M.D Romain Rey
email: romain.rey@ch-le-vinatier.fr

Ph.D Marie-Françoise Suaud-Chagny

Ph.D Anne-Lise Bohec

M.D Jean-Michel Dorey

' Amato

Ryad Tamouza

M.D Marion Leboyer

M.D Thierry D'amato

Overexpression of complement component C4 in the dorsolateral prefrontal cortex, parietal cortex, superior temporal gyrus and associative striatum of patients with schizophrenia

Keywords: Schizophrenia, Complement component 4, Neuronal plasticity, Brain, Leucocytes, Gene expression

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

Introduction

Schizophrenia (SZ) affects approximately 1% of the worldwide population [START_REF] Laidi | Factors associated with direct health care costs in schizophrenia: Results from the FACE-SZ French dataset[END_REF] and is responsible for a dramatic increase in mortality due to somatic diseases (especially those related to inflammatory processes i.e. metabolic, cardiovascular pathology and cancers) [START_REF] Laursen | Excess early mortality in schizophrenia[END_REF]. Thus, SZ can be considered as a systemic disorder in which pathological processes take place not only at the cerebral level but also in peripheral tissues [START_REF] Al-Diwani | Psychosis: an autoimmune disease?[END_REF]. Although SZ pathogenesis is partly understood, there is strong evidence that SZ is a complex trait resulting from genetic and environmental influences [START_REF] Sullivan | Schizophrenia as a complex trait: evidence from a meta-analysis of twin studies[END_REF].

Among the several susceptibility loci for SZ identified by Genome Wide Association Studies, the strongest genetic association involves variation in the major histocompatibility complex (MHC) locus (Schizophrenia Working Group of the Psychiatric Genomics Consortium, 2014). This latter hosts the human leukocyte antigens (HLA) loci that encode cell surface proteins essential for the immunological recognition of self and non-self in vertebrates. The MHC/HLA cluster is physically divided into three regions corresponding to the HLA-class I, II and III clusters. Class III genes encode components of the Complement system which consists of at least 30 circulating and cell-surface proteins that interact with each other leading to the elimination of pathogens while protecting the self from subsequent damage [START_REF] Presumey | Complement System in Neural Synapse Elimination in Development and Disease[END_REF]. At the cerebral level, components of the classical Complement cascade also participate to non-immunological processes such as the elimination of synapses [START_REF] Schafer | Microglia sculpt postnatal neural circuits in an activity and complement-dependent manner[END_REF][START_REF] Stevens | The classical complement cascade mediates CNS synapse elimination[END_REF]; this so-called "pruning" occurs during normal postnatal development. Among the various proteins involved in the classical pathway, the Complement component 4 (C4) is a critical factor [START_REF] Stevens | The classical complement cascade mediates CNS synapse elimination[END_REF] previously implicated in the pruning process of mouse models (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016).

In SZ, accumulating evidence support the hypothesis of a disruption of the synaptic pruning in the brain during adolescence [START_REF] Johnson | Pruning hypothesis comes of age[END_REF][START_REF] Rocco | Alterations in a Unique Class of Cortical Chandelier Cell Axon Cartridges in Schizophrenia[END_REF].

Consistently, recent results have established a link between the C4 locus (C4A and C4B loci) and abnormal synaptic pruning in SZ patients (Gandal et al., 2018b(Gandal et al., , 2018a;;Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016). In six different brain regions of SZ patients and healthy controls (HC), it has been shown that C4A and C4B expressions are under the genetic control of various C4 molecular structures (Gandal et al., 2018b; Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016).

Notably, the increase of C4A expression parallels that of the C4A gene copy numbers on the one hand and the insertion of a human endogenous retroviral (HERV) element on the other. Moreover, each C4 allele is associated with schizophrenia risk in proportion to its tendency to produce greater expression of C4A in the brain [START_REF] Fromer | Gene expression elucidates functional impact of polygenic risk for schizophrenia[END_REF]Gandal et al., 2018b;Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016).

Consistently, an overexpression of C4A has been identified in the total cerebral cortex (Gandal et al., 2018a), as well as in 6 different brain regions (namely, the prefrontal, anterior cingulate, orbital frontal, parietal cortices, the cerebellum and the corpus callosum) of SZ patients vs. HC (Gandal et al., 2018b;Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016). Furthermore, a C4B overexpression has been reported in the prefrontal cortex (PFC) of SZ patients vs. HC (Gandal et al., 2018b) suggesting a potential involvement of C4B in SZ pathogenesis. Altogether these data implicate both C4A and C4B overexpression in SZ pathogenesis [START_REF] Woo | The complement system in schizophrenia: where are we now and what's next?[END_REF].

To assess the clinical and biological significance of the present knowledge in SZ patients, alterations previously reported should be replicated and extended to other brain regions relevant to SZ. In this regard, C4 expression measured by microarrays, which reflects the combined expression of C4A and C4B genes, constitutes a valuable resource. Moreover, it remains unknown whether cerebral and peripheral C4 expression levels are related. A single study compared C4A expression in the peripheral blood mononuclear cells (PBMCs) of SZ patients vs. HC and no difference was found (Melbourne et al., 2018). Additional studies in peripheral tissues are needed since they are considered as promising and readily accessible surrogate systems to study the molecular mechanisms implicated in SZ [START_REF] Cai | Is human blood a good surrogate for brain tissue in transcriptional studies?[END_REF][START_REF] Kálmán | Human dermal fibroblasts in psychiatry research[END_REF][START_REF] Lavoie | Application of olfactory tissue and its neural progenitors to schizophrenia and psychiatric research[END_REF].

Using the bio-informatic application shinyGEO, we aimed to identify altered C4 expression (reflecting the combined expression of C4A and C4B genes) both at the cerebral and peripheral level in SZ patients. We compared C4 expression between SZ patients and HC (i) in postmortem cerebral samples from 7 different brain regions and (ii) in 4 peripheral tissues from independent samples. Finally, in order to evaluate the neurobiological relevance of the changes identified in peripheral tissues, we compared them to those observed in brain regions relevant to SZ.

Material and Methods

Search and inclusion criteria of primary datasets

Gene Expression Omnibus (GEO) database provides microarray expression results from postmortem brain or peripheral tissues samples from SZ patients and HC, along with demographic, clinical and quality data [START_REF] Barrett | NCBI GEO: archive for functional genomics data sets--update[END_REF]. With the aim to identify altered expression of C4 genes both at the central and peripheral level in SZ patients, we explored GEO database for datasets providing microarray expression results from SZ patients and HC.

Relevant microarray datasets were searched using the following search terms:

(("schizophrenia"[MeSH Terms] OR schizophrenia[All Fields]) AND "Homo sapiens"[porgn]) AND "Homo sapiens"[porgn] AND ("gse"[Filter] AND "Expression profiling by array" [Filter]).

We included datasets from original studies (i) involving brain or peripheral tissues samples from SZ patients and HC and (ii) using the Affymetrix Human Genome U133 plus 2.0 (HG-U133_Plus_2) or Affymetrix Human Gene 1.0 ST (Human Gene 1.0 ST) or Affymetrix Human Gene 1.1 ST (Human Gene 1.1 ST) arrays. These chips can technically interrogate C4 expression. Human Gene 1.0 ST and Human Gene 1.1 ST arrays exhibit comparable detection thresholds and are highly concordant with HG-U133_Plus_2 array [START_REF] Pradervand | Affymetrix Whole-Transcript Human Gene 1.0 ST array is highly concordant with standard 3' expression arrays[END_REF][START_REF] Robinson | A comparison of Affymetrix gene expression arrays[END_REF].

In this study, eight independent GEO datasets were included [START_REF] Barnes | Transcription and pathway analysis of the superior temporal cortex and anterior prefrontal cortex in schizophrenia[END_REF][START_REF] Cattane | Altered gene expression in schizophrenia: findings from transcriptional signatures in fibroblasts and blood[END_REF][START_REF] Chen | The transcription factor POU3F2 regulates a gene coexpression network in brain tissue from patients with psychiatric disorders[END_REF]Chen et al., , p. 2, 2013;;[START_REF] Horiuchi | Molecular signatures associated with cognitive deficits in schizophrenia: a study of biopsied olfactory neural epithelium[END_REF][START_REF] Lanz | Postmortem transcriptional profiling reveals widespread increase in inflammation in schizophrenia: a comparison of prefrontal cortex, striatum[END_REF]Maycox et al., 2009;[START_REF] Van Beveren | Marked reduction of AKT1 expression and deregulation of AKT1-associated pathways in peripheral blood mononuclear cells of schizophrenia patients[END_REF], obtained from 196 SZ patients and 182 HC. The included GEO datasets provided data from seven different brain regions relevant to SZ [START_REF] Grot | Abnormal prefrontal and parietal activity linked to deficient active binding in working memory in schizophrenia[END_REF]McCutcheon et al., 2019;[START_REF] Singh | Evidence for regional hippocampal damage in patients with schizophrenia[END_REF][START_REF] Yeganeh-Doost | The role of the cerebellum in schizophrenia: from cognition to molecular pathways[END_REF] and four peripheral tissues (Table 1). All the data used in this project were acquired in previous studies, all of which conformed to Ethical Standards [START_REF] Barnes | Transcription and pathway analysis of the superior temporal cortex and anterior prefrontal cortex in schizophrenia[END_REF]Cattane et al., 8 2015;[START_REF] Chen | The transcription factor POU3F2 regulates a gene coexpression network in brain tissue from patients with psychiatric disorders[END_REF]Chen et al., , p. 2, 2013;;[START_REF] Horiuchi | Molecular signatures associated with cognitive deficits in schizophrenia: a study of biopsied olfactory neural epithelium[END_REF][START_REF] Lanz | Postmortem transcriptional profiling reveals widespread increase in inflammation in schizophrenia: a comparison of prefrontal cortex, striatum[END_REF]Maycox et al., 2009;[START_REF] Van Beveren | Marked reduction of AKT1 expression and deregulation of AKT1-associated pathways in peripheral blood mononuclear cells of schizophrenia patients[END_REF].

Demographic characteristics and quality data

For each included GEO dataset, the quality data of the samples and demographic characteristics of the subjects who provided brain or peripheral tissues are summarized in Table 2 andTable 3, respectively. There was no significant difference in age, sex distribution, postmortem interval (PMI) and RNA integrity number (RIN) between the SZ patient and HC groups. For the brain pH, a significant difference was observed in the anterior PFC BA10 (p=0.019) and in the superior temporal gyrus (STG) (p=0.002).

Statistical analysis

XLSTAT software (XLSTAT 2017: Data Analysis and Statistical Solution for Microsoft Excel.

Addinsoft, Paris, France, 2017) was used to perform statistical analysis. For each included GEO dataset, demographic characteristics of subjects and quality data of samples in HC and SZ patient groups were compared using unpaired t-test (for age, PMI, brain pH and RIN), and Fisher exact test (for gender).

For each tissue, we used shinyGEO application to realize differential expression analysis between SZ patients and HC [START_REF] Dumas | shinyGEO: a web-based application for analyzing gene expression omnibus datasets[END_REF]. shinyGEO is implemented using R [https://www.r-project.org/] and shiny [http://shiny.rstudio.com/]. shinyGEO downloads processed gene expression datasets from GEO using GEOquery package [START_REF] Davis | GEOquery: a bridge between the Gene Expression Omnibus (GEO) and BioConductor[END_REF]. C4 expression values are then normalized using HSP90AB1 as the reference housekeeping gene. HSP90AB1 was selected based on the following criteria: (i) HSP90AB1 is one of the endogenous genes listed by Casares as potential housekeeping genes for microarray analysis [START_REF] Casares | A Simple Method for Optimization of Reference Gene Identification and Normalization in DNA Microarray Analysis[END_REF], (ii) HSP90AB1 and C4 genes are involved in different cellular functions, (iii) there was no significant difference in HSP90AB1 expression between the SZ patients and HC groups in any brain region or peripheral tissue. Normalized C4 expression values are log2-transformed to stabilize the variance.

ANCOVA testing was conducted to evaluate whether normalized C4 expression was impacted by relevant covariates. In each brain region and peripheral tissue, ANCOVA analysis was conducted using the normalized C4 gene expression as a dependent variable and with age, PMI, pH and RIN as quantitative independent variables, and sex as categorical independent variable. Normal distribution was tested using Shapiro-Wilk test. For differential expression, exact pvalues were calculated using unpaired, two-tailed t-tests. When a deviation from normality was detected, exact p-values were calculated using unpaired, two-tailed Mann-Whitney U tests. In case of violation of the equal variance assumption (Supplementary Tables 12), exact p-values were calculated using unpaired, two-tailed Welch tests. Gene expression comparisons were considered to be statistically significant for p<0.05.

Results

Demographic characteristics of the subjects and quality characteristics of the samples

ANCOVA testing of each potential covariate (age, sex, PMI, pH, RIN) revealed no significant influence on normalized C4 expression in any of the brain regions or peripheral tissues, except in the cerebellum where the pH was significant (pH=0.014).

Differential expression analysis in the brain tissues

Compared to HC, we identified a significant overexpression of C4 in the DLPFC (BA46) (fold change=1.46; p=0.005), STG (BA22) (fold change=1.78; p=0.035), parietal cortex (fold change=1.20; p=0.039) and associative striatum (fold change=1.32; p=0.034) of SZ patients (Fig. 1). In the anterior PFC (BA10) of SZ patients vs. HC, there was a trend to C4 overexpression (fold change=1.37; p=0.076). No alterations were found in the hippocampus and cerebellum of SZ patients vs. HC.

Differential expression analysis in the peripheral tissues

No significant difference in C4 expression was identified in the olfactory epithelium, skin fibroblasts, lymphoblastoid cell lines (LCLs) and PBMCs of SZ patients vs. HC (Fig. 2).

Discussion

Compared to HC, we observed a C4 overexpression in the DLPFC (BA46), STG (BA22), parietal cortex and associative striatum of SZ patients. At the peripheral level, no difference in C4 expression was observed in SZ patients vs. HC. All the original studies from which are derived the included datasets used a genome-wide approach. As a principle, the expression of all genes was analyzed, including C4. However, those results were not discussed in the original experiments. The present study re-analyzed the original data using a candidate-gene approach. Since only C4 gene expression was re-analyzed in each dataset, no requirement for multiple tests correction was needed. Such an approach allowed us to extend previous knowledge on schizophrenia-associated C4 overexpression to other brain regions.

At the cerebral level, our results expand previous evidence reporting C4A overexpression in the total cerebral, prefrontal, anterior cingulate, orbital frontal, parietal cortices, cerebellum and corpus callosum (Gandal et al., 2018b(Gandal et al., , 2018a;;Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016), C4B overexpression in the PFC (Gandal et al., 2018b;[START_REF] Pérez-Santiago | A combined analysis of microarray gene expression studies of the human prefrontal cortex identifies genes implicated in schizophrenia[END_REF] and C4A/C4B overexpression in the thalamus [START_REF] Chu | An integrated genomic analysis of gene-function correlation on schizophrenia susceptibility genes[END_REF] in SZ patients.

First, in the PFC of SZ patients vs. HC, we report C4 overexpression in BA46 and a trend to C4 overexpression in BA10. This refines previous results reporting C4A and/or C4B overexpression in the PFC (mixed data from BA46, BA9 and BA10) and C4B overexpression in BA9 of SZ patients vs. HC (Gandal et al., 2018b;[START_REF] Pérez-Santiago | A combined analysis of microarray gene expression studies of the human prefrontal cortex identifies genes implicated in schizophrenia[END_REF]. As an exploratory analysis with shinyGEO, we replicated C4 overexpression (fold change=2.03; p=0.003) in the BA46 of 29 SZ patients and 30 HC from another independent GEO dataset, GEO: GSE21138. These results suggest that C4 is overexpressed in different sub-regions of the PFC in SZ patients.

Moreover, we identified a C4 overexpression in the parietal cortex of SZ patients vs. HC. Our findings are consistent with the C4A overexpression found in the parietal cortex of SZ patients (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016) and support the correlation between C4A gene copy number and neuropil contraction observed in the parietal regions of young adult-onset SZ patients [START_REF] Prasad | Neuropil contraction in relation to Complement C4 gene copy numbers in independent cohorts of adolescent-onset and young adult-onset schizophrenia patients-a pilot study[END_REF]. Furthermore, we observed for the first time C4 overexpression in the associative striatum and STG (BA22) of SZ patients vs. HC. In the associative striatum, C4 overexpression is consistent with glial activation and neuro-inflammation, as well as increased expression of pro-inflammatory transcripts in drug-naïve first episode psychosis (FEP) patients [START_REF] Plitman | Elevated Myo-Inositol, Choline, and Glutamate Levels in the Associative Striatum of Antipsychotic-Naive Patients With First-Episode Psychosis: A Proton Magnetic Resonance Spectroscopy Study With Implications for Glial Dysfunction[END_REF][START_REF] Sivaraman | Neurometabolic abnormalities in the associative striatum in antipsychotic-naïve first episode psychosis patients[END_REF] and SZ patients [START_REF] Lanz | Postmortem transcriptional profiling reveals widespread increase in inflammation in schizophrenia: a comparison of prefrontal cortex, striatum[END_REF], respectively. In the STG, C4 overexpression is in line with the involvement of immune related genes in synaptic events in the BA22 region of chronic SZ patients [START_REF] Schmitt | Regulation of immune-modulatory genes in left superior temporal cortex of schizophrenia patients: a genome-wide microarray study[END_REF].

Notably, the C4 expression changes identified in the present study were of modest size (fold change (FC) from 1.3 to 1.8). Consistently, Sekar et al. reported that the median C4A expression in brain tissues was 1.4-fold greater in SZ patients compared to HC (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016).

Moreover, altered expression changes identified in SZ patients compared to HC are usually modest. Indeed, in the postmortem DLPFC, hippocampus and associative striatum of SZ patients versus HC, after false discovery rate correction, 99% of the differentially expressed genes exhibit a FC<|2| [START_REF] Lanz | Postmortem transcriptional profiling reveals widespread increase in inflammation in schizophrenia: a comparison of prefrontal cortex, striatum[END_REF]. Mixed results are available regarding the functional consequences of such modest gene expression changes. On the one hand, in SZ patients, small gene expression changes have been associated with abnormal brain level of the encoded protein [START_REF] Gibbons | SMAD4 protein is decreased in the dorsolateral prefrontal and anterior cingulate cortices in schizophrenia[END_REF][START_REF] Narayan | Molecular profiles of schizophrenia in the CNS at different stages of illness[END_REF][START_REF] Pandey | Abnormal gene and protein expression of inflammatory cytokines in the postmortem brain of schizophrenia patients[END_REF], and cognitive deficits [START_REF] Cai | Altered levels of immune cell adhesion molecules are associated with memory impairment in schizophrenia and healthy controls[END_REF][START_REF] Horiuchi | Molecular signatures associated with cognitive deficits in schizophrenia: a study of biopsied olfactory neural epithelium[END_REF]. In animal models of SZ as well, association between modest brain expression changes and behavioral abnormalities have been reported [START_REF] Hsueh | Immune imbalance of global gene expression, and cytokine, chemokine and selectin levels in the brains of offspring with social deficits via maternal immune activation[END_REF]. In contrast, in SZ patients, other experiments failed to report that small gene expression changes have functional consequences on the encoded protein level [START_REF] Boerrigter | Using blood cytokine measures to define high inflammatory biotype of schizophrenia and schizoaffective disorder[END_REF][START_REF] Sinclair | Dysregulation of glucocorticoid receptor co-factors FKBP5, BAG1 and PTGES3 in prefrontal cortex in psychotic illness[END_REF][START_REF] Uhrig | Reduced oxytocin receptor gene expression and binding sites in different brain regions in schizophrenia: A post-mortem study[END_REF] or clinical scales [START_REF] Ansoleaga | Decrease in olfactory and taste receptor expression in the dorsolateral prefrontal cortex in chronic schizophrenia[END_REF][START_REF] Gouvea | Gene expression alterations related to mania and psychosis in peripheral blood of patients with a first episode of psychosis[END_REF]. In this regard, while consistent with previous evidence involving C4 overexpression in SZ pathogenesis (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016), our results require additional studies to demonstrate that C4 overexpression in the brain of SZ patients is associated with abnormal C4 protein levels, disease severity and functional impairment.

Altogether our results are consistent with the hypothesis of an excessive Complement activity in schizophrenic disorders (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016). Previously, Sekar et al. showed that each of the four common C4 structural haplotypes is associated with schizophrenia risk in proportion to its tendency to produce higher C4A brain expression (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016). In SZ patients, these results suggest a genetically-determined lifelong high expression of C4. Since the average age of the brains investigated in the present study ranged from 42 to 73 years, our findings are consistent with the persistence of C4 overexpression in the brain of SZ patients long after the synaptic pruning period. However, since our samples were obtained long after adolescence, we could not demonstrate that C4 overexpression is already present during adolescence. To date and to our knowledge, no human study has explored C4 brain expression during adolescence.

This may be due to the scarcity of brain collection tissues which are mainly obtained from old subjects. Since our present results suggest that peripheral C4 expression poorly reflects C4 brain expression, future research needs to gain access to C4 expression in the central nervous system during human adolescence. In this regard, measuring C4 expression in cerebrospinal fluid, although more invasive and expensive as compared to peripheral measurements, may provide meaningful information about C4 expression during the synaptic pruning period occurring in adolescence.

Paradoxically, while increasing evidence implicate the hippocampus and the cerebellum in SZ pathogenesis [START_REF] Yeganeh-Doost | The role of the cerebellum in schizophrenia: from cognition to molecular pathways[END_REF][START_REF] Nakahara | Hippocampal subregion abnormalities in schizophrenia: A systematic review of structural and physiological imaging studies[END_REF][START_REF] Lieberman | Hippocampal dysfunction in the pathophysiology of schizophrenia: a selective review and hypothesis for early detection and intervention[END_REF][START_REF] Ding | Cerebellar structural and functional abnormalities in first-episode and drug-naive patients with schizophrenia: A meta-analysis[END_REF], no significant difference in C4 expression was found in these regions in SZ patients vs. HC. To date, findings related to C4 genes expression in these regions in SZ patients are mixed. Regarding the hippocampus, while increased predicted C4A expression was associated with poorer episodic memory performance in both SZ patients and HC [START_REF] Donohoe | Genetically predicted complement component 4A expression: effects on memory function and middle temporal lobe activation[END_REF], C4A gene copy number was not associated with hippocampic neuropil contraction in SZ patients [START_REF] Prasad | Neuropil contraction in relation to Complement C4 gene copy numbers in independent cohorts of adolescent-onset and young adult-onset schizophrenia patients-a pilot study[END_REF]. Additionally, no change was observed in the hippocampic level of C4 protein in a neurodevelopmental mouse model of SZ (Mattei et al., 2017). Regarding the cerebellum, our results are in line with those of Prasad et al. who In the olfactory epithelium, skin fibroblasts, LCLs and PBMCs of SZ patients vs. HC, we observed no significant difference in C4 expression. Although skin fibroblasts and olfactory epithelium are considered as promising surrogate systems for the study of SZ pathogenesis [START_REF] Kálmán | Human dermal fibroblasts in psychiatry research[END_REF][START_REF] Lavoie | Application of olfactory tissue and its neural progenitors to schizophrenia and psychiatric research[END_REF], our results suggest that they may not be affected by transcriptional alterations of C4.

The absence of difference in C4 expression in the lymphoblasts of SZ patients vs. HC is consistent with a previous RNA sequencing study on LCLs [START_REF] Sanders | Transcriptome study of differential expression in schizophrenia[END_REF]. In this latter study, no difference in C4 expression was observed although an overexpression of four other Complement components was reported. In SZ disorders, these results suggest that C4 overexpression may be specific to the cerebral tissue while other alterations of the Complement system may be detected at the systemic level possibly in relation with other Complement-mediated processes.

In PBMCs, the absence of significant difference in C4 expression is consistent with the single previous study exploring C4A mRNA expression in the PBMCs of SZ patients vs. HC (Melbourne et al., 2018). When considering C4 protein levels in the peripheral blood of SZ patients, discrepant results reporting increase [START_REF] Cooper | Schizophrenia-risk and urban birth are associated with proteomic changes in neonatal dried blood spots[END_REF][START_REF] Hakobyan | Classical pathway complement activity in schizophrenia[END_REF]Mayilyan et al., 2006;[START_REF] Walss-Bass | X-Aptamer Technology Identifies C4A and ApoB in Blood as Potential Markers for Schizophrenia[END_REF], decrease (Mayilyan et al., 2008) or no difference [START_REF] Ali | Redox dysregulation, immuno-inflammatory alterations and genetic variants of BDNF and MMP-9 in schizophrenia: Pathophysiological and phenotypic implications[END_REF][START_REF] Idonije | Complement factors in newly diagnosed Nigerian schizoprenic patients and those on antipsychotic therapy[END_REF][START_REF] Kopczynska | Complement system biomarkers in first episode psychosis[END_REF][START_REF] Sória | Increased serum levels of C3 and C4 in patients with schizophrenia compared to eutymic patients with bipolar disorder and healthy[END_REF] have been observed. Specifically, C4 protein level has been found increased in newborn babies who later develop SZ [START_REF] Cooper | Schizophrenia-risk and urban birth are associated with proteomic changes in neonatal dried blood spots[END_REF], Ultra-High Risk patients [START_REF] Laskaris | Investigation of peripheral complement factors across stages of psychosis[END_REF], in advanced stages of SZ disorders or in chronic patients [START_REF] Laskaris | Investigation of peripheral complement factors across stages of psychosis[END_REF] contrasting with normal C4 protein levels in FEP patients [START_REF] Kopczynska | Complement system biomarkers in first episode psychosis[END_REF][START_REF] Laskaris | Investigation of peripheral complement factors across stages of psychosis[END_REF]. However, among FEP patients, recent findings suggest that increased C4 protein levels may be restricted to treatment non-responders (Mondelli et al., 2020). The mismatch between mRNA and protein results might be related to the biological source (i.e. plasma or serum), the specific stages of SZ illness, the techniques involved in the measurement of mRNA and protein levels and the various levels of regulation between transcript and protein product [START_REF] Maier | Correlation of mRNA and protein in complex biological samples[END_REF]. Notably, while most studies investigating mRNA-protein expression correlation used a genome-wide approach (correlation between mRNA expression and protein expression across all genes), only a limited number of individual gene correlation analyses (correlation between the expression of a mRNA and its protein product across multiple samples or conditions) have been performed [START_REF] Koussounadis | Relationship between differentially expressed mRNA and mRNA-protein correlations in a xenograft model system[END_REF]. This lack of individual gene correlation analyses is relevant since higher correlations have been observed for certain classes of genes while poorer correlations have been attributed to post-transcriptional regulation [START_REF] Koussounadis | Relationship between differentially expressed mRNA and mRNA-protein correlations in a xenograft model system[END_REF]. To date and to our knowledge, no individual gene correlation analysis has explored both C4 expression and C4 protein level in brain or peripheral tissues of SZ patients vs. HC. It may thus be worthwhile for future studies to look for a correlation between C4 mRNA and C4 protein level in a given tissue.

All these findings raise the possibility that direction and distribution of C4 altered expression in brain and peripheral tissues, may depend on the characteristics of SZ patients.

On the one hand, the heterogenous clinical features of the included samples of SZ patients, especially the stage of the disorder, the acute or chronic status, the clinical severity, the level of treatment-resistance and the various antipsychotic treatments may constitute confounding factors. Regarding symptomatology, a positive correlation between C4A expression and PANSS positive factor scores was found in the PBMCs of SZ patients (Melbourne et al., 2018) while no results are available concerning such a correlation in the brain tissues. Therefore, we can't exclude that C4 brain overexpression identified in SZ patients may also reflect the severity of the pathological process. Unfortunately, we could not explore this issue since no information about severity of symptomatology was provided in the included GEO datasets. A single study reported no influence of antipsychotic treatments on C4A expression in the PBMCs of SZ patients vs. HC (Melbourne et al., 2018).

Since no previous study explored the influence of antipsychotics in brain tissues, a potential impact of such treatments on C4 brain expression could not be ruled out.

On the other hand, the biological heterogeneity of SZ patients may impact the observed C4 expression levels. Indeed, C4 overexpression may be restricted to a subset of SZ patients characterized by C4 alleles generating high levels of C4 mRNA (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016). This is in accordance with the concept of SZ disorders as a group of heterogeneous disorders underpinned by various mechanistic processes [START_REF] Clementz | Identification of Distinct Psychosis Biotypes Using Brain-Based Biomarkers[END_REF][START_REF] Mothi | Machine learning improved classification of psychoses using clinical and biological stratification: Update from the bipolar-schizophrenia network for intermediate phenotypes (B-SNIP)[END_REF]. More studies combining structural genetic data and gene expression data are warranted in brain and peripheral tissues to evaluate whether C4 overexpression is only observed in a subset of individuals with SZ disorders. A classification of SZ patients according to underlying biology rather than clinical symptomatology would be a further step to a precision psychiatry approach [START_REF] Fernandes | The new field of "precision psychiatry[END_REF].

In this study, the transcriptional alterations identified in cerebral tissues of SZ patients were not observed in the peripheral tissues. These discrepancies may be due to the fact that brain and peripheral tissues samples used in the present study were not derived from the same subjects. Alternatively, our results suggest that the olfactory epithelium, skin fibroblasts, LCLs and PBMCs do not reflect the brain expression of C4 in SZ patients. Our results are not consistent with previous studies reporting that blood shares significant gene expression similarities with brain tissues [START_REF] Sullivan | Evaluating the comparability of gene expression in blood and brain[END_REF]. Regarding C4 expression in SZ disorders, our results rather suggest that brain and peripheral tissues may be affected by distinct alterations [START_REF] Al-Diwani | Psychosis: an autoimmune disease?[END_REF][START_REF] Cai | Is human blood a good surrogate for brain tissue in transcriptional studies?[END_REF][START_REF] Liew | The peripheral blood transcriptome dynamically reflects system wide biology: a potential diagnostic tool[END_REF][START_REF] Sullivan | Evaluating the comparability of gene expression in blood and brain[END_REF] and that C4 overexpression may be restricted to specific brain regions in SZ disorders. Since C4 expression level is related to gene copy number and HERV status (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016) which are identical throughout the whole body, it may be suggested that additional epigenetic factors are involved in the regulation of C4 expression at the cerebral level, a wide concept named tissue-specificity. Consistently with this hypothesis, previous studies using mouse models have shown that early environmental risk factors for SZ disrupt the Complement system [START_REF] Duchatel | Increased complement component 4 (C4) gene expression in the cingulate cortex of rats exposed to late gestation immune activation[END_REF] even in the absence of genetic background (Mattei et al., 2017).

Finally, the microarrays used to acquire the GEO datasets included in the present study could not technically distinguish between C4A and C4B transcripts. Thus, the relative involvement of C4A and C4B transcripts in the C4 overexpression identified in the DLPFC (BA46), the STG (BA22), the parietal cortex and the associative striatum can't be specified.

We could not exclude the possibility that C4 overexpression may reflect C4B overexpression.

Although the majority of available results conclude that risk for SZ is associated with C4A overexpression (Gandal et al., 2018b(Gandal et al., , 2018a;;Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016), recent results also implicate C4B overexpression in SZ pathogenesis. Firstly, an increased expression of C4B was reported in the PFC and thalamus of SZ patients vs. HC [START_REF] Chu | An integrated genomic analysis of gene-function correlation on schizophrenia susceptibility genes[END_REF]Gandal et al., 2018b;[START_REF] Pérez-Santiago | A combined analysis of microarray gene expression studies of the human prefrontal cortex identifies genes implicated in schizophrenia[END_REF].

Secondly, in two independent samples of SZ patients, an association between C4B gene copy number and increased neuropil contractions was observed in various brain regions associated with SZ [START_REF] Prasad | Neuropil contraction in relation to Complement C4 gene copy numbers in independent cohorts of adolescent-onset and young adult-onset schizophrenia patients-a pilot study[END_REF]. Additionally, although mouse models provided the experimental evidence implicating C4 expression in the pruning processes (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016) such models are of limited interest to explore the specific role of C4A and C4B in the altered pruning process of SZ since mice lack the two isoforms of C4 found in humans. Altogether these results raise the hypothesis of the potential involvement of C4B overexpression in SZ pathogenesis. To further explore this issue, we performed an exploratory analysis with shinyGEO. We selected the GEO dataset GEO: GSE62191 which was acquired using a microarray specifically exploring C4B expression. In line with our latter hypothesis, we observed a trend to C4B overexpression (fold change = 1.17; p = 0.077) in the frontal cortex of 29 SZ patients vs. 30 HC. Additional studies are needed to further investigate C4B overexpression in SZ disorders.

Limits

Interpretation of the present results is affected by limiting factors. Firstly, brain and peripheral tissues were obtained from 8 different and modest-sized SZ samples. Brain tissues were obtained from rather old men and women (Table 2), whereas PBMCs were collected from younger men (mean age ± SD: 23.02 ± 4.03 for the controls and 23.90 ± 4.08 for the SZ patients). Therefore, the gene expression changes identified in the cerebral tissues may reflect the influence of age, while the absence of results in the PBMCs may be gender specific. However, previous studies observed no influence of age or sex on C4 expression in brain tissues (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016) or PBMCs (Melbourne et al., 2018) of SZ patients. Consistently, in the present study, ANCOVA testing did not report a significant influence of age or sex on normalized C4 expression in any of the brain regions or peripheral tissues. Thus, it is unlikely that age or sex explain our results. Moreover, it should be noted that the modest size of the samples may have led to type II errors, especially in the anterior PFC (BA10) where we identified a trend to C4 overexpression (FC=1.37, p=0.076). Independent, larger samples are thus needed to replicate our results.

Secondly, factors inherent in post-mortem brain studies, and beyond the investigator's control, might have influenced our results: (i) A concern is the effect of brain pH on our results since we observed a significant difference in brain pH between HC and SZ patient groups in the PFC (BA10) and STG (BA22). However, ANCOVA testing did not report a 20 significant influence of pH on normalized C4 expression in any of the brain regions or peripheral tissues, except in the cerebellum, (ii) Another limitation is the lack of information regarding potential confounding factors such as drug consumption, tobacco smoking or alcohol abuse history even if no significant effect of smoking on C4 transcript levels was observed in the PBMCs of SZ patients (Melbourne et al., 2018). Brain tissue collections associated with high-quality phenotype data are warranted to allow replication of the present results.

Thirdly, all the datasets included in the present study were acquired through microarray technology. Our results are thus subject to the methodological limitations that lies within the use of microarrays: (i) background hybridization limit gene expression measurement, especially for low abundance transcripts, (ii) probe performance may have led to specificity issues (through cross-hybridization and non-specific hybridization), (iii) only genes for which probes are designed can be explored. In contrast, RNA-sequencing (RNA-seq) has higher sensitivity and specificity and thus allows the detection of a higher percentage of differentially expressed genes, especially those with low expression. Moreover, RNA-seq can detect novel transcripts, isoforms and reveal splice variants [START_REF] Zhao | Comparison of RNA-Seq and microarray in transcriptome profiling of activated T cells[END_REF]. Recently, using RNA-seq in the prefrontal cortex of SZ patients compared to HC, Gandal et al. reported decreased expression levels of two C4A isoforms as well as an overexpressed and a decreased C4B isoforms (Gandal et al., 2018b). Thus, specific splice variants of C4A and C4B may be associated with the altered synaptic pruning in SZ and remain to be explored.

Additional RNA-seq studies are needed to disentangle the specific role of C4A and C4B splice variants to better understand the mechanisms underlying the dysregulation of pruning in SZ disorders.

Fourthly, postmortem tissue samples may have different white/grey matter ratios leading to different relative amounts of neuronal or glial transcripts in the extracted mRNA. Further research using single-cell RNA-seq techniques is needed to take into account this issue. Indeed, in comparison to traditional profiling methods that assess bulk cellular populations, single cell RNA-sequencing has the ability to study specific cell populations, allowing the study of white and grey matter-derived transcripts.

In the light of these different limits, replication studies in larger, independent samples using high-throughput sequencing techniques such as single-cell RNA-seq technology are needed to confirm, refine and extend our results. In this regard, high-quality brain tissue collections are needed to allow optimized cell dissociation and single-cell preparation, thus ensuring meaningful analyses and conclusions.

Finally, the gene expression changes identified in the present study were of modest size raising the question of whether or not they are associated with functional consequences.

Additional studies in SZ patients are thus needed to demonstrate that C4 brain overexpression is associated with abnormal C4 protein levels, disease severity and functional impairment. Especially, while our study provides additional clues towards an excessive Complement activity in the brain of SZ patients, our results do not allow us to link C4 overexpression to abnormal synaptic pruning. Hence, additional studies are needed, at different time points of life, to confirm that C4 cerebral overexpression disrupts the synaptic pruning during adolescence which in turn increases risk for schizophrenic disorders [START_REF] Johnson | Pruning hypothesis comes of age[END_REF].

Conclusions

C4 overexpression at the cerebral level in SZ patients. Consistently with a previous report, we found C4 overexpression in the DLPFC (BA46) and in the parietal cortex of SZ patients compared to HC. In SZ patients, C4 overexpression was further extended to the STG (BA22) and the associative striatum. Conversely, no significant alteration of C4 expression was observed in peripheral tissues suggesting that C4 overexpression may be specific to the cerebral tissue while other alterations of the Complement system may be detected at the systemic level. Our results support the hypothesis of an excessive Complement activity in various brain regions of SZ patients which may disrupt the synaptic pruning process occurring during adolescence.

hippocampus among matched tetrads of controls with subjects diagnosed with schizophrenia, bipolar or major depressive disorder. Transl Psychiatry 9, 151.

TABLE LEGENDS Table 1

Characteristics of the included GEO datasets.

Table 2

Demographic characteristics and quality data of the post-mortem brain samples.

Table 3

Demographic characteristics of the peripheral tissues samples.

Fig. 1 .

 1 Fig. 1. Expression of C4 in the postmortem brain tissues of SZ patients and HC subjects. Fold

Fig. 2 .

 2 Fig. 2. Expression of C4 in the peripheral tissues of SZ patients and HC subjects. Fold change

  reported no association between C4A gene copy number and cerebellum neuropil contraction in SZ patients but contrast with those of Sekar et al. who observed C4A overexpression in the cerebellum of SZ patients (Schizophrenia Working Group of the Psychiatric Genomics Consortium et al., 2016).

Unpaired t-tests and Fisher exact tests were conducted to assess group differences for continuous and discrete variables, respectively. *p<0.05

Acknowledgments

We would like to thank Jasmine Dumas and Garrett Dancik from the Department of Computer Science at Eastern Connecticut State University for the development of shinyGEO application and for their help in using the application.

Funding sources

This work was supported by the French National Research Agency (ANR) (microSCHIZ project: "Microglial activation in Complement C4-stratified schizophrenic patients and in a mouse model of C4 overexpression", [grant numbers ANR-18-NEUR-0008-01] to RT). The funding agency had no role in the study design, data collection and analysis, decision to publish and preparation of the manuscript. The content is solely the responsibility of the authors.

Data Availability Statement

The data that support the findings of this study are openly available in Gene Expression Omnibus (NCBI) at https://www.ncbi.nlm.nih.gov/geo/, reference numbers GEO: GSE53987, GEO: GSE17612, GEO: GSE35977, GEO: GSE35974, GEO: GSE21935, GEO: GSE27383, GEO: GSE73129, GEO: GSE62333, GEO: GSE21138, GEO: GSE62191.

Declaration of Competing Interest

The authors report no biomedical financial interests or potential conflicts of interest.

Eggen, B.J.L., Boddeke, E.W.G.M., Kaminska, B., Beule, D., Pombo, A., Kettenmann, H., Wolf, S.A., 2017. Maternal immune activation results in complex microglial transcriptome signature in the adult offspring that is reversed by minocycline treatment. Transl Psychiatry 7, e1120. https://doi.org/10.1038/tp.2017.80 Maycox, P.R., Kelly, F., Taylor, A., Bates, S., Reid, J., Logendra, R., Barnes


M Charlton

J J Choi

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K Lévêque

E Lim

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Positron production using a 9 MeV electron linac for the GBAR experiment

Keywords: positron, linear accelerator, antimatter, antihydrogen, gravitation

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

Introduction

An intense positron source is an indispensable constituent of all experimental setups which are used to study antihydrogen, the simplest anti-atom [START_REF] Aghion | Positron bunching and electrostatic transport system for the production and emission of dense positronium clouds into vacuum[END_REF][START_REF] Ahmadi | Antihydrogen accumulation for fundamental symmetry tests[END_REF][START_REF] Imao | Positron accumulation and manipulation for antihydrogen synthesis[END_REF][START_REF] Fitzakerley | Electron-cooled accumulation of 4×10 9 positrons for production and storage of antihydrogen atoms[END_REF]. Beyond their importance in antimatter research, positrons have been used for some time in materials science to study lattice defects and electronic structure in metals, semiconductors and other solids [START_REF] Tuomisto | Defect identification in semiconductors with positron annihilation: Experiment and theory[END_REF][START_REF] Krause-Rehberg | Positron annihilation in semiconductors[END_REF][START_REF] Coleman | Positron Beams and Their Applications[END_REF][START_REF] Schultz | Interaction of positron beams with surfaces, thin films and interfaces[END_REF][START_REF] Dupesquier | Positron spectroscopy of solids[END_REF] and as a sensitive probe in few-body atomic and molecular physics [START_REF] Charlton | Positron physics[END_REF][START_REF] Surko | Low energy positron interactions with atoms and molecules[END_REF][START_REF] Gribakin | Positron-molecule interactions: resonant attachment, annihilation and bound states[END_REF].

Positronium has also found application in a variety of fundamental and applied investigations [START_REF] Jean | Principles and Applications of Positron and Positronium Chemistry[END_REF][START_REF] Rich | Recent advances in positronium research[END_REF][START_REF] Cassidy | Experimental progress in positronium laser physics[END_REF]. Of particular relevance here is its use as a porosity diagnostic in polymers and porous oxides [START_REF] Jean | Principles and Applications of Positron and Positronium Chemistry[END_REF], via laser excitation in the elucidation of bound state leptonic physics and for applications in single-shot lifetime spectroscopy and the creation of Rydberg states [START_REF] Cassidy | Experimental progress in positronium laser physics[END_REF].

The advent of positron trapping and accumulation [START_REF] Murphy | Positron trapping in an electrostatic well by inelastic collisions with nitrogen molecules[END_REF][START_REF] Jørgensen | New source of dense, cryogenic positron plasmas[END_REF] has facilitated the development of non-neutral positron plasma technology, which has provided new possibilities to manipulate and better control beam properties [START_REF] Danielson | Plasma and trap-based techniques for science with positrons[END_REF].

In the majority of these studies, and indeed for most modern experiments involving positrons, the ability to produce near-monoenergetic, low-energy beams in vacuum is the enabling technology. In this paper we present a slow positron beam based on a compact linac. The device provides positrons for the GBAR experiment at CERN, but similar systems could serve as the basis of versatile positron spectrometers for most of the areas of contemporary interest in the field, as outlined above.

In the following sections we introduce the GBAR project, then describe the experimental setup of the positron source: the linear electron accelerator, the electron target with the positron moderator and the positron beam line.

In Section 7, 8 and 9 we discuss problems and solutions regarding radiation protection, beam diagnostics and electron background. Finally, we present the currently attained intensity of the positron source and characteristics of the beam in Section 10.

Positron source for the GBAR experiment

The GBAR collaboration aims at a precise measurement of the gravitational acceleration of antihydrogen in the gravitational field of the Earth [START_REF] Chardin | Proposal to measure the Gravitational Behaviour of Antihydrogen at Rest GBAR[END_REF][START_REF] Mansoulié | on behalf of the GBAR Collaboration, Status of the GBAR experiment at CERN[END_REF]. The GBAR scheme is based on the creation of a positive antihydrogen ion (consisting of an antiproton and two positrons), which can be then sympathetically cooled to low temperature and neutralised by laser photodetachment of one of the positrons. The resulting anti-atom is sufficiently cold for the direct observation of the gravitational free fall. The anti-ions are created in two consecutive reactions using a dense positronium (Ps) cloud that serves as a target for antiprotons: p + P s → H + e - followed by H + P s → H+ + e -. In the first step, an antiproton interacts with a positronium to create an antihydrogen atom. Subsequently this newly formed antiparticle reacts with a second positronium and produces a positive antihydrogen ion. The anti-ion formation cross section is thus proportional to the square of the positronium density, itself proportional to the positron flux.

The experiment will receive antiprotons at 100 keV kinetic energy from the new ELENA ring of the AD facility at CERN [START_REF] Bartmann | The ELENA facility[END_REF], which are then further slowed down to a few keV energy by an electrostatic decelerator. The expected intensity is 4 × 10 6 antiprotons per pulse. In order to create one anti-ion, this antiproton pulse must interact with a positronium target of order 10 10 cm -3 density. This high positronium density is obtained by implanting a pulse of the order of 10 10 positrons onto a converter consisting of nanoporous silica. The positronium is formed in an 1 µm thick porous silica layer. The short lived (125 ps lifetime) spin singlets decay quickly while the long lived (142 ns lifetime) spin triplets are released into the vacuum of a cavity and form the positronium target cloud. As each antiproton must react successively with two positronium atoms to form an anti-ion, the density of the target cloud, hence the positron pulse intensity, is a crucial factor for the success of the experiment. Positrons are first trapped in a buffer gas accumulator [START_REF] Murphy | Positron trapping in an electrostatic well by inelastic collisions with nitrogen molecules[END_REF][START_REF] Leite | Development of a buffer gas trap for the confinement of positrons and study of positronium production in the GBAR experiment[END_REF] and then collected in a high-field (5 T) Penning-Malmberg trap [START_REF] Grandemange | Piégeage et accumulation de positons issus d'un faisceau pulsé produit par un accélérateur pour l'étude de l'interaction gravitationnelle de l'antimatière[END_REF] during the 110 s time lapse between two antiproton pulses, before being ejected in an intense pulse onto the positron-positronium conversion target. In order to be trapped the positron energy must be in the eV-keV range (the so called slow positrons).

Low-energy positron generators most often use commercially available 22 Na radioactive sources. Their activity is however limited in practice to approximately 50 mCi (1.7 GBq), which in combination with a solid neon moderator [START_REF] Cassidy | Accumulator for the production of intense positron pulses[END_REF][START_REF] Clarke | Design and operation of a twostage positron accumulator[END_REF][START_REF] Cooper | A trap-based pulsed positron beam optimised for positronium laser spectroscopy[END_REF] can lead to a maximum of 10 7 low-energy positrons per second. Furthermore, the half-life of 22 Na is 2.6 years, thus the lowenergy beam intensity reduces over time and the source requires periodic and complicated replacement. Devices using nuclear reactors [START_REF] Hugenschmidt | Unprecedented intensity of a lowenergy positron beam[END_REF][START_REF] Van Veen | Positron extraction and transport in a nuclear-reactor-based positron beam[END_REF][START_REF] Liu | The intense slow positron beam facility at the PULSTAR reactor and applications in nano-materials study[END_REF][START_REF] Sato | Development of a mono-energetic positron beam line at the Kyoto University Research Reactor[END_REF] or large accelerator facilities [START_REF] Wagner | Positron annihilation lifetime and Doppler broadening spectroscopy at the ELBE facility[END_REF][START_REF] Kurihara | Intense positron beam at KEK[END_REF] can potentially provide a much higher positron flux. However, for the GBAR experiment, where a high positron intensity is crucial, a dedicated facility, with moderate size and cost, is the only feasible solution. We have thus chosen to construct a positron generator based on a low-energy linear electron accelerator because it has the potential to deliver a higher positron flux and at the same time it is compact enough to be placed in the available experimental area at CERN.

Electron linear accelerator

There have been a number of slow positron beam systems which used an electron linac as a positron source. The performance of a few of them is listed in Table 1. High-energy electrons hitting a dense metallic target abundantly generate positrons by pair production. However, these particles can only be used for beams after reduction of their energy by a positron moderator. The efficiency of the slow-positron production in the devices listed, defined as the number of slow positrons per electron impinging on the target, is in the 0.06×10 -7 -15×10 -7 range. Potentially, higher efficiencies can be achieved by increasing the electron energy. However, the actual performance depends on the geometry of the target-moderator structure and efficiency is not the sole design criterion in many high-energy, high-power electron accelerators.

Higher energy also requires a longer accelerator structure and a thicker biological shield. In the case of the GBAR source in the AD hall, the radiation dose rate outside the biological shield must be compatible with public access. Even with electron kinetic energies as low as 9 MeV, the electron bremsstrahlung radiation produces neutrons by interacting with some nuclei present in the surrounding structural materials via the (γ,n) reaction. This process leads to the creation of short-lived radioisotopes in the vicinity of the electron target, but the total activation level is low and the target can be approached immediately after switching off the linac. Above 10 MeV activation increases rapidly with energy. Dose-rate simulations showed that the size of the radiation shield at 18 MeV electron beam energy would be incompatible with the available volume and access to the target zone would be severely limited.

The GBAR electron accelerator (Fig. 1) is a water-cooled linac with a thermionic triode cathode, constructed by NCBJ (Poland). The microwave power is supplied by a 7.5 MW klystron (Thales 2157A), regulated by a solid-state modulator with pulse transformer from ScandiNova Systems. The accelerating section is composed of 18 cavities of 4.5 mm aperture radius with a total length of 900 mm. It is surrounded by a solenoid which provides a 59 mT longitudinal magnetic field. The cavity is mounted in a vertical position. The accelerator produces electrons at 9 MeV kinetic energy (with 0.5 MeV FWHM) in 2.85 µs long pulses (FWHM). The repetition rate can be varied from 2 to 300 Hz. The peak electron current is 330 mA. The energy distribution has been verified by a magnetic dipole spectrometer. The size and position of the beam spot have been optimised by a removable YAG (yttrium aluminium garnet) screen, placed between the linac and the electron target and observed by a camera. The viewport and the camera of this diagnostic device have to be removed in normal operation, as they cannot withstand the very high radiation dose. Focusing and position of the electron beam can be controlled by a triplet magnetic lens system at the exit of the linac cavity. The beam can be focused to a spot as small as 3 mm in diameter. In the positron-production setting, we slightly defocus the beam spot, to approximately 5 mm diameter, in order to avoid local overheating of the target. The klystron and the accelerating section are both equipped with a closed-cycle water cooling system.

We constructed a test installation in CEA-Saclay [START_REF] Liszkay | Present status of the low energy linac-based slow positron beam and positronium spectrometer in Saclay[END_REF] (in the following, we will refer to this system as the "Saclay source") which is based on a 4.3 MeV linac with a magnetron as microwave source. It provides electron pulses with 150 mA peak current, 2.5 µs pulse length and 200 Hz repetition rate. The Saclay source produced 2 × 10 6 slow positrons per second, a performance which is comparable with the yield of neon moderated isotope sources. The results proved that a source based on a low energy linac is a suitable device to supply positrons for the GBAR experiment. Some optimisation of the moderator and the target has been done with this facility.

Linac target

In electron-linac-based sources, positrons are mostly created by the bremsstrahlung radiation emitted by electrons impinging on a dense metallic target with high atomic number. The energy spectrum of positrons generated by electrons at 9 MeV kinetic energy extends to approximately 7 MeV. It must be reduced in order to allow their subsequent transport and trapping.

The "fast" antiparticles are slowed to an energy of a few electronvolts by a positron moderator [START_REF] Coleman | Positron Beams and Their Applications[END_REF][START_REF] Schultz | Interaction of positron beams with surfaces, thin films and interfaces[END_REF]. A high positron intensity requires a large power dissipated in the target, therefore both an efficient target cooling system and a sophisticated moderator configuration are important for high positron yield.

The linac target generates high energy positrons for subsequent moderation. It also produces a high flux of bremsstrahlung radiation which creates positrons in the moderator itself, this latter process being responsible for approximately 40 % of all slow positron output of the source. The target is made of tungsten, as this metal was found to be the best choice for electro-production of positrons [START_REF] Dahm | Electroproduced slow positrons[END_REF] because of its high atomic number and melting point. It has been designed to produce the highest number of slow positrons possible at 9 MeV electron energy while having sufficient cooling power to keep the target at moderate temperature. The thickness of the target has been optimized by simulating the stopping profile of positrons, created by electrons implanted into a thick tungsten plate (Fig. 2), using the Geant4 simulation toolkit [35]. As we use tungsten for both the target and the moderator, the maximum of the stopping profile gives the depth where the highest number of slow positrons are produced in the moderator behind a target of a given thickness. Figure 2 shows that the maximum of slow-positron production efficiency is at approximately 1 mm depth. In the case of the GBAR linac the optimal thickness is used with a simple static construction, without rotating target or scanning of the beam, as the cooling system is able to absorb the power deposited in a 1 mm thick target. Although the Monte Carlo simulation is reliable only down to a few hundred electronvolt positron kinetic energy, the calculated profile is very close to the actual stopping profile because positrons in this energy range do not move more than 100 nm before thermalisation. Consequently, the calculated stopping profile is a good approximation for the depth dependency of positrons which are available for the final phase of moderation. The maximum yield is a broad function of the depth, with marginal changes only at the scale of the thickness of the moderator. The target is perpendicular to the beam axis. To improve heat conduction, it is machined in the form of a 5 mm diameter, 1 mm thick disc, milled out of a thicker tungsten block. It is in turn attached to a water-cooled copper structure. When the linac works at nominal power, the target assembly absorbs 1.5 kW. On the basis of a finite element calculation we estimate the temperature of the target as 1400 K. This high temperature is localized to the electron beam spot, the rest of the target structure is efficiently cooled by the water circuit.

Positron moderator

In the positron moderation process, high-energy positrons are implanted into a solid where they lose energy until they are close to thermal equilibrium with the crystal lattice [START_REF] Schultz | Interaction of positron beams with surfaces, thin films and interfaces[END_REF]. Some of the thermalized positrons reach the surface by diffusion. In the case of tungsten and some other materials, the work function of positrons is negative, i.e., the particles gain energy when they leave the metal. Only positrons that reached thermal energy in the vicinity of the surface, in a depth range in the order of 100 nm, have a chance to be emitted from the moderator. Positronium formation and positron-electron annihilation are other possible surface processes which limit the efficiency. Altogether, moderation is a near-surface process and its efficiency increases with the useful emitting area of the moderator structure.

However, in complicated moderator structures most slow positrons can only leave the moderator after one or more collisions, with a significant probability of loss at each interaction. Intense sources based on the 22 Na isotope most often use solid neon kept at 7 K as moderator. The high power due to the scattered electron beam and high-energy gamma rays in the target zone makes application of a cryogenic moderator very difficult in the case of accelerator-based systems. In linac-based systems the moderator is usually a structure made of metallic plates or foils, annealed at high temperature. The material chosen is most often tungsten due to its high efficiency and relative stability [START_REF] Ebel | Production of slow positrons with the Giessen 65 MeV linac[END_REF][START_REF] Howell | Production and use of low-energy, monoenergetic positron beams from electron linacs[END_REF][START_REF] Hulett | The Oak Ridge National Laboratory slow positron source[END_REF][START_REF] Akahane | Stretching of slow positron pulses generated with an electron linac[END_REF][START_REF] Segers | Creation of slow positrons at the Ghent 90 MeV linac[END_REF][START_REF] Wada | Increase in the beam intensity of the linac-based slow positron beam and its application at the Slow Positron Facility[END_REF][START_REF] Tanaka | Slow positron production using an 18 MeV electron linac[END_REF]. The number of "fast" positrons created in the target increases quickly with electron energy. However, the mean energy of the positrons increases as well, which entails a decrease in moderator efficiency. This effect attenuates the gain that arises from increasing the electron energy.

The simplest type of metallic moderator is a thin foil that must be annealed at high temperature in order to release slow positrons efficiently.

High-temperature annealing removes defects and thereby increases the effective diffusion length of low energy positrons in the metal. Furthermore, it cleans surface contamination and reduces the loss of positron emission through positron trapping at the surface or positronium creation. In order to increase the slow-positron yield, we have chosen a stack of tungsten mesh pieces as a moderator because this is a structure with a large surface per unit mass, readily available and easy to heat using electrical current. Similar structures have been found to have a higher moderator efficiency than a thin tungsten foil [START_REF] Nagashima | Stable, high-efficiency moderator with tungsten mesh[END_REF][START_REF] Weng | Tungsten mesh as positron transmission moderator in a monoenergetic positron beam[END_REF][START_REF] Liszkay | Improved tungsten moderator structures for slow positron beams[END_REF]. While positrons from a 22 Na source with 180 keV mean kinetic energy are quickly absorbed in a few layers of commercially available mesh, in the case of an electron-beam-based source, the number of moderated positrons emitted per unit area is independent of the depth in the stack of moderator layers, because of the broad stopping profile. Consequently, the advantage of a larger specific surface area is expected to be even more enhanced than in the case of isotope sources where the intensity of fast positrons emitted from the source is quickly attenuated in the moderator stack. Slow positrons emitted from a surface deep in the moderator stack can only escape if they undergo a few collisions with the wires of the mesh. The loss during the collisions limits the gain attained with an increased number of layers, leading to an optimal thickness. A further factor which influences the efficiency is the temperature of the moderator, which depends on the energy deposited in the moderator, which in turn also depends on the thickness.

The stack of thin tungsten mesh pieces is mounted 2 mm behind the electron target (Fig. 3), parallel to the target. A woven wire mesh of 0.0008" (20.3 µm) thickness was used with 180 wires/inch density (141 µm wire distance). The mesh pieces were annealed in a vacuum chamber, with a pressure lower than 10 -7 mbar, using an electrical current giving a power density of about 100 W/cm 2 . They were mounted on a stainless steel moderator holder in air and moved into the target chamber in typically less than 15 minutes.

The moderator is biased at +50 V. The extraction electrode is a simple grounded plate with a 20 mm diameter hole located 27 mm downstream of the target. This simple design ensures that the electrode is not excessively heated by the electron beam. Simulations have shown that the extraction field does not have a significant negative effect on the beam quality. The slow positron yield was measured by a NaI scintillator coupled to a photomultiplier at the exit point of the biological shield.

We performed measurements using the Saclay source to optimize the positron moderator. Its ideal thickness was obtained by measuring the slowpositron yield as a function of the number of mesh layers in the moderator stack (Fig. 4). The experimental uncertainty is dominated by the difference in the properties of the electron beam between two measurements, as changing the moderator thickness is a time consuming procedure and each measurement was performed after a new start of the accelerator. We estimate this error to approximately 10 % of the signal. We found that the positron yield increases nearly linearly with the number of mesh layers up to about 9 layers, then the signal levels off. We concluded that the optimal thickness of the moderator is approximately 12 layers. In the figure, results of a simple Monte Carlo simulation are also shown, using a probability of slow positron reflection from the surface of the wire of 0.56 [START_REF] Jørgensen | Evidence of very low-energy positron reflection off tungsten surfaces[END_REF]. The simulation was normalized to give the same efficiency value as the measurement at a thickness of 12 layers. As it is also visible in the simulation, we expect a small increase in positron yield between 12 and 15 layers. The apparent decrease in the measured values is compatible with the experimental uncertainty. Nevertheless, no significant improvement can be expected by increasing the number of mesh layers beyond 12 layers. As the change in the stopping profile of positrons within the thickness of the moderator is small, the density of positrons created per unit surface area is nearly independent of the depth within the moderator. Consequently, if the moderator efficiency per unit surface is unchanged we expect that the optimal thickness is the same at 4.3 MeV and 9 MeV electron energy, for the Saclay source and at CERN, respectively. This approximation does not take into account the loss of efficiency due to the increase in temperature with increasing moderator thickness, an effect which is significant in the case of the CERN beam (see below and 10.1).

We compared the efficiency of the optimized moderator stack with that of a simple flat moderator, placed in the same position. We used pieces of 25 µm thick and 1 mm wide tungsten ribbon to construct a flat moderator. This geometry allows heating the metal by electrical current in the same chamber as done for the tungsten mesh. The difference between the geometry of the ribbon and that of the tungsten-mesh moderator was taken into account using a Monte Carlo simulation of the target-moderator structure.

The simulation provides the density distribution of moderated positrons in the plane of the moderator. The efficiency of the flat moderator was experimentally found to be only 17 ± 5 % of the efficiency of the optimized mesh configuration, which confirms the expectation that mesh moderators have significantly higher efficiency than thin foils, particularly, as here, for positrons incident with kinetic energies in the MeV range.

We also studied the effect of the temperature on the moderator efficiency at the Saclay source using in-situ heating of a single moderator mesh by electrical current (Fig. 5). The moderator was placed just behind the electron target, in a similar position as the standard moderator stack used in the setup. We estimated the temperature of the moderator on the basis of the heating power and radiative heat transfer, using an emissivity of 0.3 for the tungsten wire. As the exact value of the emissivity of the used wire is not known, the experimental error of the temperature is rather large. In the figure, the error bar represents the range of temperature determined expecting an emissivity between 0.2 and 0.4. The uncertainty in the positron signal is limited to small fluctuations in the electron beam intensity during the measurement. We found that the moderator efficiency decreases by as much as 30 % between room temperature and 800 K, then continues to decrease more slowly dropping to about 15 % at 2800 K. The result is in qualitative agreement with the measurements of Al-Qaradawi et al [START_REF] Al-Qaradawi | Re-emission of slow positrons from tungsten at elevated temperatures[END_REF]. The loss of efficiency can be attributed to the increasing positronium formation at the moderator surface at elevated temperature. As positronium formation competes with the emission of slow positrons from the surface of the tungsten mesh, this leads to a decrease in moderator efficiency.

We performed in-situ annealing of the moderator mesh using the same experimental setup. The intensity of the slow positron beam was measured after heating the mesh for 3 minutes at various heating power levels. Figure 6 shows the positron flux as a function of the estimated annealing temperature. The experimental uncertainties are the same as in the case of Figure 5. The moderator efficiency is very low in the case of an unannealed mesh.

The positron signal starts to increase above 1800 K annealing temperature and increased roughly linearly until 3000 degrees. This result illustrates the importance of annealing of the moderator at the highest temperature which is technically possible.

Positron transport

The target is surrounded by two coils in the Helmholtz configuration arranged co-axially with the same axis as that of the accelerating section.

They produce a field that can be varied up to about 20 mT at the target location. Positrons are adiabatically guided by an 8 mT magnetic field which is generated by solenoids wound around the 100 mm diameter vacuum pipe (Fig. 1). At vacuum valves, bellows and other vacuum elements, larger coils are used to provide a smooth field. At each elbow, two pairs of racetrack coils introduce a variable dipole field that can be used for steering the positron beam. The total length of the beam transfer line between the electron target and the entry point of the positron trap is approximately 7.5 m. The "S" shaped part of the beam trajectory before the vacuum valve is in the zone where the beam line crosses the biological shield and a reinforcement of the radiation shield is necessary to avoid leakage of gamma radiation from the linac bunker.

Radiation protection

The intense electron pulses produce a very high radiation dose rate (up to 30 kGy/h) in the vicinity of the target chamber. Thus, the linac and the target chamber are placed in a bunker of approximately 10 × 11 m footprint with 1.2 m thick walls, constructed from 67 % concrete and 33 % iron blocks.

A stainless steel shielding box, with 40 mm thick walls, has been installed around the target, to protect the equipment in the linac bunker. This reduces the radiation dose by about a factor of 3 inside the bunker, and consequently outside. The radiation dose rate outside the bunker is sufficiently low for unlimited access. This means that it might be possible to contemplate the use of this relatively compact type of instrumentation in small laboratories. We observed a slight short-term activation of the mechanical structure around the linac target but it never exceeded a few µSv/h equivalent dose rate at 400 mm distance from the target. Use of lead as shielding material is prohibited at this energy, as it would significantly increase the level of activation.

Positron diagnostics

In order to measure the positron flux at the end of the transport line [START_REF] Latacz | Study of the antihydrogen atom and ion production via charge exchange reaction on positronium[END_REF], a 0.5 mm thick stainless steel plate is used as a beam diagnostic target. The target is mounted on a linear drive and can also be used as a scraper to estimate the beam size. A NaI(Tl) scintillator (50.8 mm diameter, 50.8 mm length) attached to a photomultiplier tube is used to detect 511 keV photons from positrons annihilating on the diagnostic target. The detector is placed at 800 mm distance from the target, so that the systematic error caused by uncertainties of the geometry can be neglected and calibration with single annihilation gamma photons can be used. To calibrate the detector efficiency, we first measured the mean electrical charge corresponding to the 511 keV photopeak at the anode of the photomultiplier (Q 511keV ). In a second step we determined the mean energy E a that is deposited in the scintillator crystal after annihilation of one positron in the target. This was done by a Monte Carlo simulation of the detection using the Geant4 package [35]. The simulation takes into account scattering in the environment of the positron target (vacuum pipe, target holder, vacuum flanges), the solid angle of the detector and Compton scattering in the scintillator. The charge corresponding to the photopeak is corrected by the factor determined in the simulation to obtain the mean charge

Q m Q m = Q 511keV E a 511 keV (1)
from the annihilation of one positron in the target. At the detector distance used, each positron pulse produces on average only a few tens of 511 keV annihilation photons that reach the detector. This allows the determination of both the single-photon signal and measurement of the diagnostic signal with a moderate dynamic range.

In order to measure the momentum distribution of the positrons parallel to the beam axis, we used the first electrodes of the buffer-gas trap as a retarding field analyser. The relevant part of the trap consists of a series of tubular electrodes with an inner diameter of 16 mm and a total length of 149 mm. In this case the positron flux was measured by detecting the annihilation gamma signal generated by positrons impinging on a target behind the last electrode by a plastic scintillator coupled to a photomultiplier. The trap is directly behind the positron diagnostic target and the magnetic field is 60 mT at the place of the measurement. The tubular electrodes are sufficiently long to ensure that the electric potential at the center is equal to that of the electron tube. The energy distribution can be deduced from the electrode voltage -positron annihilation signal curve. A fit of the measured values with a complementary error function shows a good agreement with σ t =4.2 eV fitting parameter, corresponding to a Gaussian energy distribution with σ t standard deviation (Fig. 7).

Electron background

Electrons are generated in the linac target chamber with a wide range of kinetic energies. Low-energy electrons are adiabatically guided together with the positron beam. Below ∼100 eV the electron background is several orders of magnitude stronger than the positron flux and we observe a significant number of electrons even above 2 keV kinetic energy. This background is not noticed in most applications (positron spectroscopy) but gas ionisation by electrons is potentially deleterious in buffer-gas traps. Only a potential barrier of about -5 kV can fully eliminate the electron background. A hightransparency (90 %) metallic grid at negative potential is used to block most electrons. Acceleration and subsequent deceleration of positrons by the grid leads to a deterioration of the beam quality, therefore the potential on the grid must be limited to the lowest possible level. We found that the best trapping efficiency in the buffer gas trap is attained for a grid potential of -500 V. The positron source has been running at full power for an extended period of time (more than 1000 hours). After installing a fresh moderator, the slow-positron yield stabilized after a short transition period (typically a few hours). On a longer time scale, there is a slow deterioration with accumulated electron dose. The long term deterioration of the positron yield can be attributed to both surface contamination and accumulation of lattice defects [START_REF] Suzuki | Investigation of positron moderator materials for electron-linacbased slow positron beamlines[END_REF].

Energy distribution and beam shape

Tungsten mesh moderators are characterised by a rather broad angular distribution of the emitted positrons due to the microstructure of the moderator stack. This leads to a longitudinal momentum distribution p that can be translated into an energy E = eV FWHM) in the 9.7 mT magnetic field at the position of the moderator, using the fact that E ⊥ /B is an adiabatic invariant and the total kinetic energy E = E + E ⊥ is constant. The latter assumption is only approximately fulfilled due to the non-zero width of the energy distribution of positrons emitted from the tungsten surface. The width of the energy distribution at the moderator is comparable with the 2.1 eV FWHM value found using a 22 Na positron source [START_REF] Sueoka | Reemission intensity and energy spectrum measurements of slow positron beams for various moderators[END_REF].

The beam diameter at the positron target can be estimated from measurements with the beam scraper (Fig. 9). We found that approximately 80 % of the positron intensity falls into a 13 mm broad vertical zone. In the case of adiabatic transport the beam diameter depends on the size of the positron emitting spot on the moderator and strength of the magnetic field at both the moderator and the beam scraper. The observed size is in agreement with the expected size of the positron emitting surface of the moderator stack.

Conclusions and outlook

We built and successfully commissioned a positron generator which is based on a compact, low-energy linear electron accelerator. The system provides 5.0 ± 0.6 × 10 7 e + /s positron flux, which is fed into a buffer-gas trap. The positron flux reached is comparable to or higher than most linacbased positron beams which use significantly higher electron energy. We have demonstrated that a low-energy linac, with no persistent activation of the environment, is a good alternative to radioactive sources when a high positron flux is needed, and as such may find wide uptake. Compared to other linac-based sources (Table 1) the GBAR source provides excellent flux for its input power and energy. The source will be the first of its kind to be used to fill a high-field Penning-Malmberg trap and it can also serve as a test bench for the application of positron traps at accelerator-based positron beams.

Acknowledgements

We acknowledge support of the Agence Nationale de la Recherche (project ANTION ANR-

Figures

  fluxA steady-state positron flux of 5.0 ± 0.6 × 10 7 per second was detected at the diagnostic target at 300 Hz repetition frequency[START_REF] Latacz | Study of the antihydrogen atom and ion production via charge exchange reaction on positronium[END_REF]. The number of positrons per linac pulse measured as a function of the repetition rate is shown in Figure8. It decreases almost linearly by about 50 % between 10 Hz and 300 Hz, most probably due to the increase of the moderator temperature with increasing linac frequency. The uncertainty of the positron intensity measurement is limited to the effect of small fluctuations in the beam intensity, estimated to 5 %. The moderator is heated directly by the electron beam (estimated as 150 W at full power by simulation) and indirectly by thermal radiation of the linac target. With no efficient cooling by heat conduction, its temperature is determined by radiative equilibrium.

p 2 2m

 2 with a total width of approximately 3 eV, the work function of tungsten. The broadening may be slightly increased by the electric field which penetrates into the mesh stack and may extract some positrons which are emitted backwards. The E distribution measured by the energy analyzer depends on the magnetic field (B) at the location of the moderator and of the energy analyser. E measured at 60 mT magnetic field (Fig.7) can be fitted by a Gaussian with σ t =4.2 eV. Assuming a fully adiabatic beam transport this width translates to σ m =0.7 eV(1.6

Figure 1 :

 1 Figure 1: Schematic view of the linac (vertical structure on the left) and the positron transfer line. The transfer fields are generated by solenoids wound around the beam pipes and by the two larger coils placed around the linac target. The coil at 45 degrees position is used to fine-tune the magnetic field at the point where the positron beam turns sharply. The beam line crosses the biological shield at the "S" shaped section on the right.

Figure 2 :

 2 Figure 2: Positrons created by 9 MeV electrons and stopped in a tungsten plate (Geant4 simulation with 10 7 electrons). The number of positrons annihilating in 0.05 mm thick layers is plotted as a function of the depth. The dashed line at 1 mm shows the thickness of the actually used electron target.

Figure 3 :

 3 Figure3: Cross section of the electron target. The potential of the moderator is +50 V, the rest of the structure is at ground (GND). The copper block ("Cu cooler") is water cooled. The magnetic field of 9.7 mT is parallel with the electron and positron beams.

Figure 4 :

 4 Figure 4: Slow positron flux as a function of the number of mesh layers (solid circles). Each layer is a 18x18 mm piece of tungsten mesh with 180 wires/inch density, annealed at higher than 2700 K temperature. The measurement was performed using the 4.3 MeV Saclay linac with a 1 mm thick tungsten target. A linear fit of the data points up to 9 layer thickness is shown with a dotted line. Results of a simple simulation (see text) are displayed with open circles. The dashed line is guide for the eye.

Figure 5 :

 5 Figure 5: Slow positron flux as a function of the moderator temperature. The measurement was performed using the 4.3 MeV Saclay linac with 1 mm thick tungsten target. The temperature was estimated on the basis of the heating power and radiative heat exchange.

Figure 6 :

 6 Figure 6: Slow positron flux as a function of the moderator annealing temperature. The measurement was performed using the 4.3 MeV Saclay linac with 1 mm thick tungsten target. The temperature was estimated on the basis of the heating power and radiative heat exchange.

Figure 7 :

 7 Figure 7: Positron annihilation signal as a function of the voltage of the grid of the retarding field analyzer at 50 V moderator voltage. At low grid potential all positrons are annihilated on the target while above approximately 60 V all particles are repelled by the grid and no positron signal is detected. The continuous line is a fit with a complementary error function, giving σ t =4.2 eV. The dotted line shows the corresponding Gaussian energy distribution. The measurement was performed in a 60 mT longitudinal magnetic field.

Figure 8 :

 8 Figure 8: Slow positron yield of the GBAR positron source as a function of the linac frequency. Both the number of positrons per pulse (circles) and the number of positrons per second (positron flux) (triangles) are shown. The yield was measured after more than 30 minutes operation at a given frequency.

Table 1 :

 1 Performance of linac-based positron sources.

	14-CE33-0008), CNES (convention number 5100017115), the
	Swiss National Science Foundation (Grant number 173597), ETH Zurich
	(Grant number ETH-46 17-1), the Ministry of Education of the Republic of
	Korea and the National Research Foundation of Korea (NRF-2016R1A6A3A11932936,

NRF-2016R1A2B3008343

). Laboratoire Kastler Brossel (LKB) is a Unité Mixte de Recherche de Sorbonne Université, de ENS-PSL Research University, du Collège de France et du CNRS n • 8552. We thank to CERN for the support to construct the linac and its biological shield and for fellowships and Scientific Associateship provided to D. P. van der Werf and P. Pérez. The support of the Enhanced Eurotalents Fellowship programme to D. P. van der Werf is acknowledged. We gratefully acknowledge the help of François Butin and the CERN management and teams that were involved in this project.