conditions such as in electrical engineering, nuclear reactors or space equipment for examples. In these environments, they are often exposed to X-rays, gamma-rays, UV, protons, electrons, etc [START_REF] Du | Dynamic behaviour of surface charge on gamma-ray irradiated polybutylene naphthalate[END_REF]. Therefore, much attention has to be given to the study of the behaviour of irradiated polymers, with the aim to evaluate the change of some properties, such as insulation properties of insulated cables, and also mechanical and chemical integrity of the materials, etc. Some of the above stresses are ionizing radiations, meaning that the deposited energy is high enough to extract electrons from atoms of the material and induce chemical changes. Radiation effects on polymers consist in the generation of high-energy electrons causing ionization, bond breaking, the creation of radicals, and the possibility of cross-linking [START_REF] Mariani | Gamma irradiation of polyester films[END_REF].

Through its good electrical, chemical, physical properties, Poly (ethylene terephthalate) has become one of the most used industrial polymers. Exposition of PET to gamma radiation results in the formation of gaseous products such as carbon monoxide, Carbone dioxide (main products), hydrogen, and methane, accompanied by the formation and the scission of intermolecular bonds in the main polymer chain and in side chains [START_REF] Aliev | Comparative radiation degradation of some aromatic polyesters[END_REF]. Several experimental techniques have been implemented to understand the changes in electrical properties of polymeric materials (e.g.Isotactic Polypropylene -Poly(ethylene terephthalate) -PET, Poly(ethylene naphthalate) -PEN, low density Polyethylene -LDPE, etc.) after irradiation [START_REF] Mariani | Gamma irradiation of polyester films[END_REF][START_REF] Aliev | Comparative radiation degradation of some aromatic polyesters[END_REF][START_REF] Mouaci | Charge trapping and conduction in γ irradiated isotactic polypropylene[END_REF][START_REF] Belkahla | Influence of gamma radiation on electrical conduction of polyethylene terephthalate (PET) at ambient temperature[END_REF][START_REF] Mackersie | Gamma radiation effects in polyethylene naphthalate -electrical properties[END_REF], showing that polymers containing aromatic moieties are in general more radiation resistant than those with aliphatic chains.

This paper reports on experimental research on the effect of gamma radiation on Poly (ethylene terephtalate), PET, films, particularly with regards to the space charge behavior and conduction properties. The space charge measurements were performed by the LIMM technique (Laser Intensity Modulation Method), which is a technique suited for the determination of space charge density profiles inside relatively thin (a few tens of micrometers thickness) insulating materials. The investigation is complemented by charging-discharging current measurements aimed at analyzing transport properties of irradiated PET films.

II. EXPERIMENTAL

A. Materials and irradiation conditions

All measurements were performed on 25 µm-thick semi crystalline polyethylene terephthalate (PET) films, supplied by Dupont de Nemours, Luxembourg. The chemical structure of PET is shown in Fig. 1. The samples were exposed to 60 Co source using a gamma cell available in Nuclear Research Center of Algiers (CRNA), Algeria, with a source dose rate of approximately 31 Gy/min. Total doses of 30 kGy (16 h irradiation time) and 150 kGy (81 h) were adopted in this work. For all dielectric measurements, 30 nm-thick gold electrodes were deposited on the films. Gold layers were deposited by cold sputtering: each face of the film was exposed to a DC-powered low pressure argon discharge for 300s. The electrode diameter was 16 mm for LIMM measurements and 10 mm for charging/discharging current measurements. All the experiments were carried out at room temperature.

Terephthalate group

Ethylene group

B. Space charge measurements

Derived from the LIMM technique, the FLIMM (Focused LIMM) technique consists of heating the surface and/or volume of the sample to be studied, using an intensity and frequency modulated laser diode [START_REF] Marty-Dessus | Space charge cartography by FLIMM: a three-dimensional approach[END_REF][START_REF] Petre | Three-dimensional space charge cartographies by FLIMM in electron irradiated polymers[END_REF]. In presence of space charge and/or polarization in the sample, the interaction between the thermal source and the material creates a pyroelectric current resulting from the rebalancing of charges on the electrodes. This current, called LIMM current is detected and analyzed. The spot size can be varied from 1µm to several millimeters [START_REF] Marty-Dessus | Space charge cartography by FLIMM: a three-dimensional approach[END_REF]. In this work, as our purpose was not to get high in-plane resolution, the spot size was set to about 2 mm, which means that we essentially worked in the LIMM configuration. The modulation frequency range was 10 2 -10 4 Hz. The LIMM set-up is shown in Fig. 2. Details of the signal conditioning procedure consisting in converting the LIMM current into the charge profile and field profile based on a modelling of the temperature distribution in the sample is available elsewhere [START_REF] Marty-Dessus | Space charge cartography by FLIMM: a three-dimensional approach[END_REF][START_REF] Petre | Three-dimensional space charge cartographies by FLIMM in electron irradiated polymers[END_REF], with a recent declination of the LIMM analysis on Polyimide thin films proposed in [START_REF] Pham | Space charge formation in polyimide films and polyimide/SiO2 double-layer measured by LIMM[END_REF].

Fig. 2. Schematic of the LIMM set-up

All LIMM experiments were carried out in air at room temperature. Samples were polarized for 30 min with a DC field at different levels between 40 kV/mm and 200 kV/mm. After each polarization step, the sample was short-circuited for 30 min and then the LIMM measurement was carried out so that only residual stored charges were detected.

C. Current measurements

For conductivity measurements, PET samples were prepared as explained above. Polarization and depolarization times were 30 min, and the same field range as for LIMM measurements was considered. The current was continuously recorded and sampled in 2 s intervals using a Keithley 617 programmable electrometer driven by a microcomputer. Charging and discharging current measurements were realized under secondary vacuum at room temperature.

III. RESULTS AND DISCUSSION

A. FLIMM measurements

The space charge profiles and residual electric field obtained after 30 min of polarization followed by 30 min of depolarization are plotted in Fig. 3.Plots (a), (b) and (c) refer to virgin PET and PET subjected to 30 kGy and 150 kGy of gamma radiation, respectively. Data are provided for 5 values of the field up to 120 kV/mm except for the 150 kGy where early breakdown occur. We cannot associate for certain the early breakdown to the irradiation. Positive voltage was applied on the left electrode (therefore anode). The charge profiles were obtained by measurement made on the same electrode. In this zone (at the anode), an accumulation of homocharges (positive charge) can be noticed, for all samples, when the applied field is sufficiently high. It can be noticed that the charge profile recorded under 0-field, i.e. prior to any field application, is not flat, and is of the shape for the three tested samples: possibly the investigated PET films had specific surface properties due to its processing conditions.

For a virgin sample, at low field, the charge density is very weak and can be associated with a dipolar orientation. On the other hand, a massive charge injection (120 C/m 3 ) appears at 200 kV/mm. The penetration depth of positive charges is low, about to 3 µm from the surface: the depth is not clearly dependent on the applied field. Negative charges are also present in the bulk of the insulation and apparently spread more than positive charges. However, it must be stressed that the exact position of negative charges cannot be easily identified. The spatial resolution of the LIMM method, as for any thermal method, decreases when going from the surface to the middle of the sample, and therefore all interpretations are limited close to the left electrode.

A noticeable decrease in stored positive charge quantity is observed after irradiation of the sample. For a field of 120 kV/mm, the charge density is halved after irradiation. However the evolution with the dose is not obvious. What changes with the highest dose (150 kGy) is a deeper penetration of the positive charge and a boarder space charge peak.

Sample Driver

Lock-in Amplifier

Laser Diode

I(f) + - R Electrode LIMM Data
Residual electric field values estimated from these charge profiles decrease with the irradiation dose if one consider the field at the anode. However, in the middle of the insulation the variation is mild: the residual field is in the range 2-4 kV/mm for an applied field of 120 kV/mm. In all cases, it represents only a small fraction (<1-3%) of the applied field. This is presumably due to the fact that measurements were achieved a relatively long time (30 min) after field removal.

B/ Charging/discharging current measurements

Charging/discharging current measurements were carried out under vacuum conditions at room temperature. An example of transient current measurements is presented on Fig. 4 for the reference PET and PET irradiated with doses of 30 and 150 kGy. Both charge and discharge current are plotted as a function of time, for different values of applied electric field. The superposition of these two currents for low electric field is a sign of dominant dipolar mechanism which is not the case for high electric field, and for long times.The difference between the charging and the discharging current is more and more evident as time increases. This asymmetry is related to the contribution from conduction process to the charging current.

The transient currents are also defined by the Curievon Schweidler law with values of the exponent n close to 1 (cf. Table I). Values of n were estimated considering the linear part of the decay (in log-log plot). The slope is higher in the discharging than in the charging steps due presumably to conduction processes. It is observed that an increase occurs in the value of the current due to gamma irradiation. The increase is significant considering the amplitude of the transient current. It is also visible on the steady state current viewed as the difference between the charging and discharging currents for a given field. This increase in the charging current can be considered a result of the chain scission of the macromolecules induced by gamma radiation [START_REF] Radwan | Enhancement of the electrical performance of poly(vinyl) alcohol by doping with chlorophyll and gamma irradiation[END_REF] .This chain scission leads to a reduction in the average molecular weight of the PET, which, in turn, increases molecular mobility. Radwan [START_REF] Radwan | High gamma dose response of the electrical properties of polyethylene terephthalate thin films[END_REF] reported that chain scission results in a decrease in the number of valence electrons in PET [START_REF] Radwan | High gamma dose response of the electrical properties of polyethylene terephthalate thin films[END_REF]. Therefore, an increase in the free charge carriers occurred due to this scission, which increased the DC current.

IV. CONCLUSION

Space charge and conductivity measurements were carried out on samples of virgin and gamma irradiated poly (ethylene terephthalate). The results from the irradiated sample show some differences from the virgin sample. A decrease in the stored space charge density with irradiation dose has been observed along with an increase in conductivity. DC current voltage measurement for the irradiated sample showed a significant increase in current densities for the same applied field. Besides the increase in conductivity, changes in the field dependence of conductivity were observed, conductivity being more dependent on field after irradiation. This constitutes important results, as the dose considered here (150kGy) is mild relatively to that reported (1000kGy) for noticeable degradation of PET. The explanation for the change in electrical properties is believed to be radiation-induced chain scission in PET films.

Fig. 1 .

 1 Fig. 1. Chemical formula of Poly(Ethylene Terephtalate)

Fig. 3 .

 3 Fig. 3. Space charge density (left) and residual electric field (right) profiles for different applied electric fields (a) reference PET, (b) 30 kGy and (c) 150kGy irradiated samples. Anode and cathode were respectively at x=0 and x =25 µm during polarization.

Fig. 4 .

 4 Fig. 4. Time dependence of charge and discharge currents at various electric fields for (a) reference PET, (b) 30 kGy and (c) 150kGy irradiated samples.

Table I

 I Values of n for charging and discharging currents at a field of 40 kV/mm

	n / Dose	0 kGy	30 Gy	150 kGy
	Charging current	1.10	1	0.94
	Discharging current	1.06	1.16	1.16

ACKNOWLEDGEMENT

The authors are thankful to the Director and the staff of the Nuclear Research Center of Algiers for the irradiation of the samples.


Ascites is the most common complication of cirrhosis, as 5-10% of patients will develop this complication per year. Its management relies on symptomatic measures including restriction of sodium intake, diuretics, and paracentesis. The treatment of the underlying liver disease is always mandatory and may improve ascites. In some patients, ascites is not controlled by medical therapies and has a major impact on quality of life and survival; TIPS placement and liver transplantation have therefore to be discussed. More recently, repeated albumin infusions and Alfapump ® have emerged as new therapies in ascites. In this review, we will analyze current data available on these different options and will suggest an algorithm to help the physician in clinical decision.

Introduction

Ascites is the most common complication of cirrhosis, as 5-10% of patients with cirrhosis will develop this complication per year. Ascites has a major impact on quality of life and is associated with poor outcome. Its management can be dichotomized into 2 different aspects: the first one is symptomatic, and relies on restriction of sodium intake, diuretics, albumin infusion, and paracentesis. These symptomatic methods should always be associated with the treatment of the cause of liver disease, in order to improve liver function. The majority of patients will recover thanks to medical therapy. In patients in whom ascites is not controlled by these medical therapies, transjugular intrahepatic portosystemic shunt (TIPS) placement is the first line treatment that has to be discussed, as it has been shown that TIPS improves ascites, as well as survival when compared to repeated paracentesis. In patients with the most severe presentation, with a high MELD or a high Child-Pugh score, or with hepatic encephalopathy (HE), TIPS is contraindicated and liver transplantation is the only curative option. An age of more than 65 or 70 years is another important issue, as it may be a contra-indication for both TIPS placement and liver transplantation. In this review, we will first focus on the pathophysiology of ascites in cirrhosis, and then discuss all different therapeutic options. Last, we will suggest an algorithm to help the physician in different clinical situations. The management of hepatorenal syndrome, a severe complication that has the same pathophysiology than ascites, will not be discussed in this review.

1) Pathophysiology of ascites in cirrhosis

Ascites is defined as an accumulation of fluid in the peritoneal cavity and is due to cirrhosis in about 80% of cases. It can be graded according to its severity: grade 1 (mild ascites) if only detectable by ultrasound, grade 2 (moderate ascites) if moderate symmetrical distension of abdomen and grade 3 (large ascites) if marked abdominal distension [START_REF] Study | Electronic address eee, European Association for the Study of the L. EASL Clinical Practice Guidelines for the management of patients with decompensated cirrhosis[END_REF]. Ascites affects 5 to 10% of patients with compensated cirrhosis per year and is then considered as the most common complication of cirrhosis. Moreover, its prognosis is poor (two-year mortality of 40%), appearing later than variceal bleeding in the natural history of cirrhosis, with a more severe outcome [START_REF] D'amico | Competing risks and prognostic stages of cirrhosis: a 25-year inception cohort study of 494 patients[END_REF]. Ascites is known to be multifactorial and seems to result from the combination of portal hypertension and liver insufficiency. Several hypotheses have been suggested to explain its pathophysiology, the main one being that ascites reflects the reorganization of hemodynamics in cirrhosis. Indeed, the reorganization of hepatic structure in cirrhosis is responsible for an increase of hydrostatic pressure in sinusoid capillaries, which leads to an increase of local synthesis of vasodilators substances, such as nitric oxide. As a consequence, there is a decrease in splanchnic arterial resistance [START_REF] Fortune | Ascites, refractory ascites and hyponatremia in cirrhosis[END_REF]. Then, compensatory mechanisms occur, especially an increase of cardiac output and activation of metabolic pathways to increase effective volemia (sympathetic nervous system and renin-angiotensin-aldosterone pathway). Synthesis of anti-natriuretic substances is then increased and results in sodium and water retention in proximal tubule, loop of Henle and distal tubule (3). This can result in dilutional hyponatremia, which may worsen prognosis and makes treatment of ascites more difficult. At a final stage, the severe systemic vasodilation and subsequent renal vasoconstriction are responsible for acute kidney injury by decreasing renal blood flow, defining hepatorenal syndrome. Moreover, hypoalbuminemia due to hepatic insufficiency is responsible for a decrease of oncotic pressure, which facilitates the fluid leakage from intravascular sector to interstitial space [START_REF] Fortune | Ascites, refractory ascites and hyponatremia in cirrhosis[END_REF]. Due to the reorganization of hepatic structure in cirrhosis, capillaries are no longer fenestrated and protein concentration is then poor in this fluid. Finally, some studies suggest a role of bacterial translocation, which is frequent in cirrhosis and responsible for local and systemic inflammation. This mechanism may increase permeability of capillaries and then facilitate the fluid leakage to the peritoneal cavity (3).

2) Optimal management of ascites

We will focus on the treatment of ascites in patients: a) without refractory ascites, b) with refractory ascites, d) with spontaneous bacterial peritonitis (SBP). In patients with complicated ascites, i.e with either refractory ascites or SBP, liver transplantation (LT) has to be envisioned.

a) Patients without refractory ascites

Classical treatments

The treatment of ascites relies on symptomatic therapies, including sodium restriction and diuretics, as patients with ascites have a positive sodium balance. Dietary sodium should be moderately restricted (80-120 mmol/day) in order to avoid a reduced calorie intake, a consequence that may impair nutritional status. The aim regarding diuretic therapy is to lead to a weight loss of less than 0.5 kg/day or 1 kg/day (in the presence of peripheral edema). Patients should receive an anti-mineralocorticoid drug alone, starting at 100 mg/day, with stepwise increase to a maximum of 400 mg/day. In non-responders or in patients developing hyperkaliemia, furosemide has to be added from 40 mg/day to a maximum dosage of 160 mg/ day. Other general dispositions or treatment have also been evaluated: (1) it has not been shown that a prolonged maintenance of the supine position improves the resolution of ascites;

(2) there is evidence that the treatment of the underlying liver disease may improve ascites, such as alcohol abstinence or viral suppression; (3) the use of several drugs is contraindicated in order to avoid renal impairment, such as non-steroidal anti-inflammatory drugs, angiotensin-converting-enzyme inhibitors or aminoglycosides (except in patients with severe bacterial infections); (4) other treatments such as midodrine, or terlipressine or clonidine are not recommended.

New therapeutics in patients without refractory ascites: albumin and TIPS

Hypoalbuminemia and the synthesis of dysfunctional albumin are increasingly recognized as key factors in the pathophysiology of cirrhosis complications including ascites. Patients with moderate ascites were considered the most appropriate candidates to evaluate the efficiency of repeated albumin infusions in order to improve survival, prevent the occurrence of further complications of cirrhosis including encephalopathy, sepsis, but also reduce ascites. In the ANSWER study (4), patient with ascites under diuretics, thus not considered refractory, received either albumin (40g twice a week for two weeks and then 40g weekly) or standard medical treatment (SMT). Patients in the albumin group showed a 38% decrease of the mortality hazard ratio, fewer episodes of HE and sepsis, and a delayed need for paracentesis. Finally, during the 18 months follow-up, fewer patients were considered to have developed refractory ascites. Interestingly, a post hoc analysis (ILC 2019 presented data) of the ANSWER study showed that the albumin level after one month of treatment was strongly predictive of survival. In particular, 18 months survival reached 90% when above 40g/L. This suggests that the amount of albumin infused is highly important and may need to be adapted individually. In another RCT, patients awaiting liver transplantation received either midodrine 15-30mg/day and albumin 40g/day or placebo. There was no difference between both groups, neither in terms of survival on the waiting list, nor in terms of occurrence of cirrhosis complications or ascites control [START_REF] Sola | Midodrine and albumin for prevention of complications in patients with cirrhosis awaiting liver transplantation. A randomized placebo-controlled trial[END_REF]. A very quick access to LT (median treatment duration of 80 days in both groups) may however have precluded this trial to show more significant results.

TIPS placement induces a decompression of the portal circulation by shunting an intrahepatic portal branch into a hepatic vein. Its indications in the treatment of refractory ascites are better defined and will be discussed further away in this manuscript. The benefit of TIPS insertion in less severe patients, such as those with recurrent (or recidivant) ascites (RA) remains however uncertain. RA was first defined in a 1996 consensus as ascites that recurs at least three times within 12 months in spite of sodium restriction and diuretic treatment [START_REF] Arroyo | Definition and diagnostic criteria of refractory ascites and hepatorenal syndrome in cirrhosis[END_REF]. Recently, EASL guidelines defined early RA as ascites that recurs earlier than one month after initial control [START_REF] Study | Electronic address eee, European Association for the Study of the L. EASL Clinical Practice Guidelines for the management of patients with decompensated cirrhosis[END_REF]. None or few of these patients were included in initial RCTs comparing TIPS using bare metal stents versus standard medical treatment (SMT). Recently, a study by Bureau et al. compared the prognosis of patients with RA receiving either TIPS with PTFE-covered stents or SMT [START_REF] Bureau | Transjugular Intrahepatic Portosystemic Shunts With Covered Stents Increase Transplant-Free Survival of Patients With Cirrhosis and Recurrent Ascites[END_REF]. These patients were however more severe than according to the previous definition of RA. In order to be included, they needed to have required at least 2 LVPs within a minimum 3 weeks interval. Noteworthy, about 30% of patients had a history of variceal bleeding, and about 20% had a history of renal failure, highlighting the severity of their circulatory dysfunction. There was a significant increase of the one-year survival without transplantation rate (93% vs 52% p=0.003) in the TIPS group, which was the primary endpoint of the study. Interestingly, hepatic encephalopathy (HE) did not occur more frequently in the TIPS group. These results, obtained in patients with RA, moderate hepatic insufficiency and absence of previous overt HE, illustrate the importance of defining which patients will be the best candidates for TIPS and those more severely ill who should be listed for transplantation.

b) Patients with refractory ascites

Definition of refractory ascites

According to the International Ascites Club, refractory ascites is defined as "ascites that cannot be mobilized or the early recurrence of which cannot be satisfactorily prevented by medical therapy" [START_REF] Arroyo | Definition and diagnostic criteria of refractory ascites and hepatorenal syndrome in cirrhosis[END_REF]. This definition includes diuretic-resistant ascites, i.e ascites that cannot be mobilized or the early recurrence of which cannot be prevented because of a lack of response to sodium restriction and diuretic treatment, and diuretic-intractable ascites, i.e. ascites that cannot be mobilized or the early recurrence of which cannot be prevented because of the development of diuretic-induced complications that preclude the use of an effective diuretic dosage. From a practical point of view, it is very difficult to reach the maximal doses of diuretics and 90% of patients display intractable ascites. HE, renal failure, hyponatremia, hypo-or hyper-kaliemia and muscle cramps are the main reasons for diuretics withdrawal [START_REF] Study | Electronic address eee, European Association for the Study of the L. EASL Clinical Practice Guidelines for the management of patients with decompensated cirrhosis[END_REF].

Large-volume paracentesis

Large volume paracentesis (LVP) is the first line treatment of refractory ascites [START_REF] Arroyo | Definition and diagnostic criteria of refractory ascites and hepatorenal syndrome in cirrhosis[END_REF]. Plasma volume expansion is required in order to prevent a post-paracentesis dysfunction. In a metaanalysis of randomised controlled trials, albumin infusion has shown to be more effective than other plasma expander in the prevention of post-paracentesis dysfunction [START_REF] Sola-Vera | Randomized trial comparing albumin and saline in the prevention of paracentesis-induced circulatory dysfunction in cirrhotic patients with ascites[END_REF]. Albumin infusion should therefore be performed in patients undergoing LVP of more than 5L (8 g/L of ascites removed) [START_REF] Study | Electronic address eee, European Association for the Study of the L. EASL Clinical Practice Guidelines for the management of patients with decompensated cirrhosis[END_REF].

Albumin

Long-term administration of albumin has also been shown to reduce mortality in patients with refractory ascites. The single center, non-randomized study by Di Pascoli et al., evaluated the prognosis of patients of patients with refractory ascites treated with albumin 40g twice weekly versus SMT [START_REF] Pascoli | Long-term administration of human albumin improves survival in patients with cirrhosis and refractory ascites[END_REF]. Two-year mortality, which was the primary endpoint, was significantly lower in the albumin group (41.6% vs 65,5%, p=0.032). This study has many limitations including TIPS as an alternative therapeutic for these patients. However, a survival benefit of long-term administration of albumin in more severe patients, such as those with refractory ascites, may be particularly interesting in selected patients, especially liver transplantation candidates.

Transjugular intrahepatic portosystemic shunt

Transjugular intrahepatic portosystemic shunt (TIPS) placement induces a decompression of the portal circulation by shunting an intrahepatic portal branch into a hepatic vein. In the setting of refractory ascites, 6 prospective randomized controlled trials (RCT) compared noncovered TIPS and LVP in terms of ascites recurrence, hepatic encephalopathy, and survival (Table 1) [START_REF] Lebrec | Transjugular intrahepatic portosystemic shunts: comparison with paracentesis in patients with cirrhosis and refractory ascites: a randomized trial. French Group of Clinicians and a Group of Biologists[END_REF][START_REF] Gines | Transjugular intrahepatic portosystemic shunting versus paracentesis plus albumin for refractory ascites in cirrhosis[END_REF][START_REF] Sanyal | The North American Study for the Treatment of Refractory Ascites[END_REF][START_REF] Narahara | Transjugular intrahepatic portosystemic shunt versus paracentesis plus albumin in patients with refractory ascites who have good hepatic and renal function: a prospective randomized trial[END_REF][START_REF] Rossle | A comparison of paracentesis and transjugular intrahepatic portosystemic shunting in patients with ascites[END_REF][START_REF] Salerno | Randomized controlled study of TIPS versus paracentesis plus albumin in cirrhosis with severe ascites[END_REF]. The results were analysed in several meta-analysis, the later showing the more satisfactory methodology (meta-analysis of individual data): in this meta-analysis, ascites recurrence and transplant-free survival were better in the TIPS group, when compared to LVP [START_REF] Salerno | Transjugular intrahepatic portosystemic shunt for refractory ascites: a meta-analysis of individual patient data[END_REF]. However, the average number of HE episodes was higher in the TIPS group. It seems important to underline that those results were published before the use of PTFEcovered stents. One can hypothesise that results would be better using covered stents, when extrapolating results obtained in recurrent ascites [START_REF] Bureau | Transjugular Intrahepatic Portosystemic Shunts With Covered Stents Increase Transplant-Free Survival of Patients With Cirrhosis and Recurrent Ascites[END_REF]. To date, no prospective controlled trial has been published using covered stent in refractory ascites. In the study published by Bureau and colleagues, patients were included in case of recurrent ascites, defined by 2 LVP within a minimum of 3 weeks, excluding those who had required >6 LVP within the previous 3 months. These criteria were quite different from both the historical definition of recurrent ascites and those of refractory ascites, as previously discussed. TIPS is contraindicated in patients with heart failure, advanced liver failure, defined by a Child-Pugh score >13 or a MELD score >19, and significant HE. It seems crucial to carefully select patients for TIPS placement. Exclusion criteria were indeed heterogeneous amongst RCT, but some of them were similar, such as age >70 or 75 years, HE on the day of TIPS placement, Child-Pugh >11, HCC out of Milan criteria, and heart failure. There are 3 main complications that have a negative impact on prognosis after TIPS placement: 1) liver failure and death; 2) refractory HE; and 3) heart failure. First, a simple survival predictor has been described, combining platelets count and total bilirubin level [START_REF] Bureau | Serum bilirubin and platelet count: a simple predictive model for survival in patients with refractory ascites treated by TIPS[END_REF]: the actuarial 1-year survival rate in patients with both a platelets count above 75×10 9 /L and a total bilirubin level lower than 50 µmol/L [3mg/dl] was 73.1% as compared to 31.2%, in patients with a platelets count below 75×10 9 /L or a total bilirubin level higher than 50 µmol/ L. Second, several risk factors of further development of HE have been described: older age, a poor liver function, a previous episode of HE, sarcopenia, and minimal hepatic encephalopathy. Nevertheless, there is no predictive model to apply to select effectively patients according to their risk to develop HE. Very recently, we recommended excluding TIPS as a non-urgent option in patients with a history of at least 2 bouts of HE, or with HE on the day of TIPS placement [START_REF] Afef | Association Française pour l'Etude du Foie Clinical Practice Guidelines for the diagnosis and management of liver encephalopathy in patients with cirrhosis[END_REF]. Moreover, we suggested TIPS placement to be discussed case by case in patients older than 70. Last, regarding heart failure, a very recent prospective study has shown that cardiac decompensation occurs in about 20% of patients [START_REF] Billey | A prospective study identifying predictive factors of cardiac decompensation after TIPS: the Toulouse algorithm[END_REF]. The authors described that a combination of a BNP<40 pg/mL and a NT-proBNP<125 pg/mL before TIPS and the exclusion of diastolic dysfunction at echocardiography ruled out the risk of cardiac decompensation.

Alfapump ® Alfapump ® (AP) is a fully implantable, programmable, and rechargeable pump system that automatically diverts ascitic fluid from the peritoneal cavity to the urinary bladder, allowing fluid removal by micturition (Table 1) [START_REF] Bellot | Automated low flow pump system for the treatment of refractory ascites: a multi-center safety and efficacy study[END_REF][START_REF] Stirnimann | Treatment of refractory ascites with an automated low-flow ascites pump in patients with cirrhosis[END_REF]. A recent multicenter RCT conducted in patients with refractory ascites, AP significantly reduced the number of LVP and improved the quality of life as well as nutritional parameters [START_REF] Bureau | Alfapump(R) system vs. large volume paracentesis for refractory ascites: A multicenter randomized controlled study[END_REF]. Quality of life has shown to be improved by AP in another study [START_REF] Stepanova | Patients with refractory ascites treated with alfapump(R) system have better health-related quality of life as compared to those treated with large volume paracentesis: the results of a multicenter randomized controlled study[END_REF]. As the device may provoke acute renal failure-even if reversibleit is currently contra-indicated in patients with chronic renal failure. Moreover, some patients, especially with HE, will experience technical difficulties. Therefore, it seems reasonable not to consider AP as an alternative therapy for patients with HE without any involved relative that could take care of the device.

Liver transplantation

As survival is poor in patients with refractory ascites, LT should be discussed in all of them. Nevertheless, despite the poor prognosis of this clinical situation, some patients will present with a low MELD score that may delay LT. In these latter patients, liver transplantation could be prioritized based on a MELD score exception. Nevertheless, prioritisation will be only considered in patients with a strict contra-indication for TIPS placement [START_REF] Francoz | Model for end-stage liver disease exceptions in the context of the French model for endstage liver disease score-based liver allocation system[END_REF]. That's the reason why TIPS should first be envisioned in those patients.

Summary of available therapeutics, indications (Figure 1)

As previously mentioned, LVP should be performed in patients with refractory ascites. If LVP is the first line treatment, a second line therapy has to been envisioned as soon as the diagnosis is made in order to improve prognosis. A careful clinical, biological examination and morphological is required: 1) clinical history, including age, systematic search for a previous episode of HE or heart decompensation; 2) physical examination with screening for confusion, flapping, sarcopenia, left or right signs of heart failure; 3) biological evaluation including routine blood exams, hepatic function, renal and cardiac function with BNP and NT-proBNP; 4) morphological evaluation including abdominal ultrasound exam, CT scan, and echocardiography. TIPS seems to be the best therapeutic option in patients <65 years, without any previous episode of HE, with a Child-Pugh score <13 and a MELD score <19, a total bilirubin level <50 µmol/L, a platelets count >75×10 9 /L, a normal value of BNP/NT-proBNP, and a normal echocardiography. TIPS should be contraindicated in patients >70 years, with history of more than 2 episodes of HE. AP can be envisioned in the latter patients unless they present a correct renal function (Cl Creat ≥ 50 ml/min). A case-by-case discussion is required for patients considered at high risk, according to liver function, cardiac function, and the risk of HE after TIPS. As there is always a theoretical risk after TIPS in all patients, we believe that a liver transplantation needs to be discussed at the same time in all patients, as they are prone to develop either liver failure or refractory HE requiring LT. c) Patients with spontaneous bacterial peritonitis SBP represents the most frequent site of bacterial infection in cirrhotic patients. SBP still carries a high mortality and may trigger worsening of liver function and other complications of cirrhosis such as HE, renal failure, and bleeding. Concerning the treatment of SBP, concern has raised about the increasing prevalence of multidrug resistant organisms (MDRO). They are mainly represented by extended spectrum beta lactamases producing Enterobacteriaceae and beta lactams resistant gram-positive bacteria. The emergence of extended drug resistant organisms (XDRO), in hospitalized patients but also in the community in some parts of the world emphasizes this concern and the need for data concerning the use of newly developed antibiotics in cirrhotic patients. European data support a high prevalence of MDRO infections in decompensated or ACLF patients. About 29% of the strains isolated in the 264 culture positive infections among the 1146 patients with decompensated cirrhosis or ACLF followed in the CANONIC cohort (2011) were MDRO [START_REF] Fernandez | Multidrugresistant bacterial infections in patients with decompensated cirrhosis and with acute-onchronic liver failure in Europe[END_REF]. Wide discrepancies existed among centres and countries, with a higher prevalence in western European countries in these almost 10 years old data. The only factors significantly associated with the occurrence of MDRO were nosocomial infections, hospitalization within the previous 3 months and intensive care unit admission. Noticeably, long-term exposure to norfloxacin was not identified as a risk factor. More recent data (2017-2018) concerning 883 European patients with decompensated cirrhosis showed that 39.7% of culture positive infections among the 284 patients who developed infection were MDRO. It represents an almost 10% increase compared to 2011 data. Interestingly, there was a shift towards a higher prevalence in Eastern and Southern European countries. At a worldwide level, the study by Piano et al. reported 1302 infections in hospitalized cirrhotic patients [START_REF] Piano | Epidemiology and Effects of Bacterial Infections in Patients With Cirrhosis Worldwide[END_REF]. MDRO were isolated in 34% of cases. Risk factors were nosocomial or heath care associated infections, antibiotic exposure within the previous 3 months but also geographical origin and in particular India where the rate of MDRO and XDRO was the highest. Interestingly, the sites most concerned by MDR infections were pneumonias and urinary tract infections. Prevalence was lower in SBP (27%), in accordance with the CANONIC cohort (13.9% for SBP vs 29.3% all sites included). An Italian RCT has compared an initial antibiotic therapy with meropenem plus daptomycin versus ceftazidim to treat nosocomial SBP. There was a significantly higher response to treatment in terms of decrease of neutrophils count in ascites in the meropenem plus daptomycin group, but 90 days transplant free survival was similar in both groups. In multivariate analysis, an ineffective first line treatment was however a significant predictor of mortality, as described in the previously reported studies. Recommendations about antibiotic therapy for SBP are for these reasons very difficult and of paramount clinical importance. They must depend on local bacterial ecology and individual risk factors such as previous antibiotic therapy, health careassociated, or nosocomial infections. Concerning community acquired SBP, EASL guidelines recommend third generation cephalosporins or piperacillin plus tazobactam [START_REF] Study | Electronic address eee, European Association for the Study of the L. EASL Clinical Practice Guidelines for the management of patients with decompensated cirrhosis[END_REF]. Concerning nosocomial SBP, meropenem is recommended, in association with linezolid or daptomycin when prevalence of drug resistant Gram-positive bacteria is high. Administration of 20% albumin is also recommended during SBP at the dose of 1.5g/kg at day 1 and 1g/kg at day 3. Indeed, in the study by Sort et al., such treatment, compared to antibiotic therapy with cefotaxime alone, allowed a significant decrease of in hospital mortality (10% versus 29%, p=0.01) and occurrence of renal failure (10% versus 33%, p=0.02) [START_REF] Sort | Effect of intravenous albumin on renal impairment and mortality in patients with cirrhosis and spontaneous bacterial peritonitis[END_REF]. Severe patients (serum creatinine ≥ 88µM or total bilirubin ≥ 68µM) seemed to take most advantage of this treatment. Whether it should be administrated to all cirrhotic patients thus remains a matter of debate. Prophylaxis of SBP is another clinically relevant issue. Norfloxacin is the only drug recommended and concern is growing about its safety and efficacy regarding the increasing prevalence of MDRO. Frequent neurologic and osteo-articular side effects have led drugregulating agencies to issue warnings about this drug and advise to limit its use when no alternative is available. In primary prophylaxis, norfloxacin is recommended when ascites fluid protein level is below 15g/L is association with severe cirrhosis (Child-Pugh score ≥ 9 and total bilirubin level ≥ 3mg/L, with either impaired renal function or hyponatremia) [START_REF] Study | Electronic address eee, European Association for the Study of the L. EASL Clinical Practice Guidelines for the management of patients with decompensated cirrhosis[END_REF]. A French RCT compared norfloxacin versus placebo in Child Pugh C patients without previous SBP [START_REF] Moreau | Effects of Long-term Norfloxacin Therapy in Patients With Advanced Cirrhosis[END_REF]. Six-months mortality was only significantly lower in patients with low ascitic fluid protein level (<15g/L), confirming that primary prophylaxis should be restricted to the most severe patients. These data are however not recent enough (2010-2014) to take account of the change in susceptibility to fluoroquinolones of Gram negative bacteria, which may affect the effectiveness of this prophylaxis. Norfloxacin use in secondary prophylaxis is an even greater issue, given the high prevalence of recurrent SBP after a first episode. It has proven its effectiveness in a single RCT published in 1990, significantly decreasing the rate of recurrent SBP from 68% in the placebo group to 20% in the norfloxacin group. Such results have not been reproduced more recently. However, recent German observational data on patients under primary or secondary prophylaxis with norfloxacin are in favour of a significantly greater risk of SBP in patients carrying quinolones resistant Gram-negative bacteria. Such results, in a population with a 50% rate of baseline carriage of MDRO highlight the issue about resistance to fluoroquinolones and suggest that screening patients for MDRO could be relevant in routine practice. Finding an alternative to oral fluoroquinolones also appears to be an important question. Preliminary results and a recent meta-analysis support the effectiveness of rifaximin in primary or secondary prophylaxis of SBP [START_REF] Goel | Systematic review with metaanalysis: rifaximin for the prophylaxis of spontaneous bacterial peritonitis[END_REF]. However, the results of a RCT including a larger number of patients, comparing rifaximin and oral fluoroquinolones are still expected.

Conclusion

Prognosis is poor in patients with complicated ascites, including refractory ascites or SBP. In these situations, TIPS placement and liver transplantation have to be discussed at the same time, as TIPS may be either contraindicated or of uncertain evolution in patients at high risk of developing further liver failure, HE or cardiac decompensation. The recent study of Bureau et al. conducted in recurrent ascites suggests that TIPS placement could be indicated at an earlier stage, i.e. before the development of refractory ascites. We do believe that a multidisciplinary discussion has to be organised in order to better select patients for the best therapeutic option.

Figure 1. Algorithm for the management of refractory ascites in patients with cirrhosis

Figure 1 $

 1 Figure 1

Table 1 Main studies comparing LVP and other therapeutics in patients with refractory or recurrent ascites (Table 1a with TIPS, Table 1b with Alfapump®) Table 1a.

 1

				Enrolled patients (n)	Improvemen t of ascites (%)	Development of hepatic (%) encephalopathy	Survival (%)
				TIP S	LV P	TIP S	LVP	TIPS	LVP TIPS	LV P
			Randomised controlled studies
			Lebrec et al. 1996	13	12	38	0	15	6	29	60
			Gines et al. 2002	35	35	51	17	60	34	26	30
		Refractory ascites
			Sanyal et al. 2003	52	57	58	16	38	21	35	33
			Narahara et al. 2011	30	30	87	30	20	5	20	5
	Bare TIPS	Refractory +	Rössle et al. 2000	29	31	84	43	23	13	58	32
		recurrent ascites	Salerno et al. 2004	33	33	79	42	61	39	59	29
			Meta-analysis for refractory
			ascites
					15
			Salerno et al. 2007	149	6	58	11	58	38	56	50
	Cover		Randomised controlled study
	ed	Recurrent ascites
	TIPS		Bureau et al. 2017	29	33	89	29	34	33	93	52
	LVP: large volume paracentesis; TIPS: tranjugular intrahepatic portosystemic shunt

Table 1b . Outcome of Alfapump® for patients with cirrhosis and refractory ascites

 1b

			Len
		Enr olle d pati ents (n)	gth nths of foll ow-up (mo	Number of LVP per patient per month (median)	Development of adverse effects (n)	Child-Pugh score (mean)		MELD score (mean)	Deat h, n (%)	Improvement of Quality of life (HRQoL score)
			)
												At			At
												th			th
				At base line	At the end of follow -up	Infe ctio ns	Cat hete r issu es	Pu mp mal fun ctio	Alfa pum p® expl ant	At ba sel ine	At 6 mo nth s	e en d of fol lo	At ba sel in e	At 6 mo nt hs	e en d of lo fol	Abd omin al toms symp	Activit y scores
												w-			w-
												up			up
	Observational
	studies
						24	10	2	3						9
	Bellot et al.					(60	(25	(5%	(7.5				12.	11.	11.	(22%
	2013	40	6	3.4	0.2	%)	%)	)	%)	8.5 8.6 8.6	6	7	7	)
							28	11	27						23
	Stirnimann et						(50	(20	(48%				13.	17.	9.1	(41%
	al. 2017	56	24	2.2	0.2		%)	%)	)	8.8 9.8 7.5	42	04	1	)
	Randomised
	controlled
	study
						25	5	4	3						15
	Bureau et al.					(93	(9%	(7%	(5.4				12.		(56%	+1.2
	2017	27	6	1.6	0.3	%)	)	)	%)	8.2			2		)	5	+0.80