X Ledoux

E Bauge

G Belier

T Caillaud

A Chatillon

T Granier

O Landoas

J Taïeb

B Rossé

I Thfoin

C Varignon

V Blideanu

D Doré

F Gunsing

S Panebianco

D Ridikas

A Takibayev

M Aïche

G Barreau

S Czajkowski

CENBG B Jurado

G Ban

F R Lecolley

J F Lecolley

J L Lecouey

N Marie

LPC J C Steckmeyer

P Dessagne

M Kerveno

G Rudolf

P Bem

M Majerle

J Mrazek

J Novak

E Simeckova

Řež Npi

C Gustavsson

S Pomp

U Fischer

K Klix

S P Simakov

Kit

B Jacquot

F Farget

J P Wieleczko

L Perrot

M Avrigeanu

V Avrigeanu

C Borcea

F Negoita

NIPNE M Petrascu

S Oberstedt

A J M Plompen

M Fallot

L Giot

Subatech

G Smith

I Tsekhanovich

E Balanzat

B Ban-D'état

S Bouffard

S Guillous

J M Ramillon

The NFS collaboration

This report is a compilation of the studies performed by several teams belonging to the NFS collaboration for the use of different experimental set-ups at the Neutrons For Science facility. The list of the set-ups presented here is not exhaustive and covers only a small part of the set-ups usable at NFS. These set-ups will be used in the experiments described in the Letters Of Intent for Day One experiment submitted to the Scientific Advisory Committee of SPIRAL-2.

The NFS Facility 1 Introduction

The "Neutrons For Science" (NFS) facility will be a component of the future SPIRAL-2 facility, dedicated to the production of very intense radioactive ion beams, under construction at GANIL in Caen (France). The SPIRAL-2 facility is based on a high intensity linear accelerator (LINAG) that is designed to induce fission in the SPIRAL-2 production target. The use of intense LINAG beams will also be used in two experimental areas, the S3 spectrometer and the neutron beam-line NFS. The neutrons of the NFS facility are produced out of the reaction of the LINAG deuteron or proton beams with dedicated converters. NFS will be composed of a pulsed neutron beam for in-flight measurements and irradiation stations for cross-section measurements and material studies. Continuous and quasi-monokinetic energy spectra will be available, respectively produced by the interaction of deuteron beam on a thick Be converter and by 7 Li(p,n) reaction on a thin converter. The flux at NFS will be up to 2 orders of magnitude higher than those of other existing time-of-flight facilities in the 1 MeV -40 MeV range. NFS will be a very powerful tool for physics, fundamental research as well as applications like the transmutation of nuclear waste, design of future fission and fusion reactors, nuclear medicine or test and development of new detectors.

NFS description

NFS is mainly composed of two rooms: a converter cave and an experimental area separated by a 3 meter-thick wall of concrete (see Figure 1). The converter room includes the primary ion beam extension, the converter to produce neutrons as well as the irradiation setups. A bending magnet is placed between the converter and the collimator entrance to clean the neutron beam from protons, when a thin converter is used (see following section). Neutrons in the 0° direction are guided to the experimental room through a collimator consisting of iron and polyethylene.

The experimental area (30 m x 6 m) will allow performing measurements by using large experimental set-ups at desired distances from 5 m up to 25 m away from the converter point. This flexibility is very interesting in terms of flux and energy measurement resolution. The experimental area is designed for the use of radioactive samples up to 10 and 1 GBq for sealed and non-sealed samples, respectively.

In addition, the ion beam-line in the converter cave will be equipped with an irradiation box for cross-section measurements of proton and deuteron induced reactions by the activation technique. The use of light ions, up to carbon, is also envisaged to irradiate samples for material studies. Two production modes will be used with the pulsed proton and deuteron beams delivered by the LINAG.

First, the deuteron break-up reaction on a thick converter made of carbon or beryllium generates neutrons with a continuous energy distribution. At 0 degree, the spectrum extends up to 40 MeV with an averaged value of approximately 14 MeV as shown in Second, the 7 Li(p,n) 7 Be reaction on a thin lithium converter (1 to 3 mm of thickness) produces nearly mono-energetic neutrons as shown in Figure 2 right panel. In this case, the neutron spectrum at 0° shows a mono-energetic peak due to the 7 Li(p,n) reaction process, with a continuum tail attributed to the break-up process. The contribution of the continuum depends on the target thickness and on the proton energy. It can be removed from time-offlight measurement. The protons which did not react in the converter are swept out of the The LINAG beam frequency (88 MHz) is too high to allow for time-of-flight measurements in the considered neutron energy. In order to avoid wraparound effects, the neutron beam frequency must be reduced to a value depending on the flight path and the low energy part of the spectra. In any case it must be lower than 1 MHz. Therefore a fast beamchopper will select one over N bursts, with N>100. As a consequence the maximum ion-beam intensity in the converter cave is 50 µA, which corresponds to a maximum power deposition in the Be converter of 2 kW.

By taking into account the neutron yield production [1], the beam division and the flight path, the neutron flux can be evaluated and compared to other major time-of-flight facilities, namely n_TOF at CERN, WNR at Los Alamos (where neutrons are produced in a spallation reaction) and GELINA in Geel (where neutrons are produced by photo-fission). The length of the TOF area allows either high-intensity flux (path distance 5 m) or high-resolution (path distance 20 m) measurements. We can see in Figure 4 that NFS is very competitive in terms of average flux in comparison with n_TOF, GELINA or WNR between 1 and 35 MeV. It has to be stressed that this is achieved mainly due to the high repetition rate, compared to the other facilities. Moreover, in comparison to other neutron facilities, NFS shows some advantages relative to the neutron production mechanism itself. In spallation sources the high energy neutrons (up to hundreds MeV), may imply challenges for both collimation and background. In addition, the gamma-flash originating from the interaction of the charged primary beam (proton, electron) into the neutron-production target, which is known to be very penalizing, especially because it induces a dead time, will be probably strongly reduced at NFS. Note that high energy gammas are produced by π 0 decay in spallation sources and by bremsstrahlung in photo-neutron sources based on electron accelerators.

Neutron beam monitoring

The neutron flux will be characterized in intensity and energy with two monitoring systems. Upstream, a micromegas detector will be placed just after the collimator, and downstream the experimental set-up a fission chamber will be used. The micromegas detector does not disturb the neutron flux and therefore can be used during the different measurements, so that on-line information on the neutron flux can be a part of the experiment data flow. The fission chamber placed downstream will also be used in-beam to get a crosscheck information.

The measurement of the neutron energy relies on the time-of-flight measurement, between the neutron production (converter) and its detection. Consequently, a time-of-flight measurement electronics and data acquisition has to be installed, treating a time signal coming from the accelerator and a time signal of the monitoring detector. This ensemble of electronics and detection will be a permanent contribution to the various experimental set-ups that the NFS facility will host.

This ensemble of detectors will be first used in a commissioning phase to characterize the beam properties in energy and intensity. In addition, during this phase, a profile of the beam will be realized with a simple set-up; a small plastic detector will be moved in a plane perpendicular to the neutron beam direction in order to measure a spatial description of the beam intensity.

Physics case

Neutron-induced reactions in the NFS energy range play an important role in various applications like reactors of the new generation, nuclear medicine, Single Event Upset (SEU) appearing in electronics devices, fusion technology, or the development of nuclear model codes in general. Only very limited data exist for neutron induced reactions above 14 MeV and for many cases both fission and (n,xn) reaction cross sections are unknown. The above energy range corresponds also to the opening of new reaction channels like (n,p), (n,α), allowing the pre-equilibrium model studies, i.e. the transition between low (compound nucleus formation via capture) and high energy models (intra-nuclear cascade). The NFS characteristics are particularly well suited for studying these reactions as well as deuteron and proton induced reactions.

The (n,xn) reaction cross sections can be measured at NFS by three different methods, namely the direct detection of neutrons, the prompt gamma-ray spectroscopy of the reaction residues, or the activation technique, based on the decay spectroscopy of the reaction residues. The beam properties (energy and resolution) will allow a precise measurement of the cross-section excitation functions, from the threshold up to the maximum of cross-section for (n,2n), (n,3n) and (n,4n) reactions, where data are either unknown or known with only very bad accuracy. Double-differential cross-sections measurement for neutron-induced light-ion production (p, d and alpha particles) will also be performed. Actually, the light-ion production knowledge is essential in medical and electronic applications for accurate dose evaluation and for gas production prediction in windows or targets of several nuclear constructions. These studies are also fundamental to understand the process of pre-equilibrium emission, responsible for fusion hindrance appearing at energies above the Coulomb.

The study of fission will be an important part of the NFS physics case. Actually, the probable development of innovative fast nuclear reactors requires new high quality data for a large set of fissioning systems (from thorium to curium) for an energy range going from thermal up to the fast (~2 MeV) energy domain. Complementary to reaction cross-section data, the mass and charge distributions are needed with a high precision for burn-up calculations of the reactor fuel, because they are directly connected to the control and the safety of the reactor. A good knowledge of the cross sections is necessary for assessing the neutron balance or to predict radioactive waste inventories. The neutron multiplicity distributions as well as the energy released by gamma emission are also required.

Proton and deuteron induced activation reactions are of great interest for the assessment of induced radioactivities in accelerator components, targets and beam stoppers and are important for isotope production for medical purposes. The cross sections are needed in the energy range from the threshold of the activation reactions (2 -10 MeV) up to 40 MeV for both incident ions. Present status of the measured and evaluated data needs urgent and strong improvement. The measurement of excitation functions can be performed at NFS in an energy domain where data are not existing or known with poor accuracy. In frame of the "Day-One" program of starting investigations (LoI Phase 1 -NFS), a development of the reaction chamber hardware incorporated with pneumatic sample transport system is under way within the NPI Řež and KIT Karlsruhe collaboration.

The following sections are dedicated to a detailed description of some of the foreseen experimental set-ups.

The

Y. Watanabe

Kyushu University, Japan

Despite longstanding measurement efforts, the demand of high quality nuclear data has in recent years even increased. Among the applications with the highest demands one can mention cancer therapy and dosimetry, energy production and single-event effects in electronics. We propose measuring double-differential cross sections for neutron-induced light-ion production (p, d and alpha particles) at NFS, using the Medley detector which has been used for similar experiments in Uppsala. We also plan to upgrade the Medley facility for measuring fission fragment angular distribution and fission cross section on an absolute scale, i.e. versus the np cross section. Experimental studies of fission induced by high-energy neutrons are needed for both improving our theoretical understanding of the fission process, and for many applications. In addition, neutron-induced fission of 238 U is the most widely used standard for monitoring high-energy neutron beams, and it is used at many high-energy neutron facilities.

The Medley facility, currently installed at the neutron beam of The Svedberg Laboratory (TSL), Uppsala, Sweden is described in a number of publications, the most relevant ones are listed below as Refs. [6][13]. Schematic layouts of the chamber and telescope as well as some photographs are shown below in Figure 5 to Figure 9.

The facility has been used for measurements of neutron-induced light ion production and elastic np and nd scattering over a wide energy range. Recently Medley has been used to measure the neutron spectrum of the ANITA white neutron beam at TSL from the highest energies around 180 MeV down to about 1 MeV. Besides the local group from Uppsala University, the main collaboration partners over the past years have been LPC Caen, France, Chiang Mai University, Thailand, and Kyushu University, Japan.

Medley is designed for detection of charged particles over a wide dynamic range. It consists of eight three-element telescopes mounted inside a 240 mm high cylindrical evacuated chamber with inner diameter of 800 mm. Eight telescopes are placed at 20° intervals, covering scattering angles from 20° to 160° simultaneously. The telescopes are usually mounted in two sets, one on each side of the beam, covering the forward and backward hemispheres, respectively. All the telescopes are mounted onto a turnable plate at the bottom of the chamber and, therefore, measurements can in principle be made at any angle. The chamber is equipped with a pump to reach pressures of about 10 -5 mbar. Thus, the stopping power of the remaining air in the chamber is negligible. Thus, even alpha particles with lowest energy do not loose a measureable amount of energy on their way from the production target to the detector.

Each telescope consists of two fully depleted ∆E silicon surface barrier detectors (SSBD) and a CsI(Tl) crystal. The thicknesses of the first eight ∆E detectors (∆E 1 ) range between 50 and 60 µm. For the second one (∆E 2 ) two detector sets are available. In the thinner setup, thicknesses range between 400 and 500 µm. In addition a group of ∆E 2 detectors with thicknesses around 1000 µm is available. These SSBDs are all 23.9 mm in diameter (nominal). The last part of each telescope contains a CsI(Tl) detector to fully stop the detected particles. Two sets of CsI(Tl) detectors are available. One where the crystals are 50 mm long and have a diameter of 40 mm, and another with crystals measuring 50 mm in diameter and a 100 mm in length. The back-end part of the crystals, 20 mm and 30 mm long, respectively, has a conical shape, tapering off to 18 mm diameter, to fit the size of a read-out diode. The read-out diode is Hamamatsu S3204-08 and measures 18 x 18 mm 2 .

To obtain a well-defined acceptance, a plastic scintillator collimator can be placed in front of each telescope. A conventional collimator can cause problems like in-scattering or particle reactions before reaching the first detector. To avoid such complications, the plastic scintillator can be used as an active anti-coincidence collimator to discard the signals from particles that did not pass straight into the first detector. The plastic scintillator collimators have a 40 × 40 mm 2 square shape, with a 19 mm diameter hole at the center and a thickness of 1 mm (see Figure 7). The scintillators are read-out with photomultiplier tubes (PMT) from Hamamatsu, small enough to fit into the chamber. These PMT have been modified to be operational directly after reaching the operational pressure in the Medley chamber. The scintillators thickness is sufficient also for the most penetrating protons to produce a reasonable pulse height. Since energies at NFS are much lower, the minimum signal height would be larger than the minimum signals at TSL. Thus, the collimators could probably be used passively.

For the planned experiments at NFS, we consider adding 25 µm SSBDs for better discrimination between alpha particles and fission fragments. We furthermore work on a design for a central detector and target system for fission measurements. The system will consist of a 238 U-CH 2 -target surrounded by 2 parallel-plate avalanche counters (PPAC). One of these PPAC would be optimized for registering fission fragments, the other for detecting of forward scattered protons from elastic np scattering. Such a solution would allow Medley to work with the white neutron beam and still achieve good neutron energy resolution from time-of-flight measurements. Figure 10 shows the intended design of the upgraded Medely detector.

After passing the custom-made pre-amplifiers, the detector signals are read-out using standard electronic in NIM crates. The energy signals are amplified using Dual Amplifiers by ORTEC (Dual Spec Amp 855). These amplifiers can be considered a part of the Medley chamber. At TSL, the data-acquisition was achieved using the SVEDAQ system which is rather complex and un-stable. For NFS, use of the GANIL DAQ system is planned. This will minimize the dead time and allow for careful offline analysis of the pulse shapes, etc. The 4 π neutron detectors, often called "neutron balls" have been used for more than 50 years. The main advantage is the very high neutron detection efficiency. The development of such detector allowed measuring the fission neutron multiplicity distribution [15] and not only the average value as it was limited before. Several detectors were developed loaded with cadmium or gadolinium in order to study reactions where several neutrons are emitted. In addition to the fission neutron multiplicity [16], these detectors were intensively used for (n,xn) cross-sections measurement [START_REF] Fréhaut | Nuclear Data For Reactors[END_REF] [START_REF] Fréhaut | [END_REF]. There are also some examples of use for capture cross-section measurements [17]. Several neutrons balls were also developed for the study of hot nuclei in reactions induced by heavy ion [22][23], light charged particle [24] or antiproton [25]. Actually, the absence of coulomb barrier makes the neutron a very efficient probe of nucleus excitation energy. In particular, the neutron multiplicity is a very powerful tool for the hot nuclei study. Therefore several neutrons balls were developed for experiments the study. In the eighties, the renew interest in the study of spallation reactions open a new use to the neutron ball [26] [27]. The 4 π neutron detectors were used in with thin and thick targets, in this case liquid with very low gadolinium concentration were needed in order to measure multiplicity up to 200.

All these examples show how the large 4π neutrons detectors are a powerful tool. We have build such a detector to study (n,xn) reactions as well as fission process. A particular attention was paid to the high efficiency of this detector. Note that such set-up requires dedicated beam conditions especially with neutron induced reactions.

Detector characteristics

Description

CARMEN (Cells Arrangement Relative to the Measurement of Neutrons) is a large spherical neutron detector of high efficiency. It consists of two independent vertical hemispheres, 60 cm in outer-radius, 15 cm in inner-radius, each one filled with less than 0.5 m3 of BC521 liquid scintillator provided by Bicron. This scintillator is composed of 1-2-4trimethylbenzene loaded with 0.5 % of gadolinium. A spherical area in the centre of the detector allows placing the sample. The two hemispheres can be moved perpendicularly to the beam direction in order to perform double differential cross sections measurements. The 15 cm in radius area at the centre of the detector defines the reaction chamber. A horizontal cylindrical channel, 5 cm in radius, allows the neutron to reach the reaction chamber, the beam exit being ensured by a rectangular wide-mouthed channel. Twelve phototubes (XP4512 of five inches in diameter provided by photonis) surrounding each hemisphere collect the light produced in the scintillator. Each phototube is immerged in the liquid in order to increase the light collection efficiency. Approximately 4.5% of the external sphere surface is covered by the phototubes allowing direct and reflected light collection. Each hemisphere is supported by 2 frames moving on rails. Due to the toxicity and flammability of the sinctillator, a retention tank is placed under each hemisphere.

Detection process

CARMEN measures the neutron multiplicity event by event allowing determining the neutron multiplicity distribution of a reaction. The neutron detection process generates two signals, a prompt one in the first hundredth of nanoseconds following the reaction and a delayed one which can occur up to 50 µs later. The first one is due to the scattering of neutron on the hydrogen nuclei. The energy lost by the proton recoil produces light detected by the phototubes. The prompt peak can also be generated by gamma emitted in the studied reaction. The prompt signal being generated by all the neutrons and the gamma emitted, its intensity is related to the violence of the reaction.

The neutron then slows down by loosing its energy by inelastic and mainly elastic scattering on hydrogen and carbon nuclei until leaving the detector or being captured. In the thermal energy region, the neutron can be captured by a gadolinium nucleus thanks to the high capture cross-sections (100000 and 250000 barns for isotopes 155 and 157 respectively). The gadolinium nucleus de-excites by the emission of gamma rays, three on average per capture for a total energy around 8 MeV. Gamma rays interact by Compton effect with electrons whose recoil produces light. This signal is called delayed because due to the low gadolinium concentration, 0,5 % by weight, more than 99% of the neutrons are captured in the 50 µs following the prompt signal. The neutron capture on hydrogen is also possible, in that case a 2.2 MeV gamma ray is produced. Due to the statistical nature of neutron moderation, the simultaneously generated neutrons produces delayed pulsed separated in time. The neutron multiplicity is deduced by delayed signals counting in a 50µs long gate. The detector can be used as slave with an external trigger or in some cases the prompt signal can be used to trig the neutron counting. For each event, two 50 µs gates signal (separated by 50 µs) are generated to measure the neutron and the background multiplicities respectively. The neutron detection efficiency of CARMEN is very high, 85% for evaporation fission neutrons, but CARMEN is also very sensitive to the neutron and gamma ray background.

3

The use at NFS Due to its high efficiency, CARMEN is very sensitive to the neutron background and a particular attention was paid about that. The main sources of neutron background in the timeof-flight area have been clearly identified. They are linked to the neutron beam for the neutron collimator and the neutron beam dump or to the building design for the shafts and the heavy door between the converter room and the TOF area. Monte-Carlo simulations have been performed to evaluate the neutron background in the TOF area and to evaluate the number of captures in CARMEN (see Figure 13). A truthful description of the building and of all the components has been considered in the simulations. The center of CARMEN is placed at 150 cm from the exit of the collimator. The neutrons are produced by the interaction of 30 MeV proton on a 2 mm thick lithium converter. The number of Gd(n,γ) reactions in CARMEN as a function of time is given on Figure 14. An iterative procedure, taken into account the beam intensity and frequency, is used to estimate the number of neutron captures during 50 µs, the duration of the neutron multiplicity counting gate. The results is presented on Figure 15, two components are observed: the first one extending to 10 ms is a transition phase due to the beam setting-up; the second one is a steady state where the background becomes white. The value of the plateau gives the evaluated neutron background in 50 µs. The value of 0.09 is fully compatible with the neutron multiplicities which will be measured (between 1 and 4). Our set-up is dedicated to the study of the (n,xn γ) cross sections in view of the improvement of the (n,xn) reaction cross sections knowledge [START_REF] Kerveno | NEMEA-6: Exploring the frontiers of nuclear data and measurements, their uncertainties and covariances[END_REF]. The prompt gamma-ray spectroscopy coupled to time of flight measurements are used to measured the (n,xn γ) reaction cross sections of interest. The experiment will be performed with the GAINS set-up [START_REF] Deleanu | The gamma efficiency of the GAINS spectrometer[END_REF] which is currently used at the GELINA facility of EC-JRC-IRMM (Geel, Belgium) (see Figure 16 and Figure 17). It consists of 8 HPGe detectors placed at 110° and 150° with respect to the neutron beam direction ( Figure 17). For the neutron flux determination, we will use 238-U Fission chamber for which the efficiency will be precisely determine as it has been done for a 235-U fission chamber in our previous work [START_REF]Measurement of (n,xnγ) reactions of at high precision[END_REF]. The fission process discovered in 1938 by Otto Hahn and Liza Meitner is not completely understood, even after seventy years of intensive experimental and theoretical efforts. Experimentally, masses, charges and kinetic energies of fission fragments, energies and multiplicities of neutrons are the most studied observables. Even today, a full identification of fission fragments is a technical challenge, especially for neutron induced reactions (direct kinematics). For fission neutrons, the mean multiplicity has been measured in the past, but the neutron multiplicity associated to each fission fragment is known for very few actinides and only in the thermal region.

The goal of the FALSTAFF experiment is to benefit of the high neutron fluxes in the MeV range that will be provided by the NFS facility and the possibility to use radioactive targets in this installation to perform experiments dedicated to fission fragment measurements of some actinides. Initial (before neutron evaporation) and final (after neutron evaporation) masses of fission fragments will be identified, thus providing the neutron multiplicity associated to each fission fragment. The nuclear charge of the light fragment will be also measured together with the kinetic energy of both fragments. This type of accurate nuclear data is needed both for fundamental studies and applications.

The detection of fission fragments in coincidence with FALSTAFF (Four Arm cLover for the Study of Actinide Fission Fragment) is based on energy and time-of-flight techniques. The combined measurements of velocity and energy provide information on the mass of the fragments before and after the neutron evaporation. Neutron multiplicity as a function of the fragment mass will then be determined. The charge will be identified using the ∆E-E technique.

A sketch of the experimental setup is presented in Figure 18. For velocity measurement, secondary electron detectors (SED with gaseous electron detector) and micro-channel plate detectors (MCP) are good candidates to reach the desired resolution (σ = 100 ps) with a good efficiency [START_REF] Drouart | [END_REF] [35]. The dispersion induced by the thin emissive foils is not too large and the grids are almost transparent. MCP will be put close to and below the target as start detector. It will detect secondary electrons coming from the target. SED detectors can have large dimensions and then will be used as stop detectors and placed at about 50 cm from the target. A prototype of 20 cm x 15 cm has already been built and is being tested in Saclay and GANIL. The first tests give a resolution better than 150 ps. A position resolution of ~1.5 mm is expected. Fragment energies will be measured with segmented ionisation chambers (IC) placed behind the stop detectors. Anodes of the ionisation chambers will be segmented allowing charge identification by ∆E-E correlation up to Z~40. The charge identification provided by the ionisation chamber will allow correcting for energy losses in the different layers of the experimental setup.

GEANT4 simulations taking into account the geometry, resolutions (position, time, and energy) and uncertainties brought by the reconstruction method leads to a resolution of 2.6 amu (1.9 amu) for heavy (light) fragments. For this calculation, position, time and energy resolutions (σ) were assumed to be 1.5 mm, 150 ps and 1% respectively. A geometrical efficiency of ~1 % of 4π is reached with two arms (right panel of Figure 18). Based on an event-by-event analysis, the neutron multiplicity associated to each fragment mass has been determined. Result presented in Figure 19 shows that the foreseen resolutions will allow extracting the neutron multiplicity with a good accuracy. The large uncertainties around the mass 120 come from the low statistics. The gap between simulated and reconstructed multiplicities for 130<mass<150 can be corrected following the method developed by Terrell [36]. Simulations have shown the sensitivity of the mass determination on different parameters. In order to be more confident on the final design, we have defined three different phases for the setup development. The first one, consisting on a half-arm for the v-E measurement of one fragment, will be dedicated to the verification of the method and the simulations. The determination of the final masses of light fragments will be tested. The second one will allow checking the final masses determination of heavy fragments by the addition of a second ionization chamber for the energy measurement of the second fragment in coincidence. The experimental setup defined for this phase will be brought to NFS for D-One experiment. Finally, the last phase will lead to the initial and final mass determination of both light and heavy fragments with a good geometrical acceptance. A coherent experimental program, consisting on the measurement of a defined set of actinide targets, is foreseen to be performed at NFS with this final setup. Introduction

The use of active targets loaded with actinide open new opportunities of measurements for the study of n,xn reactions (see LoI 20) and for the study of fission reactions (see LoI 28). In particular coupling an active target with a 4π detector, like CARMEN, opens very attractive perspectives for experiments which could be performed at the NFS facility.

Direct measurement of (n,xn) reaction cross sections are difficult to perform on actinides since most of the time fission is the most probable exit channel leading also to neutron emission. The measurement of (n,xn) cross-section by detecting the x neutrons thanks to a 4π neutron detector requires to subtract the neutrons from fission inducing important uncertainties. An active target loaded with actinide gives a very efficient veto fission allowing the direct measurement of neutrons emitted in a non fission event.

The nuclear fission is a complex process not yet fully understood. One of the crucial question is the energy sharing at scission, that involves the whole physics of this complicated process. The understanding of this share requires to know nuclear deformations at scission, collective excitations, intrinsic excitation energy among other aspects. The measurement of several observable in coincidence is absolutely required to constrain or develop theoretical models. The observables that can be measured with a setup composed of an actinide loaded active target and the 4π CARMEN detector are the neutron multiplicities, the total energy released by gamma and the total kinetic energy of the fission fragments.

Description of the active target

The principle of this active target is to dissolve the actinide into an organic liquid scintillator. The advantages are the ease of fabrication, the high attainable actinide concentrations, the Pulse Shape Discrimination (PSD) capability of organic scintillators, the fast time response and the very low count losses. Moreover since the actinide is located in the active volume, this target has the potential capability of measuring the Total Kinetic Energy (TKE) of the fission fragments with no window effect, even for high sample masses. Since the scintillator response to fission fragments is not fully characterized this last feature will have to be proved.

The development of the target is inspired of the well known technique of Photon Electron Rejection Alpha Liquid Spectrometry (PERALS) which is commonly used for α spectrometry [38].

Response to fission fragments and light quenching

The experiments were performed by using Pyrex tubes inserted into a mechanical device containing a light reflector and a quantacon Burle 8850 photomultiplier associated to an ORTEC 265 base. The optical coupling was obtained with a silicone oil (Ordela Part no. LC-01). For the pulse shaping and shape discrimination a Mesytec MPD4 module was used. This module implements the zero crossing time technique for Pulse Shape discrimination (PSD) and delivers a Time to Amplitude Converter (TAC) signal. The shaped signal amplitude and the TAC were coded with a 7072 FAST Inc. ADC, associated to a FAST Inc. data acquisition system. The PH and TAC parameters were used to build a 2-dimensional histogram (PSD TAC%PH histogram). The left part of Figure 20 shows an example of histogram obtained with 1 cm 3 scintillator into which 10 µg of natural uranium and 7 Bq of 252 Cf were dissolved. Three classes of events are clearly seen. The long tailed one is associated to electrons. The 3 labeled peaks located at small amplitude and large TAC values are associated to the uranium and 252Cf α decays. Finally the bump at intermediate TAC values is associated to the 252Cf spontaneous fission. The right part of Figure 20 shows the same identification histogram obtained at a concentration of 10 mg/ml. A strong light attenuation is observed on the pulse height parameter while the pulse shape TAC is less affected for the highest concentration. Nevertheless for this last one, α-fission discrimination can still be obtained. The same study was performed with natural thorium and no light quenching was observed.

Detection efficiency

One of the major advantages of this new kind of target is its very high detection efficiency to heavy charged particles. In fact the count losses in such a system are only due to wall effects and since the associated skin has very small thicknesses, of the order of the detected particle ranges, losses are very small. Those ranges are about 50 µm for 5 MeV alpha particles and between 20 and 30 µm for typical heavy and light fission fragments. In order to determine these losses dedicated simulations were performed with the MCNPX2.6 Monte-Carlo code, and the outputs were post-processed in order obtain the spectrum of the deposited energy by fission fragment pairs. Spectra for 3 different geometries of same volume are plotted on Figure 21, for the 252Cf spontaneous fission. They exhibit small tails whose associated relative losses are 3.1x10 -6 , 9.7x10 -7 and 2.2x10 -7 events/fission for an experimental threshold of 87 MeV. It can be concluded from these simulations that such kind of active target can be used as fission trigger with almost no losses. For α-decays these losses are less than 1 %, hence the target can be used to perform very precise measurement of actinide masses. Consequently, this loaded active target can be used for (n,xn) experiments on actinides were a highly efficient fission veto is needed for precise direct measurement. Radiative capture measurements might be envisaged too.

Neutron monitoring

The main drawback of using an organic scintillator is the presence of hydrogen. But this disadvantage can be turned into benefit if a good discrimination between fission events and proton recoils can be obtained, providing the possibility to monitor the neutron flux with the active target. Experiments were performed on the CEA/DIF 4 MV accelerator with scintillators containing approximately 700 Bq of 252Cf. Neutrons were produced by the (d,T) reaction at energies around 18 MeV. Figure 22 presents a 2-dimensional identification histogram similar to the one presented in Figure 20, but obtained with a numerical data acquisition system. The y-axis here reports the ratio of the slow/fast ratio obtained by the well known charge integration method. One clearly sees a separation between fission events and proton recoils (the long "banana"). The obtained figure of merit calculated over a restrictive energy domain (associated to the region of closest approach) is 2.5. It can be concluded from this study that the target can be used as a neutron flux monitor, leading to precise measurement since the measured flux is exactly the one inducing the measured induced reaction. This technique eliminates systematic uncertainties associated to target geometry, neutron transmission.

Conclusions

The presented active target is very promising for triggering purposes in (n,xn) and fission experiments thanks to the very high detection efficiencies, and especially for fission fragments. It can also be used for neutron flux monitoring, providing very precise measurements for experiments dedicated to cross sections measurements. In the context of fission studies, its capability to measure the Total Kinetic Energy will be studied. If the energy resolution is good enough (less than 10 %) the target can be used in experiments devoted to energy sharing in fission studies.

Conclusion

The Neutrons For Science facility is designed to host a broad panel of detectors to perform experiments aiming at various physics cases, like academic and applied physics, electronic, biology or industrial applications… This report gives a short list of detection set-ups that are planned to be used at NFS. This list is not exhaustive and covers only a small part of the set-ups potentiality of NFS. The setups presented here are dedicated to the study of neutron induced fission, light charged particle production and (n,xn) reactions. Most of the presented detectors already exist and have been used at other facilities, some others are under development. In all cases, the experiment will come with its own electronics and data acquisition system. The home detection and acquisition system of NFS is limited in the neutron beam characterization, i.e. one time-offlight signal recorded in a TDS, and two signals from the beam monitoring, with their energy sampling in an ADC.

Figure 1 :

 1 Figure 1 : Schematic view of the NFS facility

Figure 2

 2 left panel.

Figure 2 :

 2 Figure 2 : Neutrons energy distribution at 0 degree produced by deuteron break-up reaction on thick converters [1][2] (left panel) and by the 7 Li(p,n) 7 Be reaction on a thin lithium target [3] (right panel).

  with a bending magnet placed downstream of the target and guided toward a beam-dump.The neutron energy measurement resolution is of prime interest for a time-of-flight facility. The time-of-flight (TOF) is measured with a Time to Digital Converter (TDC) between the trigger of the detector and a time signal delivered by the LINAG (ESCF). Flightpath and beam-time characteristics are the key parameters for the TOF technique. Taking into account the beam transport to the converter, a burst duration shorter than 1 ns is guaranteed. Taking into account a 30 m flight path and variable time resolution of different detectors, the expected resolution of the energy measurement of the impinging neutrons is given in Figure3. It may be observed that with fast detectors the energy resolution at 40 MeV is better than 1 % and even for slow detectors like, High Purity Germanium detector (∆t ≈ 8 ns), the energy resolution remains better than 5%.

Figure 3 :

 3 Figure 3 : Energy resolution as a function of the neutron energy and the detection time-resolution ∆ ∆ ∆ ∆t.

Figure 4 :

 4 Figure 4: Neutron flux at NFS for two flight paths compared to three other neutron time-of-flight facilities.

F

  Medley facility C. Gustavsson, S.Pomp, M. Lantz, A. Solders, M. Österlund Department of physics and astronomy, Uppsala University, Sweden

Figure 5 :

 5 Figure 5: Schematic layout of the detector arrangement in the Medley chamber. See text.

Figure 6 :

 6 Figure 6: Photograph of the chamber. Not seen is the mounting and the arrangement of the vacuum pumps. The table on which the telescope rails are mounted can be rotated freely from the outside. The individual telescopes are mounted on rails and can be moved along these rails to the desired distance from the target. When closed,the target frame sits in the center position (see Figure5and Figure8).

Figure 7 :

 7 Figure 7: In this photograph a sample arrangement of four telescopes can be seen. In this case the telescopes contain the small CsI detectors. The two telescopes on the left side carry the active collimator scintillators while in the two telescopes on the right side the front of the first Si detector can be seen.

Figure 8 :

 8 Figure 8: Three target frames are mounted on the lock of the Medley chamber. The frames can be moved from the outside. Thus, targets can be changed will the vacuum can be kept.

Figure 9 :

 9 Figure 9: Schematic drawing of the layout of one telescope. The drawing shows the smaller housings with the shorter CsI detectors.

Figure 10 :

 10 Figure 10 : Left: Schematic layout of the detector arrangement in the Medley chamber. (Not to scale.) In the overview sketch in the upper right corner the beam enters from above. The telescopes are placed on either side of the beam covering backward and forward scattering angles respectively. In the chamber centre sits the two-layered target, with one PPAC detector on either side (see the detailed picture at the bottom).

Figure 11 :

 11 Figure 11 : Picture of the CARMEN detector.

Figure 12 :

 12 Figure 12: View of the CARMEN detector in the NFS facility.

Figure 13 :

 13 Figure 13 : MCNPX simulation of the neutron flux in the NFS facility. The neutrons are produced by the interaction of proton at 30 MeV on a 2mm thick Lithium converter with an intensity of 5µA.

Figure 14 :

 14 Figure 14 : Neutron capture time distribution in CARMEN normalised to 1 proton source.

Figure 16 :

 16 Figure 16 : Sketch of the GAINS set-up at the Gelina facility.

Figure 18 :

 18 Figure 18 : Falstaff experimental setup. Top view (left panel) of the full setup and side view (right panel) of half of the setup.

Figure 19 :

 19 Figure 19 : Neutron multiplicity vs initial fragment mass. Theoretical (red symbols), simulated (black symbols) and reconstructed (green symbols) neutron multiplicities are shown.

Figure 20 :

 20 Figure 20: (Color online) Left: (PSD TAC)%PH histogram for a natural uranium concentration of 10 µg/cm3. Three α-peaks can be distinguished which corresponds from lower to higher energies to the 238U, 234U and 252Cf decays. Right: same for a concentration of 10 mg/cm3. The three α-peaks can not be resolved anymore due to resolution degradation associated to light quenching.

Figure 21 :

 21 Figure 21 : (Color online) Simulated spectra of the deposited energy in the most probable spontaneous fission decay of 252 Cf. The losses obtained from these three simulated spectra are respectively 3.1x10 -6 , 9.7x10 -7 and 2.2x10 -7 events/fission for the PERALS (full line), the hemisphere (dashed line) and the sphere (dotted line) geometries. The y-axis has been zoomed in order to optimize the view of the tail. Hence the full energy peak which contains 107 counts is truncated.

Figure 22 :

 22 Figure 22 : (Color online) Bi-dimensional histogram obtained with the DIN scintillator loaded with 6 kBq of 252 Cf. The neutron irradiation was performed at the CEA/DIF 4 MV accelerator.

The CARMEN detector X. Ledoux Figure 17: Photo of the apparatus.

The acquisition system is composed of TNT2D digital cards [START_REF]TNT2 Digital Pulse Processor Functionalities & TUC control software[END_REF]. We need a NIM signal from the pulsation of the accelerator and signals from beam monitors.

We bring high power supplies and racks. The electronic and DAQ is located close to the detectors and we need only internet connection to the PC's located in the experimental area.

The Fission chamber is made of a sealed 238 U sample (~ 20 mg) and P10 gas (90% argon and 10% methane) at 1 atm. (FC dimensions : ∅ = 150 mm, H = 66 mm) )

We need liquid nitrogen to cool the HPGe counters but we bring an autofill system.

Active targets based on


S Chenikher

J S Guez

F Coutte

M Pekpe

P Jacques

J P Cassar

Control of the specific growth rate of Bacillus subtilis for the production of biosurfactant lipopeptides in bioreactors with foam overflow

Keywords: Biotechnology, Fed-Batch Culture, Biosurfactant Production, Open-Loop Control, Modeling, Extraction

This paper formulates a feeding law for a bioprocess dedicated to the production of an antibiotic surfactant using Bacillus subtilis. The specificity of the process relies on the use of the surface active property of the product to extract it by foaming. The control law is designed to maintain a constant specific biomass growth rate while taking into account the particularity of the process. This law can be regarded as a generalization of the conventional exponential feeding strategy and is generic enough to encompass the case of continuous processes with partial recycling. Conventional exponential feeding strategies indeed fail to account for the loss of biomass induced by the foaming. Previous experiments have provided a model of the process and values for its parameters. From this information, a feeding rate law was computed using the feeding strategy proposed in this paper and applied to an experimental culture. This experiment allows discussion of the modeling of the biomass extraction method used in this study. The results on the estimated specific growth rate highlight the complete agreement between the expected and experimental features. Further process optimization studies can now be performed on the basis of the constant specific biomass growth rate.

Introduction

The specific biomass growth rate is considered a key parameter in many bioprocess studies [START_REF] Yee | Recombinant protein expression in high cell density fedbatch cultures of Escherichia coli[END_REF][START_REF] Loloei | Growth rate control in biotechnological fed-batch process using dynamic matrix control[END_REF][START_REF] Mart Ne | Effect of growth rate on the production of βgalactosidase from Escherichia coli in Bacillus subtilis using glucose-limited exponentially fedbatch cultures[END_REF][START_REF] Bastin | On-line Estimation and Adaptive Control of Bioreactors[END_REF]. Indeed, it is correlated to other parameters such as production rates, which are essential for the design of industrial bioprocesses. These studies need to maintain a constant specific biomass growth rate during the experiment. Since the specific growth rate depends on the substrate concentration, this objective can generally be achieved by maintaining a constant feeding rate in continuous bioprocesses [START_REF] Dauner | Bacillus subtilis metabolism and energetic in carbon-limited and excess-carbon chemostat culture[END_REF][START_REF] Vierheller | Sustained and constitutive high levels of protein production in continuous culture of Bacillus subtilis[END_REF][START_REF] Zamboni | Transient expression and flux changes during a shift from high to low riboflavin production in continuous cultures of Bacillus subtilis[END_REF] or by providing an exponential feeding rate in fed-batch bioprocesses [START_REF] Yee | Recombinant protein expression in high cell density fedbatch cultures of Escherichia coli[END_REF][START_REF] Mart Ne | Effect of growth rate on the production of βgalactosidase from Escherichia coli in Bacillus subtilis using glucose-limited exponentially fedbatch cultures[END_REF][START_REF] Lee | Enhanced production of α-amylase in fed-batch cultures of Bacillus subtilis TN 106[pAT5][END_REF][START_REF] Ic -Marco | A closed loop exponential feeding law: Invariance and global stability analysis[END_REF][START_REF] Ic -Marco | Partial stability for specific growth rate control in biotechnological fed-batch processes[END_REF]. The originality of the mycosubtilin production bioprocess described and modeled by Guez et al. [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF] is the use of the surface-active property of the product [START_REF] Maget-Dana | Surfactin/iturin A interactions may explain the synergistic effect of surfactin on the biological properties of iturin A[END_REF][START_REF] Razafindralambo | Foaming properties of surfactin, a lipopeptide biosurfactant from Bacillus subtilis[END_REF][START_REF] Razafindralambo | Foaming properties of lipopeptides produced by Bacillus subtilis: Effect of lipid and peptide structural attributes[END_REF] to extract it continuously by foaming [START_REF] Cooper | Enhanced production of surfactin from Bacillus subtilis by continuous product removal and metal cation additions[END_REF][START_REF] Davis | The application of foaming for the recovery of surfactin from B. subtilis ATCC 21332 cultures[END_REF]. However, the foam also entraps some biomass quantity and consequently reduces the biomass quantity in the broth. This phenomenon makes it difficult to treat this bioprocess as a conventional fed-batch process. Model parameters were estimated in [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF] from several exponential fed-batch experiments and were calculated for different target biomass growth rates without accounting for the foaming phenomenon. The partial loss of biomass was shown to induce increases in the biomass concentration and the specific biomass growth rate during the culturing step. To keep the specific growth rate constant, a new feeding law should consider the effect of the partial extraction of biomass introduced by foaming in future studies. In this way, the actual specific biomass growth rate can be correlated with the productivity or any other factor to be optimized.. With the very general biomass extraction model we have chosen, we can design a generic open-loop control law that is applicable to a wide variety of bioprocesses, such as those with partial recycling, fed-batch processes and our own specific process. In the literature, various approaches for bioprocess control have been proposed [START_REF] Harmand | Microbial ecology and bioprocess control: Opportunities and challenges[END_REF][START_REF] Dochain | State observation and adaptive linearizing control for distributed parameter (bio)chemical reactors[END_REF][START_REF] Huang | Bayesian methods for control loop monitoring and diagnosis[END_REF][START_REF] Dowd | Predictive modeling and loose-loop control for perfusion bioreactors[END_REF][START_REF] Lee | Control of fed-batch fermentations[END_REF][START_REF] Gadkar | Cybernetic model predictive control of a continuous bioreactor with cell recycle[END_REF][START_REF] Magyar | Globally stabilizing feedback control of process systems in generalized Lotka-Volterra form[END_REF][START_REF] Morari | Model predictive control: past, present and future[END_REF][START_REF] Zhu | Model predictive control of continuous yeast bioreactors using cell population balance models[END_REF]. Several control strategies developed in [START_REF] Ic -Marco | Globally stabilizing control of fed-batch processes with haldane kinetics using growth rate estimation feedback[END_REF] leading to a closed-loop version of the conventional exponential feeding law for the regulation of specific biomass growth rate in fed-batch bioprocess could be applied to our control law. However, open-loop control was preferred given the lack of the available measurements of the state variables during the experiment and the difficulty of indirectly estimating the value of the specific biomass growth rate at any particular time using the measurements of biomass concentrations [START_REF]Estimation of biomass concentrations in fermentation processes for recombinant protein production[END_REF][START_REF] Jenzsch | Generic model control of the specific growth rate in recombinant Escherichia coli cultivations[END_REF]. This open-loop feeding strategy was tested on an actual fed-batch culture of Bacillus subtilis involving the original foaming strategy. From the biological features of samples, as well as the measurements, the validity of the model used to compute the feeding strategy was checked, and the objective of achieving a constant specific biomass growth rate was verified. This paper is organized as follows: Section 2 presents a brief description of the biosurfactant production process. The general dynamic model of the bioprocess for the three phases is given in section 3. The design of the proposed new control law is highlighted in section 4. Section 5 is devoted to the use of the available measurements to estimate the specific growth rate and biomass concentration in the effluent foam. The results obtained are presented in section 6. Section 7 discusses the results with respect to the two following topics: the ability to obtain a constant specific growth rate and the validity of the model for biomass extraction by the foam. Finally, section 8 outlines the conclusions of this work.

Biosurfactant production

Description of the process in bioreactor

This process was developed to extract lipopeptide biosurfactants like mycosubtilin and surfactin using their foaming properties. The description of this process design from a 5 L Bioflo 3000 bench-top fermenter (New Brunswick Scientific, Edison, MA, USA) is given in Figure 1. Instead of trying to avoid foaming, the foaming capacity of the broth was increased to collect the foam, which contains a high concentration of biosurfactant. For this purpose, the lower Rushton turbine was immersed in the broth to ensure the stirring of the broth and oxygen transfer. The upper impeller was fixed just above the initial height of the broth liquid. When a feeding flow caused the volume to increase, this impeller was progressively immersed in the liquid broth, favoring mixing at the gas-liquid interface. Clearly, the effect of this unusual impeller location was to drastically increase the foaming capacity at the gas-liquid interface. The foam was collected in a cooled foam collector. The process was conducted in three main phases. In phase I, cells were grown for 10 h in a preliminary batch culture without feeding until the main carbon source was depleted. Early in this phase, foaming occurred and produced an overflow with a concomitant lowering of the liquid level. The foaming was due to the early production of mycosubtilin obtained with strain BBG100 and was caused by the replacement of the native Pmyc promoter with a constitutive one, PrepU [START_REF] Leclère | Characterization of a constitutive mycosubtilin overproducing Bacillus subtilis strain and its antagonistic activity[END_REF]. The following two phases were aimed to ensure a constant specific growth rate under carbon-limiting conditions using appropriate feeding control laws. In phase II, because of the loss of broth in phase I, the level of the liquid remained below the level fixed by the upper propeller location; thus, there was no foaming caused by this upper propeller. The cells were grown in a fed-batch culture where the volume increased according to an exponential feeding law proposed by [START_REF] Yee | Recombinant protein expression in high cell density fedbatch cultures of Escherichia coli[END_REF], whose expression is recalled in section 4.1. The parameters of this feeding law were calculated from the initial biomass quantity, which was deduced from the analysis of the biomass concentration performed at the end of phase I. This phase ended when the liquid level reached the upper propeller; its duration was predicted from the feeding law and from the initial volume of the liquid. In phase III, the liquid volume was kept constant because the feed flow was balanced by the increase of the foam overflow due to contact between the liquid and the upper propeller. In this phase, the new feeding control law developed in section 4 was applied. The evolutions with time of the volumes in the reactor and in the foam collector are given in Figure 2 in section 6.3 of the results with labels indicating the different phases of the process. The temperature was regulated to 30 °C and the pH adjusted to 6.5 by adding 3 Moles L -1 solutions of KOH or H 2 SO 4 . The aeration rate was fixed at 0.75 L h -1 , and the dissolved oxygen concentration was maintained above 15 % of the saturation concentration by maintaining the stirrer speed between 200 and 500 rpm.

Bacterial strain and growth medium

The strain BBG100 used in this study is a mycosubtilin overproducer derivative obtained previously [START_REF] Leclère | Characterization of a constitutive mycosubtilin overproducing Bacillus subtilis strain and its antagonistic activity[END_REF] from Bacillus subtilis ATCC 6633 by the replacement of the native promoter of the mycosubtilin synthetase operon with a constitutive promoter originating from the replication gene (repU) of the Staphylococcus aureus plasmid pUB110. The pre-culture was inoculated in Erlenmeyer flasks containing a modified Landy medium described in [START_REF] Guez | Respiration activity monitoring system (RAMOS), an efficient tool to study the influence of the oxygen transfer rate on the synthesis of lipopeptide by Bacillus subtilis ATCC6633[END_REF] with 1 g L -1 of yeast extract added. The reactor containing the same medium was then inoculated with mid-logarithmic grown cells. The feeding medium was a double-concentrated Landy modified medium.

Analyses and measurements

Biosurfactant lipopeptides: Overflowed foam samples containing mycosubtilin were centrifuged at 10,000 g for 10 min. A volume of 1 mL of the supernatants was purified through C18 Maxi-Clean cartridges (Alltech, Deerfield, U.S.A.) as previously described by the authors [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF]. The second derivative of the absorption spectrum between 200 and 400 nm (Diode Array PDA 996, Waters) was used to identify the eluted molecules (Millenium Software, Waters). Biomass:

The optical density at 600 nm was measured with a spectrophotometer (uV Mini 1 240, Shimadzu, Japan) whose precision is 0.005 Abs (at 1 Abs) and  0.003 Abs (at 0.5 Abs). An optical density of 1.0 Abs corresponded to a biomass concentration of 0.33 g DW L -1 . Samples were taken, and dilutions were performed using a P1000 Finnpipette (Thermo Fisher Scientific Inc., Waltham, MA, USA) whose precision is  6 L at 1000 L and  1 L at 100 L Control and acquisitions: We used the software AFS Biocommand from New Brunswick Scientific for controlling the process and acquiring data. The weight of the foam collector was measured with a balance (DA 35 Ohaus, Pine Brook, NJ, USA) at a sampling period of one minute.

Modeling

General model

The general dynamic model refers to the three phases of the bioprocess. The following model equations are deduced from volume or mass balances, in the bioreactor and in the foam collector (refer to the list of symbols for the meaning of the variables):

out out d VX VX X f dt   (1) / in in XS d VS VX S f dt Y     ( 2
)
in out dV ff dt  (3) Col Col out out dV X Xf dt  (4)
 Col out dV f dt (5)
Equation ( 2) assumes that the foam does not remove any substrate, as the substrate concentration in the bioreactor is kept at a very low level.

The specific biomass growth rate should follow Monod's law:

max S S KS     (6)

Theoretical models for phase I and phase II

The mass balance of biomass in both phases is deduced from the generic model, equation [START_REF] Yee | Recombinant protein expression in high cell density fedbatch cultures of Escherichia coli[END_REF], by zeroing the output flow (f out = 0):

d VX VX dt   (7)
In the batch phase (phase I), there is no feeding flow, so: f in = 0. Therefore, the model is reduced to equation [START_REF] Zamboni | Transient expression and flux changes during a shift from high to low riboflavin production in continuous cultures of Bacillus subtilis[END_REF], and the equation of substrate uptake is given by:

/ XS d VS VX dt Y   (8)
From equation ( 3), the volume remains constant.

In the fed-batch phase (phase II), the dynamics of the substrate equation ( 2) does not change because the substrate concentration in the feeding flow is assumed to be constant. The volume balance in the bioreactor becomes:

in dV f dt  (9)
A small foam overflow occurred in these phases but it was not taken into account in this theoretical model, which was used for simulation purposes.

Model for the phase with foam overflow (phase III)

In phase III, equations (1) to ( 5) of the model are used with the addition of an equation to take account for biomass extraction by the foam.

Computation of the feeding flow control law

The new feeding flow control law f in (t) has to be designed to maintain the specific biomass growth rate constant. In equation [START_REF] Vierheller | Sustained and constitutive high levels of protein production in continuous culture of Bacillus subtilis[END_REF], this variable only depends on substrate concentration, which has to also be kept constant. Therefore, the feeding control law required:

Conventional exponential feeding flow control law

An exponential feeding profile was proposed by Yee and Blanch, [START_REF] Yee | Recombinant protein expression in high cell density fedbatch cultures of Escherichia coli[END_REF] for fed-batch processes (phase II).

From equation (2), the substrate dynamics are given by:

/ in in XS d S d V V S VX S f dt dt Y     
Using equation ( 9), the following expression of the dynamics of the substrate concentration is derived:

/ () in in XS f dS X S S dt YV      ( 12
)
When  is constant, the differential equation ( 7) can be solved in VX and the solution is: 00  t VX V X e  (13) The feeding function can be calculated by substituting equations ( 11) and ( 13) into equation ( 12):

  / / 0 0 0 0 ( -) ( -) X S X S in in in t f t Y S S Y S S VX V X e     
4.2. Control law for phase III Using the exponential feeding equation ( 14) (Phase II), the specific growth rate was maintained at a constant value for the fed-batch culture without foam overflow. However, as soon as the foam starts to overflow the bioreactor, equations ( 7) and ( 8), which are based on the assumption that f out = 0, are no longer valid. Indeed, we demonstrated in [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF] that the exponential feeding law applied in the case of biomass extraction induces an increase of the specific biomass growth rate. Therefore, calculating a new feeding law is necessary to deal with the foam overflow and the substantial biomass extraction. Equations ( 11) and (2) require that:

/ 0 in in XS VX S f Y     , from which X can be deduced: / X S in in YS Xf V   (15)
As already explained in the bioprocess description, the volume in the bioreactor remained constant during the whole of phase III. Substituting X from equation (15) into equation ( 1) with S, µ and V constant leads to:

// X S in in X S in in out in Y S df Y S V V f X f V dt V    After simplification: / 1 1 out in in X S in X df f YS dt       (16)
Substituting X out from equation [START_REF] Ic -Marco | Partial stability for specific growth rate control in biotechnological fed-batch processes[END_REF] into equation ( 16) gives:

2 / 1 1 in in in X S in df ff YS dt V       
   This equation is in the form of a Riccati equation: Feeding control laws for specific types of bioprocess can be developed from this general solution. The conventional exponential feeding profile is obtained by setting X out to 0 and cancels out the second term of the RHS of equation ( 1), hence reverting to equation [START_REF] Zamboni | Transient expression and flux changes during a shift from high to low riboflavin production in continuous cultures of Bacillus subtilis[END_REF]. For continuous bioprocesses with recycling, where X out = α X, then β =0 and b =1, the feeding function is given by:

0 0 1 () ( 1
)
in t in in ft af e a f       (18)
If the biomass concentration in the output flow is constant then X out = β, (α=0), that leads to:

  0 in bt in f t f e   (19)

Maintenance parameter effect

The maintenance parameter characterizes the phenomenon of substrate consumption by microorganisms for physiological reasons other than the growth. In the previous model (subsections 3.1 and 3.2), the consumption of the substrate was considered to be devoted entirely to biomass growth, and the maintenance parameter was supposed to be negligible. However, some authors have previously shown [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF] that this parameter should not be neglected. Introducing the maintenance parameter into equation (2) leads to:

/ () in in S XS dS X S S f m X dt Y       (20)
The maintenance parameter does not change the parameter a, whereas the parameter b is written as:

/ / 1 1 s XS X S in m Y b YS       

Estimations from available measurements

We verified the validity of the proposed model for biomass concentration in the foam flow, as well as the efficiency of the feeding strategy to maintain the specific biomass growth rate constant, by estimating the evolution with time of these variables from the available measurements as described below.

Estimation of the biomass concentration in the foam X out

The biomass concentration in the foam collector X Col and the collected volume V Col were measured and can be estimated from these measurements by equations ( 4) and [START_REF] Dauner | Bacillus subtilis metabolism and energetic in carbon-limited and excess-carbon chemostat culture[END_REF].

( ) / ˆ/ Col Col out Col d V X dt X dV dt  (21)

Estimation of the specific growth rate

Between two consecutive biomass measurements, only the mean value of the specific growth rate, which is considered constant, can be calculated. For phase II, when neglecting the foam overflow from equation ( 7), the specific growth rate is given by:

1 1 1 1 . ln ln ( ) ln k k k kk k t t t t t k k t dX µ dt X X µ t t µt X X            1 1 ln ˆ        k k t t k kk X X µ tt (22)
In phase III, equations ( 1) and ( 4) give:

col col d V X d VX VX dt dt  
The integration between t k and t k+1 gives:

1 11 k kk kk k t tt col col tt t VX VXdt V X     
Therefore, the estimation of the mean value of µ in the interval [t k ,t k+1 ] is given by:

  1 11 [ ( ) ( )] ( ) ( ) ˆ       k k k k col col k col col k k t t VX t VX t V X t V X t µ VXdt (23)
Because the quantity of biomass grows exponentially, the integration involve in the denominator of the RHS of equation ( 23) can be estimated by the trapeze method if the time interval remains short enough:

  1 1 1 ( ) ( ) 2 k k t kk t VXdt VX t VX t    

Uncertainties of the estimations

The uncertainties of the estimations, accounting for the accuracies of the measurement devices, are estimated by simulation using the Monte Carlo procedure performed for 1000 simulated samples. The uncertainties of measurements are supposed to be normally distributed with a standard deviation equal to the third of the accuracy range. The choice of this distribution induces a probability of 0.01 of being out of the accuracy range. However, as the accuracy includes both deterministic and stochastic components, this choice overestimates the stochastic part of the uncertainties and thus the estimation of the intervals of confidence that are deduced from them.

To lower the effect of the derivation on the uncertainties, the derivate in equation ( 21) was computed from a polynomial approximation at order 2 of the evolution with time of the biomass quantity V Col X Col in the collector. This approximation was obtained by a least-squares fitting.

Results

Model parameters and experimental conditions

The specific bioprocess for producing mycosubtilin using Bacillus subtilis and product recovery through foam is presented in more detail in [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF]. In this paper, model parameters were estimated from a set of three experiments and further validated on six additional experiments. These model parameters given in Table 1 were used to compute the feeding flow control laws and were also used to simulate the bioprocess behavior using models corresponding to the different phases. The reference value of µ was fixed to 0.05 h -1. This low µ value was the result of one limitation of the process, the maximal value of the feed flow, which was around 0.18 L.h -1 . The limitation of the foaming flow and the maximum flow allowed by the feeding pump both contributed to this limitation of the feed flow. The experiment was conducted at the ProBioGEM laboratory by managing the three phases (phases I, II and III) described in subsections 3.2 and 3.3. The initial conditions of theses phases are given in Table 2. Phase I was initiated with an initial substrate concentration of 20 g L -1 . It lasted 10 hours until the residual substrate concentration reached the value of 0.001 g L -1 . For both phases II and III, the concentration of the substrate in the feeding flow was S in = 40 g L -1 . The conventional exponential feeding law for phase II (fed-batch) was calculated from the initial values of this phase so that the liquid level in the bioreactor reaches the propeller from the initial volume of 2.714 L. The equilibrium volume in the bioreactor that was obtained when the liquid reached the propeller was 2.8 L, The feeding profile for phase III was calculated from equation ( 17) using the values of parameters and those of the initial conditions at the 16 h time point. The experiment was continued until the feeding flow pump maximal capacity around 0.18 L h -1 was reached, i.e., 40 hours after the beginning of the feeding.

Volumes evolution with time

Figure (2) provides the evolutions with time of the simulated and measured volumes both in the reactor and in the collector vessel. The three phases that were explained in section 2.1 are also presented here because they are closely related to the evolution with time of the volumes. In phases I and II, no foaming was expected from the simulation. In fact, the foam overflow already started in the middle of the batch phase and led to an increase in volume in the collector. This phenomenon also explains the quasi constant gap between the expected and measured values of volume in the collector during phase III of the experiment. The volume in the collector vessel was simulated using an exponential feeding law and is also given here for the purpose of comparison. The exponential feeding clearly led to a more important feeding flow and thus to a more important volume in the collector. The foam overflow during phases I and II induced a loss of liquid volume in the bioreactor, which made it necessary to continue with phase II to recover the initial volume, while keeping constant the specific growth rate. In phase III, the broth volume in the bioreactor remained constant as the flow of foam balances the entire feeding flow.

Biomass quantities

The biomass quantities in the bioreactor and in the foam collector were calculated from volume and concentration measurements, which are given in Figure [START_REF] Mart Ne | Effect of growth rate on the production of βgalactosidase from Escherichia coli in Bacillus subtilis using glucose-limited exponentially fedbatch cultures[END_REF]. Intervals of confidence of 0.01 are depicted around the estimated values and are the result of the Monte Carlo procedure explained in section 5.2. The polynomial approximation of the order of 2 for the evolution with time of the biomass quantity in the collector that was introduced in subsection 5.3 is also given in this figure. It provides the values of the biomass quantity in the bioreactor that was predicted by a dynamic simulation covering the three phases using the model of equations ( 1) to ( 5) with the feeding flow calculated according to equations ( 14) and (17).

Estimation of the specific biomass growth rate

The objective of the control laws calculated from equations ( 14) and ( 18) for phase II and phase III was to maintain the specific biomass growth rate at a constant value; Figure [START_REF] Bastin | On-line Estimation and Adaptive Control of Bioreactors[END_REF] presents the estimations of this variable, which can be deduced from the measurements presented in the previous subsections by using equations ( 22) and [START_REF] Gadkar | Cybernetic model predictive control of a continuous bioreactor with cell recycle[END_REF]. Intervals of confidence at the 1% level are depicted around the estimated values and result from Monte Carlo simulation explained in section 5.2. The curves obtained by simulation for exponential feeding and the feeding calculated from [START_REF] Harmand | Microbial ecology and bioprocess control: Opportunities and challenges[END_REF] are also provided for the purpose of comparison.

Measurements and estimations of the biomass concentration in the foam

The measured values of the biomass concentration in the foam, X out , were plotted against the measured concentration in the bioreactor in Figure [START_REF] Dauner | Bacillus subtilis metabolism and energetic in carbon-limited and excess-carbon chemostat culture[END_REF]. Some additional data for the measurement of the biomass concentration in the foam were obtained from an independent experiment performed under the same conditions. Thus, a larger range of biomass concentrations in the reactor was covered. The biomass concentration in the foam, X out , was also estimated using equation [START_REF] Dowd | Predictive modeling and loose-loop control for perfusion bioreactors[END_REF]. This estimation involved the time derivative of the quantity of biomass in the collector performed from the polynomial approximation of the time evolution with time of this variable, as depicted in Figure [START_REF] Mart Ne | Effect of growth rate on the production of βgalactosidase from Escherichia coli in Bacillus subtilis using glucose-limited exponentially fedbatch cultures[END_REF]. The slope of this curve provided the numerator of equation [START_REF] Dowd | Predictive modeling and loose-loop control for perfusion bioreactors[END_REF]. The denominator was estimated from the slope of the time plot of the liquid volume in the collector in Figure [START_REF] Loloei | Growth rate control in biotechnological fed-batch process using dynamic matrix control[END_REF]. This information provided the basis for the discussion of the proposed linear model given in equation [START_REF] Ic -Marco | Partial stability for specific growth rate control in biotechnological fed-batch processes[END_REF]; the parameters  and  of this model obtained from previous experiments are given in Table [START_REF] Yee | Recombinant protein expression in high cell density fedbatch cultures of Escherichia coli[END_REF].

Mycosubtilin production

Table (3) shows the quantities of mycosubtilin produced during the bioprocess. For experiments operated at a constant specific growth rate of 0.05 h -1 , the mycosubtilin productivity measured in our experiment at 0.71 mg g -1 h -1 agreed with the one obtained in a previous report [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF] i.e. 0.7 mg g -1 h -1 .

Discussion

Modeling of biomass extraction

In Figure [START_REF] Dauner | Bacillus subtilis metabolism and energetic in carbon-limited and excess-carbon chemostat culture[END_REF], the estimation of the biomass concentration, X out , reached lower values than those measured in the foam. The latter can be explained by the dynamics of the foam in the collector vessel; the foam was driven into the collector with a delay and was slowly concentrated into a liquid. Therefore, the biomass concentration in the liquid did not take into account the total amount of biomass in the foam. The difficulty in collecting a sufficient amount of foam to obtain analysis that was accurate enough led to a more important variability in the measurements of the biomass concentration in the foam. In Figure [START_REF] Dauner | Bacillus subtilis metabolism and energetic in carbon-limited and excess-carbon chemostat culture[END_REF], the results of the experiment show that the relation between X out and X did not exactly fit the model given by the equation [START_REF] Ic -Marco | Partial stability for specific growth rate control in biotechnological fed-batch processes[END_REF] and the parameters of Table 1. The minute value of  from the previous experiments implies that the biomass concentration in the foam was almost constant; it was equal to 2 g L -1 . This value was estimated for experiments conducted under different feeding conditions; few measurements were taken for each experiment. For X=0, the biomass concentration in the foam must equal zero, and the proposed model did not take this constraint into account. The curvature of the experimental points scattering in the first experiment suggests that a non-linear model might better to fit these points, while satisfying this constraint. However, for concentrations greater than 3 g L -1 ; the points that were added from a second experiment do not confirm this hypothesis. This suggests that the structure of the proposed model can be validated with a greater value of the  parameter. A computational prediction of the feeding control law using a value of  =3. leads to a 17 % increase of the feeding flow at the end of the experiment..

Results of the proposed control law

The main result of this paper is highlighted in Figure [START_REF] Bastin | On-line Estimation and Adaptive Control of Bioreactors[END_REF], which plots the estimated specific biomass growth rate over time. The estimated values remained close to the expected value of 0.05 h -1 . In phase III, the specific growth rate differed significantly from the target value during three separate periods. At the beginning of the application of the proposed feeding strategy, between times 15 h and 29 h, the specific growth rate was close to the reference value. From 18 h until 21 h 30 min, it increased significantly above the reference value and then ended below it from 25 h 25 min to 29 h. The mean value of the specific growth rate during the second period is close to the reference value. The third period from 35 h 75 min to 45 h 75 min, in which the specific growth rate was significantly lower than the target value, could reflect a substrate limitation problem. This effect was visible in Figure (3), and the limitations presumed start is indicated by an arrow. The limitation in carbon substrate may be due to the open-loop control, which did not consider higher biomass concentrations than expected values. At the end of the fermentation, the value of  was again very close to the reference value. Interestingly, this result was obtained with open-loop control, demonstrating the relevance both of the model that was derived from previous experiments and of the calculated control law for the feeding flow. It is clear that a closed-loop scheme, based for example on predictive control, would limit all the observed fluctuations. Introducing a maintenance parameter in the model led to a specific growth rate lower than the reference value. Indeed, in section 4.3, parameter b increased when taking into account the maintenance phenomenon; thus the feeding was greater and led to a higher value of . The estimated values of  were not influenced by the maintenance and were close to the reference. This indicates that this parameter could be eliminated as a contributing factor. The comparison with the values of  calculated for an exponential feeding shows that the proposed feeding strategy avoided an increase of the specific growth rate. Indeed, the equilibrium value of  for an exponential feeding and a constant value of X out have been demonstrated in [START_REF] Guez | Setting up and modelling of overflow fed-batch cultures of Bacillus subtilis for the production and continuous removal of lipopeptides[END_REF] and it led to a value of 0.074 h -1 under the conditions of our experiment. However, under the new feeding law, this value cannot be reached because the feeding flow limitation only enables to run the experiment for 45 h instead of 50 h.

Conclusion

A new feeding control law has been proposed to keep the specific biomass growth rate constant even when biomass was partially extracted from the bioreactor. The new feeding control law differs fundamentally from the conventional exponential law. For instance, this feeding law was applied to keep the specific biomass growth rate at 0.05 h -1 . The estimations of the specific biomass growth rate based on the experimental measurements show the ability of the calculated control strategy to reach this objective, even in an open-loop configuration. Applying a closed-loop strategy, as a predictive control method based on the proposed feeding law, would improve these performances. This study also provides better knowledge about biomass extraction using the foam overflow. For biomass concentrations in the bioreactor over 3 g L -1 , the relationship between the biomass concentration in the foam and in the bioreactor can be considered linear. The structure of the model proposed in a previous report is thus confirmed. Parameters of the biomass extraction model have been modified to express a constant biomass concentration in the foam at 3 g L -1 . This new experiment confirms the correlation between the specific biomass growth rate and productivity of mycosubtilin obtained in previous works. Consequently, our results provide the basis for studies to maximize productivity of biosurfactants.

 max maximum specific growth rate (h -1 ) K s saturation constant (g L -1 ) Y X/S actual growth yield on substrate (g g -1 ) m s maintenance coefficient (g g -1 h -1 )  proportional coefficient of the linear model of biomass concentration in the foam  constant coefficient of the linear model of biomass concentration in the foam (g L -1 ) Volume in the collector calculated with an exponential feeding profile, Volume in the collector calculated with the proposed feeding profile. Table 1: Parameter values of the bioprocess model. Table 2: Initial values of the variables X, S and V for the three phases (I, II and III). . Table 3. Mycosubtilin production and productivity during the experiment.

  general model can thus deal with the three following scenarios: X out is proportional to X ( ≤ 1 and  = 0), corresponding to a partial recycling process, X out is equal to X ( = 1 and  =0), the bioprocess is considered continuous, without recycling,  <1 and  0, corresponding to the foaming process and differs from existing bioprocess models.

Figure 1 :Figure 2 :

 12 Figure 1: Apparatus layout

Figure 3 :

 3 Figure 3: Biomass and substrate quantities in the bioreactor and in the collector vessel: (▲) Quantity of biomass in the bioreactor, (■) Quantity of biomass in the collector vessel, Simulated biomass quantity in the bioreactor, Polynomial approximation of the biomass quantity in the collector vessel, Simulated quantity of substrate in the bioreactor.

Figure 4 :

 4 Figure 4: Estimation of the specific biomass growth rate, estimated value of µ Interval of confidence of the estimated value of µ,Expected evolution with time of µ with an exponential feeding, Simulated value of µ.

Figure 5 :

 5 Figure 5: Biomass concentration in the foam as a function of biomass concentration measured in the bioreactor, (□) X out in the foam data from the experiment (o) X out in the foam from additional data, () estimated values of X out ., () estimated values of X out from additional data.

Process Biochemistry Volume 45, Issue 11, November 2010, Pages 1800-1807

Acknowledgements

This work was supported by the Agence Nationale de la Recherche (ANR) and the European Funds for the Regional Development. The authors would like to thank Dr. William Everett for kindly reading the manuscript and Laurent Bonneau from Polytech-Lille for his technical assistance.

List of symbols

V volume of culture medium in the bioreactor (L) V Col volume of culture medium in the collector (L) V 0 volume of culture medium at the start of the feeding (L)

biomass concentration in the bioreactor (g L -1 ) X out biomass concentration in the foam (g L -1 ) X Col biomass concentration in the collector (g L -1 ) X 0 biomass concentration in the bioreactor at the feed beginning (g L -1 ) S substrate concentration in the bioreactor (g L -1 ) S in substrate concentration in the feed (g L -1 ) S 0 substrate concentrations in the bioreactor at the feed beginning (g L -1 )  specific growth rate (h -1 )