Experimental Dispersion Relation of Surface Waves Along a Torus of Fluid Filip Novkoski, 1, * Eric Falcon, 1, † and Chi-Tuong Pham We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatio-temporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous and sloshing modes. Standing azimuthal waves are also studied leading to polygon-like patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.

Introduction.-Vortex rings or toroidal droplets are ubiquitous in nature [1][2][3][4][5][6][7][8][9], but they are unstable. On flat surfaces, they break up into droplets or close their central hole [START_REF] Worthington | Proc. R. Soc. Lond[END_REF][START_REF] Pairam | [END_REF][12][13][14][15]. Generating stable tori of fluid thus remains a formidable challenge. It can nevertheless be achieved in toroidal plasma [16,[START_REF] Gharib | Proc. Natl. Acad. Sci. USA[END_REF], in biophysics [START_REF] Šimkus | [END_REF], or in fluid mechanics by using an unwetting liquid at the periphery of a cylinder [19], by injecting a liquid within a rotating fluid [START_REF] Pairam | [END_REF][START_REF] Pairam | Proc. Natl. Acad. Sci[END_REF], or by levitating a liquid over its vapor film (Leidenfrost effect) on particular substrates [START_REF] Perrard | [END_REF]22].

Due to its periodic boundary condition, a stable torus of fluid is a good experimental system to study the wave propagation in curved and periodic media. For hydrodynamic waves, the curved conditions have been achieved experimentally only for spherical-liquid shells [23][24][25], whereas periodic conditions in planar geometry can be reached (e.g. in an annular water tank [26,27]), as well as in curved geometry but without periodicity (e.g. along the border of a liquid cylinder [28,29]). In this last case, the wave dispersion relation found experimentally [28,29] and theoretically [30][31][32] differs from that in planar geometry [START_REF] Lamb | Hydrodynamics[END_REF]. For a fluid torus, the dispersion relation of waves along the inner and outer torus borders as well as their interaction, are still unreported to our knowledge, the only existing experiment [19] and the theoretical predictions [19,22] being performed with strong torus constraints.

Here, we report an original experimental technique to create a stable torus of liquid moving almost completely unconstrained. By means of a simultaneous space and time resolved measurement, we highlight the dispersion relation of azimuthal waves propagating along the torus borders as well as their interaction. Several branches occur with a complex structure reminiscent of forbidden gaps in periodic media in condensedmatter physics [START_REF] Griffiths | [END_REF]35]. Standing waves are also studied showing polygon-like patterns. Our system with these particular boundary conditions (periodic, curved and one-dimensional) including different propagation modes could evidence nonlinear waves, solitons or wave turbu- lence [START_REF] Falcon | Discrete Contin[END_REF]37] in this geometry.

Experimental setup.-A circular duralumin substrate (19 cm in diameter) is machined to have an axisymmetric wedge-shaped groove, with angle α = 4.5 • to the horizontal, running along its perimeter as shown in Fig. 1. The substrate is coated with a superhydrophobic spray providing a liquid/substrate contact angle of 160 -170 • [START_REF]Multi-surface liquid repelling treatment, NeverWet ™ from Rust-Oleum ®[END_REF][START_REF] Gupta | [END_REF]. The gentle substrate inclination of angle α constrains the liquid (distilled water) to move along the sloped surface, thus preventing the torus from closing its hole, and experiencing a reduced gravitational acceleration g eff = g sin α with g = 9.81 m • s -2 .

After being deposited on the substrate, we excite the the borders of the torus using a teflon cylinder connected to a shaker oscillating vertically as shown in Fig. 1. For a given fluid volume, a frequency-sweep forcing is applied, i.e., its frequency f is varied linearly in time over 2 min from 0 to 20 Hz. The typical amplitude of vibrations is 3 mm. A camera located above the torus records its interface displacements. Using a border detection algorithm written using OpenCV [START_REF] Novkoski | Circular border detection in Python[END_REF], we extract from the video the horizontal displacements, η(θ, t), of the two borders with respect to their stationary positions. The procedure is repeated by adding water to change the width, W , of the torus in the range 1.2-3.2 cm, the center of the section remaining at the groove radius R c = 7 cm. These values correspond to torus aspect ratios ξ = (2R c /W ) from 4.3 to 11.7. For each volume, we perform a 2D fast Fourier transform on the inner-and outer-border signals, moving from real space η(θ, t) to Fourier space η(k θ , ω). This leads to the dispersion relation, ω(k θ ), of the azimuthal waves, ω being their angular frequency and k θ their azimuthal wave number, that takes integer values n.

Dispersion relation.-As the torus is excited, linear waves propagate along its borders (see video in Supp.

Mat. [41]

). We observe that the injected energy is redistributed in different regions of the Fourier space, localized around several branches (see Fig. 2a for the inner, and Fig. 2b for the outer border). The dimensionless wave number k θ is used to compare the wave spectra along both borders. It takes discrete values because the system is periodic. We will set R i = R c -W/2 and R o = R c + W/2 (see Fig. 1).

The different branches observed in Fig. 2 correspond to different modes of wave propagation. The branch passing through zero, denoted V and visible in both spectra, is the dispersive branch stemming from the usual gravity-capillary waves (see below). The first branch starting above zero, marked S, has a cutoff frequency ω S 0 ≡ ω S (k θ = 0) which depends on the torus volume (see below). Other branches (denoted Sl i with i = 1, 2, 3 or 4) correspond to sloshing modes clearly different from the V and S branches. In Fig. 3, we superimpose the two spectra of Fig. 2 to better understand their structures. All these modes are described below in detail.

V mode.-The V branch is well described by a dispersion relation of gravity-capillary waves (see solid line in Fig. 3) of the form

ω 2 V = g eff k θ R o + σ eff ρ k 3 θ R 3 o tanh k θ W R o 2R 2 c ( 1
)
with ρ = 1000 kg/m 3 the fluid density, g eff = g sin α 0.77 m s -2 , and σ eff = 60 mN m -1 , an effective surface tension inferred by fitting the data (regardless of W ∈ [1.6, 3.2] cm); g eff and σ eff are notably linked to the geometry of the substrate [32]. For k θ → 0, Eq. ( 1) reads ω V = Ω ϕ k θ . The angular phase velocity of gravity waves Ω ϕ is inferred by fitting the V branch in Figs. 2 or 3 near k θ = 0. By changing the torus volume, we infer

Ω ϕ ≡ [ω V (k θ )/k θ ]| k θ =0
as a function of the width W , on the inner and outer borders separately, as shown in the top inset of Fig. 4. Ω ϕ is experimentally found to match for both borders at a given volume, and to scale as W 1/2 . It is well described (see solid line in top inset of Fig. 4) by

Ω ϕ = g eff W/2 R c (2)
with no fitting parameter, in agreement with Eq. ( 1) when k θ → 0. S mode.-The S branch has a very different behavior, intersecting the upper sloshing branches (see Fig. 3). The S branch is found to display a pure capillary regime (i.e., ω 2 ∼ k 3 θ ) for k θ 0, and to be well described (see dashed line in Fig. 3) by

ω 2 S = ω S 0 2 + σ eff ρ k θ R i 3 . (3)
with no fitting parameter, ω S 0 being the cutoff frequency. The S mode being more significant for the inner border (see Fig. 2), it is thus consistent that Eq. (3) involves the inner radius R i as a length scale. Moreover, ω S 0 is experimentally found to be dependent on the torus width as W -1/2 (see main Fig. 4 and bottom inset). Since this cutoff corresponds to the motion of the center of mass of the torus section, we model it as (see Supp. Mat. [41])

ω S 0 = π 2 g sin(2α) 2W (4)
Eq. ( 4) is found in good agreement with the data with no fitting parameter (see dashed line in main Fig. 4 and bottom inset). Sloshing modes.-The Sl i branches in Fig. 3 are ascribed to sloshing modes driven by gravity. These branches are well described (see dot-dashed lines in Fig. 3) by

ω 2 Sli = ω (i) 0 2 + c 2 k θ R c 2 , (5)
with c = √ g eff R c , and ω (i) 0

the cutoff frequencies at k θ = 0. These nondispersive sloshing modes (ω 2 ∼ k 2 θ ) for k θ 0 differ from theoretical results on sloshing in 4) with no fitting parameter. Bottom inset: Log-log plot of the cutoff frequencies versus W for sinuous and sloshing branches: ω S 0 ∝ W -1/2 for the S branch, and ω (i) 0 ∝ W -1 for all Sli sloshing branches. Top inset: Angular phase velocity Ω of the outer (blue) and inner (orange) borders for different W (inferred from the V branch). The solid line corresponds to Eq. ( 2). Insets: Sinuous and varicose mode schemes for a slim torus.

toroidal containers [START_REF] Ibrahim | Liquid Sloshing Dynamics: Theory and Applications[END_REF] or in non-rectangular ones [START_REF] Groves | [END_REF]. Moreover, the cutoffs are found to scale as ω (i) 0 ∼ W -1 (see bottom inset of Fig. 4), and are well described (see solid lines) by ω

(i) 0 = M (i) √ g eff R c /W with M (i) a func- tion computed numerically (see Supp. Mat. [41]).
Thin torus.-For slim tori, the inner and outer border motions interact. The S and V branches are then visible both on the inner and outer border spectra (see Supp. Mat. [41]). The V branch corresponds to a varicose mode, i.e., waves propagating along both borders in anti-phase motion (see inset of Fig. 4). The S branch is related to a sinuous mode (also called zigzag mode [44,45]) for which waves on both borders are inphase (see inset of Fig. 4). Indeed, by summing (resp. subtracting) signals of the outer and inner borders and taking the spectrum of the resulting signal, the sinuous (resp. varicose) branch in the total spectrum is removed, as expected for in-phase (resp. anti-phase) motions. For wide tori, interaction between the two borders vanishes for almost all k θ , and these modes are no longer phase related. The wide torus criterion is W > 2R 2 c /(k θ R o ), from Eq. (1).

Polygons.-We now force the torus at a fixed frequency, f , to generate standing azimuthal waves along both borders of the torus. The torus boundary condition being periodic, the wave dispersion relation is quantized (k θ is an integer). This quantization is studied more closely here, as well as the coupling between the outer and inner torus borders.

We consider two different torus volumes, a slim one (W = 1.5 cm), and a wider one (W = 3 cm). For each f , a short video of the torus is taken (see Supp. Mat.

[41]). Once the standing wave regime is established, a polygonal pattern is observed (see inset of Fig. 5a). We then measure the number n of sides of the pattern. By varying f ∈ [0.8, 3] Hz, we plot n as a function of f . In the slim case, n is found to be the same for both the inner and outer borders within this frequency range (see inset of Fig. 5b). The maximal number of sides that is possible to observe can be predicted. It occurs when the wavelength is of the order of the effective capillary length, i.e., λ = c = σ eff /(ρg eff ) ≈ 8 mm. For R o = 8.5 cm, the maximal number is given by n m = 2πR o / c = 67. Note that such azimuthal patterns were previously observed up to n = 25, but only along the outer border of a torus [19].

The measurements are repeated for a wider torus where the interaction between both borders is weak. Figure 5b shows the superimposition of the outer and inner border wave spectra together with the number of sides n for a given forcing frequency f . For both borders, they are the same and follow the V branch, up to a given frequency (f ≤ 1.2 Hz). Once f is large enough, n becomes different on the two borders: the number n for the outer border ( -symbol) keeps on following the Vbranch, while for the inner border (+-symbol), n switches to the upper S -branch. This effect is due to a decoupling between the two interfaces. For the slim torus, energy on the inner and outer borders is distributed on both S and V branches (see Supp. Mat. [41]), and n matches only the V branch as a varicose mode (see inset of Fig. 5b). For the wide torus, the inner border localizes its energy much more on the S branch (see Figs. 2a) whereas the energy on the outer border is mainly distributed on the V branch (see Figs. 2b). Except for large scales, i.e., k θ ≤ 2R 2 c /(W R i ) or k θ ≤ 6 for W = 3 cm, the two borders are decoupled (see main Fig. 5b).

Conclusion.-We developed an original technique to create a stable torus of fluid moving almost completely unconstrained, and offering a system with atypical boundary conditions, i.e., periodic, curved and onedimensional. We reported direct measurements of the dispersion relation of azimuthal waves propagating along the boundaries of this stable torus of fluid. The dispersion relation is quantized since the periodicity induces a wave number selection for a given forcing frequency band. The wave energy distribution in Fourier space is complex and exhibits several modes modeled as varicose, sinuous or sloshing ones. In the future, this new system could highlight nonlinear phenomena such as nonlinear waves and solitons in curved geometry. It could also address the role of finite-system size effects in wave turbulence [36, 37,46], as well as the coupling of waves propagating on two curved interfaces [45,47].

FIG. 1 .

 1 FIG.1. Top: Cut-out of the experimental setup showing the water torus on the groove. Bottom: Profile of the setup including the teflon plug connected to a shaker and camera centered above the circular plate.

FIG. 2 .

 2 FIG. 2. Dispersion relation η(k θ , ω) of azimuthal waves along the (a) inner and (b) outer borders of a torus of width W = 3.2 cm, obtained using sweep-sine forcing. The energy is distributed along distinct branches corresponding to different propagation modes. The S branch along the inner border (a) is more pronounced than the V branch, in contrast with the outer border (b). The sloshing Sl i branches are the same for both borders.

FIG. 3 .

 3 FIG.3. Superimposition of the two spectra of Fig.2, as well as the predicted branches. V branch corresponds to Eq. (1) (solid line), S branch to Eqs. (3) and (4) (dashed line), and (Sli) branches to Eq. (5) (dot-dashed lines). W = 3.2 cm.

FIG. 4 .

 4 FIG. 4. Cutoff frequency ω Sof the sinuous S branch versus the torus width W . Solid line displays Eq. (4) with no fitting parameter. Bottom inset: Log-log plot of the cutoff frequencies versus W for sinuous and sloshing branches: ω S 0 ∝ W -1/2 for the S branch, and ω

FIG. 5 .

 5 FIG. 5. (a) Polygonal patterns generated as standing waves along the inner border n = 8 (octagon), and the outer border n = 12 (dodecagon). Forcing frequency f = 2.5 Hz. W = 3 cm. Torus is colored in magenta. (b) Number of sides n of the polygonal pattern on the outer ( ) and inner (+) border of a wide torus (W = 3 cm) for different f , together with the superimposed dispersion relations. For f ≥ 1.2 Hz, the two borders decouple and n differs on the two borders: the outer n keeps following the V branch, while the inner n switches to the S branch. Inset: Same for a slim torus (W = 1.5 cm): n on both borders matches for all f .

  2, ‡ 1 Université de Paris, MSC, UMR 7057 CNRS, F-75013 Paris, France 2 Université Paris-Saclay, LISN, UMR 9015 CNRS, F-91405 Orsay, France (Dated: August 16, 2021)

We thank A. Di Palma and Y. Le Goas for their technical help on the experimental setup. Part of this work was supported by the French National Research Agency (ANR DYSTURB project No. ANR-17-CE30-0004), and by a grant from the Simons Foundation MPS N o 651463.


D P P Higginson

L Vassura

M M M Gugiu

P Antici

M Borghesi

S Brauckmann

C Diouf

A Green

S Kar

L Palumbo

H Petrascu

S Sofia

M Stardubtsev

O Willi

F Negoita

J Fuchs

Temporal Narrowing of Neutrons Produced by High-Intensity Short-Pulse Lasers

HAL is

Due to their direct interaction with nuclei, neutrons penetrate deep into materials and can probe ion population properties directly. This leads to unique insights into many aspects of matter beyond the capability of charged particles or x-rays. However, as neutron probing techniques advance, a challenge is to create a source that is short in time for the observation of ultra-fast (ps to ns) phenomena. For neutron energies in the MeV-range, neutron damage can be understood at the atomic scale: creating collision cascades, point defects, dislocation or melts that could be observed in real time [1]. This is a highly topical subject for many technological applications: radiation hardness testing of semiconductors in aerospace, materials for fusion/fission reactors [2][3][4][5], particle accelerator vessels or containers for storing radioactive nuclear wastes. For slightly lower (keV) energies, understanding of the dynamic behavior of warm dense matter (WDM) [START_REF] Drake | High-Energy-Density Physics[END_REF] is a key application area for short neutron bursts [START_REF] Yuan | [END_REF]8]. As neutrons are uniquely sensitive to ion properties, such a source would allow (e.g. via resonance spectroscopy [START_REF] Yuan | [END_REF]) measurement of ion distribution temperatures when synchronized with a WDM-driving laser or free-electron laser (FEL) source, which have short (fs-ns) temporal duration.

Sub-ps duration lasers are superb candidates for the production of short-pulse neutron probes. In fact, such high-intensity lasers have previously produced monoenergetic neutron bunches of 0.2 ns duration [9] via irradiation of deuterium clusters (D-D reactions). However, this method is limited to mono-energetic neutrons and has a low neutron yield (∼ 10 5 n/J) compared to methods based on laser-accelerated protons impinging on solid material slabs, a technique shown to create up to and above 10 8 n/sr/shot (∼ 10 7 n/J) [5,8,[10][11][12][13]. On the other hand, a major challenge when using solid targets is that the interaction creates large numbers of highenergy charged particles and x-rays, which could damage a test sample and create a high-noise environment for sensitive diagnostics. Also, while picosecond-duration at the source, the laser-accelerated protons are broadband in energy and divergent in angle, thus both their temporal cohesion and flux decrease rapidly over large distances. While techniques exist to focus and select ions via pulsed or passive magnetic fields [14][15][16][17], these devices require large distances to function which leads to increased time-of-flight broadening and takes up valuable space for shielding of unwanted particles.

In this Letter, we show, by modifying the proton spectrum, that a high-flux, short-duration and narrow band laser-generated neutron source can be produced far from the secondary radiation generated in the laser-interaction using laser-techniques alone. This is achieved using a laser-driven micro-lens [18][19][20], to both transport the protons and to narrow their energy spread and temporal duration, which results in a neutron source that is similarly improved. This method is shown to produce a neutron bunch with a ∼3 ns full-width-at-half-maximum (FWHM) duration at 0.56 m from the primary target, thus allowing the neutrons to be produced and used in a region free of high-energy secondary particles.

This study was preformed in three stages, as illustrated in Figure 1. Stage I (S1) accelerated protons from the primary 50 µm solid PET plastic target (coated with 14 nm Al to improve laser absorption) using the main beam of the ELFIE laser [21] (10 J, 350 fs pulse length, 10 µm focal spot, 1057 nm wavelength, 20 minute shot rate) located at the Laboratoire pour l'Utilisation des Lasers Intenses (LULI) in France. The laser accelerates electrons which generate a strong electric field (MV potential) and accelerate protons via the Target Normal Sheath Acceleration (TNSA) mechanism [22][23][24][25]. The protons generally have broadband energy spectrum and divergence half-angles of 5 -30 • [26,27].

In Stage II (S2), the protons were chromatically focused using a plasma-based micro-lens [18,19]. The hollow Al cylinder (φ = 0.86 mm, thickness = 0.10 mm, length = 3.0 mm) used as a micro-lens was placed 1.0 mm from the proton source and irradiated with the secondary ELFIE laser beam (similar parameters as the main beam) at a time delay of 86 ps following the primary pulse. The secondary laser pulse creates a strong transient electric field (as in TNSA) normal to the cylinder surface, which forces the protons towards the cylinder axis. Lower energy protons spend more time in the field, thus they are focused more strongly and subsequently have a higherdivergence, 8 • , compared to higher energy protons which are focused less and obtain a lower divergence, 1 • . The timing of the secondary laser is important, as this determines the maximum energy of protons that will be focused by the cylinder, since protons arriving prior to this time will feel no effects of the field.

In Stage III (S3) the chromatic nature of the focus is used to reduce the fluence of lower-energy protons arriving at a distances of 0.56 m from the proton source. Since the lower energy protons are more divergent (as the associated focal length of the micro-lens is shorter for them [18,19]) they become more diluted than the higher energy protons (see Fig. 1c), which increases the ratio of the high-to-low energy protons. At this point, in the center of the beam the energy bandwidth and, thus, the temporal duration of the proton beam, is narrowed compared to the intrinsic beam, and can be used to create a short-pulse neutron beam through nuclear reactions.

In our discussion of the experimental results, we begin with the diagnosis of the proton beam. Both the proton beam widths and spectra were measured using layers of Gafchromic R Radiochromic Film (RCF) [26]. In the S1 and S2 cases, both HD and MD films were used to increase the dynamic range of the measurement, while in the S3 case only the MD film (more sensitive, but lower energy-resolving) was used due to the lower proton fluence at this distance.

Figure 2a shows the protons in the unfocused (S1) case using RCF placed at 30 mm. These protons have a divergence angle that decreases with increasing proton energy, as visible in the diameters (35 mm at 1.3 MeV and 6 mm at 8.9 MeV). The next set of images (Fig. 2b) show the focused protons 30 mm from the target (S2), here the beam diameter is significantly reduced and the diameter decreases as function of energy (8 mm at 1.3 MeV and 2 mm at 7.7 MeV) due to the focusing effect discussed previously. However, protons with energies above 7.7 MeV transit the cylinder before the electric field has developed, are not focused and thus their shape represents the projection of the cylinder aperture.

Finally, in Figure 2c, the focused beam is shown at 0.56 m (S3) from the target. The beam is not completely centered on the film (by an offset of 1.8 • ), and thus we capture around a quarter of the proton beam. Also, we note that the beam appears more annular at this larger distance. The diameter is still energy dependent (67 mm at 3.8 MeV and 34 mm at 6.3 MeV), and corresponds well to the expected diameter using simple trigonometric ratios of the focal distances measured in the S2 setup (81 mm at 3.7 MeV and 50 mm at 6.1 MeV).

Figure 3a shows the energy spectra of the proton flu- ence inferred from the RCF stacks using the unfolding method described in Ref. [START_REF] Higginson | High Energy Density Physics[END_REF] Section 3.1. The intrinsic spectrum (S1) decreases monotonically and shows a decrease in proton number by a factor of 100 between 1.3 and 6 MeV. When the protons are focused (S2, S3), the spectrum changes considerably. Instead of decreasing monotonically, the spectrum has a second peak around 6 MeV, where the proton number is 10 times higher than the intrinsic spectrum at this energy, and is relatively flat from 4 to 8 MeV. At the high energies protons are less divergent than the lower energy ones and thus produce a higher fluence at far distances. Since we will use a small LiF neutron converter at this location, only protons in the central portion of the beam will contribute to neutron production (illustrated in Fig. 1c). This takes advantage of this increase in high-to-low energy protons to narrow the energy and temporal duration of the neutron bunch.

Figure 3b shows exponential fits to the proton spectra that are used later as inputs for neutron generation simulations. These fits show that the focusing technique has an efficiency of around 15%, which is the efficiency that we expect from the geometry of the Al cylinder and the intrinsic proton divergence, and could thus be increased by using a wider diameter cylinder.

Neutrons were produced by placing a LiF disk (φ = 25 mm, thickness = 2 mm) in the path of the proton beam at 2 mm and 0.56 m away in the S1 and S3 cases, respectively. The protons produce neutrons via nuclear reactions in the LiF, mainly 7 Li(p,n). The neutron yield at 0 • was diagnosed using CR-39, a plastic damaged indirectly by neutrons (∼0.5 to 6.0 MeV) through scattered ions [START_REF] Frenje | [END_REF], and bubble detectors, a supercritical solution that creates bubbles when neutrons (1.0 to 2.5 MeV) scatter in the solution [START_REF]Bubble technology industries inc[END_REF][START_REF] Green | Annual Report, Central Laser Facility[END_REF]. The CR-39 detectors and bubble detectors were placed 20 and 40 mm from the LiF disk, respectively. To improve statistics, they were integrated over 3 to 4 shots. The CR-39 was shielded from direct protons (<21 MeV) with 1 mm of Pb. The CR-39 and bubble detectors recorded yields of 7 ± 4 and 8 ± 4 ×10 5 n/MeV/sr/shot, respectively, in the S1 case. We note that these yields are lower than those presently achievable on some laser systems due to the higher laser intensity and contrast of such systems [5,8,[10][11][12][13].

To measure the spectrum and temporal duration of the neutron bunch, a neutron time-of-flight (ntof) detector was employed. The ntof used a 40x40x120 mm BC400 scintillator (placed so neutrons traverse the 40 mm length) coupled to a Photonis XP2972 photomultiplier and recorded with a 1 GHz oscilloscope. This was placed at 2.2 m and 30 • from the S1 LiF position, which corresponds to 2.0 m and 33 • from the S3 LiF position. The ntof was shielded with 200 mm of Pb to reduce the x-ray signal produced in the scintillator.

Figure 4 shows a comparison between the ntof signals without (S1) and with (S3) spectral modification of the incident protons. The light-colored lines show experimental results when no neutrons are expected (i.e. RCF was used instead of LiF). The earliest signal, at ∼10 ns (peak not visible due to the scale), is due to x-rays induced by electron bremsstrahlung in the primary target, decays based on the response time of the scintillator and is used to synchronize to the time-zero of the laser. We show this non-neutron case to highlight the clean exponential decay of the scintillator signal (i.e. no reflections or spurious signals).

The dark lines in Fig. 4 show the experimental signal recorded when using LiF for neutron production. The upper axis (Neutron Energy) is derived from the location of the ntof with respect to the LiF (taking into account the flight-time of the protons in the S3 case). We see that the first neutrons arrive around 100 ns, corresponding to an energy of ∼3 MeV. In the S1 case, the neutron signal extends many hundreds of nanoseconds in time and with energies down to 100 keV. In contrast, the S3 neutron signal is much shorter in duration and has a significant reduction of lower energy neutrons due to the modified incident proton spectrum.

The narrow peak in the signal (at ∼100 ns, with a peak of 2.0 V, thus out of the graph) in S3 is likely due to single neutron hitting the scintillator. This is because, at this energy (3 MeV) the scattering probability is only 50% in our scintillator and the neutron flux on the detector is low, only ∼0.1 n/ns. This explanation is corroborated by the observed similarity between this narrow pulse and the detector's temporal response (both 9 ns FWHM). We note that this statistically limited feature is less important as energy decreases since the average scattering probability is already 90% at 1 MeV. In order to better understand these signals, the Monte-Carlo particle transport code MCNP6 [START_REF] Pelowitz | MCNP6 User's Manual, Ver. 1[END_REF] was run. This code includes particle scattering, energy loss and nuclear interactions. The proton-induced nuclear reactions included were 7 Li(p,n) 7 Be, 6 Li(p,n) 6 Be and 19 F(p,n) 19 Ne, which have cross-sections resolved in angle. The simulation did not include reactions producing excited states in the final nuclei or other reaction channels yielding neutrons such as break-up, however these have crosssections below 10% of the main reactions. When benchmarking the code, we noticed that the standard 7 Li(p,n) cross-section (ENDF/B-VII.0 [START_REF] Chadwick | [END_REF]) used by the code differed considerably from experimental data [34], as does TENDL-2013 [35] below 15 MeV. Thus a recently reworked cross-section was used instead [36].

The geometry of the simulation reproduced the experimental setup with protons injected from the location of the primary target and directed, using straight trajectories, towards a LiF disk at the S1 or S3 position. The protons were given the measured exponential spectra described in Fig. 3b . For the S1 case, our simulations recorded a neutron yield in the forward direction of 2.8 and 3.9 ×10 5 n/MeV/sr/shot in the energy range of the CR-39 and bubble detectors, respectively, which is consistent with the experimental measurements.

To reproduce the neutron time-of-flight data, detectors were placed in the simulations at the same location and dimensions as the scintillators used in the experiment. The simulations included the neutron scattering induced from Pb-shielding along the line-of-sight from source to detector, as well as scattering sources near to the detector (e.g. the steel chamber, concrete walls, concrete floor, other Pb walls). MCNP6 collected the number of neutrons passing through the detector and binned them in energy and time. The neutron detector efficiency was determined in the following manner: First, the spectrum of protons scattered via neutrons (at these energies scattering of C and nuclear processes can be neglected) was determined using other simulations with MCNP6. Next, the light response (in units of electron-equivalent response) of the protons was determined by applying the light response function from Birks' formula [37], (kB value from Ref. [37] for NE-102). Finally, the electron equivalent response was converted to a signal using a calibration performed with a 60 Co gamma-source to complete the absolute calibration. Additionally, the 60 Co source was used to fit the detector's temporal response with two exponential decays (1/e = 8, 60 ns), which was then convolved with the calibrated neutron signal to give a simulated signal, as well as an x-ray falloff.

The simulated signals of the simulations are shown as dashed lines in Fig. 4. These are in agreement with the experimental shape of the data and, especially, the absolute number, which has not been arbitrarily normalized. This agreement highlights the importance of including nearby structures, as we found these scattering structures (i.e. those not along the direct line-of-sight) contributed from 40% to 80% of the neutrons detected at 3 MeV, in the S1 and S3 cases, respectively.

To determine the loss of neutrons through the selection process, we look at the yield of 3.0 MeV neutrons on the scintillator, which are 4.0 and 1.2 ×10 4 n/MeV/sr/shot for the S1 and the S3 cases, respectively. This shows that the neutron yield was only reduced to 30% of the original yield, despite the large, 0.56 m, distance traveled by the protons. As mentioned previously, this reduction is due to the geometry of the microlens. Using the simulations, we investigate the temporal narrowing achieved by placing a virtual detector consisting of a neutron counting sphere of 2.5 mm radius at 0.5 m from the proton emission (i.e. 5 mm from the LiF in the S3 case) to record all of the neutrons that pass through it. This measurement shows a FWHM duration of 30 ns in the S1 case and 3.4 ns in the S3 case, thus a factor of around 10 in temporal narrowing. This reduction is due to the energy selection of the protons hitting the LiF. Since the low-energy protons are dramatically reduced (see Fig. 3) the time-of-flight broadening is reduced as well. This duration compares well with existing accelerator driven devices [38, and references therein]. Additionally, we note that moving the LiF slab to 100 mm would lower the pulse to sub-ns duration, while at the same time staying a long distance away from the laser-interaction to allow for proper shielding.

In summary, we have shown that a narrowing of the pulse duration of protons and neutrons generated by laser-acceleration is achievable, showing that laseraccelerated neutrons can be useful in researching and probing material properties at ultra-fast timescales. The ability of the micro-lens to focus ions is expected to scale with the electron temperature (thus laser intensity) [39] and has previously been shown via simulations to focus proton beams up to 270 MeV [START_REF] Humières | AIP Conf. Proc[END_REF], which will be important when using higher laser energies (up to kJ, instead of 10 J) and emerging ion-acceleration mechanisms to give rise to much higher neutron yields [13]. Additionally, the upcoming increase in repetition rate of these lasers (now a few shots/hour) will soon increase with the development of fiber [START_REF] Mourou | [END_REF] or diode-pumped lasers [42,43]. The smooth electric field profiles [19] and simple structure (potentially a single target [44]) of the micro-lens make this technique compatible with quick, repeatable lasers making laserbased short-pulse neutron sources even more attractive.

FIG. 1 .

 1 FIG. 1. Diagrams of the different setups used in this study: (a) S1: the broadband, unfocused proton beam, (b) S2: proton focusing using the micro-lens, irradiated by the secondary beam, and (c) S3: focused protons at longer distances, where the higher divergence of the lower-energy protons decreases their contribution to the measured spectrum.

FIG. 3 .

 3 FIG.3. Measured single-shot energy-spectra of the proton fluence from S1 (circles), S2 (squares) and S3 (diamonds). Error bars for S1 represent variation across multiple shots, whereas S2 and S3 are single shots with 10% film batch variability uncertainty. The top plot shows the average fluence which is determined by dividing the total signal on the film by the solid angle subtended by the signal. The bottom plot shows the total number of protons hitting the film stack, where lines show exponential fits to the spectra, dN /dE = (N/T )e -E/T . Where N is 1.9 × 10 11 , 2.5 × 10 10 and 5.5 × 10 9 , and T is 1.72, 1.96 and 5.32 MeV for the S1, S2 and S3 cases, respectively.

1 FIG. 4 .

 14 FIG.4. Plot of the ntof traces from the experimental data without neutron production (light lines), with neutron production (dark lines) and the simulated neutron signal (dashed lines). Time zero corresponds to the arrival of the laser. The plots (a) and (b) refer to setups S1 and S3, respectively.

We are grateful to Dr. K. Parsons and Dr. G. Hale for evaluating a newer 7 Li(p,n) 7 Be cross-section that agrees better with previous experimental results. We acknowledge the support of the LULI technical teams. This work was supported by Grant E1127 from Région Îlede-France. The research leading to these results has received funding from Laserlab-Europe (Grant Agreement No. 284464, Ec's seventh framework program) and Grant No. 001528. This work was was partly done within the LABEX Plas@Par project and supported by Grant No. 11-IDEX-0004-02 from Agence Nationale de la Recherche. L. V. was funded by a DGA-MRIS scholarship. H.P., M.M.G. and F.N acknowledge support of Romanian National Authority for Scientific Research, CNCS UEFISCDI, under the project number PN-II-ID-JRP-2011-1. This work also partly supported by the DFG GRK 1203 program and by EPSRC grants EP/K022415/1 & EP/J002550/1. M.B. acknowledges co-financing by the European Social Fund and the state budget of the Czech Republic (project numbers CZ.1.05/1.1.00/483/02.0061 & CZ.1.07/2.3.00/20.0279). This work was supported in part by the Ministry of Education and Science of the Russian Federation under Contract No. 14.Z50.31.0007.


Sepaldeep Singh Dhaliwal

Sarah Wilby

Martijn De Vries

Brou Kévin

Sina Boni

Stefan Escaida Firouzy

Abdelkader Navarro

Vincent Belarouci

Othman Coelen

David Lakhal

Pasquier

Firouzy

Cobra

K Boni

Escaida Navarro

A Belarouci

V Coelen

O Lakhal

D Pasquier

A L Palmer

Q Polak

A Labib

Sanz Lopez

C Duriez

& Merzouki

CoBra robot for localized cancer treatment and diagnosis under real-time MRI guidance

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

We present the CoBra (Cooperative Brachytherapy) project 2018 -2022. The CoBra purposes an integrated concept to perform localized cancer treatment and biopsy of soft-tissues under real-time (RT) MRI guidance [START_REF] Dhaliwal | Cooperative Brachytherapy for Prostate Cancer Under MRI Guidance[END_REF]. The robot executes needle insertion within the MRI-scanner, performing adaptive prostate brachytherapy under RT-imaging. An active steerable-needle under closed-loop control is used to achieve precise positioning of the seeds with the increased reach of the needle to pubic arch and organs-at-risk occluded areas. Dose calculation under RT-MRI is achieved by the generation of synthetic-CT datasets based on a Machine-learning algorithm. Needle trajectory planning based on a steerable needle with minimal entry points is optimized by an algorithm depending upon the target, seed plan, and prostate contours attained from MRI. A bio-inspired active phantom (BIP) is designed for concept validation. The CoBra project is funded by the EU Interreg 2 Seas programme, led by the University of Lille partnering with multiple institutions and industrial observers.

Conclusion

This poster presents the recent progress attained from the CoBra project, as it reaches the phantom testing stage.

• BIP developed to mimic the actual condition of prostate intervention, with sensory feedback dynamic in nature, and resulting rotation and twist motion.

•

The CoBra concept contributes towards adaptive treatment and diagnosis, which consists of adapting the control of the robot for precise deposition of seed with a minimal perineum entry points and reducing the tissue damage.

•

The steerable needle concept helps further to reach the targets which are inaccessible to conventional prostate brachytherapy treatment with straight needles in a grid.

•

The CoBra concept, a multi-system model, integrates the robotic sub-systems using MRI-guidance in closedloop feedback to implement an adaptive MR-robot control, for the treatment of localized cancers.

Results

The CoBra robot was tested under a 3 T Philips MRI scanner at Lille Hospital.

CoBra robot for localized cancer treatment and diagnosis under real-time MRI guidance

Materials and Methods

The MR-conditional robot has been developed to perform in-bore prostate adaptive-BT and biopsy (BX) with the aid of a steerable needle targeting the lesion sites under RT-MRI. The steerable needle is able to reach pubic arch obstructed zones and a new target position when pre-defined target shifts during needle insertion, prostate motion, tissue deformation, or inflammation. Targets are planned based upon an initial dosimetry plan under RT-MRI, then tracked and updated in parallel using rapid creation of accurate synthetic-CT (sCT) datasets from the live MR images and are used to update the needle trajectory planning software NPS to deliver the seed with more accuracy using active steerable needle. Thus, the dosimetry plan integrated to NPS and robot helps to deliver dose to the new target position.

In order to attain an RT dosimetry plan using sCT datasets, the team use an augmented cycle Generative Adversarial Network (AugCGAN) algorithm [START_REF] Boni | MR to CT synthesis with multicenter data in the pelvic area using a conditional generative adversarial network[END_REF]. AugCGAN is more robust with the erraticism of MR-images as compared to the standard cycleGAN. This study incorporated T2w MR and CT pelvic images of 38 patients from 5 centers. The AugCGAN was trained on 2D transverse slices of 19 patients from 3 different sites. The network was then used to generate sCT images of 19 patients coming from two other sites. Mean Absolute Errors (MAE) for each patient were evaluated between real and sCT. The novel steerable needle has been manufactured and omnidirectional steering at the distal tip can be achieved by a jointless integrated pull-push mechanism. The degree and direction of needle steering are controlled by four piezoelectric motors at the proximal end of the robotic BT module as shown in Figure 1 (a). The inner needle and outer catheter with a 1.4 mm and 2.0 mm diameter, respectively. After needle placement, the inner needle can be retracted leaving behind a channel for seed delivery. Artifact formation of the needle and piezoelectric motors is evaluated in 3 T MRI. CoBra's needle path planning algorithm is designed for steerable needles based on the seed plan and prostate contours received from MRI. It clusters the seeds and creates candidate path plans to reach all seed positions, using a single insertion point. Acceptable results are those that allow all seed positions to be reached, while keeping a minimum, pre-set distance between the needle and the urethra. From all candidates, the one that causes the least amount of tissue damage is chosen. For CoBra robot testing, the team developed a bio-inspired prostate phantom, depicting the motion, deformation, and inflammation of the prostate seen clinically during needle insertion.

•

  The absolute encoder and USM actuators resulted in normal functioning under 3 T field without influencing the MR-images during the scan. • Developed software for needle path planning with single entry point, Figure 6. • Robotized needle insertion in BIP under RT-MRI resulting features with good fidelity and the needle tip identified under T1w, T2w, and DYN-B FEE sequences, Fig 3. • sCT datasets showed a mean MAE of 59.8 HU and 65.8 HU for first and second test sites, taking on average 8.5 s to generate a complete sCT (90 slices) on our GPU (Nvidia Quadro P6000), Fig 5.

  The active BIP is connected to SOFA (Simulation open framework architecture) to estimate the changes in the prostate, thus enabling tracking of target position interactively (Figure1 (b)).

Figure 5 :

 5 Figure 5: From left to right, Dose distribution from the same radiotherapy external plan computed on the CT, sCT and the dose difference related to the prescribed dose.Figure6: Seed plan using single perineum entry point using steerable needle.

Figure 6 :

 6 Figure 5: From left to right, Dose distribution from the same radiotherapy external plan computed on the CT, sCT and the dose difference related to the prescribed dose.Figure6: Seed plan using single perineum entry point using steerable needle.

Figure 4 :

 4 Figure 4 : Conventional straight needle vs. steerable needle concept for 1) accurate targeting & 2) increased needle reach

Figure 3 :Figure 1 :

 31 Figure 3: Needle insertion to bio-inspired active prostate phantom


Pierre Garcia
email: pierre.garcia@cea.frb

Jérôme Pouvreau
email: jerome.pouvreau@cea.fr

High Temperature Combined Sensible-Latent Thermal Energy Storage

This work aims at proposing innovative Thermal Energy Storage (TES) systems for CSP power plants able to operate with high efficiency thermodynamic cycles working at 600°C. To do this, for CSP plants with gases or molten salts as Heat Transfer Fluid (HTF), high thermal capacity molten salts can be used in thermocline tanks with encapsulated Phase Change Material (PCM) top layer to limit the temperature degradation during discharge and thus increase the utilization rate of the storage system. Aluminum silicon (AlSi) has already been identified to have superior properties for a PCM: high specific energy density and volumetric heat of fusion, good thermal conductivity, low cost, and low environmental impact. A one dimensional dynamic model of combined sensible-latent TES system is presented, taking into account thermal transfer by conduction and convection in axial direction, measured thermo-physical properties for the storage media, and realistic heat losses to the environment. A prototype of molten salt single media thermocline tank is designed and modeled, and a parametric analysis is performed with different amounts of PCM for the same total tank volume. This numerical study shows that a combined sensible-latent molten salt thermocline concept with AlSi as PCM material can slow down the outlet temperature degradation during discharge and increase the storage capacity compared to a sensible only thermocline TES with the same tank volume.

INTRODUCTION

IN-POWER H2020 project aims at developing and integrating new innovative material solutions into CSP technology to increase the efficiency while simultaneously decreasing the energy production cost. These advanced material solutions consist of self-healing and anti-soiling coated mirrors, optimized mirror support structure, hightemperature absorber coating, and high-temperature Thermal Energy Storage materials and designs leading to the reduction of storage system size. Proposed innovative TES materials could operate with high efficiency thermodynamic cycles working at 600°C. To do this, for CSP plants with gases or molten salts as HTF, high thermal capacity molten salts will be used in thermocline tanks with encapsulated PCM top layer to limit the temperature degradation during discharge and thus increase the utilization rate of the storage system. Below the PCM layer, the storage tank operates as a thermocline tank without filler materials (single media thermocline) or with filler materials (dual media thermocline), as shown in Figure 1.

MATERIAL AND SYSTEM DESCRIPTION Combined Sensible-Latent TES Systems

Combined sensible-latent TES systems were already reported in the literature. Galione [1] considered a dual media thermocline tank (solar salt and quartzite) with two PCM layers (potassium hydroxide), at the top and at the bottom of the tank, with the objective to reduce the thermocline degradation throughout charge/discharge cycles thanks to the thermal buffering effect of the PCM layers. Such TES concepts were numerically tested and their thermal performances were compared against other designs of single-tank systems and with a reference two-tank molten-salt system, showing that this multi-layered solid-PCM concept is an interesting option for thermal storage in CSP facilities.

Other recent studies consider combined sensible-latent TES systems with AlSi12 as PCM [START_REF] Kotzé | High temperature thermal energy storage utilizing metallic phase change materials and metallic heat transfer fluids[END_REF][3][START_REF] Zavattoni | High-temperature thermocline TES combining sensible and latent heat -CFD modeling and experimental validation[END_REF][START_REF] Hernández | AIP Conference Proceedings of the 23 rd SolarPACES Symposium[END_REF][START_REF] Rea | Experimental Demonstration of a Latent Heat Storage System for Dispatchable Electricity[END_REF] but none of them using molten salts as Heat Transfer Fluid (HTF). Kotze [START_REF] Kotzé | High temperature thermal energy storage utilizing metallic phase change materials and metallic heat transfer fluids[END_REF] proposed a storage system concept integrating TES and steam generator into one unit with eutectic sodium-potassium alloy (NaK) as HTF and metallic PCM as storage medium. As NaK is highly reactive with water, this TES concept requires a safe physical separation between NaK and water-steam: the TES tank consists in a shell-and-tube heat exchanger with PCM (AlSi) on the shell side, and two separate tube circuits for the primary HTF loop (NaK) and steam generation loop. The storage tank is divided into three separate sections, each serving as a distinct part of the steam generator (boiler, superheater, and reheater). In commercial implementations of this concept, three different PCM would have to be selected to better match temperature of the steam. Thermodynamic and heat transfer analyses showed that such a design is feasible, even if the author points out that further analyses are necessary to assess its economic benefit. A prototype thermal energy storage test rig has been built and tested as to better understand the behavior of latent heat thermal energy storage, using AlSi as PCM and quenching oil as HTF in the unique tube of the test section [START_REF] Kotzé | Simulation and testing of a latent heat thermal energy storage unit with metallic phase change material[END_REF]. A numerical model was developed and compared with the behavior of the test rig during discharge, showing reasonable accuracy to simulate the latent heat thermal energy storage.

Zanganeh [3] investigated a high-temperature thermocline TES concept, using air as the heat-transfer fluid and integrating PCM to stabilize the discharging outflow air temperature. A lab-scale prototype was built and tested, containing layer of encapsulated phase change material (AlSi12 in stainless steel tubes) on top of a packed bed of rocks. A two-phase transient heat transfer model of the thermal storage cycle was experimentally validated with measured temperatures from the lab-scale prototype. Tests show a stabilization of the outflow air temperature around the melting temperature of AlSi12, possibly extending the discharge time for the downstream application. The thermofluid dynamics behavior of this prototype was later analyzed by a computational fluid dynamics approach, both sensible and latent heat sections of the storage being modeled as porous media [START_REF] Zavattoni | High-temperature thermocline TES combining sensible and latent heat -CFD modeling and experimental validation[END_REF].

Hernandez [START_REF] Hernández | AIP Conference Proceedings of the 23 rd SolarPACES Symposium[END_REF] developed and validated a two-phase model in order to describe the thermal performance of a combined sensible-latent thermal storage system, using steel slag as sensible packed-bed material, encapsulated AlSi metal alloy as phase change material and air as heat transfer fluid. The model was validated with data from the From Solar Field

High-temp PCM Layer 575°C

To Power Block

To Solar Field

From Power Block

MS 300°C to 600°C

Thot = 600°C Tcold = 300°C
200020-2 literature [3,[START_REF] Izquierdo-Barrientos | Modeling and experiments of energy storage in a packed bed with PCM[END_REF], showing the enhanced performance of combined sensible-latent storage compared to purely sensible system. The analysis of the proposed real scale TES system with different thickness of PCM layers showed that an optimal design with a 5% vol. top PCM layer can overcome the limitations of the only sensible packed bed technology, without oversizing the storage.

Rea [START_REF] Kotzé | Simulation and testing of a latent heat thermal energy storage unit with metallic phase change material[END_REF] presented the design and initial experimental results of a lab-scale prototype of a latent heat thermal storage system using 50 kg of Al-Si alloy as a PCM, embedded sodium heat pipes to distribute heat, and a valved thermosyphon to control heat flow from the thermal storage tank to thermoelectric generators. This system was able to distribute heat from an electrically generated heat input simulating solar flux to and from the PCM with small temperature gradients, and controllably dispatch the heat to thermoelectric generators.

PCM Selection

TES materials must have a high energy density per-unit mass or per-unit volume, that is to say a high density and a high specific heat (for sensible heat storage) or a high latent heat (for latent heat storage). The following technical requirements should also be taken in consideration when selecting a PCM for thermal storage purposes: thermal conductivity, mechanical and chemical stability, chemical compatibility with heat exchanger and/or container, low cost, and process-adapted temperature and pressure operational ranges. Contrary to many PCMs, metallic phase change materials have high thermal conductivity, allowing high charging and discharging rates of TES system, and can operate at temperatures exceeding 500°C. Many metals were found to be highly suitable as PCMs (in the temperature range of 400-750°C), with advantages over inorganic salts (higher heat of fusion and thermal conductivity, lower volume required per stored energy). Aluminum silicon (AlSi12 with melting temperature of 575°C) has been identified to have superior properties for a PCM: high specific energy density and volumetric heat of fusion, good thermal conductivity, low cost, and low environmental impact [9]. As compatibility between PCM and containers is a critical point, innovative anti-corrosive layers under development at CEA are currently tested in the framework of the IN-POWER project to avoid creep corrosion. Kotzé et al. [START_REF] Kotzé | High temperature thermal energy storage utilizing metallic phase change materials and metallic heat transfer fluids[END_REF][START_REF] Kotzé | Simulation and testing of a latent heat thermal energy storage unit with metallic phase change material[END_REF] also selected the eutectic alloy of aluminum and silicon, AlSi12, as one of the best candidates as metallic PCM based on a review of the literature. Finally, aluminum-silicon alloys are relatively stable through several heating and cooling cycles [START_REF] Li | The influence of heating-cooling cycles on the thermal storage performances of Al-17% Si alloy[END_REF].

MODEL DESCRIPTION AND VALIDATION

A one dimensional dynamic model of combined sensible-latent TES system was developed, taking into account thermal transfer by conduction and convection in axial direction (along the height of the tank), measured thermophysical properties for the storage media, and realistic heat losses to the environment. To do this, existing continuum thermodynamics models of dual-media thermocline systems [START_REF] Esence | AIP Conference Proceedings of the 23 rd SolarPACES Symposium[END_REF] were extended with the additional use of a top PCM layer. This model has been adapted in Modelica language within the Dymola platform.

To our knowledge, there is no existing experimental facility of molten salt thermocline storage with PCM top layer. To validate our model we chose to compare its results with experimental data from a combined sensible latent packed bed tank of rocks and AlSi with air as HTF [3]. AlSi and stainless steel capsules are considered as a unique material by using mean values of specific heat, density, and thermal conductivity. Thermal gradients inside solids (PCM capsules and rocks) are considered negligible: this assumption can be made when the conduction resistance in the solids is negligible compared to the convection resistance, that is to say when the dimensionless Biot number is lower than 0.1 [START_REF] Bergman | Fundamentals of Heat and Mass Transfer[END_REF]. A quite good agreement of the simulated results can be observed in Figure 2 for both latent and sensible section. Radiative heat transfers are neglected, which could partially explained the deviations from experimental results.

200020-3 (a) (b) FIGURE 2.
Experimentally measured (markers, from [3]) and simulated (curves, this work) temperatures during charge and discharge: packed bed and inlet (top) temperatures in the sensible section (a); PCM and air temperatures in the latent section (b)

STORAGE DESIGN

As previously reported, some recent studies have shown the interest of adding a top layer of PCM in a packed bed [START_REF] Hernández | AIP Conference Proceedings of the 23 rd SolarPACES Symposium[END_REF] or in mid-temperature molten salt thermocline [1] TES. IN-POWER combined sensible-latent TES design has been modeled and its thermal performances are compared to thermocline storage without PCM. The TES system consists in a molten salt (Solar Salt, 60% NaNO 3 and 40% KNO 3 by weight) single media thermocline tank, with a top layer of encapsulated AlSi. Solar Salt properties are taken from Ferri [START_REF] Ferri | Molten salt mixture properties in RELAP5 code for thermodynamic solar applications[END_REF], and AlSi capsules properties are taken from Zanganeh [3]. The reference design of the simulated tank is presented in Table 1. A parametric study was done replacing a variable fraction of the salt by a PCM top layer, the total tank volume being left constant. In Figure 3a, simulated outlet temperatures profile in discharge are presented for TES subjected to the same charge and discharge conditions such as inlet temperatures and flow rates and final charging outlet temperature (350°C) for a TES previously charged at 585°C. In such conditions a 15% (in volume) PCM layer can extend the discharge time with outlet temperature over 550°C by up to 12% for the same TES volume. In Figure 3b, the same simulation is done for a TES previously charged at 600°C. In such conditions a 15% (in volume) PCM layer can extend the discharge time by up to 10% for the same TES volume. In both cases it can be observed that the PCM layer lowers the outlet temperature during the first period of the discharge, and then then increases the outlet temperature in the second part of the discharge for outlet temperature below 570°C. In Figure 4, the amount of energy coming out of the TES during discharge is shown as a function of the temperature degradation in discharge (defined as the difference between the nominal inlet temperature in charge and the outlet temperature in discharge), for different PCM fractions in a tank previously charged at 600°C. Temperature degradation in discharge is a restrictive parameter for the downstream component of the facility (power block, process heat consumer, …), that is why it is often considered as a relevant criterion to define the end of discharge. If the heat can be recovered at a temperature level down to 100 K lower than it was produced, about 60 MWh th can be discharged from a 100% molten salt thermocline tank, whereas 72 MWh th can be discharged from a storage where 20% of the molten salt is replaced by PCM.

OUTLOOK

This numerical study shows that a combined sensible-latent molten salt thermocline concept with AlSi as PCM material can slow down the outlet temperature degradation during discharge and increase the storage capacity compared to a sensible only thermocline TES with the same tank volume.

However, compatibility issues between AlSi and molten salts may raise safety concerns. Indeed, contact between molten aluminum and nitrates or other oxidizers may cause an explosion. To mitigate this risk, the following options may be considered: -to decrease the leakage risk of AlSi capsules within the salt through an innovative TES design, -to change the PCM: back-up solutions have been identified, but with lower thermal performances, -to use the PCM in alternative regenerative-type TES with gas as heat transfer fluid instead of nitrate salts.

This simulation model of the PCM storage will be further validated with tests results from IN-POWER partners. It will be used to design and size high temperature thermocline storage for commercial scale CSP plants. Parametric studies will be performed to optimize tank geometry and operating strategies. Through this work, we will develop a cost-performance model to determine the unit cost of storage capacity (€/kWh) for a given operating temperature range and storage materials combination. This techno-economic model will allow to determine the optimal PCM fraction for this combined sensible-latent TES system.

  SolarPACES 2018 AIP Conf. Proc. 2126, 200020-1-200020-6; https://doi.org/10.1063/1.5117735Published by AIP Publishing. 978-0-7354-1866-0/$30.00

FIGURE 1 .

 1 FIGURE 1. IN-POWER combined sensible-latent thermocline TES without fillers (left) and with filler (right)

FIGURE 3 .

 3 FIGURE 3. TES outlet temperature during discharge for different amounts of PCM, for a 90 MWhth storage tank (left: TES charged at 585°C; right: TES charged at 600°C)

FIGURE 4 .

 4 FIGURE 4. TES discharged thermal energy as a function of the outlet temperature degradation for different amounts of PCM, for a 90 MWhth storage tank

TABLE 1 .

 1 Reference design of a 90 MWhth molten salt thermocline tank

	Design parameter	Unit	Value
	Hot temperature	°C	600
	Cold temperature	°C	290
	Design mass flow	kg/s	34.9
	Design salt mass	tons	754
	Tank height	m	14
	Tank diameter	m	7.57
	Tank volume	m 3	630

ACKNOWLEDGMENTS

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 720749.