N M Doll

S Bovio

A Gaiti

A-C Marsollier

S Chamot

S Moussu

T Widiez

Gwyneth Ingram
email: gwyneth.ingram@ens-lyon.fr

The endosperm-derived embryo sheath is an anti-adhesive structure that facilitates cotyledon emergence during germination in Arabidopsis

Keywords: Embryo, Endosperm, Surface, Adhesion, Germination, Cotyledon, Arabidopsis

Germination sensu stricto in Arabidopsis involves seed coat and endosperm rupture by the emerging seedling root. Subsequently the cotyledons emerge rapidly from the extraembryonic tissues of the seed, allowing autotrophic seedling establishment. Seedling survival depends upon the presence of an intact seedling cuticle that prevents dehydration, and which has hitherto been assumed to form the interface between the newly germinated seedling and its environment. Here we show that in Arabidopsis this is not the case. The primary interface between the emerging seedling and its environment is formed by an extra-cuticular endosperm-derived glycoprotein-rich structure called the sheath, which is maintained as a continuous layer at seedling surfaces during germination, and becomes fragmented as cotyledons expand. Mutants lacking an endosperm specific cysteine-rich peptide (KERBEROS (KRS)), show a complete loss of sheath production. Although krs mutants have no defects in germination sensu stricto they show a delay in cotyledon emergence, a defect not observed in seedlings with defects in cuticle biosynthesis. Biophysical analyses reveal that the surfaces of wild-type cotyledons show minimal adhesion to silica beads in an aqueous environment at cotyledon emergence, but that adhesion increases as cotyledons expand. In contrast krs mutant cotyledons show enhanced adhesion at germination. Mutants with defects in cuticle biosynthesis, but no sheath defects, show a similar adhesion profile to wild-type seedlings at germination. We propose that the sheath reduces the adhesiveness of the cotyledon surface under the humid conditions necessary for seed germination, and thus promotes seed coat shedding and rapid seedling establishment.

RESULTS AND DISCUSSION

The embryo sheath, and not the cuticle, forms the primary interface with the environment upon cotyledon and hypocotyl emergence.

Arabidopsis seed development, is triggered by a double fertilization event that leads to the production of two tissues; the embryo (from the fertilized egg cell) and the endosperm (from the fertilized central cell of the female gametophyte). The coordinated development of these two tissues is critical for the production of fully viable seeds. In Arabidopsis the initial growth of the seed is driven by the expansion of the endosperm, which is then progressively replaced by the invasively growing embryo. Only one viable layer of endosperm cells remains at seed maturity (reviewed in [START_REF] Marsollier | Getting physical: invasive growth events during plant development[END_REF]). During this process a structure called the embryo sheath, composed of material rich in EXTENSIN epitopes, is produced in the endosperm surrounding the developing embryo and deposited at the embryo surface, outside the embryonic cuticle [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF]. Sheath deposition correlates with an apparent reduction in the adhesion of the embryo to the endosperm during seed development both temporally and in a variety of backgrounds defective in sheath deposition, and facilitates the invasive growth of the embryo through the endosperm in developing seeds.

We tested whether the sheath remains within the seed at germination or whether it adheres to the seedling surface upon emergence. Immunolocalisations of resin sections with the anti-EXTENSIN JIM12 antibody [START_REF] Smallwood | Localization of cell wall proteins in relation to the developmental anatomy of the carrot root apex[END_REF] revealed that the newly emerged embryoderived surfaces of wild-type seedlings at 2 Days After Stratification (DAS) are covered with a continuous sheath (Figure 1A). We previously reported [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF], that this structure could also be detected with the LM1 anti-EXTENSIN antibody [START_REF] Smallwood | An epitope of rice threonine-and hydroxyproline-rich glycoprotein is common to cell wall and hydrophobic plasmamembrane glycoproteins[END_REF], and we could also detect it using the JIM19 anti-EXTENSIN antibody [START_REF] Smallwood | Localization of cell wall proteins in relation to the developmental anatomy of the carrot root apex[END_REF] (Figure S1). Previous work has shown that the KRS protein is necessary for sheath production. However a structure-function analysis suggested that KRS likely regulates sheath production rather than forming a structural component of the sheath [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF]. Consistent with the previously reported absence of sheath production by the endosperm of developing kerberos (krs) mutant seeds, sheath material is absent at the surface of krs mutant seedlings (Figure 1D-F, Figure S1). This result was confirmed by whole-mount immunolocalisations with JIM12, which show a strong and continuous signal on all aerial parts of wild type seedlings at 2 DAS, but no signal in the krs background (Figure 1G,J). Finally, analysis of cotyledons by transmission electron microscopy confirmed the presence of an extra-cuticular matrix, corresponding to the embryo sheath on the surface of wild-type seedlings at 2DAS (Figure 1M,O). This structure is entirely absent at the surface of krs-3 seedlings (Figure 1 O,P). Consistent with the observation that the sheath is strictly seed-derived [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF], JIM12 signal on the surface of wild-type seedlings was progressively fragmented as seedlings expanded. At 4 DAS, the sheath on the wild type cotyledons was discontinuous (Figure 1B), and at 7 DAS, only a few patches remained on the cotyledon surface (Figure 1C). These results were confirmed by whole mount immunolabelling in which the JIM12 signal decreased strongly in intensity during cotyledon expansion (Figure 1H,I). As expected, JIM12 signal was found to be absent on post embryonic structures such as leaf primordia (Figure 1A). In the primary root, occasional patches of sheath-like material were observed, which may be derived from the embryonic root apex (Figure S1).

These results show that the assumption [START_REF] Aharoni | The SHINE Clade of AP2 Domain Transcription Factors Activates Wax Biosynthesis, Alters Cuticle Properties, and Confers Drought Tolerance when Overexpressed in Arabidopsis[END_REF][START_REF] Jenks | Cuticular Waxes of Arabidopsis[END_REF][START_REF] Para | The Dehydratase ADT3 Affects ROS Homeostasis and Cotyledon Development[END_REF][START_REF] Suh | Cuticular Lipid Composition, Surface Structure, and Gene Expression in Arabidopsis Stem Epidermis[END_REF][START_REF] Tanaka | A subtilisin-like serine protease is required for epidermal surface formation in Arabidopsis embryos and juvenile plants[END_REF][START_REF] Todd | KCS1 encodes a fatty acid elongase 3-ketoacyl-CoA synthase affecting wax biosynthesis in Arabidopsis thaliana[END_REF] that the Arabidopsis seedling cuticle forms the primary interface between the seedling and the environment upon germination is false, and that this interface is, in fact, formed by the embryo sheath; an endosperm derived structure.

Sheath deposition and embryonic cuticle formation are genetically separable processes.

Our previous work, combined with the above results, suggest that the embryo sheath is tightly associated with the embryo cuticle, the structure commonly thought to impart specific physical properties to plant surfaces (reviewed in [START_REF] Bernard | Arabidopsis cuticular waxes: advances in synthesis, export and regulation[END_REF][START_REF] Ingram | The roles of the cuticle in plant development: organ adhesions and beyond[END_REF]). To identify backgrounds that would allow us to discriminate between the specific functions of these structures, we analysed cuticle integrity in krs mutant seedlings which lack the embryo sheath. Staining with the lipophilic dye auramine O showed that krs mutants have a continuous and apparently normal cuticle after germination (Figure 2A-D). As previously proposed the reported slight increase in permeability of the krs cuticle after germination may be due to mechanical damage at cotyledon tips sustained during development or emergence [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF]. No endosperm debris was observed on the surface of krs seedlings during staining, indicating that although the embryo and endosperm show an abnormally tight association during seed development [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF] this cuticle ultimately allows a clean separation of the embryo from surrounding endosperm tissues. The krs cuticle was also found to be indistinguishable from that of wild-type seedlings later in cotyledon development (Figure 1M-P, Figure S1). We conclude that krs is only deficient for sheath deposition but not for cuticle establishment. In addition we investigated sheath production in a mutant reported to have a defect specifically in cuticle biosynthesis, the glycerol-3-phosphate acyltransferase 4 and 8 (gpat4 gpat8) double mutant [START_REF] Creff | A stress-response-related intercompartmental signalling pathway regulates embryonic cuticle integrity in Arabidopsis[END_REF][START_REF] Li | Identification of acyltransferases required for cutin biosynthesis and production of cutin with suberin-like monomers[END_REF]. As previously reported, gpat4 gpat8 mutant seedlings do not completely lack an embryonic cuticle [START_REF] Creff | A stress-response-related intercompartmental signalling pathway regulates embryonic cuticle integrity in Arabidopsis[END_REF].

Nonetheless the cuticle of gpat4 gpat8 mutants stains only very weakly at 2 and 4 DAS, consistent with the role of these enzymes in cutin biosynthesis (Figure 2E,F, Figure S1) [START_REF] Creff | A stress-response-related intercompartmental signalling pathway regulates embryonic cuticle integrity in Arabidopsis[END_REF][START_REF] Li | Identification of acyltransferases required for cutin biosynthesis and production of cutin with suberin-like monomers[END_REF]. It is important to note that the complete lack of an embryonic cuticle is thought to lead to early embryo lethality (reviewed in [START_REF] Ingram | The roles of the cuticle in plant development: organ adhesions and beyond[END_REF][START_REF] Delude | Plant Surface Lipids and Epidermis Development[END_REF]). Sheath production and deposition is not affected in gpat4 gpat8 and the sheath is maintained on the cotyledon surface post germination in this background (Figure 2G,H). Consistent with this, embryoendosperm separation occurs normally in gpat4 gpat8 mutants (Figure 2G). Our results suggest that this genetic background shows defects only in cuticle biosynthesis, but not in sheath deposition. Thus, embryo sheath deposition can be functionally separated from cuticle biosynthesis. The gpat4 gpat8 and krs mutants therefore represent valuable tools to separate the function of the embryonic cuticle from that of the embryo sheath during germination.

The presence of an intact embryo sheath facilitates the emergence of cotyledons

from the seed coat.

The germination of krs, gpat4 gpat8 and WT seeds was observed. 48h after stratification, krs plantlets have a significantly higher frequency of retention of the cotyledons within the extra embryonic tissues of the seed than either WT or gpat4 gpat8 mutants (Figure 3C-F). Kinetic analysis in three independent mutant alleles of KRS revealed a significant delay in cotyledon escape in the presence of sucrose (Figure 3C, Figure S2). This effect was amplified in the absence of sucrose (Figure 3E, Figure S3). However, radicle emergence was not delayed, showing that germination stricto sensu is not affected in krs mutants (Figure 3D,F Figure S2). The fact that gpat4 gpat8 plantlets do not present defects in cotyledon escape, indicates that this phenotype is specifically caused by the absence of the embryo sheath rather than by cuticle defects. The dynamics of cotyledon escape were also assessed in dark-grown seedlings in which cotyledons do not expand dramatically (Figure 3 G-J). Similarly to a growth in presence of light, a delay in cotyledon escape was observed in krs compared to the WT and gpat4 gpat8. At 4 (96h) DAS, cotyledons frequently remain inside the extra-embryonic tissues in krs seedlings but very rarely in WT and gpat4 gpat8 (Figure 3G,H).).

Based on our results, we hypothesise that the sheath promotes robust cotyledon escape from the seed even in absence of significant cotyledon expansion, reinforcing the hypothesis that the sheath is involved in reducing adhesion of cotyledons to surrounding tissues, and in lubrication during seed coat shedding. In further support of this hypothesis we found that seed coat shedding in wild-type seedlings, and radicle emergence in either wild-type or krs mutants, were only weakly affected by restriction of water availability by increasing agarose concentrations in the media [START_REF] Verger | A tension-adhesion feedback loop in plant epidermis[END_REF]. In contrast, a decrease in water availability increased seed coat retention in krs mutant (Figure S3 B-D). Similarly, germination on media with abnormally high or low pH increased seed-coat retention in krs mutants but only marginally affected cotyledon escape in wild-type (Figure S3 I-N).

The presence of an intact embryo sheath promotes robust plant establishment.

We found that, in the absence of sucrose, a significant proportion (around 20%) of krs mutants arrest before the first leaves appear (Figure 3 K-M, Figure S2C). Levels of seedling arrest were correlated with cotyledon trapping, suggesting that cotyledon trapping may impede the establishment of autotrophic growth (Figure 3N). Consistent with this idea, seedling arrest was not observed in the presence of sucrose (which attenuated, but did not abolish the cotyledon trapping phenotype of krs mutants), or on soil (Figure 3C-D, K and Figure S2C). To investigate further whether defects in krs mutants translate into altered fitness, we carried out competition assays between wild-type and krs-3 seeds sown as mixed populations at very high density on soil. Under normal growth conditions (1 plant per pot) krs mutants show no delay in bolting compared to wild-type plants.

Genotyping revealed that only 16.33% (+/-2,05% n=3, 100 bolts per sample) of bolts produced under high density conditions were derived from krs mutants, suggesting that loss of KRS function significantly impacts plant establishment under these conditions.

Changes in the adhesive properties of the cotyledon surface correlate with the presence of an intact sheath.

The fact that the sheath is maintained on the surface of young seedlings provides an opportunity to measure the biophysical properties of surfaces with and without a sheath, and notably to assess the adhesive properties of these surfaces. To assess this parameter we used atomic force microscopy (AFM) with a spherical silica tip (as in [START_REF] Burton | Hydrophobicity, adhesion, and friction properties of nanopatterned polymers and scale dependence for micro-and nanoelectromechanical systems[END_REF][START_REF] Burton | Surface characterization and adhesion and friction properties of hydrophobic leaf surfaces[END_REF]) . Initial scans were carried out to acquire the topography of the sample and to identify cells (Figure 4A). Smaller areas (10 x 10 µm²) were then selected for the generation of 8 x 8 grids of force curves for adhesion measurements (Figure 4B)(see materials and methods).

Several grids were generated per cotyledon. Under our conditions little, if any, adhesion was measured at the surface of wild-type cotyledons at 2 DAS, whereas at 5 DAS, higher levels of adhesion were observed. krs cotyledons showed similar values of adhesion at 2 DAS and 5 DAS, and these values were similar to those observed in wild-type cotyledons at 5 DAS (Figure 4C,D). This is likely due to the fact that krs mutant cotyledons at 2 and 5 DAS, and wild-type cotyledons at 5 DAS, all have surfaces composed of a similar cutin matrix. Similar results were observed on both the adaxial and abaxial surface of cotyledons (Figure S4), and we therefore concentrated on adaxial surfaces which, being slightly convex, are more accessible to measurement. As previously observed in cuticle staining experiments, AFM scans and scanning electron microscopy analysis showed the absence of endosperm debris at the cotyledon surface of krs mutants (Figure S4). Thus, the presence of an intact sheath correlates with reduced adhesion both temporally in wild-type seedlings, and in the krs mutant. (Figure 4C,D) (Figure S4). These results suggest that the sheath is less adhesive under hydrated conditions than the cuticle, which is considered to be a non-adhesive structure [START_REF] Burton | Surface characterization and adhesion and friction properties of hydrophobic leaf surfaces[END_REF].

Consistent with the fact that gpat4 gpat8 mutants produce a normal sheath, their properties were identical to those of wild-type seedlings at 2 DAS (Figure 4C).

Interestingly however, at 5 DAS, the surface of gpat4 gpat 8 mutant cotyledons tended to be less adhesive than that of wild-type and krs seedlings (Figure 4D). This could reflect changes in cuticle composition caused by, or compensating for, the loss of the products of the GPAT4 and GPAT8 enzymes at this developmental stage. Such compensatory alterations, have been reported in studies of other cuticle biosynthetic mutants [START_REF] Aharoni | The SHINE Clade of AP2 Domain Transcription Factors Activates Wax Biosynthesis, Alters Cuticle Properties, and Confers Drought Tolerance when Overexpressed in Arabidopsis[END_REF][START_REF] Sieber | Transgenic Arabidopsis plants expressing a fungal cutinase show alterations in the structure and properties of the cuticle and postgenital organ fusions[END_REF][START_REF] Bessire | A permeable cuticle in Arabidopsis leads to a strong resistance to Botrytis cinerea[END_REF][START_REF]Functional analysis of the LACERATA gene of Arabidopsis provides evidence for different roles of fatty acid omega -hydroxylation in development[END_REF][START_REF] Wellesen | Functional analysis of the LACERATA gene of Arabidopsis provides evidence for different roles of fatty acid omegahydroxylation in development[END_REF].

In conclusion, our work reveals that, contrary to the situation at other aerial plant surfaces, the primary interface of the newly emerged Arabidopsis embryo with its environment is not the cuticle, but the extra-cuticular endosperm-derived embryo sheath.

We demonstrate that the sheath renders the embryo surface less adhesive under humid conditions, which likely explains its role in permitting the growth of the embryo through the endosperm during seed development, and in facilitating robust cotyledon escape from the seed coat. Our results highlight a previously unsuspected role for endosperm-derived apoplastic components in the emergence of cotyledons during germination, and in seedling establishment, and also have potentially important implications for understanding the interactions of germinated seedlings with their environment.

Supplementary

STAR METHODS LEAD CONTACT AND MATERIALS AVAILABILITY

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Gwyneth Ingram (gwyneth.ingram@ens-lyon.fr). This study did not generate new unique reagents.

EXPERIMENTAL MODEL AND SUBJECT DETAILS Plant materials

The Columbia-0 (Col-0) accession was used as a reference in this study. Three KRS loss of function alleles were used, a t-DNA allele (krs-1) and two CRISPR lines alleles (krs-3 and krs-4), all described in [START_REF] Moussu | ZHOUPI and KERBEROS Mediate Embryo/Endosperm Separation by Promoting the Formation of an Extracuticular Sheath at the Embryo Surface[END_REF]. The double mutant gpat4 gpat8 used corresponds to loss of function of both GPAT4 (AT1G01610) and GPAT8 (AT4G00400) by t-DNA insertion and has been described previously [START_REF] Li | Identification of acyltransferases required for cutin biosynthesis and production of cutin with suberin-like monomers[END_REF].

Plant growth

Unless otherwise specified, Arabidopsis seeds were gas-sterilized and sown on MS media (pH = 5,7) with 0.8% Plant agar (Meridis) and 0,5% sucrose and stratified for 2 days at 4°C. Plants were then transferred to long day conditions (16h light) at 21°C.

For generating the seed stocks used, seedlings were transferred to compost (Argile 10 (favorit)) after 7 days, and grown under long day conditions (16h light) at 21°C.

For cotyledon escape tests under light conditions, seeds were sown in rows on MS plates in the presence or absence of sucrose as specified.

For etiolated seedlings, plates were wrapped in aluminium foil for stratification, exposed to a 6h light flash to synchronise germination, re-wrapped and placed in the growth chamber. Observations were carried out in a light free chamber with optional green lighting for observation purposes.

For cotyledon escape tests with varying agarose concentration, 0.5% to 5% of agarose (Sigma-Aldrich) was added to the liquid MS media as specified. For cotyledon escape tests with varying pH, 0.05% w/v of MES hydrate (Sigma-Aldrich) was added to the MS media and pH was adjusted by addition of hydrochloric acid or sodium hydroxide.

For seedling arrest tests, seeds were sown in rows on compost (Argile 10 (favorit)) or on MS plates lacking sucrose, stratified for 2 days at 4°C before transfer to the growth chamber (16h light at 21°C).

For the competition assay, equal weight of krs-3 and Col-0 seeds (containing a YFP marker expressed in the anthers), were thoroughly mixed and sown at high density on soil. Seeds lots were from mother plants that were grown in identical conditions. The estimated density of seeds on soil was 120 seeds/cm². 2 days of stratification were then performed and trays were then transferred to growth chambers. Plants that had bolted after 4 weeks were genotyped by YFP visualisation (Axio Imager 2 microscope (Zeiss)). 3 repetitions of the experiments were performed with seed batches from independent mother plants.

METHOD DETAILS Germination and cotyledon escape tests

Seeds were grown as described in the previous section. Three batches of 100 seeds, each from independent mother plants, were used as biological replicates. Seeds were observed under a binocular microscope at different times after transfer to the growth chamber and the percentage of radicle emergence and cotyledon escape were recorded. A seedling was considered as showing cotyledon escaped when at least one cotyledon had been released from the seed-coat. Pictures of seedlings in Figure 3 were taken with a Leica MZ12 light microscope.

Cuticle staining

2 DAS and 4 DAS seedlings were fixed with 4% paraformaldehyde (Sigma-Aldrich) in 1X PBS with at least 1 hour of vacuum treatment as described in [START_REF] Ursache | A protocol for combining fluorescent proteins with histological stains for diverse cell wall components[END_REF]. Fixed seedlings were then washed twice for 1 min in 1X PBS before being transfer for at least 6-days to ClearSee solution (10% w/v xylitol (Sigma-Aldrich); 15% w/v sodium deoxycholate (Sigma-Aldrich); 25% w/v urea (Euromedex) in water) at room temperature with gentle agitation. Cleared seedlings were then stained with a 0.5% solution of Auramine O (Sigma-Aldrich) in ClearSee. After 12-16 hours of incubation in the dark, seedlings were washed in ClearSee rapidly, then for 30min and then again for at least 1h before being mounted in ClearSee solution. Confocal imaging was performed using a Zeiss LSM700 with a Plan-Apochromat 63x/1,4 oil DIC M27 (ref 420782-9900) objective. Auramine O fluorescence was imaged with a 488nm diode laser excitation and detected with a 505-530nm PMT. Images were then processed using the Zeiss LSM Image Browser Program. AFM experiments were performed on a stand-alone Nanowizard III microscope (JPK, Bruker), driven by JPK Nanowizard software 6.0. The experiments were performed in filtered MS media (without sucrose) that was used to flood the petri dish as soon as possible after cotyledon immobilisation and 15' to 2 hours before the beginning of the measurements. A silica spherical tip (Special Development SD-sphere-NCH, Nanosensors) mounted on a silicon cantilever with a nominal force constant of 42 N/m, and a radius of 400 nm was used. Cantilevers were cleaned before each experiment in a Hellmanex III (VWR, Ref. 634-0666)/water solution (2% v/v) for 10', then rinsed in water for 10' and finally in ethanol (either pure or 70% solution), in order to remove organic contaminants. This procedure was repeated if there was any suspicion of tip contamination.

Atomic Force Microscope (AFM)

Cantilever calibration was performed following the standard thermal noise method. The deflection sensitivity was measured by performing a linear fit of the contact part of a force curve acquired on a sapphire sample in MQ water. The spring constant was determined by acquiring the thermal noise spectrum of the cantilever and by fitting the first normal mode peak using a single harmonic oscillator model. To reduce the offsets in force that introduced by each new calibration, we followed the SNAP protocol developed by [START_REF] Schillers | Standardized Nanomechanical Atomic Force Microscopy Procedure (SNAP) for Measuring Soft and Biological Samples[END_REF].

Since the cantilevers used for this study were not independently calibrated by the manufacturer, we considered the spring constant value found at the first calibration as the reference value. In subsequent calibrations, we corrected the deflection sensitivity following SNAP, in order to obtain the same spring constant each time by thermal tune analysis. Then, the new deflection sensitivity and the reference spring constant were set in the instrument's software.

The acquisitions were performed as follows: a first acquisition in Quantitative Imaging (QI) modality at low force (75 nN) and over large areas (90 x 90 µm² or 100 x 100 µm²) gave a first topographic scan for selecting the regions of interest. The first topographic scan was also used to verify that the areas selected were free from contaminants and as flat as possible to minimise tilting of tip-sample contacts. 3 to 4 smaller maps (10 x 10 µm², with 8 x 8 force curves) were then acquired in Force Mapping mode, each restricted to 1 single cell. Force curves were acquired with a 4 µm ramp size (2048 data points per curve), with approach and retract speed of 20 µm/s and a force setpoint of 100 nN: This setpoint is rather small (giving indentations around 50 nm), but high enough to ensure a stable contact for each force curve. Between approach and retract curve, a 2 second pause segment at constant force (100 nN) was imposed, to give a controlled contact time at each point.

• Data analysis

Data analysis was carried out using JPK Data Processing software 6.0. Adhesion force was measured as the minimum value of force found on the retract segment of the force curve. To filter out spurious adhesion events, the following strategy was used:

an RMS value was calculated on a portion of the baseline, then curves were separated into 2 groups depending on whether adhesion passes a threshold value defined as 5 * RMS. This coefficient was selected by visually verifying the correct separation into the 2 groups for several samples. Using a Python routine, an adhesion of 0 nN was assigned to all adhesion events below the previously defined threshold.

Statistical analysis was performed in GraphPad Prism 7.05. For each cotyledon the average of adhesions measured on all the regions of interest defined was calculated. Data were then grouped per genotype and represented as scatter plots, where means +/-SEMs are displayed. T-tests were run if only 2 genotypes were present, for the rest of the comparisons we used one-way ANOVA, comparing each genotype with every other genotype.

Immunolabelling

• On sections Seeds or seedlings were fixed in PEM buffer (15.2g.L-1 PIPES (Sigma-Aldrich), 1.6g.L-1 EGTA (Sigma-Aldrich), 1.2g.L-1 MgSO4,7H2O (MERCK), pH 6.9, in water) containing 4% the seedlings were mounted in water between slide and coverslip. Observations were made using an Imager M2 (Zeiss) microscope images treated using ImageJ software. `

Transmission electron microscopy (TEM)

For TEM analysis, 2 DAS seedlings grown on MS plates with 0,5% sucrose were highpressure frozen with a Leica EM-PACT-1 system. One or two seedlings were inserted into a flat copper carrier with hexadecene, fast-frozen, and cryosubstituted into the Leica AFS1 device. The different freeze-substitution steps were as follows: 54 h at -90°C in acetone solution containing 0.2% glutaraldehyde (50% aqueous, EMS), 1% osmium tetroxide (EMS), and 0.1% uranyl acetate (EMS). The temperature was then raised with a ramp of 2°C/h before being held for 8 hours at -60°C. The temperature was raised again to -30°C for 8h00 before being increased to 4°C. Samples were washed three times for 10 min in 100% acetone before embedding in Spurr's resin (Spurr Low Viscosity Embedding Kit, Polysciences). Embedding was performed progressively (8 h in 25% Spurr's resin in acetone, one day in 50% Spurr's resin in acetone, one day in 75% Spurr's resin in acetone, and two times overnight in 100% Spurr's resin). Polymerization was performed at 70°C for 18 h. Samples were sectioned (70 nm sections) on a UC7 Leica ultramicrotome with a diamond knife and imaged at 120 kV using a Phillips CM120 TEM with 2k x 2k Gatan Orius 200 ccd.

QUANTIFICATION AND STATISTICAL ANALYSIS

  extraembryonic tissues of the seed. G-L) JIM12 whole mount immunolabelling. JIM12 labelling is shown in green. G) 2 DAS WT seedlings. H) 4 DAS WT cotyledon. I) 7 DAS WT cotyledon. J) 2 DAS krs-3 seedlings. K) 4 DAS krs-3 cotyledon. L) 7 DAS krs-3 cotyledon. Scale bars = 200µm in G-L. M-P) Transmission electron microscopy images on 2DAS seedlings. M,O) Col-0 seedling. N,P) krs-3 seedling. ECW = epidermis cell wall, cut = cuticle, ES = embryo sheath. Scale bars = 1µm in M and N, = 200nm in O and P.

Figure 2 :

 2 Figure 2: Sheath deposition and cuticle biosynthesis are genetically separable processes. A-F) Auramine O staining of the cotyledon cuticle 2 DAS. Arrows indicate the cuticle A) in Col-0, B) magnification of A, C) in krs-3, D) magnification of C, E) in gpat4 gpat8, F) magnification of E. G-H) JIM12 immunolabelling on section in the gpat4 gpat8 mutant. JIM12 signal is in green and cell walls are stained with fluorescent brightener 28 (in blue). cot = cotyledon, sc = seed coat, emb = embryo, end = endosperm. Scale bars = 20µm in A,C,E, 2µm in B,D,F and 50µm in G and H.

Figure 3 :

 3 Figure 3: Absence of sheath leads to defective cotyledon emergence and induces a premature seedling arrest in the absence of sugar. 2 DAS Col-0 seedling, B) 2 DAS krs-3 seedling with the two cotyledon inside the seed coats. C) Percentage of seedlings with escaped cotyledons at different times after stratification for Col-0, krs-3 and gpat4 gpat8 lines. N = 3 (repetitions from independent mother plants), 100 seedlings per repetition. Seedlings were grown on MS plates supplemented with 0,5% sucrose. D) Percentage of radicle emergence in the same experiment as that shown in C. E) Percentage of seedlings with escaped cotyledons at different times after stratification for Col-0, krs-3 and gpat4 gpat8 lines. N = 3 (repetitions from independent mother plants), 100 seedlings per repetition. Seedlings were grown on MS plates lacking sucrose. F) Percentage of radicle emergence in the same experiment as that shown in E. G) 5 DAS etiolated Col-0 seedlings. H) 5 DAS etiolated krs-3 seedlings with the two cotyledons inside the seed coats. I) Percentage of seedlings with escaped cotyledons at different times after stratification for Col-0, krs-3 and gpat4 gpat8 lines. N = 3 (repetitions from independent mother plants), 100 seedlings per repetition. Seedlings were grown in absence of light, on MS plates lacking sucrose. J) Percentage of radicle emergence in the same experiment as that shown in I. K) Quantification of seedling growth arrest (at 12

Figure 4 :

 4 Figure 4: Absence of the sheath leads to altered adhesive properties at the cotyledon surface. A) Large scale topographical maps of cotyledon surfaces were acquired in QI mode (scan size 90x90 or 100x100 µm) in order to identify cells and define regions for adhesion measurements. 4 smaller (10x10 µm) regions of interest were then selected for extracting force curves. B) In each region of interest 64 curves were performed and then analysed to measure the adhesion force. The approach curve is shown in blue and the retract curve in red. Adhesion corresponds to the difference between the minimum of the retract curve and the base line. C,D) Cotyledon adhesion measurements for the three genotypes described above at 2 DAS and 5 DAS respectively. Average adhesion scatter plot. Each dot corresponds to the average adhesion measured for 1 cotyledon. Average +/-SEM is indicated on each scatter plot. One-way ANOVA tests were performed for betweendataset comparisons, with an a-value of 0.05. *** indicates p-value ≤ 0.001, **** indicates p-value ≤ 0.0001, ns indicates p-value > 0.05 in a subsequent Sidak post-hoc test.

Figure S1 :

 S1 Figure S1: Supplementary analyses of seedling surface composition and structure. A-C) Immunolabelling on sections of 2DAS seedlings. Immunolabelling is shown in green and cell walls stained with fluorescent brightener 28 are shown in blue. A) JIM19 labelling in Col-0. B) JIM19 labelling in krs-3. C) JIM12 immunolabelling on a transverse section of

Figure S2 :

 S2 Figure S2: Three independent null alleles of KRS show similar phenotypes regarding delay in cotyledon escape and premature seedling growth arrest (Related to Figure 3). A) Percentage of seedlings with escaped cotyledons at different times after stratification for Col-0 and three null-alleles of KRS. N = 3 (repetitions from independent mother plants), 100 seedlings per repetition. Seedling were grown on MS plates supplemented with 0,5% sucrose. The seed batches used in this study was older than the other used in this article. ** represents statistically significant differences (p-value < 0.01) obtained after one-way ANOVA and subsequent Tukey HSD tests. B) Percentage of radicle emergence in the same experiment as that shown in A. +/-SD are represented on each bar plot. C) Quantification of seedling growth arrest (at 12 DAS) in different conditions for Col-0 and three null-alleles alleles of KRS.

Figure S3 :

 S3 Figure S3: Variations in water availabilty and pH of growth media affect the cotyledon escape phenotype of krs mutants (Related to Figure 3). A-D) Percentage of seedlings with escaped cotyledons at different times after stratification for Col-0 and krs-3 lines. N = 3 (repetitions from independent mother plants), 100 seedlings per repetition. Seedlings were grown on MS plates lacking sucrose and with varying concentrations of agarose. A) 0,5% agarose, B) 1% agarose, C) 3% agarose, D) 5% agarose. E-H) Percentage of radicle emergence in the same experiment as that shown in A-D). E) 0,5% agarose, F) 1% agarose, G) 3% agarose, H) 5% agarose. I-K) Percentage of seedlings with escaped cotyledons at different times after stratification for Col-0 and krs-3 lines. N = 3 (repetitions from independent mother plants), 100 seedlings per repetition. Seedlings were grown on MS plates lacking sucrose and with differing pH. I) pH = 4,0 J) pH = 5,7 (standard condition) K) pH = 8,5. L-N) Percentage of radicle emergence in the same experiment as that shown in I-K). I) pH = 4,0 J) pH = 5,7 (standard condition) K) pH = 8,5. +/-SD are represented on each bar plot.

Figure S4 :

 S4 Figure S4: Supplementary biophysical and microscopic analysis of seedling surface properties (Related to Figure 4). A) Average adhesion scatter plot on adaxial and abaxial surfaces 2 DAS. Each dot corresponds to the average adhesion measured for 1 cotyledon. Average +/-SEM is indicated on each scatter plot. One-way ANOVA tests were performed between dataset comparisons, with an a-value of 0.05. B) Variability of adhesion maps between cotyledons. Breakdown of adhesion distribution in multiple cotyledons of Col-0, krs and gpat4 gpat8 at 2 DAS. Each dot corresponds to the average adhesion measured for an adhesion map of 64 measurements . Average +/-SEM is indicated on each scatter plot. *** indicates p-value ≤ 0.001, ** indicates p-value ≤ 0.01 and ns indicates p-value > 0,05 in a subsequent Sidak post-hoc test C-H) Comparison of the surfaces of wild-type and krs mutants seedlings. C, E, G) Col-0; D, F, H) krs-3. C-F) Scanning electron micrographs of cotyledon surfaces 2 DAS. Scale bars = 100µm in C,D) and 10 µm in E,F). G,H) Topographical scans of cotyledon surfaces at 2 DAS obtained using the Atomic Force Microscope. Scales are indicated.

  Force vs Height Measured curves were first flattened by removing the result of a linear fit performed over a portion of the non-contact part (baseline) of the curve, in order to set this part to a force of 0 N. A first estimation of the point of contact (POC) was obtained, considering it as the first point crossing the 0 of the force, moving backward along the approach curve, starting from its last point (i.e. force setpoint position). The force vs. tip-sample distance curves were then obtained calculating a new axis of distances as Height Measured [m]cantilever deflection [m].

For

  all the experiments, detail of statistical tests used and error-bars on barplots are indicated in the figure legends.

  Cotyledons were dissected under a binocular microscope and fixed to the bottom of plastic Petri dishes (Falcon 600 mm x 15 mm, Corning Ref. 351007) using 2-components, bio-compatible glue (Reprorubber-Thin Pour, Flexbar Ref. 16135).

• Measurements

Acknowledgements

We would like to thank A. Lacroix, J. Berger, P, Bolland, H. Leyral and I. Desbouchages for assistance with plant growth and logistics, and A. Patole, S. Maurin, B. Martin-Sempore and C. Vial for administrative assistance. AG was funded by the Erasmus student network. N.M.D was supported by the French Agence National de Recherche (ANR-17-CE20-0027 ; Mind the Gap)

DATA AND CODE AVAILABILITY

• This study did not generate/analyze [datasets/code].

Declaration of Interests

The authors declare no competing interests. (W/V) paraformaldehyde (Sigma-Aldrich) for 1 hour under vacuum, on ice and then overnight at 4°C. Samples were washed 2 times in PEM buffer and dehydrated by incubation in increasing concentrations of ethanol, (50%, 70%, 80%, 90% and three times 100%). Incubations were performed on ice, for one hour and under vacuum. Samples were then infiltrated with increasing concentrations of LR white resin (Euromedex) in absolute ethanol, (30%, 50%, 70% and three times 100%), for 1 hour on ice under vacuum followed by an overnight incubation at 4°C for each bath. Samples were then transferred to small Beam capsules (Electron Microscopy Sciences) and incubated overnight at 60°C for polymerisation. Seed and seedling sections of 1μm were cut on a Leica RM6626 microtome and fixed onto superfrost gold slides (Thermoscientific). For immunolabelling, sections were first incubated for 45 minutes in PBS containing 2% (W/V) of bovine serum albumin (BSA). They were then incubated with a 10-fold dilution of the primary antibody in PBS containing 0.1% (W/V) BSA overnight at 4°C followed by one hour at room temperature. Primary antibodies used for this study were JIM12 and JIM19 (plant probes) [START_REF] Smallwood | An epitope of rice threonine-and hydroxyproline-rich glycoprotein is common to cell wall and hydrophobic plasmamembrane glycoproteins[END_REF][START_REF] Smallwood | Localization of cell wall proteins in relation to the developmental anatomy of the carrot root apex[END_REF]. Sections are then washed three times in successively PBS for 5 minutes, PBS and 0.1% of tween 20 (W/V) (Sigma-Aldrich) for 10 minutes and PBS for 5 minutes. Incubation with a 1000-fold dilution of anti-rat secondary antibody (AlexaFluor 488 conjugate, Invitogen) in PBS with 0.1% BSA for 1 hour in darkness, in a wet chamber was performed. The sections were washed three times as previously described. Sections were counter-stained with a solution of 0.25 ng.L-1 of calcofluor (Fluorescent Brighter 28 (Sigma Aldrich)) in PBS for 5 minutes. Sections were washed rapidly three times in PBS and mounted in VECTASHIELD solution (Eurobio).

Main

Observations were made using an Axio Imager 2 microscope (Zeiss) and images were treated using ImageJ software.

• Whole mount immunolabelling

Seedlings were first fixed as described above, then washed two times for 5 minutes in PBS under rotation (30rpm) in 5ml tubes. Immunolabelling was immediately performed using the same protocol as describe above, but with the differences listed below. For the washes, seedlings were put in 5ml tubes with rotation at 30 rpm. For incubation with the primary and the secondary antibodies, the seedlings were carefully transferred to 0.25ml tubes and incubated in 200μL of antibody solution. The counter-staining was not performed and


D Galassi
email: davide.galassi@epfl.ch

H Reimerdes

C Theiler

M Wensing

H Bufferand

G Ciraolo

P Innocente

Y Marandet

P Tamain

Eurofusion Mst1 Team

Numerical investigation of optimal divertor gas baffle closure on TCV

A first set of divertor gas baffles has recently been installed in the TCV tokamak. In order to explore the physics determining the benefits and limitations of divertor baffling and to guide the design of a possible second generation of baffles, the effect of baffle closure is investigated using the 2D transport code SolEdge2D-EIRENE with realistic wall geometries. The baffle extension is scanned, first imposing the same upstream conditions as in previous SOLPS-ITER studies, then extending the parameter space to access detached plasma conditions. In attached plasma cases, divertor neutral compression is maximised by a Low-Field Side baffle length with an opening between the separatrix and the baffle tip of approximately 5 λ q , resulting in an increase in compression by a factor 4 with respect to the unbaffled case. In detached cases this ratio can be improved by up to a factor 25 using higher baffle closures. This difference in behaviour between attached and detached conditions is explained by a model based on the ionisation mean free path of neutral particles recycled from the target. In some conditions, the optimal baffle extension in terms of neutral compression is found to be subject to high levels of intercepted upstream heat flux, which results in a peak heat flux on the baffles comparable to the one impinging on the outer 1 target. The individual roles of the High-Field Side and Low-Field Side baffles are disentangled by means of dedicated simulations, which show a lower global impact of the inner baffle. This study suggests that an outer baffle with a gap of approximately 3 λ q , slightly longer than the one presently installed, could further enhance the neutral compression ratio in cases where the ionisation front is detached. The biggest unknown in these simulations is related to far SOL particle transport, which could result in higher levels of baffle recycling and thus limit baffle performance.

Introduction

Divertor baffling and the resulting improvement of the confinement of neutral particles in the divertor region of tokamaks is known to facilitate the access to detached divertor conditions (see e.g. [START_REF] Leonard | Plasma detachment in divertor tokamaks[END_REF]). Several baffling solutions have been conceived (see e.g. [START_REF] Loarte | Effects of divertor geometry on tokamak plasmas[END_REF]), including advanced solutions such as a tight baffling along divertor legs [START_REF] Umansky | Attainment of a stable, fully detached plasma state in innovative divertor configurations[END_REF], baffles enclosing the target region in a Super-X divertor [START_REF] Havlíčková | SOLPS analysis of the MAST-u divertor with the effect of heating power and pumping on the access to detachment in the super-x configuration[END_REF], small-angle slot divertors [START_REF] Guo | Small angle slot divertor concept for long pulse advanced tokamaks[END_REF] and V-shaped divertors [START_REF] Liu | Modeling study of the onset density for divertor detachment on east[END_REF]. Even though the baffle geometry can change according to specific tokamaks, several physical problems are common to all of them, such as the maximisation of the neutral confinement in the divertor, the interplay with plasma plugging and the requirement to assure acceptable heat and particle fluxes impinging on the baffles. In this work, we numerically study gas baffling and its limitations for the specific solution currently implemented on the Tokamak à Configuration Variable (TCV) [START_REF] Coda | Physics research on the TCV tokamak facility: from conventional to alternative scenarios and beyond[END_REF], which consists in a narrow throat at a height close to the X-point. The main goal of this study is to understand the effects that determine the optimal baffle design for different divertor conditions. The TCV baffle is formed by an inner baffle, located on the High-Field Side (HFS) of the vessel at a vertical location of about Z = -0.3 m with respect to the midplane, and by an outer baffle located at the Low-Field Side (LFS) at a similar height, as visible in figure 1 ( [START_REF] Fasoli | TCV heating and in-vessel upgrades for addressing DEMO physics issues[END_REF], [START_REF] Reimerdes | Tcv divertor upgrade for alternative magnetic configurations[END_REF]). A unique characteristic of the TCV baffles is their capacity to largely preserve the flexibility of the divertor magnetic geometry. The vertical positioning of the baffles, relatively far from the bottom where the outer strike point usually sits, is compatible with multiple magnetic geometries, including Lower Single Null, X, Super-X and Snowflake divertors [START_REF] Reimerdes | Tcv divertor upgrade for alternative magnetic configurations[END_REF]. As a result of the baffles, an increased density of neutral atoms and molecules recycled from the wall is expected in the divertor volume, along with a decrease in neutral density at upstream locations. The increased neutral density in the divertor should enhance momentum and power losses from the plasma, facilitating the access to the detached regime and extending the operational range of dissipative divertor operation in L and H-mode plasmas on TCV.

The dimensions of the first generation of baffles, recently installed in TCV, were designed ( [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF]) to maximise the neutral compression ratio:

c D ≡ n div n /n main n , (1)
where n n = n D 0 + 2n D 2 is the neutral density, and the superscripts div and main indicate the divertor and the main chamber regions, respectively. The design is based on edge plasma simulations performed with the code SOLPS-ITER ( [START_REF] Wiesen | The new solps-iter code package[END_REF], [START_REF] Bonnin | Presentation of the new solps-iter code package for tokamak plasma edge modelling[END_REF]). In this code, the fluid solver B2 is coupled with EIRENE [START_REF] Reiter | Progress in two-dimensional plasma edge modelling[END_REF], a Monte-Carlo code which solves a kinetic model for neutrals, allowing the description of plasma-neutrals and plasmawall interactions. A current limitation of SOLPS-ITER is that the plasma solver grid is not allowed to intercept solid objects other than the target plates, and in particular it is limited in radial extent by the position of the baffle tips. As a consequence, sheath boundary conditions are only applied at the target plates. Plasma flux radially out of the simulation domain is dependent on ad-hoc boundary conditions, e.g. imposed on the radial density decay length, which can become a sensitive input parameter if the simulation domain is limited in radial extent. Therefore, the plasma flux impinging on gas baffles cannot be modelled self-consistently. SOLPS simulations carried out in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF] suggested that the largest neutral compression would be obtained with a baffle placed at a distance from the separatrix corresponding to approximately 5 characteristic heat flux widths λ q . For longer baffles (Baffles 4 and 5 in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF]), however, the mesh grid had to be shrunk in the radial direction, making the results more sensitive to the boundary conditions imposed at the outer boundary of the plasma grid. On the contrary, in cases where the grid did not extend up to the baffle tip, an artificial channel was possibly left open for neutrals to leak from the divertor to the main SOL, yet without any plasma transport into the divertor. These limitations and the sensitivity of the recycling at the outer boundary of the plasma grid on ad-hoc boundary conditions warrant further studies. In the present paper, we investigate in more detail the optimal choice of the baffle length and the plasma-baffle interaction with the SolEdge2D-EIRENE code [START_REF] Bufferand | Numerical modelling for divertor design of the west device with a focus on plasmawall interactions[END_REF], which allows for a plasma grid extension and realistic boundary conditions up to the first wall and the baffles. The aim is to better understand the physics mechanisms determining the benefits and limitations of divertor baffling, to complement experimental findings from the first baffled campaign on TCV and guide the design for a second set of baffles. The paper is organised as follows. In section 2, the SolEdge2D-EIRENE code and simulation setups will be described. In section 3 we present a scan in outer baffle length, fixing upstream plasma conditions. The individual roles of the inner and the outer baffle will be assessed for the same input parameters, by carrying out simulations with each of these components alone. This analysis is useful as well since some restrictions given by the TCV baffles on magnetic geometry could be relaxed if just one of the baffles, the HFS or the LFS one, is proven to be sufficiently effective. In section 4 we extend the outer baffle scan to different upstream conditions, in particular to higher upstream density and lower power, and we discuss the variation of the neutral compression ratio in all the simulated cases. In section 5 we will present a simple model useful to understand the impact of the baffles on the achieved neutral compression ratio in different divertor plasma conditions. Conclusions are presented in section 6.

SolEdge2D-EIRENE simulations setup

SolEdge2D is a 2D multi-fluid code solving Braginskii equations, with a diffusive ansatz on cross-field transport. Being coupled with EIRENE, it also includes plasma-neutrals interactions. In this code, the above-mentioned limitation on the plasma mesh grid is overcome by means of a numerical technique called "penalisation" [START_REF] Paredes | A penalization technique to model plasma facing components in a tokamak with temperature variations[END_REF]. In SolEdge2D-EIRENE, the grid of the plasma solver and the one of EIRENE are superimposed. A mask function determines if a grid cell belongs to the wall or to the vacuum. In case of a wall cell, an additional term is solved in the equations, that forces the evolved quantity to a certain value. One can demonstrate [START_REF] Paredes | A penalization technique to model plasma facing components in a tokamak with temperature variations[END_REF] that, with an adequate choice of the penalisation parameters, this technique allows to recover the Bohm boundary conditions at the interface between plasma and plasma-facing components. In this work, we simulate the divertor performance of a standard TCV single-null magnetic configuration that had already been used in previous studies [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF], with several shapes for the baffle geometry, as illustrated in figure 2. The Baffle 1 considered in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF] has been omitted, since it was found to be far from the optimum design. The design of the first version of the baffles installed on TCV is similar to Baffle 3, shown in figure 2. The X-point is centered between the baffles, whose tips are tangent to the same flux surface. In order to determine the distance across flux surfaces, we use the coordinate ρ = √ ψ -ψ 0 / √ ψ x1 -ψ 0 , where ψ 0 is the poloidal flux at the magnetic axis, and ψ x1 is the one at the separatrix. widths λ q . This is also a useful parameter to characterise the baffle extension, since the optimal neutral compression must be determined assuring a sustainable heat flux on the baffles. At the LFS baffle poloidal location λ q 4.3 mm, corresponding to a ∆ρ ∼ 0.014. This value depends on the transport coefficients imposed in the simulations, and it varies by less than 10% percent among all simulations, when transport coefficients are kept constant. The SolEdge2D grid is flux-surface aligned. The resolution of the grid in the poloidal direction is of the order of 1 cm at locations far from the strike points, while it is refined to 1 mm near the strike points and of 5 mm close to the baffle tips, where large gradients are usually expected. The radial resolution at the outer midplane is of the order of 1 mm near the separatrix, and increases further out. Transport coefficients are imposed to be constant in time and in the radial direction. In the poloidal direction, they follow a Gaussian profile centered on the midplane, in order to mimic a ballooning-like turbulent transport. The poloidal average of the transport coefficients for particles, electron heat flux and ion heat flux, of D ⊥ = 0.2 m 2 /s, χ e ⊥ = 1.0 m 2 /s and χ i ⊥ = 1.0 m 2 /s correspond to the values chosen in the SOLPS investigation [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF] to match heat flux experimental profiles at the outer target in a particular non-baffled TCV L-mode discharge (#52312). Similarly, drifts are not taken into account in this work. Deuterium molecules are puffed at the location shown in figure 2, which corresponds to the location of the standard fuelling valve in TCV. A feedback loop adjusts the simulated gas puff to control the electron density at the outboard midplane separatrix. The actual density can differ up to ∼ 3% with respect to the target value. The deuterium recycling coefficient on the carbon wall is set to R = 0.986, which results in a relatively good agreement between gas puff levels in the simulations and in the experiment. The simulations include carbon ionised states, where the only source of carbon atoms are physical and chemical sputtering. The physical sputtering is calculated with the Bohdansky formula [START_REF] Bohdansky | A universal relation for the sputtering yield of monatomic solids at normal ion incidence[END_REF], while the chemical sputtering yield is set to 3.5%, as in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF]. The imposed value for the carbon recycling coefficient on carbon tiles is 0.4: since this coefficient is hard to be actually determined from experiments, the value has been chosen in order to obtain a reasonable radiated power in the SOL. Only the continuity and the momentum conservation equations are solved for carbon ions, which are considered in thermal equilibrium with the main ions. The upstream conditions imposed in the simulations discussed in this paper are summarised in table 2 In high-power simulations, 1/3 of the power is assigned to electrons and 2/3 to ions, as in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF], while in low power simulations it is evenly distributed between the two species.

Baffle closure scan at fixed upstream condition

In this section, we inspect the effect of different baffle closures on both outer midplane (upstream) and target profiles, fixing n u = 1.8 • 10 19 m -3 and P in = 1.2 M W . These are the same low-collisionality upstream conditions as in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF].

Upstream profiles

While the upstream electron density at a flux surface just inside the separatrix is fixed, the upstream neutral density varies substatially with the baffle dimensions, as shown in figure 3c. It decreases monotonically with increasing baffle length up to Baffle 4, where a reduction of approximately a factor 10 is achieved. Beyond this point, it increases again in the case of Baffle 5. This behaviour is due to a competition of a better neutral confinement in the divertor with increasing baffle length and increasing levels of recycling on the baffle. It should also be noted here that neutrals recycled from the baffles get mostly ionised in the close vicinity of the baffle. Therefore, even more than to the upstream neutral density, they contribute to the average main chamber neutral density, which is the quantity used in section 4 to determine neutral compression. The neutral particle density at the outer midplane is the main difference with respect to former SOLPS simulations [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF], where it increased considerably with respect to the optimum case for Baffles 4 and 5 (by one order of magnitude with Baffle 5). However, these were also the cases for which, in SOLPS, the plasma grid was radially narrowed. As a result, these simulations were particularly sensitive to the choice of the radial outer boundary condition, i.e. the value set for the radial density decay length. Comparison with the present SolEdge2D-EIRENE simulations indicates that the choice of this boundary condition in [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF] resulted in an overestimation of the level of main chamber recycling. This effect, together with a different poloidal distribution of main chamber recycling (predominantly from the baffles in SolEdge2D-EIRENE) is likely the cause of the discrepancy in the two simulations. Electron density at the outer midplane changes modestly from case to case, as it is shown in figure 3a. In the first flux surfaces of the SOL, density with the baffles is up to 15% higher (Baffle 3 case) as compared to the unbaffled case. This is due to the fact that Baffle 3 is the one characterised by the lowest ionisation in the confined region. Therefore, a lower density gradient at the separatrix is necessary to transport particles outwards. Since we fix the electron density just inside the separatrix, a flatter density gradient leads to higher densities in the first SOL flux surfaces. This difference in the steepness of density profile is more visible in the closed flux surfaces. The flattening of the density profile in the confined region has also been observed on Gas Puff (10 [START_REF] Casali | Modelling the effect of divertor closure on detachment onset in diii-d with the solps code[END_REF]. The electron and ion temperatures (only shown here for electrons) follow an opposite trend in the confined region with respect to density: this happens because of the fixed power imposed in the simulations, and from the assumption of a diffusive cross-field heat transport. One can also notice from figure 3b) that temperature in the SOL remains unaffected by the baffle dimensions. This is consistent with previous SOLPS-ITER simulations [START_REF] Wensing | SOLPS-ITER simulations of the TCV divertor upgrade[END_REF].

The gas puff required to keep the upstream density constant increases in the presence of the investigated baffles by ∼ 40%, but depends little on the dimensions of the baffle, Table 3. This can be understood since in the presence of baffles, the divertor volume is better decoupled from the main chamber and thus a higher gas puff is needed to achieve the same separatrix upstream density. Two additional simulations have been performed, featuring the same plasma upstream conditions, although imposing the gas puff at the top of the machine (at (R, Z) = (0.92, 0.75) m). These simulations were once performed without baffle and once with Baffle 3. Also in this case, the simulation with the Baffle 3 results in a higher gas puff than in the unbaffled geometry. However, this increase is lower (∼ 20%) than in the case where the gas puff is at the bottom. This is interpreted to be due to the fact that puffed neutrals now reach the closed-field lines region in the same way in baffled and unbaffled cases, while the baffle still partially screens the neutrals recycled at the strike points. The increase in gas puff values in baffled cases has also been observed in simulations with higher upstream density, with gas puffing both from the bottom and from the top of the machine.

Target profiles

In baffled cases, the electron density at the outer target increases by up to 40% with Baffle 3, with respect to the simulation with no baffle (figure 4a). It is weakly sensitive to a change in the outer baffle extension and does not show a systematic trend. The peak neutral density at the outer target follows a similar trend as electron density, with a maximum for Baffle 3 (not shown). The electron and ion temperatures at the target (only shown for electrons, in figure 4b) are considerably more strongly affected by the choice of the baffle, decreasing monotonically with the baffle length. To explain this strong variation in target temperature with the baffles, we show the total heat flux impinging on the outer strike point, superimposed with the one affecting the outer baffle, in figure 5a. This heat flux includes the contributions from ions, electrons and neutrals. At ρ < 1.02, the heat flux is approximately the same in all cases, meaning that the radiative power losses are not significantly affected by the baffles in these low-collisionality plasmas. Nevertheless, even at these locations the electron temperature in the baffled cases is lower with respect to the unbaffled one. This is due to the fact that the total pressure is approximately conserved on the flux surfaces, so an increase in target density leads to the observed decrease in target temperature.

Even for ρ > 1.02 the target heat flux is not significantly affected by radiated power levels. Table 3 shows that the total radiated power (which is mainly due to weakly-ionised states of carbon in the relatively cold divertor region) does not change dramatically with different baffle geometries and it is maximised in the Baffle 2 and 3 cases, because of the high values of electron density near the targets. The strong reduction in target temperature with increasing baffle length for ρ > 1.02 can instead be explained by a stronger and stronger interception of the heat flux by the outer baffle, as visible in 5a. Therefore, the longer the baffle, the smaller the integrated heat flux reaching the outer strike point, and the lower the target temperature. In the Baffles 4 and 5 cases, the peak heat flux intercepted by the outer baffle corresponds to ∼ 25% and ∼ 50% of the peak heat flux at the target, respectively. Clearly, such high heat flux fractions on the baffles might be a concern in the design of baffle tiles in a reactor. In addition, such baffle interaction can cause enhanced levels of impurity sputtering and resulting impurity fluxes towards the confined plasma. In the present simulations, however, carbon sputtered from the baffles does not penetrate significantly into the closed field-line region.

Besides the parallel heat flux, the parallel particle flux is also affected by the presence of the baffles. However, as visible in figure 5b, the peak ion flux on the baffle tip, even in the Baffle 5 case, is significantly lower than at the strike points. In fact the overall particle source in the flux tubes connected to the baffle is small, if compared to the flux tubes connected to the target, leading to small ion fluxes and elevated temperatures at the baffle surface. Moreover, the smaller connection length between the midplane and the outer baffle, with respect to the one between midplane and target, leads in our simulations to a sheath-limited regime in the low-field side of the flux tubes connected to the baffles, with high peak temperatures (up to ∼30 eV) at the baffle tip, as visible in figure 5b. The ion flux on the baffles may depend on transport properties. Simulations with D ⊥ increased by a factor 2 and 6 have been run with the same baffle geometries as before to check the sensitivity to these parameters, while the other transport coefficients have been kept constant. Even with these higher values of D ⊥ , and thus broader midplane density profiles, the peak particle flux on the outer baffle has been found to be much lower with respect to the one at the outer target, not changing the trends observed in figure 5. The ion flux is weakly sensitive on D ⊥ since the majority of the ions stays confined in a recycling pattern around the divertor target, and it is weakly affected by upstram transport conditions. The balance between intercepted fluxes of heat and particles by the baffles, although found to be weakly dependent on the values of D ⊥ explored here, would probably change for flat far-SOL density profiles and in particular in presence of a "density shoulder" [START_REF] Vianello | Modification of SOL profiles and fluctuations with line-average density and divertor flux expansion in TCV[END_REF]. The result would be a higher recycling on the baffle, and thus higher neutral particle fluxes to the confined region. The study of this problem should be addressed by dedicated edge turbulence simulations. At the inner target the electron density increases in baffled cases, as visible in figure 6a, by a larger factor than at the outer target. The peak density follows the same trend as a function of the baffle length as at the outer target. Electron and ion temperatures are lowered (only shown for T e ) by the presence of the baffle, figure 6b. This reduction in target temperature is consistent with weak changes in upstream and target pressures for varying baffle length. Contrary to the outer target, there is no substantial interception of parallel heat flux by the inner baffle and consequently no monotonic decrease of the temperature at the inner target with an increasing outer baffle extension.

The effect of the inner and outer baffles

In order to evaluate the separate effects of the inner and of the outer baffles, we analyse the two simulations where only the HFS baffle, or only the LFS baffle 4 are included. Among the different LFS baffles, we simulate the one corresponding to Baffle 4, since it results, in most of the cases, in the highest neutral compressions. The inner baffle alone lowers the electron temperature at the inner target by approximately 30%, as visible in figure 7b. At the outer target, instead, it has a very weak effect on the electron temperature, figure 7a. The neutral compression (see section 4.1 for details) is increased by only 20% with the inner baffle alone. The outer baffle 4 alone, besides cooling down the outer target, also lowers the peak electron temperature at the inner target by approximately 15%, without intercepting directly the heat flux directed to the HFS (figure 7b). At the outer target, the outer baffles leads to plasma conditions very similar to the full Baffle 4. Neutral compression is increased in this case by a factor 3 with respect to the unbaffled case, similarly to the Baffle 4 case. We observe therefore a global effect of the outer baffle quantitatively stronger than the one of the inner baffle. This is also backed up by the fact that the gas puff values for the inner and the outer baffle cases are respectively of 1.6 • 10 21 el/s and 1.8 • 10 21 el/s, consistent with a lower core ionisation for the case with the outer baffle. Nevertheless, both inner and outer baffles appear to locally have an impact similar to a full set of baffles, although the inner baffle has a reduced effect on the other target. As in TCV it is generally easier to obtain detached plasma at the outer target [START_REF] Theiler | Results from recent detachment experiments in alternative divertor configurations on TCV[END_REF], the inner baffle could, therefore, be important to access detached regimes also at the inner target.

Baffle closure scan at variable upstream conditions

We focus now on the effect of the baffle closure for all the different upstream parameters listed in Table 2, and in particular for higher collisionality conditions than the cases discussed in section 3. Qualitatively, changing input power and upstream density, the baffle closure affects upstream profiles in the same way as in the formerly presented cases, with Baffle 4 or Baffle 5 generally minimising upstream neutral pressure. Since we will later show the importance of the ionisation front position in determining the performances of the baffle, it is interesting to evaluate the spatial distribution of the net ion source. In figure 8, the spatial distribution of the ion source is shown for higher upstream density and same input powers as the cases discussed in Sec. 3, for different baffle configurations. In the case without baffle, the ionisation source is strongly localised in the vicinity of the strike points. When increasing the baffle length, the ionisation front at the outer strike point moves towards the X-point, while recombination becomes dominant near the target. This does not necessarily mean that the plasma is completely detached from the target or that the density roll-over has occurred (see [START_REF] Stangeby | The Plasma Boundary of Magnetic Fusion Devices[END_REF], Chapter 16 and references therein, for a review on this subject). Recombination starts to dominate below approximately 2 eV in all cases (see contour lines in figure 8). The ionisation events due to particle recycling on the baffle tip accounts only for up to ∼ 3% of the total recycling flux. The ionisation source at the inner target remains attached to the target surface for all inspected baffle lengths. Figure 9 illustrates the position of the ionisation front for the different baffle closures and all the upstream conditions listed in table 2. Here we define the ionisation front as the position along the outer divertor leg, where the sum of ionisation and recombination events is equal to zero. While in the high power, low density case discussed in section 3, the ionisation front remains attached to the target independently of the baffle closure, in more collisional upstream conditions the ionisation front moves progressively away from the target as the baffle closure is increased. In the high density, low power case, the ionisation front reaches the X-point height, so that any further increase of the baffle length is not expected to have beneficial consequences. The increasing poloidal distance of the ionisation front from the target is caused by the progressive cooling of the divertor plasma with an increasing outer baffle extension. Considering more specifically the high-power, high-density case, we note that the divertor dissipated power fraction (i.e., the ratio of the power dissipated in the outer divertor via photons and neutrals and the total power entering the outer divertor) increases monotonically with the outer baffle length, leading to a decrease in the peak heat flux at the outer target. This additional dissipation is mainly due to deuterium radiation and charge exchange losses. For long baffles (Baffles 4 and 5), however, large fractions of the power directed towards the outer divertor (up to 40 % in the Baffle 5 case) get intercepted by the outer baffle, thus substantially contributing to the cooling and the total heat flux reduction at the outer target.

Effect of baffle closure on neutral compression

In order to evaluate the compression ratio, we average the neutral density, including the molecular one as defined in section 1, over the "main chamber"and the "divertor"volumes:

c D = n n div n n main , (2)
where the divertor and main chamber regions are separated by a line connecting the tips of the inner and of the outer baffle. In the case without any baffle, or with just the inner baffle, a horizontal line is set as separation between the divertor and the main chamber, at the vertical position of the inner baffle tip. Note that the c D values calculated with (2) can be sensitive to the choice of the line separating the divertor and the main chamber regions. This is because neutral density usually drops rapidly at the X-point height. In the present simulations, however, the c D values are only weakly sensitive to this choice. In the low-collisionality case described in section 3, the neutral compression ratio is approximately 30 without baffle, and it increases by a factor of approximately 4 with Baffle 3, figure 10a, as a result of a factor 2 increase in the average neutral density in the divertor, and of a factor 2 decrease in the main chamber. This increase is slightly lower than SOLPS-ITER predictions [START_REF] Wensing | SOLPS-ITER simulations of the TCV divertor upgrade[END_REF]. The possibility that these quantitative differences were due the more comprehensive set of chemical reactions used in SOLPS-ITER has been ruled out by a dedicated set of simulations with the same reactions, which did not substantially change our results. In the Baffle 4 and 5 cases, the ion flux recycled on the LFS baffle, even if much smaller than the one at the strike points, represents the main source of particles for the main chamber, and thus affects the neutral compression ratio. We remind that in these cases, the ionisation front remains attached to the wall. At low density and low input power, the neutral compression factor increases monotonically with the outer baffle length, figure 10a. While the ionisation front is attached in the no-baffle case, it moves towards the X-point, with increasing baffle dimensions. It is worth noting that for these conditions, while the neutral compression increases the longer the baffle, peak heat fluxes on the baffles become very high for the Baffle 4 and the Baffle 5 case (∼ 75% and ∼ 140% of the peak target fluxes, respectively). Increasing the upstream density at high input power, the ionisation front is still attached in the no-baffle case. In this case, the neutral compression is relatively high, due to an elevated molecule density in the Private Flux Region (PFR). These results are in line with SOLPS-ITER simulations [START_REF] Wensing | SOLPS-ITER simulations of the TCV divertor upgrade[END_REF], which showed an improvement in the neutral compression ratio with increasing upstream density. The best neutral compression is achieved with Baffle 4, while with Baffle 5 the recycling on the outer baffle leads to a higher ionisation source in the main chamber, and to a slightly lower c D . In the high-density, low-power case, the baffle is particularly efficient in confining neutrals. As explained later, this is due to the fact that in these conditions the ionisation front is detached. A saturation is reached, again, for the Baffle 4 case. With Baffle 5, the ionisation front is close to the X-point, so that neutrals partially leak to the main chamber, in the SOL region between the HFS baffle and the separatrix, leading to a slightly lower neutral compression.

Neutral density asymmetry in the divertor

The change in neutral compression between a baffled and an unbaffled plasma appears to be larger when the ionisation front is detached. One can see that the improvement in neutral compression with respect to the unbaffled case (figure 10b) follows the same trends as the distance of the ionisation front from the outer target (figure 9). In order to understand this behaviour, we consider two cases without baffle at the same upstream density (n u = 3.5 • 10 19 m -3 ), but different input power (1.2 M W and 0.3 M W ).

Figure 11a, corresponding to a high density, high power attached case, shows a difference in neutral density between the PFR and the SOL of approximately one order of magnitude. In this case, without baffles, the neutral compression is particularly elevated (c D ∼ 80), and the PFR contains the majority of neutral particles. Figure 11b shows the same case, but at low input power: here the asymmetry between SOL and PFR is much smaller. Although the ion flux to the outer target is lower than in the high power case, the neutral density in the SOL region is actually higher, and the neutral compression factor consequently lower (c D ∼ 30). Since this asymmetry in neutral density affects the impact of the baffles, we need to explain its origin. The main source of neutrals is located at the targets, where impinging ions are re-emitted as "first-generation"D 2 molecules, with an energy corresponding to wall temperature (set to 310 K in these simulations). In the configuration investigated here, the poloidal angle between the separatrix and the wall is close to 90 • , so the average molecule flux is directed along the separatrix direction. Therefore, the asymmetry in neutral density is not caused by the inclination of the target with respect to the separatrix (this last effect is investigated in e.g. [START_REF] Sang | SOLPS analysis of neutral baffling for the design of a new diverter in DIII-d[END_REF], [START_REF] Moulton | Neutral pathways and heat flux widths in vertical-and horizontal-target EDGE2d-EIRENE simulations of JET[END_REF], [START_REF] Fil | Separating the roles of magnetic topology and neutral trapping in modifying the detachment threshold for TCV[END_REF]). The majority of recycled molecules are dissociated when they enter in a region where T e >∼ 3 eV ([21], [START_REF] Post | Models for poloidal divertors[END_REF]). While the resulting ions travel back to the target, the D 0 atoms, with typical energies around 3 eV , can escape from the divertor leg. Subsequently, they can be reflected or absorbed by the wall, and re-emitted as molecules. The resulting slow "second-generation"molecules can travel for a relatively long time, in regions such as the PFR or the far SOL, until they get sufficiently close to the plasma to be dissociated again. In the attached case at high input power, one can see from figure 12a that the source of neutral atoms is radially located close to the separatrix, and poloidally at few centimeters from the target. This distance approximately corresponds to the mean free path for molecules dissociation (based on dissociation rate coefficients in [START_REF] Post | Models for poloidal divertors[END_REF]). The total atom flux in this case, which does not have, a priori, a preferential direction, is stronger towards the PFR than towards the SOL, as shown in figure 12b, where we calculate the atom and molecule fluxes across the control surfaces defined in 12a. This difference can be explained by the different ionisation mean free path of neutral atoms towards the PFR and the SOL, due to higher densities and temperatures on the SOL side of the strike point with respect to the PFR side. Figure 12b also shows that the net flux of molecules (mainly "first-generation", with source centered close to the strike point) across the same surface is relatively low with respect to the atoms flux, so they are less important in determining the overall neutral densities in the PFR and in the SOL. As a result, in the attached case, neutral density is significantly higher in the PFR than in the SOL, with molecules (mainly "second-generation") accounting for approximately 90% of neutral particles in the divertor and deuterium atoms for approximately 10%. In the detached case illustrated in figure 12c, the source of neutral atoms is not peaked at the target, but extends along the entire divertor leg. The electron temperature in the SOL is insufficient to ionise the resulting neutral atoms directed towards the main SOL, similarly to the PFR. Additionally, a non-negligible net flux of molecules reaches the SOL, as shown in figure 12d. Globally, a higher share of neutrals, with respect to the attached case, is directed to the main chamber through the Common Flux Region, and is blocked by the baffles. In the detached case, so, baffles lead to higher changes in neutral compression ratios. Moreover, this effectiveness in reflecting neutrals increases with the baffle length. In the attached case, instead, the PFR acts as a reservoir that temporarily encloses neutrals, before they get ionised in divertor legs, so that the baffle closure plays a weaker role.

Discussion: a simple evaluation of neutral flux asymmetries

A simple model is presented here in order to evaluate the asymmetry in neutral content in the PFR and in the divertor SOL. We assume, for simplicity, that the divertor leg is perpendicular to the wall in the poloidal plane and we call x the radial coordinate along the outer target. We also suppose that all the neutral atoms are generated at the position x M along the target, corresponding to the peak of the ion flux. Then, the ratio of the fluxes perpendicular to two surfaces placed at x SOL > x M and x P F R < x M is simply:

Γ n SOL Γ n P F R exp - x SOL x M 1 λ i (ne(x),Te(x)) dx exp x P F R x M 1 λ i (ne(x),Te(x)) dx , (3)
where λ i = v n /(n e σv e i ) is the ionisation mean free path, with v n the atom velocity and σv e i the ionisation rate coefficient. The asymmetry in radial density and temperature profiles in the PRF and the main SOL then leads to a different integrated ionisation mean free path for the two sides, which usually results in Γ n SOL /Γ n P F R ≤ 1. In order to calculate the flux ratio, we assume that neutral atoms are originated from the dissociation of desorbed molecules, and that half of them fly towards the SOL at the thermal speed corresponding to 3 eV , while the other half is directed towards the PFR with the same velocity. As a general approximation for our plasma profiles at the outer target, we consider now a simple Eich-like profile for electron temperature, with λ T e = 0.015 m and S T e = 0.01 m, and a profile of electron density with λ n = 0.01 m and S n = 0.006 m [START_REF] Eich | Inter-elm power decay length for jet and asdex upgrade: Measurement and comparison with heuristic drift-based model[END_REF]. These values have been found to be representative of most of the profiles resulting from our simulations. While for density this function fits well the density profiles at the target, we note that it is less so for temperature, that is difficult to fit satisfactorily with an Eich function [START_REF] Wagner | A study of the perpendicular particle transport properties in the scrape-off layer of asdex[END_REF]. No background value is considered for these fields. We can now multiply these density and temperature profiles by arbitrary constants, and infer the ratio in neutral flux between SOL and PRF in this ideal situation using equation (3). We fix the two boundaries of integration x SOL and x P F R , where the fluxes to the SOL and to the PFR are respectively calculated, at the locations represented in figure 12a. Then, we characterise the profiles by their maximum value, and we plot the ratio of fluxes as a function of these maximum values in figure 13, in the form of contour lines. The model predicts the asymmetry to increase with the maximum temperature and density at the target, although with a weaker dependence on density in the considered parameter range.

In the same plot, we represent the same quantity, calculated for each of the SolEdge2D-EIRENE simulations considered in this work. In this case, the fluxes are averaged over the poloidal extension indicated in figure 12a. The model can fail if the dissociation region of first-generation molecules is far from the target, where radial plasma profiles can differ substantially from the ones at the target. This happens for example in some high density cases, where the temperature profiles at the target is approximately flat, but it is not at the location of the atoms source. In most of the cases however, the simple model introduced here can catch qualitatively, and almost quantitatively, the imbalance in neutral fluxes directed towards PFR and SOL. This suggests that we have identified the right mechanisms that determine the asymmetry in neutral density in these attached and detached TCV simulations. The choice of atom velocity determined by molecular dissociation processes is justified for the parameter space explored in this work and for carbon walls. In the case of a tungsten divertor, for example, a higher share of ions impinging on the target would be reflected as neutral atoms, thus leading to a higher average neutral velocity [START_REF] Zhang | Effect of carbon and tungsten plasma-facing materials on the divertor and pedestal plasma in EAST[END_REF]. Different assumptions should therefore be made on the neutral average velocity v n , which would change the mean free paths to be inserted in (3), but not the validity of the model, as long as the geometric hypotheses of the model hold (half of the atoms directed towards the PFR and half to the SOL at the atom source location). This simple model can be easily tested in experiments, where the ratio of neutral pressures in the SOL and in the PFR could be considered as an approximation of the ratio of the neutral fluxes to the two regions, while the temperature and density at the target can be inferred from Langmuir probes measurements.

Conclusion

The effect of the baffle closure on the TCV edge plasma has been investigated by means of 2D fluid simulations performed with the SolEdge2D-EIRENE code, taking into account the realistic geometry for plasma-facing components. A first set of simulations of low collisionality plasmas, comparable to previous SOLPS-ITER cases [START_REF] Fasoli | TCV heating and divertor upgrades[END_REF], has been analysed. Results show that an intermediate-length baffle, similar to the one installed at present on TCV, is able to optimise the neutral compression ratio, increasing it by at least a factor 4 with respect to the unbaffled case in these attached conditions. These results confirm previous SOLPS-ITER simulations, although the degradation of neutral compression ratio for longer outer baffles is found to be substantially weaker in SolEdge2D-EIRENE, probably because of an overestimation of the outer boundary recycling in the past work. In such low-collisionality, attached plasmas, the average neutral pressure in the divertor is not primarily determined by the outer baffle. Instead, the main reservoir of neutral particles is the PFR. The reason for this is that the D 2 molecules recycling from the target get dissociated in the divertor leg, and the resulting deuterium atoms are more likely to reach the PFR than the main SOL. As shown by a simplified analytical model, this behaviour is related to the asymmetry of the divertor radial profiles of electron density and temperature, and associated differences in the ionisation probability of the neutral atoms travelling towards the PFR and the main SOL, respectively. Therefore, as long as the divertor leg is not transparent to the deuterium molecules traveling back towards the leg after desorption from the wall, neutral particles can be well confined into the PFR. In the same upstream conditions, the roles of the inner and of the outer baffle have been disentangled by performing two simulations where only one of the two components is present at a time. The case including only the outer baffle is quantitatively the one approaching most the performances obtained by the complete baffle. Both baffles, nevertheless, are effective in lowering locally the temperature, and thus the inner baffle is still potentially interesting for detachment studies at the inner target. The parameter space explored by previous SOLPS baffle length scan has been extended considering multiple combinations of input power and upstream electron density, in particular considering cases at higher collisionalities. Increasing baffle closure is found to increase monotonically the ionisation front distance from the outer strike point, allowing recycled neutral atoms to freely fly to the SOL and then to the main chamber. As a result, the efficiency of the baffle in inhibiting the movement of neutrals to the main chamber is improved with respect to attached cases, leading to compression factors up to 25 times higher than unbaffled cases. For high densities, the optimum compression ratio is obtained with Baffle 4, while for Baffle 5, depending on the level of input power, either a significative recycling occurs on the baffle tip, or the ionisation front moves too close to the X-point, reducing plasma plugging and allowing neutrals to escape from the divertor region. A key observation is also that in some cases (low density, low power), even though an increase in the outer baffle length can still lead to an improved compression ratio, the peak heat flux on the baffle tip becomes a large fraction of the peak target flux, which would be a concern for a reactor. A baffle length corresponding to the presented Baffle 4 scenario may lead to increased neutral compression ratios with respect to the ones obtained with the present baffle, and this without an excessive heating of the outer baffle. While in this work we have considered a purely diffusive perpendicular transport, sim-ulations including drifts will be carried out in a near future. Drifts are expected to lead to a different imbalance between inner and outer divertor (see e.g. [START_REF] Christen | Exploring drift effects in TCV single-null plasmas with the UEDGE code[END_REF]), depending on toroidal field direction, and possibly cause an additional neutral influx into the confined region [START_REF] Reimold | The high field side high density region in solps modeling of nitrogen-seeded h-modes in asdex upgrade[END_REF]. The results of more complex simulations will be interpreted also following the guidelines given by this work, where we have highlighted how the target conditions and the ionisation source distribution can affect the neutral compression ratio for a given baffle geometry. A more precise description of cross-field transport in the far SOL could also quantitatively impact the particle recycling on the baffles. This calls for turbulent simulations including neutral dynamics and a realistic wall geometry.

Figure 1 :

 1 Figure 1: Example of parallel Mach number distribution in the SolEdge2D domain for a baffled TCV plasma. The baffle tiles are coloured in grey.

Figure 2 :

 2 Figure 2: Simulated wall geometry in the different baffle cases. The geometry of the inner baffle is the same in all cases.

Figure 3 :

 3 Figure 3: a): Electron density at the outer midplane in the low-collisionality case, in function of the baffle length. The dashed black vertical line represents the separatrix, while the red vertical line represents the first wall. b) Upstream (outer midplane) electron temperature. c) Upstream neutral density n n = n D 0 + 2n D 2 .

Figure 4 :

 4 Figure 4: a): Electron density profiles at the outer target in the low-collisionality case, as function of the baffle length. b) Electron temperature at the outer target.

Figure 5

 5 Figure 5: a) Total heat flux projected on the wall surface at the outer strike point, superimposed to the one on the outer baffle, for different baffle lengths. b) Ratio of the peak particle flux (Γ) projected on the wall surface at the baffle and at the outer strike point, and maximum temperature at the baffle.

Figure 6 :

 6 Figure 6: a): Electron density at the inner target in the low-collisionality case, in function of the baffle length. b) Electron temperature at the inner target.

Figure 7 :

 7 Figure 7: a) Electron temperature at the outer target in the low-collisionality case, for geometries without baffle, with HFS or LFS baffle 4 only, and with the full Baffle 4. b) Electron temperature at the inner target.

Figure 8 :

 8 Figure 8: 2D map of the net ion source (ionisation plus recombination) in the different baffle cases, with n u = 3.5 • 10 19 m -3 and P in = 1.2 M W . In the first panel, contour lines indicate electron temperature levels. In the other panels, the values of the electron temperatures used for contours are the same as in the first panel.

Figure 9 :

 9 Figure 9: Ionisation front distance from the outer strike point, along the outer divertor leg, for simulations with different input power and upstream density. The red dashed line corresponds to the position of the X-point.

Figure 10

 10 Figure 10: a) Neutral compression factor for simulations with different input power and upstream density. b) Ratio of compression factor with respect to the unbaffled case.

Figure 11 :

 11 Figure 11: Neutral density in a non-baffled case at high density (n u = 3.5 • 10 19 m -3 ) and a) high power (1.2 M W ), and b) low power (0.3 M W ).

Figure 12 :

 12 Figure 12: a): D 0 flux near the outer strike point in the case with no baffle, n u = 3.5•10 19 m -3 and P = 1.2 M W . Arrow lengths are proportional to the flux magnitude. Cyan lines represent flux surfaces, and the magenta one represents the separatrix. The blue and the red lines are the portion of flux surfaces over which the flux is evaluated. b) D 0 atom and D 2 molecule fluxes across the blue and red surfaces indicated in the a) panel. The flux is positive if directed from the separatrix towards the considered surface. c) Same plot as a), for the case with n u = 3.5 • 10 19 m -3 and P = 0.3 M W . d) Same plot as b), for the case with low input power.

Figure 13 :

 13 Figure 13: Ratio of the neutral atom fluxes to the Scrape-Off Layer, and to the Private Flux Region. The contour line represent the simple model described by (3), the coloured dots represent the values calculated from SolEdge2D-EIRENE simulations.

Table 1

 1 lists the distance of the baffle tip from the separatrix for each considered case.The distance of the baffle from the separatrix is also measured in SOL heat flux

		ρ b	∆ρ/λ q
	No Baffle	1.083	5.9
	HFS Baffle	1.057	4.1
	LFS Baffle 2 1.120	8.6
	LFS Baffle 3 1.069	4.9
	LFS Baffle 4 1.043	3.1
	LFS Baffle 5 1.025	1.8

Table 1 :

 1 Normalised flux coordinate of the closest point of the baffle (or of the outer wall in the No Baffle case), with respect to the separatrix, and distance from the separatrix of the same point, measured in λ q .

Table 2 :

 2 . The LFS baffle 4 in table2indicates the geometry, that will be discussed in section 3.3, including only the outer baffle of Baffle 4. Summary of the electron upstream density and input power imposed in the presented simulations. The density value is imposed at the outer midplane, at the separatrix position.

		n e,u (10 19 m -3 ) P in (M W )
	No Baffle	1.8; 3.5	0.3; 1.2
	HFS baffle	1.8	1.2
	Baffle 2	1.8; 3.5	0.3; 1.2
	Baffle 3	1.8; 3.5	0.3; 1.2
	Baffle 4	1.8; 3.5	0.3; 1.2
	LFS baffle 4	1.8	1.2
	Baffle 5	1.8; 3.5	0.3; 1.2

Table 3 :

 3 21 el/s) Radiated power (kW ) In the second column, values of the gas puff in the different baffle configurations needed to ensure a fixed upstream density. In the third column, the values of the power radiated in the simulation domain.

	No Baffle	1.4	360
	HFS Baffle	1.6	390
	Baffle 2	1.9	400
	Baffle 3	2.0	410
	Baffle 4	1.9	380
	LFS baffle 4	1.8	330
	Baffle 5	2.1	340

DIII-D, in experiments where a closed divertor configuration was compared to an open one

Acknowledgements

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work was supported in part by the Swiss National Science Foundation. This work was performed within the 3rd cycle of MARCONI-FUSION HPC. The required computational resources were allocated under the project PEXUPG.