Mechanical characterization of yarns made from carbon nanotubes for the instrumentation of particle beams at CERN

Existing copper-coated carbon (cid:28)bers used in wire scanners to measure the transverse beam pro(cid:28)le in the accelerators at CERN are approaching material limits. A new instrument design has showed that the main limitation now comes from the centerpiece of the instrument: the wire. Large amplitude vibrations increase the risk of failure during scans. New required speci(cid:28)ca-tions concerning the beam measurements for the Future Circular Collider (FCC) project cannot be met. Fortunately, the commercial development of long microscopic yarns made of spun carbon nanotubes has paved the way for possible alternatives. The objective of this study is to determine if those Carbon NanoTube Yarns (CNTY) could replace the current carbon (cid:28)bers (CF) for beam instrumentation, and if so, to determine the best con(cid:28)guration in terms of diameters and mounting system. To do so, we have made extensive testing and microscopy on CNT yarns with diameters of 10, 20 and 30 (cid:181)m, with two di(cid:27)erent mounting systems, the Paper Frame conditioning (PF) or partial Copper-Coated conditioning (CC). A Weibull approach was used to extrapolate our results to the real length of the wires used in operational instruments. This study shows that considering the Weibull criteria, the best con(cid:28)guration to increase the accuracy of the beam pro(cid:28)le measurement is to


Introduction
In high-energy physics, physicists are pushing for an increase in beam energy and intensity as well as smaller beam sizes.New technically challenging projects are planned.The LHC Injector Upgrade (LIU) [1], High Luminosity LHC Project (HL-LHC) [2] and Future Circular Collider (FCC) [3] will improve the beam brightness at CERN in the next years.Wire-scanners (WS) are devices used since the 1980s [4,5] to measure the transverse beam density prole, by moving a thin wire across the particle beam and detecting the secondary particles.The interaction between the beam and the wire creates secondary particle showers with an intensity proportional to the number of particles crossing the wire.These secondary particles are intercepted by a scintillator positioned downstream of the wire, coupled to a photo-multiplier which amplies the resulting signal.The acquisition of the wire position and the signal intensity are combined to reconstruct the transverse beam density prole.The rst WS moved linearly with stepper motor [6,7] which required very low scan speeds, of up to 1 m.s -1 [8,9].Various studies on this instrument were carried, from the inuence of the diameter of the wire [10] to its thermal behavior [7,11,12].Another generation of rotary WS was then designed to meet higher specications [13] in the Proton Synchrotron Booster (PSB) and the Proton Synchrotron (PS).However, in the coming years, the beam will progressively be smaller and more intense.This will lead to two main issues with the current generation of WS: an overheating of the wire [1416] and an insucient resolution for the beam size.In order to address the overheating issue, a new generation of fast wire-scanners [17,18] was developed at CERN (Fig 1), for the whole accelerator chain, from PSB to the Super Proton Synchrotron (SPS).The whole engineering concept has been redesigned with new machining and manufacturing concepts [19,20].
The major improvement is the increase of the scan velocity up to 20 m.s -1 , which allows to reduce the beam/wire interaction time and consequently the increase of temperature.Everything in this new WS was changed, except the centerpiece of the instrument: the wire.The same material with the same mounting system has been used from the beginning, i.e. partially copper coated carbon ber.The problem is that rst, most common wires (carbon ber, gold coated tungsten,. . . ) will be destroyed in the HL-LHC conditions [15] and second, the precision of the wire installation is currently mainly dependent on the technicians who install the wire manually and is prone to large variations in the calibration results.
As an alternative to conventional carbon bers, we considered bers made of Carbon NanoTubes (CNT), a new exciting material formed by one (Single Wall Carbon NanoTube -SWCNT) or several (Multi Wall Carbon Nan-oTube -MWCNT) sheets of graphene, coiled on themselves.It seems that such nanotubes were already observed in the 50s [21] but really highlighted only 30 years later, by Sumio Iijima [22].For isolated nanotubes, experimental studies and theoretical simulations showed a combination of excellent mechanical [2325], electrical [2629], and thermal properties [3032].Its very light weight for a solid, with relative densities that can be as low as 0.5, depending on the CNT structure and packing [33] is also an interesting characteristic.The nanometric size, with diameters varying from less than 1 nm for SWCNT [34] to more than 50 nm for the bigger MWCNTs [35] and typical lengths of the order of the micrometer, [35], the millimeter [3638] or even the centimeter [39], are particularly adapted for new technologies such as nanoelectronics [26,40] or material composites [27,4143].The "macromechanics" would also be interested in these fabulous characteristics, but individual tubes are not practical for most engineering applications due to their size.More recently, the technology to assemble these tubes together to make long stranded yarns has opened up a new world of potential applications.Dierent methods were developed such as dry spinning [44], wet spinning [45,46], in situ direct spinning [34] and spinning from gas phase [47] that oer a wide panel of possible congurations.
Many academic institutes and industrial companies are interested in investing and developing these new Carbon NanoTube Yarns (CNTY) further.
Nevertheless, several studies [4850] showed a large dierence between the properties of a single nanotube and the properties of the wire assembly.Indeed, the bonds between carbon atoms inside the coiled graphene layers are strong covalent bonds, whereas the inter-tubes bonds inside the wire are weak van der Waals forces.It led to a disappointment for some applications needing high mechanical properties and a microscale structure.Methods to improve the mechanical properties of pristine yarns exist such as chemical treatment [5153] or densication by twisting [5456].However, the inuence of a partial copper-coating on the mechanical properties has not been stud- ied.Hence, the goal of our study is to determine the best conguration for this new material considering several diameters (10, 20 and 30 µm), and two dierent mounting systems: 1-glued on a paper frame (PF) and 2-partially copper coated (CC).This new input will be carefully analyzed and will be determinant for the upgrade of the wire scanners used at CERN.
We will rst describe the material, methods and protocols used, then describe the results of our measurements and the Weibull analysis done to estimate the maximum tensile stress that we will be able to impose safely to the yarns during their installation on wire scanners of the new generation.
This point is crucial to achieve fast scan speeds with minimal deformations as required to monitor with a sucient precision the beam prole in enhanced luminosity conditions.An in-depth discussion of our results, with a comparison with other results from the literature will then lead us to give some perspectives and propose recommendations for the conguration to be used at CERN.

Preparation of the tensile tests
The wires used for this study were provided by Hitachi Zosen Corporation.
CNTs were obtained by Chemical Vapor Deposition, producing a vertically aligned sheet.[5759].The as-grown CNTs have an outer diameter of 10 to 12 nm.These are typical values which can be found in many productions [44].The average number of walls composing the tubes are between 5 and    Our study concerns the eects on the mechanical properties (strain at failure (ε max ), tensile strength (σ max ), Young's modulus (E) and toughness (T )) of the PF or CC preparations and of the diameters of the wires.Tensile tests were made using a Dynamic Mechanical Analyzer (DMA) (Bose Elec-troforce3200) at ambient temperature (21 °C) equipped with a 22 N load cell (precision of ± 5 mN) and displacement sensor of ± 1.5 mm (precision of ± 1 µm).The gauge length of the specimens were 10 and 30 mm for the PF and CC preparations, respectively.
Tests were performed with a displacement control at a speed of 1 mm.min -1 .
The Young's modulus quanties the tensile stiness of a material.It was determined by linear regression of the stress/strain curves on a range of strain comprised between 0 and 1 %.
As already mentioned, two dierent mountings have been prepared (PF and CC).For PF, we used a self-adhesive paper frame [60]

Focused Ion Beam (FIB) microscopy
To prepare the samples, mechanical cutting with scissors was performed.
The specimens were glued with silver paste to an aluminum stub (standard consumables for SEM).In order to gain improved insight into the microstructure of the CNTs, a cross section was milled by FIB into the samples.For the transverse cross-section, a 20 (radial) × 2 (axial) × 1 (thickness) µm 3 platinum (Pt) polishing barrier was initially deposited onto the sample surface at a current of 300 pA in order to facilitate eective polishing.A milling current of 3 nA and accelerating voltage of 30 keV were then used to mill out a section using the silicon (Si) ablation ratio.Subsequent polishing milling steps were performed at 700 pA and 100 pA and accelerating voltage of 30 keV and a nal polishing was performed at a milling current of 50 pA and accelerating voltage of 30 keV to leave a smooth surface that could be eectively imaged.
For the longitudinal cross-section, a milling current of 3 nA and accelerating voltage of 30 keV was used to mill out the material up to approximately half of the wire diameter.Subsequent polishing milling steps were performed at 1.5 nA and 700 pA and accelerating voltage of 30 keV and a nal polishing was performed at a milling current of 100 pA and accelerating voltage of 30 keV to leave a smooth surface that could be eectively imaged.

Analyzing tools
The data analysis was performed by using a combination of Excel worksheets (Microsoft, Redmond, Washington, USA) and python Jupyter Notebooks [61].Graphs and statistics have been plotted with GraphPad Prism 9 (GraphPad Software, San Diego, California, USA).Images were processed with ImageJ [62] to set up brightness, contrast and get measurements.Fig- ures have been assembled with the free software Inkscape [63].The void density was calculated using a python script developed internally.

Internal structure analysis
A CNTY can be described as a hierarchical structure.Individual CNTs self-assemble forming bundles and bundles are bonding together in successive layers to form the nal yarn [64].A good knowledge of the characteristics of the individual CNTs composing the yarn and their packing would be an asset for developing an eective composite model for the yarn [64,65].
A transverse cross-section has therefore been milled in several yarns using gallium ions from the FIB, to observe their internal structures (see the surface).It was observed with a magnication of 7700 (Fig 3-c).This image was binarized (Fig 3-d) from a grey level picture using a threshold manually set to 122 in the python script, in order to visually preserve the extents of the voids while ltering out artifacts.The void density is then estimated by the ratio of black pixels over white pixels.For SOI-1 of the 185 20 µm yarn, we found 0.63 %.SIO-2 (Fig 3-b) is located at mid distance between the outer part and the center of the layer.A picture was taken with a magnication of 52000 3-e) and binarized 3-f ).Using a threshold of 110, the void ratio was then estimated to be 0.28 %.
The same approach has been used for a 30 µm yarn ( From the above results, we can see that the packing is denser (less voids) for the 20 µm yarns than for the 30 µm yarns, which is in the continuity of the results of a previous study carried out with yarns with diameters varying from 30 to 83 µm [66].This study showed a decrease of the apparent density from 1.2 to 0.6 g.cm -3 with increasing diameter.However, despite the fact that various previous studies showed that the packing of twisted yarns increases with the twist angle [55,56,67,68], our observations do not seem to support this correlation, since we nd quite dierent packings for similar twist angles (20 ± 2°and 19 ± 1°for wires of 20 and 30 µm respectively (Table 1)).This discrepancy may be due to the non-uniformity of packing in the 30 µm CNTY versus the uniformity of the packing in the 20 µm CNTY.Indeed, we found that the void ratio at the site of interest located on the outer layer of the 20 µm yarn is twice larger than the one at the site of interest located midway between the center and the surface of the yarn.This indicates that for this diameter, the packing is not radially uniform.For the 30 µm, both sites of interest show very similar packings, given the uncertainties inherent to the manual setting of the binarization threshold.

copper-coating
Wires used in the current wire scanners are copper coated on the extremities for integration reasons.However, coating the yarns with copper is a delicate step in the wire preparation.Therefore, we prepared a new batch of copper-coated wires in order to study the dispersion of their geometrical and mechanical characteristics.Results on the copper-coatings external diameters were very variable compared with the design specications.They also showed dierent proles for a same batch (Fig 4-a).To observe the interface between the yarn and the copper-coating, we performed transverse cross-section using the FIB method.The samples were positioned with the The observation of the interface between the copper-coating and the yarn could lead to the supposition that while lling the voids in the structure of the wire, copper could form new bonds stronger than the weak van der Waals forces between CNTs, which could reinforce the yarn.It would then lead to mechanical properties slightly better than for a pristine yarn, by strengthening the coating region.However, we observed that the strength results of the tensile tests for d20_CC and d30_CC batches are well below the results for the d20_PF and d30_PF batches, which would prevent use of higher tensile forces in order to straighten the wires and, consequently, to improve the accuracy of the WS by decreasing the amplitude of the vibrations.Our FIB/SEM/EDXS observations of cross-sections of CNTYs before tensile tests showed that the coating does not modify the shape of the yarn but that copper penetrates in the supercial layer of the CNTY.However, we have no information on the type of bonds created between the CNTs and the coating.Furthermore, all the samples broke at the end of the copper plating showing that there is probably a stress concentration at this point, leading to a point of weakness.Hence, it seems that partial copper coating is denitely not a good solution from a mechanical perspective.Solutions to improve the mechanical properties by fully coating the wire have been suggested [69], but not adopted in our case.The goal is to reduce the number of interactions with the beam.A coating with a high Z material would lead to an increase of beam interactions.Another alternative solution would be to use iron or tungsten coatings, since these elements are more soluble in carbon than copper and can form carbides, but this solution implies to add an signicant mass, which could be a problem.Indeed, a local increase of mass implies larger deections during the scan due to the acceleration.Moreover, we saw that the reproducibility of the coating process is not very high and is depending on a lot of factors, such as the cleanliness of the tank, precision of the current going through the grid, but also the thickness and the width of the copper layer on the printed circuit board during the grid preparation.This is not acceptable for such a high precision project.The goal of this study is to nd which kind of yarn, with which mounting, could replace the existing carbon bers used in the current WS.To do so, tensile tests have been performed on 93 samples, combining the two parameters of interest: diameter (10, 20 and 30 µm) and mounting conditioning (PF and CC).Labels and numbers of samples tested are given in Table 2.  16) d30_CC (25) Typical raw tensile stress/strain curves show various behaviors for our samples depending on the diameter and conditioning (Fig 5).The left axis of each graph indicates the load (in N) applied to the wire during the test while the right axis is for the corresponding stress (in GPa) calculated as load divided by the previously measured real cross-sections of the yarns.For the CC samples, the diameter used to calculate the stress is also the diameter of the yarn.We consider that the coating parts are part of the clamping system.
Looking at the three PF gures corresponding to the three diameters (Fig 5-a, b and c), we can see that the curves are quite similar since they all correspond to a brittle behavior of these non-coated CNTY, with a strain to failure about 2 %.There is a linear increase of the stress between 0 and 90 % of the strain to failure (ε max ) and a very short plastic zone before the failure.The behavior for the CC samples is more disparate.Samples from batch d10_CC more or less have the same brittle response as for the PF conditioning, whereas samples of d20_CC and d30_CC batches show a much larger discrepancy between samples, with larger intervals of variation than for the PF conditioning, since the strain at failure varies from 1.4 to 4 % and from 1.7 to 5 % for 20 and 30 µm respectively.The maximal load before the failure also shows large variations, from 140 to 357 mN and from 229 to 638 mN for 20 and 30 µm respectively, corresponding to maximal stresses smaller than in the PF and d10_CC cases.
Strain at failure (ε max ), average strength (σ max ), Young's modulus (E)   and toughness (T ) were evaluated from the raw curves of  Young's modulus.The Young's modulus (E) (Fig 6-c) was calculated using the slope of a linear regression of the stress-strain curve between 0 and 1 320 % of strain.It is interesting to notice that for the yarns with a nominal 10 µm diameter, the modulus is a larger for CC with 51 ± 3 GPa than for  PF with 44 ± 14 GPa.For the diameters of 20 and 30 µm, it is the opposite, with a modulus for PF twice larger than CC, with 58 ± 7 and 26 ± 15 GPa and 43 ± 11 and 20 ± 12 GPa respectively.We can see that the relative uncertainty is much larger for the d20_CC and d30_CC batches than for the other batches, as already visually evident in Fig 5).
Specic toughness.The specic toughness (T ) expressed in J.g -1 quanties the ability of a material to absorb energy by deforming elastically without breaking.It is dened as the area under the stress/strain curve up to the elastic limit, divided by the density.The average specic toughness (Fig 6-d) for the d10_PF batch is 66 ± 18 J.g -1 , 78 ± 14 J.g -1 for d20_PF and 89 ± 16 J.g -1 for d30_PF.These data could be tted by a linear increase with diameter of equation T = 1.2d + 54.7.The yarns with the CC conditioning show another behavior with a specic toughness quite similar for the three diameters, with 62 ± 12, 59 ± 21 and 71 ± 44 J.g -1 for d10_CC, d20_CC and d30_CC respectively.We note that for this conditioning, this is the standard deviation which increases linearly.

Weibull parameters calculation
For many years, scaling models for composite materials have been the subject of intense research.Empirical, phenomenological or progressive damage methods, all aim to optimize and improve the performances of these materials [70].Our study also ts in this framework, with the idea of testing small-sized samples of short CNTYs and adapting the results to the longer wires used in wire scanners, using Weibull methods.Main tests are performed with small gauge length samples [71,72] as limits on translational stroke of the tensile machine does not accommodate samples of length used in WS.This kind of analysis allows scaling the dispersion of the mechanical strength results without explicitly modeling the defects, using the hypothesis that a higher degree of similarity of defect type and uniformity results in a smaller dispersion of failure stresses.In this approach, the state of the material (failed or not) is represented by a random variable which is distributed according to a probability law that depends on the applied stress and can be experimentally identied by a series of tests (see e.g.[73,74]).The probability of survival follows a Weibull distribution and is then expressed as [75,76]: where σ is the applied stress, σ 0 , the scale parameter, and m the shape parameter (Weibull modulus).V * is the reduced volume equal to the actual volume divide by a reference volume.First, to get the scale and shape parameters, we consider that the volume of reference is the volume of the sample, so that V * = 1.In order to compute σ 0 and m, we rst sort the samples by stress at failure (σ max ) from lowest to highest.Each sample then has an associated probability of survival that can be evaluated using its rank in the list (n rank ) with formulas that depend on the number of samples (N samples ).
For moderate size samples [76] P Then (for V * = 1), we can obtain m and σ 0 thanks to a linear t using the following equation derived from Eq. 1 Indeed, using a plot (Fig 7) of ln(− ln(P s )) as a function of ln(σ), the slope of the linear regression gives the modulus m and the Y-intercept y 0 gives σ 0 = exp(y 0 /m).Results for m and σ 0 for the three diameters and two conditionings, are summarized in Table 3 along with r 2 which characterizes the quality of t.
For the 10 µm batches, Weibull moduli are 19.18 and 28.11 respectively, for PF and CC conditionings.This is quite high compared with the results for the 20 and 30 µm batches (between 3.05 and 8.25).This is normal since a mathematically known property of the Weibull modulus is that the lower m, the greater the dispersion of the variable characteristic of the failure.
This has been seen for composite materials with bers oriented at random, lower values of m corresponded to greater dispersions of the tensile strength.Hence, the high m for the low diameter indicates a defects distribution more homogeneous than for the larger diameters, which agrees with the previous observations of the packing.
The results for σ 0 show 6 % of dierence between the PF and the CC conditionings for the diameter of 10 µm, while this dierence increases up  3, in italic.they give a modulus of 11.8 and a σ 0 of 928 MPa.With r 2 = 0.93, the t is as good as for the CNT yarns.
Our study for diameters from 10 to 30 µm, completes the study of Sugano et al. [66] in which 4 yarns with diameters larger than 30 µm were used.

Operational parameter calculation
The interest of this study is to verify if these new yarns could be installed on operational WS.If so, the length of the yarns will not be 12 or 30 mm as in the tests, but 150 mm.In order to extrapolate our experimental results to yarns of 150 mm, Weibull analysis is a good approach, since the stress-strain curves showed a brittle behavior, sometimes with signicant variations, which excludes using the classic sizing criteria used for ductile materials [7779].
Furthermore, CNTYs broke at maximal stresses (σ max ) which varied greatly from a sample to another, particularly for the d20_CC and d30_CC batches.
This dispersion, probably due to the presence of defects in variable quantities and distributions, undermines the classical assumption of homogeneity of mechanical behavior.
To make this extrapolation, we used an equivalent reduced volume V * expressed as V * = V op /V sample , with V op the volume of the operational wire and V sample the volume of the samples used for the mechanical tests [80], either for PF or CC conditionings.Using Eq.1, we see that the larger the operational volume, the smaller the survival probability, which is normal since the number of defects is increased.In fact, we can also dene V * = 150/l cond , since the wires in the operational future WS will have one of the diameters used during the tests and consequently the same cross-section as the CNTYs with that diameter.We therefore nd V * PF = 12.5 for the PF conditioning (gauge length of 12 mm) and V * CC = 5 for the CC conditioning (gauge length of 30 mm).The problem is now to dene a new characteristic strength σ 0−op lower than σ 0 if V * > 1.Since the Weibull modulus m characterizes the inhomogeneity in the population of defects population (the bigger m, the more homogeneous the population), it can be considered independent of the gauge length.In the test case (V * = 1), P s (σ) = 1/e if σ = σ 0 .Similarly, in the operational case (V * > 1), we dene σ 0−op such that P s (σ 0−op ) = 1/e.This implies that V * (σ 0−op /σ 0 ) m = 1, which gives: Using the values of σ 0 and m from Table 3, the new σ 0−op for the PF conditioning decreases by 12 % with respect to σ 0 for a diameter of 10 µm and by around 25 % for diameters of 20 and 30 µm.The values decrease much more for the CC conditioning and diameters of 20 and 30 µm, due to the combination of a larger reduced volume and smaller modulus, up to a 41 % decrease for the diameter 30 µm (Table 4).34 764 (-18 %) -The impact of the gauge length has also been studied by Zhang et al. on bers composed of MWCNT of around 6-8 nm but they found that variations of the gauge length between 1 and 20 µm gave apparently randomly scattered results without any specic trend [48].However, Wang et al., while studying CNTY transformed in rolled ribbons [55], found a large evolution of the curve shape, with a linear increase followed by a long period of plastic deformation for 10 mm gauge length vs. almost no plastic deformation for 20 mm gauge length.Finally, the dierences in strength and strain at failure were +17 % and +50 % respectively in favor of the 10 mm samples.This is slightly dierent with our observations, where the shape of the curves is very similar for the three diameters, with a sharp increase up to failure.As the gauge length is correlated with the copper coating, it is dicult to determine if the increase of the strain to failure of the CC conditioning is due to the gauge length or to the coating.It is particularly true if we consider the 10 µm where the variation is only 5 %.

Comparison of mechanical parameters
The Weibull survival probability distribution for a given stress, dened in Eq.1, is complementary to the probability of failure before that stress corresponding to the following probability density function (PDF) (in the case V * = 1): that both for the PF and CC conditionings, the transition from 0 to 1 is quite sharp for d = 10 µm and smoother for the other two diameters.We also see that for the operational conditions, the dierence between σ 0 and σ 0-op shifts this transition to lower stresses, which is due to the higher number of defects in the increased volume.For the 10 µm yarns, the shift is small (11 % and 5 % for PF and CC respectively), but much larger ((46,36 %) and (28,41 %) for (PF,CC) and for d = 20 and 30 µm respectively.However, the slopes of the transition remain much smaller for d = 20 and 30 µm than for d = 10 µm, corresponding to a broader range of stress at failure, i.e an increased range of strengths for the two larger diameters.
The average strength can be computed from the PDF f dened by Eq.6, by:  where Γ is the gamma special function.Results for the average strengths are summarized in Table 5, along with values for other mechanical parameters that will be discussed later.We observe that considering the length of an operational WS, Weibull analysis show a reduction of the average strength decreasing by around 10% with respect to the lengths used for the mechanical 490 tests, for d = 10 µm, for both conditions.For the diameters 20 and 30 µm, the variation is much higher with 28% for d20_PF, and up to 40% for d30_CC.
For comparison, we note that σ varies by only 20% for the d = 34 µm CF.
Table 5: Strain to failure (ε max ), maximum stress at failure (σ max ), average strength in the test conditions (σ raw , calculated using σ 0 ), average strength for operational WS (σ op , calculated using using σ 0-op ), Young's modulus (E) and toughness (T ), rst for the CNTYs with d = 10, 20 and 30 µm, then for the 34 µm CF (only the strengths in that case).5.6 ± 2.5 4.4 ± 0.4 6.7 ± 1.0 6.0 ± 2. The mechanisms increasing the strength of the yarn for the packing factor is mainly the reduction of the distance between CNTs and CNT bundles.
Stronger bonds are created at a nano-scale for individual tubes and at a micro-scale for bundles with increasing the shear strength.This is coherent with the results of Vilatela et al. [64] where he reported the increase of yarn strength with the increase of the CNT length and so, the surfacic area in contact with other tubes.Moreover a high packing factor implies a higher probability to create entanglements between individual tubes and bundles The question of the optimal material to be used for the wire in the CERN WS has already been extensively studied.Materials such as beryllium [4] or carbon bers [14] (already used at CERN for WS) or tungsten [6] (not used for fast WS) were considered.These studies have been extended for the mechanical aspect to other materials (copper, iron and titanium) [83].
Our goal in this study was to assess whether the CNTYs could stand the pre-tension imposed to reduce the uncertainty on the wire position due to its vibrations during the scan.To get the maximal deection δ max , as a function of diameter, applied load and angular scan velocity, we consider a simplied stationary model, where the wire is ying parallel around the shaft at a constant angular speed ω (details of the calculations in Annex).Thus, we neglect the transitory regime arising during the angular acceleration of the wire by supposing that its characteristic decay time is much smaller than the 10 ms of the constant angular speed phase.Thus, the accelerated phase is supposed to be there only to excite the stationary oscillations.The maximal deformation, located at the center of the wire is found to be: with where R and L are the length of the forks and the wire (equal to 150 mm and 183 mm) respectively, ρ the density of the wire, and F p the pre-tension of the wire.For existing designs, a load of 30 g is applied during assembly, corresponding to a stress of 327 MPa on current carbon ber of 34 µm.As the installation procedures are sensitive, all the changes in the accelerator complex require in-depth studies.That is why nowadays the load has not been increased.The result for δ m ax gives us an opportunity to evaluate the inuence of the pre-load.
The maximal deection is therefore plotted as a function of the pre-load for the CNTYs with diameters 10, 20 and 30 µm (density of 1.3 g.cm -3 , cf.
subsection "Preparation of the tensile tests") and the CF of diameter 34 µm (density of 1.7 g.cm -3 ) (Fig 10-a).We observe for all the diameters, a decrease of 80 % of the maximal deection between 10 and 50 g of pre-load.For the same pre-load, there is a dierence of 75 % between 10 and 20 µm and 90 % between 10 and 30 %.Looking at the 30 g pre-load, the maximal deection is 4 µm, 15 µm and 34 µm for 10, 20 and 30 µm respectively.This corresponds to an applied stress σ p = F p /S = 4F p /(πd 2 ) of 2318, 777 and 356 MPa (computed with the measured real cross-sections areas: 127, 379 and 826 µm 2 respectively).We note that the stress applied for the CNTY of diameter 10 µm is much higher than its average strength calculated previously, which would forbid us from using that diameter.However, we must remember that these results are obtained for a given pre-load while Eqs.7 and 8 show us that the important quantity is not the pre-load, but the pre-stress.As already said, in the conguration currently used, we obtain an applied stress for the 34 µm CF and 30 g of preload of 327 MPa.Using this applied stress, ρ = 1.3 g.cm -3 and ω = 133 rad.s -1 in Eqs.7 and 8, we get the same δ max = 25 µm for the CNTYs independently of the diameter, whereas using ρ = 1.7 g.cm -3     for the CF, we get δ max = 34 µm for the CF ( This analysis shows the importance of a high pre-load stress during the installation in order to decrease the maximal deection and thus increase precision of the beam prole measurement, with respect to the current CF. In our simplied model, the important quantity is the stress and not the force (in α).Hence, thinking in terms of load, as usually done, can be misleading.

590
The comparison of the performances of the CNTYs with dierent diameters, for a same stress, thus seems to be more appropriate in our case.For a constant stress of 327 MPa, we observe a decrease of 25 % of the maximal deection with respect to the current CF, for the CNTYs with d = 10 and 20 µm in the PF conditioning.The copper-coating seems to degrade the 595 properties leading to a δ max twice and three times larger for the 20 and 30 µm CNTYs than for the CF.However, these results have to be considered carefully, keeping in mind that the real density could be dierent as the one used for the calculation, and that our model relies on assumptions.Considering the results from the Weibull analysis, we can evaluate the probability of failure for a stress of 327 MPa, for each yarn diameter and both PF and CC conditionings.Table 6 summarizes the results before and after the σ 0 correction.We observe that for d = 10 µm, both for the raw test data and for the operational WS, the probability of failure is quite small for both conditionings, but lower for the CC conditioning than for the PF conditionings.The behavior is partly dierent for d = 20 and 30 µm, with an increase of the failure probability P f for the CC conditioning with respect to the PF one.However, we still have an increase of P f for operational WS, with respect to the shorter wires used for the tests.P f reaches 67 % for d = 30 µm in CC conditioning after the σ 0 correction.

Conclusion
This work focused on the comparison of the mechanical properties of CNT wires between a conventional assembly of pristine wires on a paper frame and other wires copper coated at their ends.The study of the cross sections has shown that the structure of these threads is not homogeneous with, in particular, a greater packing at the core than at the surface.In addition, the overall packing seems to increase with the increase in diameter.
The direct copper plating without an intermediate layer on this type of wire is a novelty and has been tested to be able to meet the current specications of the new generation wire-scanner.The study of the copper-coating was rst of all hindered by the bad reproducibility of the samples, with very variable diameters and surface conditions which lead to much higher variations in the mechanical properties compared to the PF case.The copper / carbon interface shows copper penetration into the interstices of the wire in the surface layer.The tensile tests show an increase in the disparity of the mechanical properties with the increase in diameter.Furthermore, the mechanical strength was on average 30 % higher for the PF conditioning (910 MPa) than for the CC conditioning (640 MPa), for the three diameters.Weibull analysis also shows the importance of considering changes in the length of the sample which induces changes in σ 0 [80].The tensile tests carried out with PF conditionings used gauge lengths of 12 mm while CC batches had gauge lengths of 30 mm and the design length for the wire to be put in the WS is 150 mm.We therefore corrected σ 0 so that the average strength and probability of failure for a given load corresponds to the same 150 mm length for all the batches.We found, as expected, that the lower the m parameter, the larger the signicance of that correction on the strength results.The decrease of the scale parameter (σ 0-op ) when shifting to a larger volume model is coherent with the increase of the number of defects and their distribution in the volume.This conrmed our observations under the microscope on the non-uniformity of the structure and the variations of the numbers and types of defects.The Weibull modulus for the batch with a 10 µm nominal diameter is much larger than for the 20 and 30 µm batches, which indicates a more uniform distribution of the defects in the structure, possibly with less defects than for the 20 and 30 µm batches.Clearly, a solution to improve the reproducibility of the copper-coating process necessary to weld the wire in the inserts of the WS must be found or the entire insertion sub-system should be redesigned.
The calculation of the failure probabilities for conventional installation loads of 10 to 50 g showed the impossibility of installing 10 µm wires with these loads without breaking them.However, our model for the maximal deection of the wire, for a given pre-load applied during the installation of the wire, showed that the relevant quantity is not the load but the stress.
For a smaller diameter, a smaller load is required to get a given stress, the failure probabilities for a given stress show a much dierent tendency, with the smaller diameter being the most interesting, partly due to the smaller variability of the failure stress during our tests.
The conclusion of this study is that to increase the measurement accuracy on existing instruments during scans, it will be preferable to use small

Perspectives
In the present study, we saw (in Table 6) that the yarn that can carry the highest load is the one with the largest diameter.However, the highest tensile strengths are obtained for the 20 µm diameter.A possibility to combine these two parameters would be to braid yarns of small diameter and high mechanical resistance in order to get an equivalent diameter equal to 35 µm, which is the maximal diameter required for accelerator physics.This would lead to increase the cross-section of the new yarn, keeping the best mechanical properties of the bers.A braiding machine prototype has been developed at CERN and the rst braided yarns have been created using 100 µm CNTYs.
Mechanical tests will be performed on these new braided yarns to assess their strength distribution.
In the old WS we used carbon bers.This kind of material has been extensively used in research and industry.This has led to a good understanding of their mechanical properties.On the contrary, the development of CNTYs is more recent, and little is known about their properties, especially for applications in beam instrumentation which are very rare [84,85].Previous studies of these wires after proton [86], ions [87], electrons [88,89] or gamma ray irradiation [90,91] at low energies showed an improvement of mechanical resistance under certain conditions, possibly due to the creation of chemical bonds between layers of CNTs or between CNTs themselves.However, we currently have no results at very high energies -GeV / TeV.This is why projects are currently ongoing to irradiate CNTYs in the SPS at CERN, with protons of 450 GeV and integrated intensity of 3.2 × 10 15 particles.
Post irradiation analysis should give some answers concerning the evolution of their mechanical properties (and survival probability) under such harsh conditions.

Figure 1 : 4 C
Figure 1: (a) 3D CAD model of the new generation of fast wire-scanners (WS) for SPS, (b) illustration of the wire vertical movement and interaction with the beam.During a scan, the wire crosses 86 times the beam for a beam size of 500 µm and a scan speed of 20 m.s -1 , represented here by p1p86.(c) Beam prole reconstruction combining the signal, proportional to the number of interactions, and the wire position.

Figure 2 :
Figure 2: (a) Mounting of the wire on the Paper Frame (PF) and (b) assembly for clamping system in the tensile machine.(c) Typical preparation grid for the copper-coating of the extremities.(d) Quality control of the coating for a yarn of diameter 20 µm and (e) clamping systems for the CC conditioning test 140

Figure 3 :
Figure 3: (a) Transverse cross-section of a 20 µm diameter yarn with (b) two sites of interests.(c,d)SOI-1 (outer position) and SOI-2 (inner position) have been zoomed in and (e,f) binarized for the external position with grey level thresholds set at 122 and 110 respectively.(g to l) The same process has been performed for the 30 µm yarn with thresholds of 60 and 45 for SOI-1 and SOI-2 respectively.

Fig 3 -(
g), but due 190 to the larger dimensions, only the external diameter area of the wire was prepared by FIB cross section milling.Two sites of interests have been chosen Fig 3-h), the rst on the external layer of the yarn (Fig 3-i) and the second slightly lower but still on the outer layer (Fig 3-k).Both images have a magnication of 50000.The binarisation gives for SOI-1 a void density of 11 % with a threshold of 60 (Fig 3-j) and 10 % with a threshold of 45 for SOI-2 (Fig 3-l).The cross-section at the external layer of the 30 µm presents a similar aspect in the two sites compared.Groups of well aligned nanotubes are discernible and also, locally, small groups of non-aligned nanotubes are visible in the voids.SOI-1 and SOI-2 had a similar aspect with discernible groups of well aligned nanotubes and also, locally, small groups of non-aligned nanotubes, visible in the voids.

Figure 4 :
Figure 4: (a) extremities of three yarns, two (left and center) only coated with copper, the third (right) was also welded in silver paste.(b) Samples after FIB milling for crosssection observations.(c) Grey level SEM images of one cross-section at dierent zoom levels (x200, x2000, x5000 and x20000).copper-coating appears grey while the CNTY appears black.(d) Energy-dispersive X-ray spectrum of a sample highlighting the presence of copper, carbon, oxygen and sulfur.(e) maps of these four elements showing the presence of oxygen and sulfur in the transition region between the inner carbon yarn and the outer copper-coating.

Figure 5 :
Figure 5: Typical stress / strain curves for the PF (a, b and c) and CC conditionings (d,e and f).For each of these conditionings, response of samples from three dierent diameters: 10 µm (a and d), 20 µm (b and e) and 30 µm (c and f) have been plotted

to 32 %
for the 20 µm batches and 43 % for the 30 µm batches.The r 2 values indicate a fair quality of the linear ts, with a minimum of 0.88 for the d20_CC batch and a maximum of 0.96 for the d30_PF batch.In order to compare the new CNT yarns with the existing CF wires, other tests have been performed with 8 samples of carbon bers (as used in current WS) of diameter 34 µm and length 10 mm, with a PF conditioning only.Results for those tests are summarized in the last line of Table

Figure 7 :
Figure 7: Linear ts of results of tensile tests using a Weibull failure probability law.(left) PF samples, (right) CC samples

On Fig 8 ,
we plot the Weibull probability of failure before a given stress (P f (σ) = 1 − P s (σ)), rst for the raw test data (Fig 8-a,b) and then for the operational WS (Fig 8-c,d) with a solid blue line for d = 10 µm, dotted orange line for d = 20 µm and dashed purple line for d = 30 µm.We observe

Figure 8 :
Figure 8: Probability of failure before a given stress for the PF (a) and CC conditionings (b) for d = 10 µm (continuous blue line), d = 20 µm (dotted red line) and d = 30 µm (purple dashed line) for the raw test data and (c and d) for the operational WS.

[ 81 ]Figure 9 :
Figure 9: (a) Beam structure of the HiRadMat experiment after extraction from the SPS.The beam is structured with 4 batches spaced by 120 ns coming from the PS.Each batch are composed of 72 bunches spaced by 25 ns for a LHC beam.(b) Theoretical angular speed (in blue, left scale) and angular acceleration (in red, right scale) proles for a SPS wire-scanner at nominal angular speed (133 rad.s -1 ) (c) Model of the sub-assembly shaft -forks -wire and representation of the maximal deection (δ max ) for a stationary state case.

Figure 10 :
Figure 10: Maximal deection at the center of the wire using a stationary state model (a)as a function of the pre-load for CNTYs of 10, 20 and 30 µm with density of 1.3 g.cm -3 and a CF with a diameter of 34 µm and density of 1.7 g.cm -3 (b) for an applied stress of 327 MPa and (c) considering an applied stress of 80 % of the operational strength corresponding to a given couple (diameter, conditioning).
low density, provided they exhibit the same homogeneity of strengths than during ours tests, and that it would be useful to design a new xing system to use pristine wires without copper coating.

28
with α = ω λ/F p = ω ρ/σ p .Eq. 10 is an inhomogeneous linear ordinary dierential equation with constant coecients that can be solved explicitly in terms of trigonometric functions.The solution can be written as y stat (x) = 2R sin( αx 2 ) sin( α(L−x)

Table 2 :
Labels and numbers of samples for each couple of parameters

Table 3 :
Weibull parameters m and σ 0 and goodness of t r 2 They found a decrease of the shape parameter m from 9.4 to 3.1, and scale parameter σ 0 from 938 to 217 MPa with the increase of the diameter, which is coherent with our results.

Table 6 :
Probabilities (in %) of failure for a stress of 327 MPa, corresponding to a load of 30 g applied on a 34 µm CF yarn during the installation