Mario Merino

Pablo Fajardo

Gabriel Giono

Jón-Tómas Tómas Gudmundsson

Nickolay Ivchenko

Stéphane Mazouffre

Dimitry Loubère

Käthe Dannenmayer

Collisionless electron cooling in a plasma thruster plume: experimental validation of a kinetic model

I. INTRODUCTION

The interaction of the plasma thruster plume with the surrounding elements of the spacecraft poses a major concern for the integration of electric propulsion systems like gridded ion engines (GIT) and Hall effect thrusters (HETs) in space missions [START_REF] Tverdokhlebova | Plasma plume/spacecraft interaction. state of the art in investigation methodology[END_REF][START_REF] Id Boyd | Interactions between spacecraft and thruster plumes[END_REF][START_REF] Goebel | Fundamentals of Electric Propulsion: Ion and Hall Thrusters[END_REF]. The main threat are the charge-exchange ions generated in the plume near-region, which can impinge on neighboring surfaces and interact mechanically, electrically, or chemically with them. These ions originate from collisions between primary ions and low-velocity neutrals outside of the thruster, and their motion is dominated by the local electric field. For this reason, determining accurately the electric potential in the plume near-region is a key step toward the predictive simulation of charge-exchange ion effects.

The electric potential map φ(x) arises from the expansion of the primary ions and the neutralizing electrons, but depends especially on the electron thermodynamics, i.e., on the evolution of the electron temperature T e in the plume, with hotter electrons leading to larger electric fields (∆φ ∼ T e /e). Due to computational constraints, the majority of existing simulation codes follow a fluid de- * mario.merino@uc3m.es; http://ep2.uc3m.es scription for the electrons, using a simple electron cooling law in the form T e ∝ n γ-1 e as the closure relation, where n e is the electron density and γ is a polytropic exponent. The limit γ = 1 means an isothermal electron expansion and results in Boltzmann's relation. Unfortunately, in the near-collisionless regime of plasma thruster plumes, the fluid approach is unjustified, and a fully kinetic model must be used to obtain physically-correct solutions. The inadequacy of the fluid approach is evidenced, in particular, in the case of an isothermal electron species, which leads to an infinite potential fall as the electron density drops to zero. Moreover, even accepting the fluid approximation and a polytropic closure with γ > 1, the parameter γ must be regarded as an extra degree of freedom of the fluid model, which has to be determined for each thruster and each operating condition, bringing an additional source of uncertainty to the simulations.

In order to address these shortcomings, a kinetic electron model for plasma plumes expanding into vacuum [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF] (and the open-source AKILES code [START_REF] Merino | AKILES code: Advanced Kinetic Iterative pLasma Expansion Solver 2D[END_REF]) was recently developed to compute self-consistently the near-collisionless electron expansion. The results of this model show the gradual electron cooling and development of anisotropy in the plume, and can be used to inform existing plume/spacecraft interaction codes like EP2PLUS [START_REF] Cichocki | Hybrid 3D model for the interaction of plasma thruster plumes with nearby objects[END_REF] or SPIS [START_REF] Roussel | SPIS open-source code: Methods, capabilities, achievements, and prospects[END_REF], providing more accurate electron fluid closure relations than the currently-used isothermal and polytropic laws, or at the bare least, choosing a value for γ that is consistent with the kinetic electron response.

As with any physical model, contrasting the predictions of the kinetic model against actual experimental measurements is a necessity to validate it and gain confidence on its accuracy. To this end, a set of dedicated experiments on the plasma plume of a HET have been carried out at ESA-ESTEC, which were reported in references [START_REF] Giono | Experimental determination of the plasma properties in the far-plume of an SPT-100 hall thruster[END_REF][START_REF] Giono | Non-maxwellian electron energy probability functions in the plume of a SPT-100 hall thruster[END_REF]. The present paper compares the kinetic model with those experimental results, analyzing the differences found for six different thruster operating conditions. The validity of the model, and its different predictions, for these operating points is assessed by comparing the axial plasma profiles of the model and the experiments. The paper concludes with the estimation of the polytropic cooling exponent γ in the different experimental cases, as this parameter is widely employed in current simulation codes, and discusses the limitations of such single-γ approximations to model the electron response in plasma thruster plumes.

The rest of the paper is structured as follows. For the sake of self-containment, Section II summarizes the hypotheses and the main aspects of the electron kinetic model of [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF]. Likewise, Section III reviews the experiments of [START_REF] Giono | Non-maxwellian electron energy probability functions in the plume of a SPT-100 hall thruster[END_REF]. Section IV explains the comparison procedure followed, and presents the comparison results to determine the error of the model. The discussion of the effective polytropic fluid closure law as an approximation to be used in fluid electron models is then carried out in Section V. Finally, the main conclusions of this work are gathered in Section VI.

II. KINETIC PLASMA PLUME MODEL

The model of [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF] describes the steady state expansion into vacuum of a plasma jet composed of singly-charged ions and electrons. The reader is directed to that reference for a full account of the model derivation; in this section, only the major aspects of the model, such as its assumptions and parameters, are summarized.

The plasma plume is considered to be collisionless, quasineutral, unmagnetized, and slowly-diverging (i.e., paraxial). The electric potential φ is assumed to decrease monotonically downstream and radially, and is modeled as

φ(x, r) = φ x (x) - C h(x) 4 r 2 , ( 1
)
where C is a constant, and φ x (x), h(x) are a slowlyvarying functions of x to be determined as part of the solution, which represent the potential along the plume axis (r = 0) and the radial widening of the plume as it expands. In essence, expression (1) prescribes the shape of the radial profile for φ to be parabolic. The resulting electric field -∇φ causes a small acceleration on the already-hypersonic ions that stream out of the thruster, and effectively confines most of the electrons, except for the highest-energy tail of their distribution. These free, escaping electrons are responsible for balancing out the ion current in the plume, making it globally current-free.

A typical confined electron trajectory involves many radial reflections between two axial reflections. Under these conditions, the mechanical energy E, the angular momentum about the plume axis p θ , and the adiabatic invariant given by the radial action integral [START_REF] Goldstein | Classical mechanics[END_REF] J r of each individual particle,

E = 1 2 mv 2 ; p θ = mrv θ ; J r = mv r dr, (2)
are conserved. The latter integral accepts a closed form, J r = J r (x, r, v r , v θ ).

Ions are treated as a cold species, and their bulk density and velocity are integrated directly from their continuity and momentum equations, expressions (32) and (33) in reference [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF], whereas the electron distribution function f e = f e (x, r, E, p θ , J r ) is averaged over the radial electron motion into fe = fe (x, E, p θ , J r ) and solved for using the paraxial Vlasov equation,

v x ∂ fe ∂x = 0. ( 3
)
This equation states that fe is constant along x for each (E, p θ , J r ), as long as v x = 0. The condition v x (x, E, p θ , J r ) = 0 defines the turning manifold at which electrons are axially reflected, and is given by

E -U eff (x, p θ , J r ) = 0, (4)
where U eff is an effective potential for the axial motion of the electrons,

U eff (x, p θ , J r ) = -eφ x (x) + 2eC m e J r /π + |p θ | h 2 . (5)
Observe that the turning manifold depends on J r and p θ only through p ⊥ = J r /π + |p θ |, which allows to reduce the dimensionality of the model. The manifold in equation ( 4) splits the electron phase space into four distinct regions, according to the connectivity of electron trajectories with the boundaries of the domain (x = 0 and x = ∞): (i ) reflected electrons, i.e., low-energy electrons that are emitted from the plasma source and eventually reflected back to it by the potential fall along the plume; (ii ) free electrons, i.e., high-energy electrons emitted from the source that can reach infinity downstream; (iii ) doubly-trapped electrons, i.e., isolated electrons whose trajectories do not connect neither with x = 0 nor with x = ∞; and (iv ) empty regions, which connect only with x = ∞ and are therefore not occupied.

At the upstream boundary (x = 0), conditions on the ion density n i0 and axial bulk velocity u i0 must be provided. Likewise, the forward-going (v x > 0) part of the radially-averaged electron distribution function fe is required at that position. In the present work, a semi-Maxwellian electron population is prescribed. These boundary conditions suffice to obtain the solution of the reflected and free electrons, but additional information is required to solve for the isolated doubly-trapped population. The model assumes that either the transient set-up process of the plume [START_REF] Sánchez-Arriaga | Kinetic features and non-stationary electron trapping in paraxial magnetic nozzles[END_REF] or the occasional collisions help populate these regions with a fraction α of the same distribution as in other electron regions.

After assuming an initial guess for the φ(x) and h(x) functions, the ion and electron models are used to obtain the ion and electron density n i and n e along the plume axis. The quasineutrality condition, n i -n e = 0 and the current-free condition n i u i -n e u e = 0 are then used to compute the error of the solution and set up an iterative scheme that allows to find the self-consistent solution for φ(x) and h(x).

The resulting model has three remaining degrees of freedom, which can be parametrized as the filling parameter α that characterizes the doubly-trapped electron regions; the initial ion Mach number, M i0 ; and the square root of the ion-to-electron mass ratio µ:

α; M i0 = u i0 T e0 /m i µ = m i m e (6)
In this work, α = 1 is chosen (fully occupied doublytrapped regions), and µ = 2.39 • 10 5 (xenon). Observe that T e0 and n e0 depend on the backward-going part of the distribution function fe at x = 0, which is not known a priori and must be computed as part of the solution.

Finally, note also that the initial values of φ x (x) and h(x), i.e. φ 0 and h 0 , as well as the constant C introduced in (1), can be fixed after solving the model, as long as the solution is rescaled appropriately.

III. PLASMA PLUME MEASUREMENTS

This section overviews the main aspects of the experimental campaign carried out in April-May 2017 at the ESA/ESTEC Electric Propulsion Laboratory. The measurements have been obtained in the plume of a 1.5 kWclass SPT-100-ML Hall thruster [START_REF] Giono | Non-maxwellian electron energy probability functions in the plume of a SPT-100 hall thruster[END_REF]. A more detailed account of the experiments can be found in that reference. The plasma properties of the plume were mapped for six different operating points of the thruster by changing the discharge voltage and the mass flow rate of Xenon to: A) 150 V, 2 mg/s; B) 225 V, 2 mg/s; C) 300 V, 2 mg/s; D) 400 V, 2 mg/s; E) 150 V, 4 mg/s; and F) 300 V, 4 mg/s. The six cases are shown in I. Two different probe diagnostics were used in the campaign: cylindrical Langmuir probes and Faraday cups.

Cylindrical Langmuir probes (5 mm long Tungsten wire with a 0.2 mm diameter, aligned parallel along the plume axis) were installed on two two translation stages mounted on the large CORONA vacuum chamber at ESA-ESTEC (2 m in diameter and 4 m in length). The first translation stage was mounted on the chamber rotating arm, allowing to scan angular position from -20 • FIG. 1. Maps of the electron density ne (top) and electron temperature Te (bottom) for a discharge voltage of 300 V and a mass flow rate of 4 mg/s (case F). The SPT-100-ML thruster was position at the origin, with the plume direction along positive x. The dots show were measurements were performed and a 2D interpolation is displayed in-between.

to +90 • at distances between 550 to 750 mm from the thruster, while the second translation stage was placed further downstream, providing measurements along the plume axis 850 mm to 1550 mm from the thruster exit. The current-voltage characteristic (i.e. I-V curve) of the Langmuir probe was measured using a Keithley 2440 sourcemeter, sweeping the probe voltage from -15 V to +35 V. The plasma parameters, namely the electron density n e , the electron temperature T e and the plasma potential φ, were derived from the I-V curve both by fitting the appropriate expression of the current and by using the Druyvesteyn method [START_REF] Lieberman | Principles of plasma discharges and materials processing[END_REF]. Figure 1 shows an example of measured electron density and temperature in the plume region, for a discharge voltage of 300 V and a mass flow rate of 4 mg/s. With the exception of operating point B, which showed noisy measurements, the rest of cases have smooth axial profiles of electric potential φ and electron density n e . The obtained values of electron temperature T e also present smooth variations, except for cases B, E and F.

Faraday cup (FC) measurements were used in the test campaign to obtain the angular distribution of the ion current density in the plasma plume. Details about FC design and operation can be found in [START_REF] Mazouffre | Evaluation of various probe designs for measuring the ion current density in a hall thruster plume[END_REF]. The graphite probe collimator aperture is 10 mm in diameter; it defines the collection area. The cup is 16 mm in diameter and 20 mm in length. Electrical insulation between the cup and the collimator is achieved with PEEK spacers. The FC is mounted onto a floating aluminum holder fixed to the chamber rotating arm. The FC faces the center of the thruster exit plane, i.e. it is parallel to ion current streamlines. The HT to probe distance is x F = 797 mm. The current was recorded with a Keithley 2400 calibrated sourcemeter. The latter is also used to polarize the cup at -100 V for all measurements. The FC was positioned in the horizontal plane that contains the SPT-100-ML Hall thruster centerline. Ion current density measurements were performed over a hemisphere. In this work the Hall thruster was not aligned with the rotating arm pivot. As a consequence, the FC angle with respect to the thruster exit plane does not correspond to the arm angle, but at 0 • when the arm is aligned with the thruster axis. Correction has been applied to all measured current angular distributions to retrieve the effective distributions. Figure 2 shows raw and corrected ion current density angular profiles for case F.

Figure 3 shows the current-voltage curve at various angles. The results show the great advantage of using Faraday Cups to measure the ion current density, since the saturation current does not depend on the voltage. This means the plasma sheath expansion effect is cancelled; thus current density measurements are more accurate with FCs compared to other probe types.

IV. COMPARISON RESULTS

The procedure used to compare the experimental results with the model can be summarized as follows.

Firstly, the available experimental data for each operating point is prepared for the comparison. Since the spatial locations where the Faraday cup data and the Langmuir probe data were obtained are not identical, interpolation is carried out when needed to evaluate a plasma property. Also, the average of the plasma properties obtained from Langmuir probe measurements processed with the IV-curve method and the Druyvesteyn method is computed and used as the reference data for the model validation, after checking that the differences between the two are small.

Secondly, we determine the input parameters of the model for each case. The value of M i0 is obtained by using the ion current density from the Faraday probe at point F , x F = 797 mm, i.e., j i (x F ). The value of n e (x F ) at that point is then interpolated from the Langmuir probe data, and ion velocity is determined as u i (x F ) = j i (x F )/n e (x F ). Next, the ion velocity at the most upstream point L where measurements exist, x L = 550 mm, is computed with the energy equation,

u i (x, 0) = u 2 i (x F ) -2e∆φ(x, 0)/m i (7)
at x = x L , where ∆φ(x, 0) = φ(x, 0) -φ(x F , 0), with φ(x F , 0) interpolated from the Langmuir probe data at x F . Finally, the ion Mach number for the kinetic model is computed as M iL = u i (x L )/ T e (x L )/m i , where T e (x L ) is obtained from Langmuir probe data. Under the assumption that the ions are hypersonic, so that Mach number variations along the plume axis are small, the initial Mach number is estimated as M i0 = M iL . The values leading to this calculation and the resulting M i0 are shown in rows 3-8 and row 9 of table I for each experimental case. In the six test cases studied here, M i0 is in the range of 9-15. While the ion Mach number M i0 is one of the main input parameters of the kinetic model, analysis shows that the sensitivity to this parameter is large only for low values of M i0 , and that when the plume is hypersonic (say, M i0 > 5), the model results are only weakly dependent on the value of M i0 . Therefore, the dimensionless simulation results do not vary much among the different test cases. In the nomenclature used in reference [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF], all cases have χ 0.02. As it can be observed, electron density n e , ion velocity u i , electric potential φ, and electron temperature T e increase with the discharge voltage V d , with the exception of case B, which has the worst quality experimental results and is slightly off this trend. The increase of n e can be attributed to a less divergent plume as V d increases. The estimated ion velocity at x F following the procedure above is seen to be consistent in all cases with the estimation based on the discharge voltage u i ≈ 2βeV d /m i , with β ∈[0.4-1]. Lastly, it is seen that electron density n e increases and u i decreases with increasing ṁ, while there is no clear trend with ṁ for φ and T e . The behavior of the ion Mach number M i0 , which results from the combination of the behavior of u i and T e , is also non-trivial; however, overall it can be stated that it increases with the discharge voltage, V d .

Thirdly, the beam width function, h(x)/h(x P ), is computed from the experimental data using the paraxial continuity equation:

h 2 (x) h 2 (x P ) = n e (x P )u i (x P ) n e (x, 0) u 2 i (x P ) -2e∆φ(x, 0)/m i (8)
where ∆φ(x, 0) = φ(x, 0) -φ(x P , 0). The beam width function was inspected for all test cases and seen that it could be accurately approximated as a straight line in the measurement region with a relative RMS error of less than 0.1%. This is consistent with a nearly-conical expansion in the far plume region. Hence, a linear h(x) fit with a constant slope dh/dx (dependent on the operating case) is used in the comparison in the range where experimental data are available. The value of dh/dx, which represents the plume divergence rate, is seen to decrease with increasing discharge voltage V d . This is consistent with a more collimated plasma beam as the discharge voltage increases.

Fourthly, the remaining parameters of the model, i.e., h(x P ), φ 0 , n e0 , and C, are determined for each test case by minimizing the mean square error in potential, density and temperature with the experimental data at the plume axis, for all points between 550 and 1550 mm from the thruster exit plane where Langmuir probe data are available. These parameters are shown in rows 10-14 of table I. With the exception of the previously mentioned noisy case B, the general trend of the upstream potential, φ 0 , and electron density, n e0 , is to increase with the discharge voltage as could be expected.

It should be noted that the kinetic model returns the axial, radial, and azimuthal electron temperature T ex , T er , T eθ as distinct values, showing the development of electron anisotropy in the expansion even if the distribution is initially Maxwellian. As separate temperature component data is not experimentally available, only the average temperature T e = (T ex +T er +T eθ )/3 can be used in this comparison study. Once all the model parameters are fixed, simulations have been carried out for each experimental case. Below, the comparison and discussion of results is presented.

A. Radial electric potential profile

One of the hypotheses of the kinetic model is that the electric potential profile φ has a parabolic shape in the radial direction. The radial electric potential profile at x 1 = 550 mm is shown in Figure 4 for test case A. This figure is representative of the rest of test cases, which are not shown in the sake of conciseness. As it can be observed, the experimental data are well approximated by the parabolic electric potential profile up to about y = 150 mm; from there outward, the measured potential decreases at a lower rate than the one considered in the model.

As the majority of the electron population has low energy E, most of the electrons cannot travel to large values of r, and hence they do not perceive the the difference between the radially-parabolic and the measured electric potential. The deviation from a radially-parabolic electric potential profile is expected to introduce an error in the model due to the change in the mathematical expression of the radial action integral, J r , of the higher-energy electrons that can travel far in the radial direction before being radially reflected. In essence, the higher value of the potential at large r means that those electrons with high J r will display a larger radial oscillation period than in the parabolic case. Future work must assess the importance of this assumption further by considering other radial profiles for the electric potential model. F. We can conclude that the potential, electron density, and electron temperature on the plume axis are well described by the model in all cases, which supports the validity of the model. The comparison error in electric potential is below 0.5 V everywhere, with the sole exception of a small region of case D. This error is below 10-20% of the local value of T e in all cases, except in the noisy simulation B where it reaches 30%. The relative error of electron density n e is less than 5-10% in all the experimental cases.

B. Plasma properties along the plume axis

Regarding the electron temperature measurements, they are more noisy than the other variables. This is evident from the erratic experimental curves in these figures, especially in cases B, D, E. Notwithstanding this, the model clearly reproduces the average trend of the experimental data, which clearly proves that electron cooling is taking place in the near-collisionless expansion, which is one of the major predictions of the kinetic model. It is worth noticing that the experimental error in the electron temperature T e affects the determination of constant C in the model, a fundamental sizing parameter for the radial electric potential profile, and thus an error in its determination affects the electric potential and electron density as well. Since the parameter fitting procedure followed here ensures that the error is as small as possible in φ, the electron density n e , and the electron temperature T e simultaneously, these three fits are not independent from each other.

The differences between model and experiment are in all cases comparable to the expected experimental error of a Langmuir probe in a plasma thruster plume, and indeed, most of the differences have a noisy oscillatory behavior, which can be attributed to the measurements themselves. The model can be extrapolated in each test case to x = 0 and x = ∞ to investigate additional aspects of the plume expansion and further validate it. In the experiments, the thruster was electrically floated with respect to the vacuum chamber walls, to which the potential is referenced (φ = 0). Two major difference between the free plasma expansion in space and in a vacuum chamber are the higher background pressure and the limited plume length in the latter case. These effects make it more difficult to validate the kinetic model with laboratory experiments. It is noted that the validity of the model relays on the expansion being non-magnetized and collisionless. Thus, as the model is extrapolated toward the exit plane of the thruster (x = 0), the error committed is expected to increase, as these assumptions are not longer satisfied there. In fact, it is not expected that h(x) has the same slope dh/dx in this near region as in the far region. Notwithstanding this, the model can be used to estimate φ 0 , n e0 , and T e0 , the upstream values of the electric potential, electron density, and the electron temperature. Indeed, the former two were obtained as part of the parameter fitting process in Section IV and the three of them are shown in table I. These values roughly correspond to the potential, density and temperature close to the thruster, but they cannot be directly related to any specific location for the reasons above. As it can be observed, with the exception of test case B, φ 0 , n e0 and T e0 increase with increasing discharge voltage V d . Increasing the Xenon mass flow rate increases the electron density n e1 . However, it also increases the background pressure in the vacuum chamber, which translate into a larger plasma collisionsionality. This goes against the collisionless assumption in the kinetic model, so it can be expected that cases E and F will be worse represented While in the laboratory the presence of the chamber wall interrupts the plasma expansion to infinity, the plasma forms a sheath at the chamber wall downstream to ensure a net current-free plume, such that the total potential fall from the thruster to the chamber wall, i.e., including the sheath, is essentially the same as the total potential fall in space from the thruster to infinity. In other words, φ ∞ should roughly correspond to the potential of the vacuum chamber, φ = 0. As it can be observed in table I, φ ∞ is slightly greater than 0 in all test cases, but within one electron temperature T e0 from it, i.e., eφ ∞ /T e0 < 1. This consistency further supports the validation of the model.

V. APPROXIMATE FLUID CLOSURE LAW

As previously mentioned, most of the existing plasma plume simulation codes follow a fluid description for the electrons and many of them use as closure relation a simple law relating the electron density and temperature by means of a simple polytropic exponent, γ, i.e., T e = T e0 (n e /n e0 ) γ-1 . The kinetic results of the model of reference [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF] can be used to compute an approximated, effective electron polytropic cooling exponent γ for each experimental case. The value of γ can be chosen to give the same potential fall φ ∞ -φ 0 along the plume as in the kinetic model. Integrating the collisionless electron momentum equation 0 = -∂(n e T e )/∂x+en e ∂φ/∂x between FIG. 6. Experimental (red segment lines) and fitted model (blue lines) curves for the plasma potential, φ, electron density ne, and electron temperature Te, along the plume axis (y=0), for test cases C and D. The difference between the two lines in the region of measurement is displayed in the inset plots.

x = 0 and x = ∞,

γ = | φ ∞ -φ 0 | | φ ∞ -φ 0 | -T e0 /e . (9)
The last row of table I presents the values of effective γ for the considered conditions. The value of this effective, lumped-model polytropic cooling exponent γ is in the range [1.26-1.31] for all cases. There is no clear trend to the behavior of this parameter with the discharge voltage or the propellant mass flow rate. These values are in line to those reported experimentally by [START_REF] Giono | Non-maxwellian electron energy probability functions in the plume of a SPT-100 hall thruster[END_REF] for the same experiments. They are also in agreement with the measured values in a PPS-1350-ML and a PPS-100-ML [START_REF] Dannenmayer | Electron flow properties in the far-field plume of a hall thruster[END_REF], as well as a BHT-200 [START_REF] Nakles | Experimental and numerical examination of the BHT-200 Hall thruster plume[END_REF] in the far plume region. Finally, while it might provide a first approximation to the plasma expansion, it should be noted that a lumped model like this one conceals the local variation of the cooling rate in the collisionless expansion, which does not fit well with a single polytropic exponent. And although the value of φ ∞ is correctly captured by a polytropic approximation (indeed, γ has been defined to match φ ∞ , the local electric potential map in the plume differs substantially from that of the kinetic model [START_REF] Nuez | Fluidkinetic propulsive magnetic nozzle model in the fully magnetized limit[END_REF]. Moreover, a simple polytropic model neglects the anisotropy in electron temperature that develops as the collisionless electrons expand [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF].

VI. CONCLUSIONS

The kinetic electron model of a paraxial, unmagnetized, collisionless plasma plume expanding into vacuum of [START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF] has been compared against the six experimental test cases of a SPT-100-ML Hall Effect Thruster from FIG. 7. Experimental (red segment lines) and fitted model (blue lines) curves for the plasma potential, φ, electron density ne, and electron temperature Te, along the plume axis (y=0), for test cases E and F. The difference between the two lines in the region of measurement is displayed in the inset plots. [START_REF] Giono | Non-maxwellian electron energy probability functions in the plume of a SPT-100 hall thruster[END_REF]. A comparison procedure has been established that first computes the input parameters of the model M i0 , dh/dx for each test case and then fits the normalization constants (φ 0 , n e0 and C) to minimize the difference error. The kinetic model, which follows exploits the conservation of mechanical energy, angular momentum about the plume axis and the adiabatic radial action integral to solve the electron Vlasov's equation is seen to match well the laboratory measurements. This is a first step toward the validation of the model; additional and more detailed measurements, such as of the electron temperature anisotropy in the plume, are necessary to assess the accuracy of all the predictions of the model and fully validate it.

The accuracy of the radial parabolic potential profile used by the model has been confronted against real data, showing good agreement in the central part of the plume, and increasing differences in the plume radial periphery. The deviation from the assumed profile introduces a computation error in the the radial action integral of electrons, J r , which is expected to affect only high energy electrons, i.e., only a minority of the population. Kinetic models with other radial potential profiles, closer to the measured ones, can be developed to better approximate this aspect of the problem.

The agreement on the fundamental plasma parameters along the plume axis (potential φ, electron density n e , and electron temperature T e ) has been evaluated and discussed using the available measurements, in the range x = 550-1550 mm. The error in potential and electron density is small in all six test cases and within experimental uncertainty. The evolution of T e clearly follows the trend recovered experimentally, but the measurements are noisier.

The departure of the laboratory test conditions from in-space conditions presents a surmontable hurdle toward the validation of the model. In particular, the higher background pressure and presence of the vacuum chamber wall that interrupts the plume expansion to infinity can affect the results of the comparison. It is noted that the electron response in the collisionless plume is global, meaning that an effect downstream can alter the expansion upstream, and vice-versa. However the model shows a fitted φ i nf ty value that is only slightly higher than 0, consistent with the potential of the vacuum chamber wall.

Finally, an approximated, effective electron polytropic coefficient was computed that gives the same total potential fall than the model. The values computed for the different operating conditions tested are in the range γe = 1.26-1.31, in agreement with other values reported in the literature.

FIG. 2 .

 2 FIG. 2. Ion current density distribution measured for 300 V, 4 mg/s (case F). Raw and corrected profiles are shown.

FIG. 3 .

 3 FIG. 3. Current to voltage curve for the Faraday probe measured at different angles from the centerline.

FIG. 4 .

 4 FIG. 4. Radial electric potential profile at x = 550 mm, the first plane of the plume where experimental data are available, for test case A. The thick line shows the interpolated experimental profile. The dashed line shows the approximated radially-parabolic electric potential profile used by the kinetic model.

Figures 5 ,

 5 Figures 5,[START_REF] Cichocki | Hybrid 3D model for the interaction of plasma thruster plumes with nearby objects[END_REF] and 7 compare the electric potential φ, the electron density n e , and the electron temperature T e between the fitted model and the experimental results in the region of measurement for all test cases A through

  C. Model extrapolation to x = 0 and x = ∞

FIG. 5 .

 5 FIG.5. Experimental (red segment lines) and fitted model (blue lines) curves for the plasma potential, φ, electron density ne, and electron temperature Te, along the plume axis (y=0), for test cases A and B. The difference between the two lines in the region of measurement is displayed in the inset plots.

TABLE I .

 I Operationg conditions (rows 1-2), experimental and intermediate data[START_REF] Goebel | Fundamentals of Electric Propulsion: Ion and Hall Thrusters[END_REF][START_REF] Merino | Kinetic electron model for plasma thruster plumes[END_REF][START_REF] Merino | AKILES code: Advanced Kinetic Iterative pLasma Expansion Solver 2D[END_REF][START_REF] Cichocki | Hybrid 3D model for the interaction of plasma thruster plumes with nearby objects[END_REF][START_REF] Roussel | SPIS open-source code: Methods, capabilities, achievements, and prospects[END_REF][START_REF] Giono | Experimental determination of the plasma properties in the far-plume of an SPT-100 hall thruster[END_REF], fitted model parameters 9-14 and results (15-18) for cases A through F.

		A	B	C	D	E	F
	V d [V]	150	225	300	400	150	300
	ṁ [mg/s]	2	2	2	2	4	4
	ne(xF ) [10 15 m -3 ] 1.29 2.59 2.77 3.30 4.78 7.29
	ui(xF ) [m/s]	14484 15691 18000 24576 11759 12840
	φ(xF ) [V]	7.22 7.68 9.58 10.21 7.73 10.31
	φ(xL) [V]	9.25 9.15 12.35 13.17 8.45 12.70
	ui(xL) [m/s]	14381 15622 17886 24488 11714 12702
	Te(xL) [eV]	2.86 1.96 3.57 3.66 1.44 2.60
	Mi0 [-]	9.92 13.02 11.04 14.94 11.40 9.19
	h(xF ) [mm]	301.5 155.6 123.3 76.7 254.3 82.23
	dh/dx [-]	0.301 0.144 0.135 0.088 0.22 0.09
	φ0 [V]	24.83 14.69 33.15 56.12 12.61 28.56
	ne0 [10 16 m -3 ]	8.48 3.96 17.6 45.2 5.08 46.8
	C [Vmm 2 ]	7385.4 4811.8 1688.9 551.45 14274 567.43
	Te0 [eV]	4.81 2.77 6.55 12.04 2.20 4.98
	φ∞ [V]	1.28 1.95 1.79 2.43 2.17 3.73
	γ[-]	1.27 1.29 1.28 1.31 1.28 1.26

ACKNOWLEDGMENTS

The authors would like to thank the support and use of the facilities at the Electric Propulsion Laboratory at ESTEC. This work was performed in the framework of the 'Model and Experimental validation of spacecraftthruster Interactions (erosion) for electric propulsion thrusters plumes' (MODEX) project (ESA contract number 4000116180/15/NL/PS). MODEX is a collaboration between Airbus-DS, UC3M, ONERA, CNRS-ICARE and KTH aiming to provide a better understanding of the plasma properties in the farplume of a Hall thruster. Additional funding for M. Merino and P. Fajardo came from Project ESP2016-75887 (Spain's National Research and Development Plan -MINECO/FEDER).


Leila El-Bassi
email: l.elbassi@gmail.com

Amel Ibn Ferjani
email: amel.ibn-ferjani@uha.fr

Mejdi Jeguirim
email: mejdi.jeguirim@uha.fr

Simona Bennici
email: simona.bennici@uha.fr

Salah Jellali
email: s.jellali@squ.edu.com

Hanene Akrout
email: hanene.akrout@gmail.com

Nicolas Thevenin
email: nicolas.thevenin@rittmo.com

Lionel Ruidavets
email: lionel.ruidavets@rittmo.com

Anne Muller
email: anne.muller@rittmo.com

Lionel Limousy
email: lionel.limousy@uha.fr

Production of a biofertilizer from exhausted grape marc waste: agronomic and environmental impact on plant growth

Keywords: Exhausted grape marc waste, biochar, biofertilzer, soil stability, suppressive effect

Biochars produced from exhausted grape marc waste were considered as a potential source for agriculture biofertilization. Results indicated that the biochar application didn't show a significant effect on Ryegrass fresh weight increase. The pyrolysis temperature influenced the fresh and dry matter yield since it interferes with phosphorus bioavailability for plant growth.

Potassium intakes were positively affected but not statistically significant. The % of soil stable aggregates decreased after 60 days. In the short term, there is no significant effect on soil structural stability. Biochar incorporation led to domination of large macro-aggregates, which are instables comparing to small macro-aggregates. A dose of 15 t ha -1 considerably reduced the leached soil and thus improved water retention by changing soil porosity. Soil pH and electric conductivity markedly increased for all treatments after 60 days of incubation. Biochar extract had a significant inhibitory effect on Fusariun oxysporum and Phytophtora sp.The use of exhausted grape marc waste to produce a biochar has shown a good potential for carbon and water sequestration in soil.

Introduction

Annually, an amount of 282 million hectolitres of wine is produced all over the world [START_REF] Oiv | World vitiviniculture situation[END_REF]. The grape marc (GM), also called grape pomace, is a residue of the vineyard processing industry. It mainly consists of skins, stalks and seeds that remain after grape pressing (Vitis vinifera). The GM contains high amounts of flavonoids, anthocyanins [START_REF] Auger | Phenolics from commercialized grape extracts prevent early atherosclerotic lesions in hamsters by mechanisms other than antioxidant effect[END_REF], fat, tanins [START_REF] Spanghero | Chemical composition, including secondary metabolites, and rumen fermentability of seeds and pulp of Californian (USA) and Italian grape pomaces[END_REF], and phenols [START_REF] Spigno | Cellulose and hemicelluloses recovery from grape stalks[END_REF].

Thus, the direct diposal of GM in the environment is of great impact on water resources' biochemical oxygen demand. The grape marc represents 10 to 30 wt% of the total mass of grapes processed in winemaking industries [START_REF] Muhlack | Sustainable wineries through waste valorisation: a review of grape marc utilisation for value-added products[END_REF]. The Food and Agriculture Organization (FAO) of the United Nations estimates that the grape marc generated worldwide from winemaking industries exceeds 70 million tons annually, which need to be valorized [START_REF] Oiv | World vitiviniculture situation[END_REF].

Various methods were apropriated to valorize this residue such us moderate or intense lowoxygen combustion to be used as biomass fuel [START_REF] Saha | Burning characteristics of grape marc under mild combustion conditions[END_REF]; crimping and silage to be used as ingredient in cattle diet [START_REF] Caetano | Effect of ensiled crimped grape marc on energy intake, performance and gas emissions of beef cattle, Animal Feed[END_REF]; microbial bioconversion to produce a functional ingredient, dietary supplement or pharmaceutical preparation [START_REF] Campanella | Exploitation of grape marc as functional substrate for lactic acid bacteria and bifidobacteria growth and enhanced antioxidant activity[END_REF], composting [START_REF] Bustamante | Study of the composting process of winery and distillery wastes using multivariate techniques[END_REF] and distillation for ethanol and alcohol production [START_REF] Corbin | Grape marc as a source of carbohydrates for bioethanol: Chemical composition, pre-treatment and saccharification[END_REF]. Some processes have rather focused on the extraction of valuable substances contained in GM like polyphenols and specially proanthocyanidins to be used as antioxidant, anti-aging, preventing cardiovascular deseases and anti-microbial substances [START_REF] Natolino | Kinetic models for conventional and ultrasound assistant extraction of polyphenols from defatted fresh and distilled grape marc and its main components skins and seeds[END_REF][START_REF] Rockenbach | Phenolic compounds and antioxidant activity of seed and skin extracts of red grape (Vitis vinifera and Vitis labrusca) pomace from Brazilian winemaking[END_REF][START_REF] Sessa | Exploitation of polyphenolic extracts from grape marc as natural antioxidants by encapsulation in lipidbased nanodelivery systems[END_REF], lignocellulose, cellulose and lignin to be used as a source of fermentable sugars [START_REF] Spigno | Cellulose and hemicelluloses recovery from grape stalks[END_REF].

Hence, recent studies have focused on the exploitation of GM for its potential as renewable energy generation. The thermochemical conversion of GM has been carried out through various processes [START_REF] Muhlack | Sustainable wineries through waste valorisation: a review of grape marc utilisation for value-added products[END_REF] namely, combustion [START_REF] Kraiem | Energy recovery from Tunisian agri-food wastes: Evaluation of combustion performance and emissions characteristics of green pellets prepared from tomato residues and grape marc[END_REF] , gasification [START_REF] Lapuerta | Effect of biodiesel fuels on diesel engine emissions[END_REF] , hydrothermal carbonization [START_REF] Mäkelä | Experimental design and response surface methodology in energy applications: A tutorial review[END_REF],

and pyrolysis [START_REF] Ferjani | The use of exhausted grape marc to produce biofuels and biofertilizers: Effect of pyrolysis temperatures on biochars properties[END_REF]. The major issue associated to GM combustion is the NO x emission [START_REF] Kraiem | Energy recovery from Tunisian agri-food wastes: Evaluation of combustion performance and emissions characteristics of green pellets prepared from tomato residues and grape marc[END_REF].

The pyrolysis is proposed as an adequate alternative ensuring efficiency and eco-friendly treatment of this residue [START_REF] Ferjani | The use of exhausted grape marc to produce biofuels and biofertilizers: Effect of pyrolysis temperatures on biochars properties[END_REF]. The recovery of GM through this technique generates three different fractions; gazeous and bio-oil fractions that could be used as biofuels for energy generation [START_REF] Jeguirim | Olive mill wastewater: From a pollutant to green fuels, agricultural water source and bio-fertilizer. Biofuel production[END_REF]; and a solid fraction called biochar mostly used as soil biofertilizer and bioremediation tool. The pyrolysis temperature is the key parameter to determine the characteristics and appropriate applications of biochar [START_REF] Khiari | Thermal conversion of flax shives through slow pyrolysis process: in-depth biochar characterization and future potential use[END_REF][START_REF] Sun | Effects of feedstock type, production method, and pyrolysis temperature on biochar and hydrochar properties[END_REF].

Interest on using biochar as soil amendement for its biofertilizing potential, has recently increased [START_REF] Shalini | Biochar from biomass waste as a renewable carbon material for climate change mitigation in reducing greenhouse gas emissions-a review[END_REF]. Many studies demonstrated and reported positive effects of biochar on soil physical properties by altering soil porosity and increasing soil surface area [START_REF] Hardie | Does biochar influence soil physical properties and soil water availability?[END_REF], soil moisture retention and hydraulic conductivity [START_REF] Obia | In situ effects of biochar on aggregation, water retention and porosity in light-textured tropical soils[END_REF]. The application of biochar can also affect the soil chemical properties like pH [START_REF] Tian | Biochar derived from corn straw affected availability and distribution of soil nutrients and cotton yield[END_REF][START_REF] Butnan | Biochar characteristics and application rates affecting corn growth and properties of soils contrasting in texture and mineralogy[END_REF], cation exchange capacity (CEC) [START_REF] Agegnehu | Benefits of biochar, compost and biochar-compost for soil quality, maize yield and greenhouse gas emissions in a tropical agricultural soil[END_REF], carbon content [START_REF] Jiang | Controls and dynamics of biochar decomposition and soil microbial abundance, composition, and carbon use efficiency during long-term biochar-amended soil incubations[END_REF], nitrogen (N) bioavailability [START_REF] Levesque | Mitigation of CO 2 , CH 4 and N 2 O from a fertigated horticultural growing medium amended with biochars and a compost[END_REF] and phosphorus (P) [START_REF] Chathurika | Woodchip biochar with or without synthetic fertilizers affects soil properties and available phosphorus in two alkaline, chernozemic soils[END_REF] for culture use. Moreover, biochar amendement significantly impacted the biological properties of the soil by decreasing the metabolic quotient of carbon value (qCO 2 ) used to estimate the stress level of microbial communities [START_REF] Levesque | Mitigation of CO 2 , CH 4 and N 2 O from a fertigated horticultural growing medium amended with biochars and a compost[END_REF], increasing the bacteria-to-fungi ratio [START_REF] Khadem | Responses of microbial performance and community to corn biochar in calcareous sandy and clayey soils[END_REF], enhancing the microbial diversity [START_REF] Wang | Biochar stability in soil: meta-analysis of decomposition and priming effects[END_REF] and reducing soil-born pathogens [START_REF] Jaiswal | Linking the belowground microbial composition, diversity and activity to soilborne disease suppression and growth promotion of tomato amended with biochar[END_REF]. Consequently, the biochar application on the soil increased the plant productivity and crop yield under differents pedoclimatic conditions [START_REF] Hussain | Biochar for crop production: potential benefits and risks[END_REF][START_REF] Warnock | Mycorrhizal responses to biochar in soil-concepts and mechanisms[END_REF]. Biochar is also receiving increasing attention as a remediation tool in agricultural soils by immobilizing heavy metals and reducing their bioavailability [START_REF] Khalid | A comparison of technologies for remediation of heavy metal contaminated soils[END_REF] as well as their great potential for sorption of organic compounds like pesticides [START_REF] Khorram | Biochar: a review of its impact on pesticide behavior in soil environments and its potential applications[END_REF]. However, it is worthy to mention that the biochar effect on agronomic and biological properties of the soil is highly dependant on biomass, pyrolysis operating conditions and soil types [START_REF] Sun | Assessment of herbicide sorption by biochars and organic matter associated with soil and sediment[END_REF][START_REF] Brassard | Effect of six engineered biochars on GHG emissions from two agricultural soils: A short-term incubation study[END_REF].

As far as we know, the reuse of GM-derived-biochars as amendment for agricultural purposes in comparison with synthetic fertilizers and their effect on plants growth, nutrients (P and K) bioavailability, phytopathogens suppressive effect and agricultural soil stability has not yet been investigated. Thus, the aim of this work is to evaluate the potentialities of exhausted grape marc derived biochars produced at three pyrolysis temperatures: 300, 400 and 500°C; to be used as soil biofertilizer. The biochar amendement on the soil was performed under different doses with analysis of nutrients bioavailability, soil aggregates stability parameters, physico-chemical parameters monitoring and suppressive effect on phytopathogens.

Materials and Methods

Biochars production and characterization

Prior to be used in agronomic tests, exhausted grape marc (EGM, supplied by the industrial distillery located in Sigolsheim, France), obtained after ethanol extraction by distillation process, were subjected to pyrolysis in a vertical tubular furnace under three pyrolysis (slow) temperatures (300, 400 and 500°C) as described previously [START_REF] Ferjani | The use of exhausted grape marc to produce biofuels and biofertilizers: Effect of pyrolysis temperatures on biochars properties[END_REF]. Obtained biochars were grounded and fractions with size between 250 and 400 µm were collected and characterized (Table 1). BC1, BC2 and BC3 correspond to biochars obtained respectively at 300, 400 and 500°C.

Biodisponibility of potassium and phosphorus

Bioavailibilities of biochars nutrients, K and P, were assessed using the three biochars (BC1; BC2; BC3). The micro-cultures technique was used as summarized by [START_REF] Lombaert | Micro-cultures methode Chaminade[END_REF] [START_REF] Lombaert | Micro-cultures methode Chaminade[END_REF].

The italian Ryegrass, used as a model plant, was cultivated in pots containing 1 kg of dry soil with seeding density of 1.2 g pot-1. It was a loamy sandy soil, it contained 76.2%wt, 14.4%wt, and 9.1%wt of sand, silt and clay respectively. It had a pH and a conductivity of 7.3 and 0.5 mS cm-1. Furthermore, it was a relatively poor soil with organic matter content of 0.75% wt and low contents in N, P, K with average contents of 0.03% wt, 0.036% wt, and 0.13% wt, respectively. Experimentations was done in greenhouses at constant temperature of 25°C during 16 h and at 20°C during 8 h, with a minimal brightness of 175 W m -2 during 14 h.

Watering was realized by sub-irrigation to avoid leaching losses and maintained to a relative humidity of 70% throughout the duration of plant growth. The use of exhausted GM derived biochars for soil amendement was performed using 15 modalities described below ( For soil structural stability estimation, we used the method of [START_REF] Kemper | Aggregate stability and size distribution[END_REF] [START_REF] Kemper | Aggregate stability and size distribution[END_REF] with slight modifications. In brief, soil pots containing 500 g dry matter (DM) of soil with increasing doses of biochar were incubated at 28°C in the darkness for 60 days. Soil humidity was maintained constant at 70% humidity during the assay to maintain the microbiological activity of the soil. Soil surface samples were sampled at defined times to test the stability of the aggregates (0, 7, 14, 28, 45 and 60 days). Soil pots were replicated for eah sampling period.

Samples were then air-dried at ambient temperatures (3 days) before being sieved to obtain the 1-2 mm fraction. Air-dried 1-2 mm fractions were inserted in the 200 µm sieves of the Bartoli device. Cylindric containers were filled with 150 mL of distilled water, in order to soak sieves in a 0.5 cm layer of water. The device was launched for 10 minutes of 20 mm amplitude and 1.6 Hz sieving. After 10 minutes, the aqueous phase (containing water unstable aggregates in suspension) was recovered and dried (16h at 105°C). Meanwhile, undissolved aggregates stay in sieves, and underneath plastic containers were filled with 150 mL of a dispersing solution (NaOH: 2g L -1 ). The wet sieving device was relaunched for 20 minutes. After 20 minutes, underneath recipients containing liquid dispersant phase (in which water stable aggregates in suspension) were recovered. Their integral content was transferred in weighted crystallizers and dried (55°C, 16 h). Every crystallizer was weighed. Water stable aggregates percentage was given by the ratio between mass of stable aggregates and the addition of stable + unstable aggregates masses.

Tested modalities with soil at different biochar doses were (DM basis):

 Control : soil without biochar  Soil+BC1 (300°C) : 5 t biochar ha -1 (15g BC1/kg) , 12.5 t biochar ha -1 (39g BC1/kg) , 15 t biochar ha -1 (47g BC1/kg) (BC1/5, BC1/12.5 and BC1/15 resp.)

 Soil+BC2 (400°C) : 5 t biochar ha -1 (15g BC2/kg), 8.33 t biochar ha -1 , 15 t biochar ha -1 (47g BC2/kg) (BC2/5, BC2/8.33 and BC2/15 resp.)

 Soil+BC3 (500°C) : 3.13 t biochar ha -1 (9.8g BC3/kg), 5 t biochar ha -1 (15g BC3/kg), 6.25 t biochar ha -1 (19g BC2/kg), 15 t biochar ha -1 (47g BC3/kg) (BC3/3.125, BC3/5, BC3/6.25 and BC3/15 resp.)

The monitored parameters are the aggregates stability and soil losses under water action (erosion of soil particles).

The rate of stable aggregates (SAG water ) was calculated as follows (Eq.( 1)):

Eq.( 1)

The mean weight diameter MWD of aggregates (corresponding to the same samples used to determine SAG water ), was estimated according to equation (2):

Eq.( 2)

With:

 w >200 : weight of particles which real diameter is higher than 200 µm (resistant to water degradation)

 w <200 : weight of particles which real diameter is less than 200 µm  w tot : total weight of the tested dry soil

Impact on soil losses

To estimate soil losses by water infiltration, the trays containing the different pots used on §2.3.1

were placed under a rain simulator, in term of 60 days' incubation. The trays were placed on slope plan of 6% and cutted to the surface to allow water to trickle out of the tray. Rain simulator (SPRAI, P-B24-IN-NF0-0032, France) was used with a continuous standard rain scenario during 4h for a final volume between 40 to 60 mm of water. Surface water and leached water were collected in pots every hour, and dried at 60°C. Once dried, pots were weighed to assess the mass of dry soil particles transported by water.

pH and conductivity

Soil samples collected for aggregates stability were used to measure pH and electrical conductivity for each modality.

Suppressive effect of biochars on phytopathogens

The suppressive effect of amended biochars on the soil was assessed using four telluric The suppressive effect is estimated by measuring the colony radial diameter of fungi grown on petri dishes and then compared to control. All modalities were repeated 3 times.

Statistical analysis

All reported data were analysed using SPSS for Windows with one-way analysis of variance (ANOVA). This analysis enables the discrimination of average values according to the procedure of Fisher's minimum significant differences, at the 5% threshold (P<0.05). Each value was represented as the mean ± standard deviation of three or four individuals (n = 3 or 4).

Results and discussions

3.1. Effect of biochar amendement on P and K biodisponibilities 3.1.1. Effect of biochar amendement on ryegrass growth Fig. 1.a reported the cumulative fresh matter average of ryegrass after the first and second harvest. Corresponding results showed no significant effect of all tested modalities on the ryegrass fresh matter (P-value= 0.0802); the higher fresh matter increase observed for BC3-200 treatment was around 2 wt% compared to control sample. However, the dry weight monitoring (Fig. 1.b) showed a significant effect of the treatment (P-value=0.0026). The amendement of BC1 and BC2 on the soil have a slight negative effect on dry matter of the ryegrass. This result could be explained by a limited availability of nutrients with biochar amendements treatment as well as a possible phytotoxic effect of these biochars on ryegrass growth. Indeed, Spokas (2011) [START_REF] Spokas | Qualitative analysis of volatile organic compounds on biochar[END_REF] showed that volatile organic compounds (VOCs) such as acetone and benzene in biochar were found to have severe phytotoxic effects. The P content for BC1-300, BC2-400 and BC3-500 was 3.4, 4.9 and 6.2 g kg -1 and K content about 11, 16.40 and 21.70 g kg -1 respectively (Table 1).

Moreover, carbon content increased considerably with increasing pyrolysis temperature.

Hadroug (2019) [START_REF] Hadroug | Pyrolysis Process as a Sustainable Management Option of Poultry Manure: Characterization of the Derived Biochars and Assessment of their Nutrient Release Capacities[END_REF] demonstrated that P and K concentrations increase when increasing the pyrolysis temperature; the P and K contents increased by 53.9%, 19.5% for biochar produced at 400°C and by 88.7% and 73.7% for biochar obtained at 500°C. Thus, an amendement with BC3 (produced at 500°C) generated an increase in dry matter with a dose of 200U. BC3-200U

treatment showed an increase in dry matter of 6% compared to the control treatment. The biochar application could act directly on soil by promoting the carbon release and reducing the nutrients leaching, which positively influence the improvement of crop yield [START_REF] Hussain | Biochar for crop production: potential benefits and risks[END_REF]. Chen et al.

(2018) [START_REF] Chen | Effects of biochar on the ecological performance of a subtropical landfill[END_REF] have reported that enhanced plant growth after biochar application was mainly attributed to modifications on soil bacterial and fungal communities. Some bacterial functions mainly related to nutrient cycling including ammonia and nitrite oxidation and sulphur respiration were emphasized. The biochar acts also by increasing available nutrients for plants and enhancing water retention by soil [START_REF] Zhao | Apply biochar to ameliorate soda saline-alkali land, improve soil function and increase corn nutrient availability in the Songnen Plain[END_REF]. As shown in the previous results, the pyrolysis temperature influenced the fresh and dry matter yield as it can interfere with P bioavailability for plant growth.

When applying inorganic fertilizers such as KNO 3 (for K fertilization) and TSP (for P fertilization) with respect of the same doses provided by biochars, a significant enhancement of fresh and dry weights was observed compared to the control and biochar amended soils. This result is explained by the high bioavailability of contained nutrients. Thus, many reports have recommended mixing biochar with an organic or inorganic fertilizer for a better crop yield and soil productivity and a synergetic effect would be involved [START_REF] Hussain | Biochar for crop production: potential benefits and risks[END_REF]. 3.1.2. P and K biodisponibility Fig. 2 reported the average of K intake in the ryegrass plant for 2 cumulative harvests under the modalities described previously. The average of exported K was significantly different for all modalities (P-value = 0.0005). Interestingly, the application of biochar BC1, obtained at 300°C, generated a potassium adsorption significantly high compared to the control, and very similar to the Ref K-200 treatment in which the soil was amended with 200 U of inorganic fertilizer KNO 3 .

When applying BC2 and BC3 amendement to the soil, the K intakes was positively affected but not statistically significant which explain the dry matter increase for BC3 treated cultures. The increase of K intakes was mainly achieved through the CEC improvement and others conductive nutrients [START_REF] Gul | Biochemical cycling of nitrogen and phosphorus in biochar amended soils[END_REF]. Previous studies have shown that biochar amendement enhanced the K exported amounts via their absorption by biochar pores and slow release to the soil [START_REF] Xu | What is more important for enhancing nutrient bioavailability with biochar application into a sandy soil: direct or indirect mechanism[END_REF]. It is worthy to notice that the K intakes for treatment with addition of KNO 3 and TSP were less than treatment with KNO 3 alone, possibly due to the effect of TSP. The measurements of P intakes under the described modalities (Fig. 3) showed no significant effect for all tested treatments (p-value = 0.0763). The P intakes in modalities using mineral TSP fertilizer are increasing when higher doses are used, and it is considerably important for the synthetic K-100+TSP-60.5 amendment. A synergetic effect seems to be existant between mineral fertilizers for low doses. The amendement with BC3-100 positively affected P adsorptions without significant effect. When adding BC1-200, BC2-200 and BC3-200, P adsorptions are similar to the control. It was previously reported that pyrolysis temperatures affected the P bioavailability to the soil; high pyrolysis temperature enhances the P bioavailability with a slow release for plants [START_REF] Tan | Returning biochar to fields: a review[END_REF]. Actually, biochar produced at high pyrolysis temperatures provided important surface areas with the presence of microporosities and consequently P release [START_REF] Lehmann | Biochar sequestration in terrestrial ecosystems: a review[END_REF]. [START_REF] Deluca | Biochar effects on soil nutrient transformation[END_REF] have shown that P content was significatly enhanced when using biochar produced at temperature higher than 300°C. However, pyrolysis temperature higher than 700°C could significantly increase P retention [START_REF] Zhang | Roles of biochar in improving phosphorus availability in soils: a phosphate adsorbent and a source of available phosphorus[END_REF]. To overcome the inavailability of P in biochar amended soils, inoculation with P-solubilizing fungi like Penicillium fungi or Penicillium aculeatum was suggested [START_REF] Efthymiou | Augmentation of the phosphorus fertilizer value of biochar by inoculation of wheat with selected Penicillium strains[END_REF].

Deluca et al. (2009)

Effect of biochar amendements on soil physico-chemical characteretics

Biochar incorporation into soil affect: physical (porosity, stability), chemical (pH, conductivity) and biological (bacterial communities, enzymes) properties of the soil depending on biochar production conditions and dose. The direct impact of biochar amendement on aggregate stability, soil losses by water runoff and soil pH are decribed below.

Aggregate stability

The structural stability of the soil was assessed by the amount of stable aggregates to water action comparing to unstable ones. A high amount of stable aggregates is considered as an indicator of an improvement in soil structure to prevent soil runoff and erosion.

As shown in Fig. 4, the evolution of the stable aggregates rate in water is almost similar for all treatments (P-value = 0.6111). The % SAG water was between 10 and 15% in the begining of the experiment and decreased to about 5 to 11% at 60 days. The decrease of %SAG water is not related to biochar amendement. In the short term, there is no significant effect on soil structural stability.

Similar results were demonstrated by Hardie (2014) [START_REF] Hardie | Does biochar influence soil physical properties and soil water availability?[END_REF] showing that after thirty months of biochar incorporation into soil (acacia green waste biochar), no siginificant effect was observed on aggregate stability, soil water retention parameters and permanent wilting point. [START_REF] Peng | Temperature-and duration-dependent rice straw-derived biochar: characteristics and its effects on soil properties of an Ultisol in southern China[END_REF] [52] also reported that the amendement with rice straw biochar had no effect on aggregate stability despite of its positive impact on soil fertility. Contreversial results have reported a significant positive effect of biochar on aggregate stability in laboratory and field experiments [START_REF] Obia | In situ effects of biochar on aggregation, water retention and porosity in light-textured tropical soils[END_REF]. The differences regarding this parameter are mainly due to initial fedstock and amended soil characteristics.

Figure 4 Water-stable aggregates (%SAG water ) for soil containing different biochar types and quantities.

To have an insight on the biochar effect on stable aggregate size, the mean weight diameter (MWD) of aggregates was estimated according to equation (2) (Fig. 5). From the first experimental day, the average of aggregates diameter was around 0.5 mm for all tested modalities which means that initially the soil was instable. Along with time, the mean weight diameter decreased due to the loss of stable agregates. In term of 60 days, the MWD slightly decreased to 0.4 mm giving more instability to the soil. Although, there is no significant difference between biochar produced at different temperatures and added in different doses (P- [START_REF] Wang | Sorption of four hydrophobic organic contaminants by biochars derived from maize straw, wood dust and swine manure at different pyrolytic temperatures[END_REF] demonstrated that the pyrolysis temperature can significantly impact the sorption capacity of biochars for hydrophobic organic compounds. Biochar pyrolysed at temperatures between 250 and 400°C contain more aliphatic organic compounds and cellulose structure while biochar produced at higher temperatures (400-700°C) showed rigid surfaces colonised by considerable pores adapted to the adsorption of hydrophobic organic compounds.

Soil losses

Fig. 6 reported the cumulative weight of soil particles recovered by leaching or by runoff, for the same modalities than tested for aggregates stability. After 4 hours of simulated rain, soil losses by surface runoff were insignificant or weak for all modalities except for control and soil amended with BC1 at a dose of 5 t ha -1 (BC1/5), and a thin crust of clap was created. However, an important decrease in the soil losses by leaching was observed in all the modalities amended with biochar compared to the control. A dose of 15 t ha -1 for BC1, BC2 and BC3, which is the maximum applied dose in this study, considerably reduced soil leaching, especially for BC1 treated soil. Thus, it is obviously clear that the biochar amendement reduced the soil losses and improved water retention by changing the soil porosity [START_REF] Basso | Assessing potential of biochar for increasing water-holding capacity of sandy soils[END_REF][START_REF] Han | Biochar's stability and effect on the content, composition and turnover of soil organic carbon[END_REF], which considerably influences soil moisture and hydraulic conductivity. However, the relationship between pyroloysis temperature and water retention abiliy is still subject of debate ; Yi at al. (2015) [START_REF] Yi | The origin and reversible nature of poultry litter biochar hydrophobicity[END_REF] have shown that biochar produced at temperatures below 450°C retained hydrophilic organic compounds, however Kameyma (2014) [START_REF] Kameyama | Influence of biochar incorporation on TDR-based soil water content measurements[END_REF] demonstrated that biochars produced at high temperatures have high water retention capacity due to their pore volume and pore tortuosity.

The ability of biochar to retain water and other chemicals is a function of its surface area, its porosity and its functionnal charged groups. These properties are mainly conditionned by originated feedstock [START_REF] Bolognesi | Biochar production from sewage sludge and microalgae mixtures: properties, sustainability and possible role in circular economy[END_REF] and pyrolysis temperatures [START_REF] Gul | Physico-chemical properties and microbial responses in biochar-amended soils: mechanisms and future directions[END_REF]. It is worthy to mention that physicochemical properties of biochar are not maintained constant over the time; the retention capacity of biochar might be reduced with time due to decrease of pH, loss of reactive surface sites and weathering parameters such as erosion [START_REF] Spokas | Impact of biochar field aging on laboratory greenhouse gas production potentials[END_REF].

It was demonstrated in the section 3.2.1 that the biochar amendment had an insignificant effect on the structural stability of soils. Thus, it is highly probable that there is no effect on the resistance of soils to water losses by runoff in time. Others soils properties (microbial activities, pH, nutrient retention, …) need to be measured to confirm this finding.

pH and CEC

The biochar application also affected the pH of amended soils. The measurement of pH and CEC of treated soils after 60 days of incubation (Fig. 7) showed a significant impact of biochar on pH (P-value = 0.0001). Most of tested biochars increased the soil pH excepted the BC1 amended with a dose of 5 t ha -1 (BC1/5). For a given biochar, the pH increased with the used amended dose. Except for BC1/5, the effect is significant and it increases with the pyrolysis temperature of the biochar. Intersingly, the pH of amended soil is as higher as the pyrolysis temperature and used dose are high. The pH increased by one unit for all doses of BC3 doses. The initial pH of biochar could impact the final pH of the soil; the pH for BC1, BC2 and BC3 biochars is 7.2, 8.7, 9.9 respectively (Table 1). At identical dose, the pH increase is higher for BC3 in any case, as expected. It was previously reported that biochars can alter the pH of amended soil [START_REF] Ren | Biochar and PGPR amendments influence soil enzyme activities and nutrient concentrations in a eucalyptus seedling plantation[END_REF] with alkalizing effect on the soil [START_REF] Brassard | Biochar for soil amendement[END_REF][START_REF] Han | Biochar's stability and effect on the content, composition and turnover of soil organic carbon[END_REF]. This alkalizing effect is probably due to the basic cations (potassium, calcium and magnesium) in biochar decreasing the exchangeable ions of aluminium and hydrogen by adsorption [START_REF] Tan | Returning biochar to fields: a review[END_REF], and its chelation with organic compounds contained in biochar [START_REF] Butnan | Biochar characteristics and application rates affecting corn growth and properties of soils contrasting in texture and mineralogy[END_REF]. pH increase of soils in the range of 5.5 to 7 could improve the nutrients availability on agricultural soils and consequently facilitate their uptake by plant roots which favorised their growth [START_REF] Matsubara | Incidence of Fusarium root rot in asparagus seedlings infected with arbuscular mycorrhizal fungus as affected by several soil amendments[END_REF]. However, biochar amendement (1% and 2% w/w) in alkaline soils significantly increased the pH values (until 9.5) which limits the bioavailability of nutrients for plants [START_REF] Chathurika | Woodchip biochar with or without synthetic fertilizers affects soil properties and available phosphorus in two alkaline, chernozemic soils[END_REF]. The pH variation on soils may also affect the bacterial and fungal communities' distribution in the soil as well as the fungi-to-bacteria ratio since these two communities operate differently in the incorporation and turnover of carbon. An increase of pH also highly impacts the rates of carbon loss from soils [START_REF] Chen | Effects of biochar on the ecological performance of a subtropical landfill[END_REF].

As biochar amendement significantly increased the pH, it also affects the cation exchange capacity CEC of soil. The CEC evolution is similar to pH evolution; CEC values increased with amended dose and the pyrolysis temperatures of biochars as shown in Fig. 7. This is due to the reduction of cation leaching by establishment of bonds with negatively charged sites of biochars, organic matter and organo-mineral complexes [START_REF] Gul | Biochemical cycling of nitrogen and phosphorus in biochar amended soils[END_REF]. Thus, the magnitude of CEC variation is dependant on initial organic matter content of soils. The CEC enhancement could be also explained by the presence of an electrostatic attraction force initiated by carboxylic and phenolic groups present at the surface of biochars [START_REF] Tian | Biochar derived from corn straw affected availability and distribution of soil nutrients and cotton yield[END_REF].

Suppressive effect of amended biochars on phytopathegens fungus

The biochar amendement as reported to have significant effect on biological properties. Thus, the suppressive effect of amendend biochar against selective phytopathogens was investigated in this study. Fig. 8 (a, b, c) reported the average radial diameter of fungi for soil amended biochar, under different doses, in the presence of four telluric phyotopathogens fungi; Rhizoctonia solani, Fusarium oxysporum, Pythium ultimum and Phytophtora sp.

The effect of treatment using soil extract and BC1 extract (Fig. 8.a) on Rhizoctonia solani is significant compared to the control (p-value: 0.001), but obviously this effect is only due to the soil since there is no statistical difference between the soil effect and different doses of biochar (p-value = 0.6017). Same behaviour was noticed for Pythium sp. in which the suppressive effect is due to the soil and not to biochar BC1 (p-value=0.2229). However, interesting results were noticed for Fusariun oxysporum and Phytophtora sp. assay in which the inhibitory effect of BC1 extract is significant comparied to the soil extract (p-value of 0.0001 and 0.0004 respectively), and interestingly for B1/12.5 treatment.

By observing the treatment using BC2 extract (Fig. 8.b), the significant effect of biomass reduction of Rhizoctonia solani and Pythium.sp was entirely related to the soil, since no statistical difference between the soil and biochar (p-value = 0.3474 for Rhizoctonia sp., p-value = 0.2979 for Pythium sp.) was noticed. The amendement of BC2 biochar didn't affect significantly Fusarium oxysporum growth. Thus, the 4 treatments using soil and BC2 biochar have a significant effect on tested phytopathogens, but this effect is mostly due to the soil since 1 the difference between soil and BC2 treatment is not significative (p-value = 0.0769). However, 2 a small dose effect with BC2 was observed on Fusarium oxysporum for BC2/15 treatment.

3

Possibly for higher doses of BC2 biochar, a significant suppressive effect will be noticed in a 4 better way. Moreover, for Phytophtora sp, a significant effect of BC2 could be observed between 5 soil and BC2 treatments (p-value = 0.0355). Using the BC3 biochar (Fig. 8.c), there is no significant effect of the biochar amendement on the suppressive effect of phytopathogens. The inhibitory effect is mainly due to the soil since the statistic differences between modalities using soil and biochars are insignificant; (p-values are respectively 0.1099 ; 0.0579 ; 0.0712 ; 0.1656 for Rhyzoctonia solani, Fusarium oxysporum, Phytophtora sp., Pythium ultimum respectively). However, it is important to mention that low doses of BC3 biochar could have a significant suppressive effect on Phytophtora sp. Surprinzingly, nevertheless the BC3 amendement seems to promote Rhyzoctonia growth.

Regarding the results reported above, the treatment using BC1 biochar limited the phytopathogens growth and clearly have a suppressive effect, especially on Fusarium sp. and Phytophtora sp. The addition of BC2 biochar to the soil has a suppressive effect on phyotophtora sp. and a potential effect on Fusarium oxysporum at high doses. However, there is no significant effect of BC3 biochar for the tested soil borne phytopathoegens. The suppressive effect of biochar was previously reported for soil borne pathogens [START_REF] Matsubara | Incidence of Fusarium root rot in asparagus seedlings infected with arbuscular mycorrhizal fungus as affected by several soil amendments[END_REF][START_REF] Zwart | Biochar amendment increases resistance to stem lesions caused by Phytophthora spp. in tree seedlings[END_REF] and fungal phyto-pathogens in tomato, sweet pepper, and strawberry [START_REF] Elad | The biochar effect: plant resistance to biotic stresses[END_REF]. In our case, better suppressive effect was observed for biochar obtained at 300°C rather than for biochars BC2 and BC3 obtained at 400°C and 500°C respectively. Increasing pyrolysis temperatures could reduce the biochar effect on phytopathogens. Contrarily, previous researches have shown that biochar produced at high and low temperatures have an equal effect on Rhizoctonia solani [START_REF] Jaiswal | Rhizoctonia solani suppression and plant growth promotion in cucumber as affected by biochar pyrolysis temperature, feedstock and concentration[END_REF] and Fusarium sp. [START_REF] Jaiswal | Linking the belowground microbial composition, diversity and activity to soilborne disease suppression and growth promotion of tomato amended with biochar[END_REF].

Moreover, it was demonstrated that increasing pyrolysis temperature lead to a decrease in fungibacteria ratio in amended soil [START_REF] Khadem | Responses of microbial performance and community to corn biochar in calcareous sandy and clayey soils[END_REF]. Therefore, the biochar effect on phytopathogens growth is not attributed to any indigenious consortium of microorganisms on biochar but it is mainly due to its content on organic compounds, which is directly related to the feedstock source, pyrolysis temperature and concentration of the added amendment [START_REF] Jaiswal | Linking the belowground microbial composition, diversity and activity to soilborne disease suppression and growth promotion of tomato amended with biochar[END_REF][START_REF] Swagathnath | Influence of biochar application on growth of Oryza sativa and its associated soil microbial ecology[END_REF]. The biochar contains tars with multiple organic compounds [START_REF] Schnitzer | The conversion of chicken manure to biooil by fast pyrolysis II. Analysis of chicken manure, biooils, and char by curie-point pyrolysis gas chromatography/mass spectrometry (Cp Py-GC/MS)[END_REF] and some tars fractions are involved in biocidal effect and seed germination promoting [START_REF] Amonette | Characteristics of biochar: microchemical properties[END_REF].

As shown in Fig. 8, the biochar effect is improved with increasing amendement levels. Thus, it is important to define the best dose stimulation for a high inhibition effect [START_REF] Graber | Biochar impact on development and productivity of pepper and tomato grown in fertigated soilless media[END_REF]. It also important to mention that biochar can promote the abundance of soil biota and important modifcations on microbial communities [START_REF] Lehmann | Biochar effects on soil biota-a review[END_REF]. These changes may have an important effect on fungi suppression.

Conclusion

The application of biochar from EGM waste at three pyrolysis temperatures (BC1-300°C, BC2-400°C and BC3-500°C) and at different amended doses increase the K and P intakes on Ryegrass, specially for BC3-100U; which have a direct influence on the dry weigh of ryegrass.

Although, the applied biochar didn't have a significant effect on soil structural stability in short term conditions, the soil losses by runoff or leaching were significantly reduced for high amended doses of biochar (15 t ha -1 ). These transformations were followed by an alcanisation of inoculated soils as well as an increase on their CEC specially for biochar produced at high temperatures. However, pronounced phytopathogens suppressive effect was observed for BC1 produced at 300°C, probably due to VOC residues. Thus, an extended scale for long-term studies were required to have a comprehensive insight for the use of EGM biochar impact as biofertilizer in soil as well as agroenvironnemental impact. The transformation of EGM waste into valuable biochar can be of interest for carbon and water sequestration in the frame of a circular economy approach.

  phytopathogens species: Rhizoctonia solani, Fusarium oxysporum, Pythium ultimum et Phytophtora sp. The phytopathogens were grown on PDA (Potato Dextrose Agar) solid medium in presence of soil and biochar extract (aqueous extraction 2% w/v). The soil and biochar mixture used in this test were collected from structural stability test after 60 days of incubation for all tested modalities. Mycelial discs (diameter of 5 mm), taken from the periphery of an actively growing PDA culture of each tested pathogen, were placed at the center of the PDA Petri dishes. 1 mL of each extracts were dropped-off (100 µL) at the two opposite sides of the Petri dishes. Resulting Petri dishes were incubated in the dark at 25 (± 2)°C for 12 days. In this experiment, the considered control sample is the phytopathogen grown on PDA without soil and biochar extract.

Figure 1 .a

 1 Figure 1.a Cumulative weight average of the fresh ryegrass harvest (g) obtained for all the tested modalities (BC1, BC2, BC3 amendment, references and Dose 100 U K 2 O) after the second harvest.

Figure 2

 2 Figure 2 Average of cumulative exported potassium obtained for all the tested modalities (BC1, BC2, BC3 amendment, references and Dose 100 U K 2 O) after the second harvest (g of potassium per kg of dry rye grass).

Figure 3

 3 Figure 3 Average of cumulative exported phosphorus obtained for all the tested modalities (BC1, BC2, BC3 amendment, references and Dose 100 U K 2 O)after the second harvest (g of phosphorous per kg of dry ryegrass).

Figure 5

 5 Figure 5 Mean Weight Diameter (MWD) of soil aggregates depending on biochar type and quantity.

Figure 6

 6 Figure 6 Evaluation of soil losses through leaching or runoff experiments on soil containing different amounts of the different biochars compared with a control (soil only).

Figure 7

 7 Figure 7 Evolution of soil pH and conductivity after 60 days of contact with the different biochar modalities.

Figure 8

 8 Figure 8 Evaluation of the average radial diameter of fungi for different phytopathogens colonies in presence of soil and biochar BC1(a), BC2 (b), BC3 (c) under different doses.

Table . 1

 . Main biochars' characteristics of produced biochars (BC1-300°C ; BC2-400°C ; BC3-500°C)

Table 2

 2

	)

Table 2 .

 2 Summary of modalities used for the assessment of K and P bioavailabilities under K 2 O (kg ha -1 ) and P 2 O 5

	(kg ha -1 ) amendements

Sample name Experiment K 2 O (kg ha -1 ) amendement P 2 O 5 (kg ha -1 ) amendement

	Control	Soil	---	---
	B1-200	Soil+BC1(39g BC1/pot)	200 (12.5 t DM biochar ha -	106
			1 )
	B2-200	Soil+BC2 (26g BC2/pot)	200 (8,33 t DM biochar ha -	93
			1 )
	B3-100	Soil+BC3 (9.8g BC3/pot)	100 (3.13 t DM biochar ha -	60.5
			1 )
	B3-200	Soil+BC3 (19g BC3/pot)	200 (6.25 t DM biochar ha -	121
			1 )
	Ref K 100	Soil+mineral K fertilizer (KNO 3 )	100	0
	Ref K 200	Soil+ KNO 3	200	0
	Ref TSP 60.5	Soil+mineral P fertilizer (TSP)	0	60.5
	Ref TSP 93	Soil+ TSP	0	93
	Ref TSP 106	Soil+ TSP	0	106
	Ref TSP 121	Soil+TSP	0	121
	Ref K 100 + TSP	Soil+KNO 3 +TSP	100	60.5
	60.5
	Ref K 200 + TSP 93	Soil+KNO 3 +TSP	200	93
	Ref K 200 + TSP 106 Soil+KNO 3 +TSP	200	106
	Ref K 200 + TSP 121 Soil+KNO 3 +TSP	200	121
	DM : Dry Matter
	2.3. Aggregates Stability and soil losses by infiltration and runoff
	2.3.1. Structural stability

,33 BC2 /15 BC3 /3,125 BC3 /5 BC3 /6,25 BC3 /15 value

  = 0.2705). The decrease of MWD was rapidly achieved for soils amended with BC3 amended with a dose of 15 t ha -1 .Wang et al. (2016)

		30%
	(%SAgW)	25%
	agregates rate	15% 20%
	water-stable	5% 10%
		0%
		0	10	20	30	40	50	60	days	70
		Control	BC1 /5		BC1 /12,5	BC1 /15	BC2 /5		BC2 /8

Acknowledgements

The authors thank the "Comité Mixte franco-tunisien pour la Coopération Universitaire (CMCU) for the support. Authors would like also to thank the Carnot MICA Institute for funding the experimental tests in the frame of CARBOVIT project.