Generation and Measurement of Sub-Micrometer RelativisticElectron Beams

Simona Borrelli ∗1, Gian Luca Orlandi1, Martin Bednarzik1, Christian David1, Eugenio Ferrari2,Vitaliy A. Guzenko1, Cigdem Ozkan-Loch1, Eduard Prat1, and Rasmus Ischebeck1

1Paul Scherrer Institut, 5232 Villigen PSI, Switzerland2Ecole Polytechnique Federale de Lausanne EPFL, Lausanne, Switzerland

April 13, 2018

The generation of low-emittance electron beams has received significant interest in recent years. Driven by the re-quirements of X-ray free electron lasers, the emittance of photocathode injectors has been reduced significantly, witha corresponding increase in beam brightness. At the same time, this has put increasingly stringent requirements on theinstrumentation to measure the beam size. These requirements are even more stringent for novel accelerator develop-ments, such as laser-driven accelerators based on dielectric structures or on a plasma, or for linear colliders at the energyfrontier. We present here the generation and measurement of a sub-micrometer electron beam, at a particle energy of330 MeV, and a bunch charge below 1 pC. An electron beam optics with a β -function of a few millimeters in the verticalplane had been set up. The beam was characterized through a wire scanner that employs a 1 µm wide metallic structurefabricated using the electron beam lithography on a silicon nitride membrane. The smallest (rms) beam size presentedhere is less than 500 nm.

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Nowadays, scientists are striving for electron beamswith extremely small transverse sizes and emittances,driven by the high demand of X-ray free-electron-lasers(XFELs) and novel accelerators development. In linearcolliders one of the main design goals is to achieve asmall beam size at the interaction point to maximize theluminosity. The design of the International Linear Col-lider, for example, uses a nanometer-sized beam at theinteraction point [1, 2]. Similar requirements have to bemet for advanced accelerator concepts, such as dielectriclaser accelerators [3, 4] and plasma wake-field accelera-tors [5, 6, 7]. These schemes utilize micron scale trans-verse accelerating structures, defined by either the plasmaor laser wavelength, and have been shown to achieve highaccelerating gradients. In a dielectric laser accelerator,the electron beam is accelerated through a dielectric mi-crostructure that requires beam transverse dimensions inthe sub-µm scale [8]. In the field of plasma based ac-celeration, reducing the transverse emittance down to thenanometer scale would open a path towards many differ-ent applications of this technology, such as colliders andlight sources [9]. Concerning XFELs the reduced beamemittance would allow for a compact design with lowerbeam energy and shorter undulator length [10, 11, 12].

The challenge of designing ultra-low emittance accel-erators brings the need for transverse beam size diagnos-tics with sub-micrometer resolution. However, the reso-lution limit of commonly used beam profile monitors hin-ders the possibility to measure sub-micrometer spot sizes[13, 14, 15] (details are provided in ’Discussion’).

We designed a novel wire scanner (WSC hereinafter)with resolution in the sub-micrometer range. In a WSCmeasurement a thin metallic wire scans the beam transver-sally. The generated particle shower (loss signal) is de-tected downstream, enabling the reconstruction of thebeam transverse profile (see ’Methods’). The design of aWSC with improved resolution requires a reduction of thewire width. We developed a high-resolution profile mon-itor exploiting nanofabrication techniques to produce a 1µm wide metallic stripe on a membrane by electron beamlithography and electroplating. The proposed design is abreak-through in the state-of-the-art of transverse profilemonitors ensuring sub-micrometer resolution as well asenabling the integration of a wire scanner on-a-chip. Wepresent in this paper the generation and characterizationof an electron beam with a 53 nm normalized emittance

Figure 1: Layout of the SwissFEL injector. The elec-tron beam is emitted in an RF photoinjector and then ac-celerated up to an energy of 330 MeV by an S-band RFbooster linac (Booster 1 and 2). An experimental cham-ber is located downstream of a bunch compressor and of-fers the possibility to insert into the beamline the designedwire scanner on-a-chip. We show a picture of the exper-imental chamber (bottom right) and the wire scanners in-stalled on sample holders in the load-lock pre-chamber(bottom left).

in the vertical plane, for a particle energy of 330 MeV anda bunch charge below 1 pC. This nanometer emittance hasbeen attained at SwissFEL [11, 16], the X-ray free elec-tron laser at the Paul Scherrer Institute. We achieved sub-micrometer spot sizes setting up an electron beam opticsto meet a 2.61 mm β -function in the vertical plane. Thepresented acceleration setup, beam optics and wire scan-ner on-a-chip, have enabled the generation and measure-ment of beams with rms sizes less than 500 nm. To thebest of the author’s knowledge, this is the smallest rela-tivistic electron beam measured at an FEL accelerator.

Results

Generation of sub-micrometer relativistic electronbeams. Figure 1 shows the layout of the SwissFEL injec-tor, where we generated and characterized the relativisticelectron beams with rms transverse sizes below 500 nm.

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In the SwissFEL injector, electron beams are emittedin an RF photoinjector gun [17] and initially acceleratedin an S-band RF booster linac (consisting of two sections:Booster 1 and 2) up to a maximum energy of 330 MeV[18]. In the last injector section, an experimental chamber[19] located downstream of a bunch compressor, offersthe possibility of scanning the novel wire scanner on-a-chip vertically through the beam to measure the verticalbeam profile.

The beam size was brought down to sub-micrometerscale by minimizing the beam emittance at the photoin-jector and the vertical β -function at the interaction pointwith the wire scanner (see section ’Methods’). The emit-tance was minimized by suitably reducing the laser spotsize on the cathode and by operating the gun at a very lowcharge (below 1 pC) where space-charge effects are neg-ligible. The measured vertical normalized emittance was53 nm, with estimated errors of ∼ 10%.

Once the gun is optimized for the smallest emittance,the achievement of a sub-micrometer size hinges on theminimization of the vertical β -function. For this pur-pose, we calculated and implemented in the acceleratora specifically suited optics. The computed vertical β -function at the wire scanner location was 2.61 mm.

Using an electron energy of 330 MeV and the presentedvertical normalized emittance and β -function, we wereable to generate a beam with an expected vertical size of460±20 nm at the wire-scanner location.

Beam profile measurements with sub-micrometer res-olution. The goal of measuring sub-micrometer beamsizes can not be achieved using conventional profile mon-itors such as screens and wire scanners, since their resolu-tion is typically limited to the micrometer scale (see sec-tion ’Discussion’). Among them wire scanners are highlypromising devices in terms of spatial resolution, whichmainly depends on the wire width. In the conventionaldesign this dimension is constrained to a few microme-ters [20] (see section ’Methods’). To overcome this lim-itation, we exploited the possibilities offered by nanofab-rication techniques to develop a novel WSC on-a-chipwith improved sub-micrometer resolution. The device wepresent here consists of a silicon chip with a silicon nitridemembrane at the center (cf. Fig. 5). On the membranetwo gold stripes are produced by electron-beam lithogra-

Figure 2: Wire scanner beam profile measurements.Beam vertical profile measurements performed scanningthrough the beam a 5 µm tungsten wire (in blue), a 2 µm(in green) and a 1 µm (in purple) gold stripe. For eachwire, we show three sequential and suitably normalizedbeam profile measurements.

phy and electroplating. They are characterized by differ-ent widths, namely w1 = 1 µm and w2 = 2 µm. Conse-quently, their rms geometrical resolutions are 0.3 and 0.6µm respectively (see ’Methods’). A vertical scan throughthe beam is performed for each stripe independently tomeasure the beam profile. For comparison, we also scanthrough the beam a conventional cylindrical 5 µm tung-sten wire (cf. Fig. 5(b)) whose rms geometrical resolutionis 1.25 µm [15].

In Fig. 2 we present measurements of the beam verticalprofile obtained scanning each of the three wires throughthe beam and acquiring the corresponding loss signal by abeam loss monitor (BLM). For each wire, we show threesequential beam profile acquisitions. We evaluated therms size of each of the three profiles. In Table 1 we reporttheir mean values σrms, with their associated statistical er-rors. Only the σrms from the 1 µm gold stripe measure-ments is comparable with the expected beam dimensionof 460± 20 nm. This behavior can be attributed to theresolution limits of the 5 µm tungsten wire and the 2 µmgold stripe. The measured traces are indeed the convolu-tion of the beam profile with the wire cross section. Thecylindrical shape of the 5 µm wire is clearly visible in Fig.2.

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Nevertheless, the beam size can be extracted from themeasured profiles fitting the data with the convolution ofa function describing the wire shape and one describingthe beam, which we assume to be Gaussian (details areprovided in section ’Methods’). Figure 3 shows one ofthe three beam profiles measured by means of the conven-tional 5 µm W wire, the novel 2 and 1 µm gold stripes,and the corresponding fit curves. It also shows the re-constructed Gaussian profiles obtained by the describeddeconvolution. The profile measured by the 1 µm goldstripe and the corresponding reconstructed Gaussian pro-file are comparable. This confirms the goodness of ourinitial assumption of a Gaussian beam shape.

The beam vertical sizes σy derived from the fit proce-dure are summarized in Table 1. Each value is the aver-age of the fit sigma over the three sequential beam profilemeasurements, with the corresponding standard devia-tion. The measured sizes are in good agreement with eachother and with the expected beam dimension of 460±20nm. The results support the conclusion that by apply-ing this analysis we can reconstruct the beam size fromthe profiles acquired with all three wires. It should benoted though that this analysis is only valid for Gaussianbeams. Conversely, the 1 µm stripe can be used to accu-rately measure the profile of beams with transverse sizeof 400-500 nm and directly extrapolate the beam dimen-sion, without the need of an analysis demanding a-prioriassumptions on the beam shape. Since the resolution limitis lower than the beam dimension the effects of the con-volution in the measured profile are negligible, whereassmall details would be washed out by the convolution witha larger wire. The σy and σrms of the profile measuredwith the 1 µm stripe are indeed in good agreement, withan error below 9%.

Discussion

We have demonstrated the generation of sub-micrometerrelativistic electron beams at SwissFEL and their charac-terization via wire-scanner profile measurements.

This is a particularly promising result in view of ad-vanced accelerator concepts experiments. A notable ex-ample is the development of an all-on-a-chip dielectriclaser accelerator, pursued by the Accelerator on a ChipInternational Program [21]. A proof-of-principle exper-

(a)

(b)

(c)

Figure 3: Beam vertical size reconstructions from wirescanner measurements. One of the three profiles mea-sured scanning through the beam (a) the conventional 5µm W wire and the novel (b) 2 µm and (c) 1 µm Austripes. We show in dotted black line the fit curve and insolid colored line the reconstructed Gaussian beam pro-file. Refer to Table 1 for the corresponding beam sizes.

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5 µm W 2 µm Au 1 µm AuResolution (nm) 1250 600 300

σrms (nm) 1967 ± 16 890 ± 2 449 ± 32σy (nm) 462 ± 11 491 ± 4 491 ± 5

Table 1: Beam vertical size and wire resolution. Thefirst row shows the wire resolution. σrms is the averagerms beam size over three beam profile measurements. σyis the mean value of the sigmas from the fit of the threeprofiles.

iment of high gradient dielectric laser acceleration willbe conducted at PSI using the SwissFEL high-brightnesselectron beam [19, 22]. Generating electron beams withsub-micrometer spot size will be mandatory in order toachieve full transmission through the accelerating struc-ture [8].

The characterization of sub-micrometer beams requirethe development of diagnostics with unprecedented spa-tial resolution. Several different techniques are commonlyused to measure the beam transverse profile. Screens arethe most used two-dimensional beam profile monitors. Inthe case of the SwissFEL YAG:Ce screens the spatial res-olution is 8 µm with a smallest measured beam size of 15µm [14]. A higher spatial resolution has been achieved atthe UCLA Pegasus laboratory utilizing a 20 µm YAG:Cecrystal with an in-vacuum infinity-corrected microscopeobjective coupled to a CCD camera. This set-up allowedmeasurements of beam sizes down to 5 µm and transverseemittances of 5 nm × 10 nm [23]. The spatial resolu-tion of optical transition radiation screens (OTRs) is onlylimited by the camera sensor and optics [13]. In the Ac-celerator Test Facility 2 at KEK, a vertical beam size of750 nm has been measured by means of OTR monitors[24, 25]. Nevertheless, OTRs are limited by the emissionof coherent optical transition radiation from compressedbunches, which prevents their usage in FELs [26]. Laserwire scanners are one-dimensional profile monitors thatrequire a laser beam focused to a diffraction-limited waist.The minimum achievable laser waist and therefore mea-surable beam size is limited by the laser wavelength. Atthe SLAC Final Focus Test Beam, scientists have mea-sured an electron beam vertical size of 70 nm by means

of a laser beam split and folded onto itself to produce aninterference fringe pattern [2]. The minimum achievablelaser wavelength coupled with space constraints and costsrepresents the main limitation of such profile monitors[13].

In this work we focused on wire scanners, since theyare the most promising profile monitors in terms of spatialresolution. The latter is limited by the encoder readout,the wire diameter and vibrations. In SwissFEL, a wire-geometry dominated resolution of 1.25 µm was reachedwith a 5 µm tungsten wire. This was achieved thanks to amotion system provided of an encoder with resolution of0.1 µm and measured wire-vibrations largely below thegeometrical resolution [15, 20]. Therefore, a natural wayto push the geometrical resolution of a WSC towards thesub-micrometer scale was by decreasing the wire diame-ter. However, the strength of a wire reduces with its di-ameter. Thus, the conventional manufacturing techniqueof stretching a wire onto a wire fork limits its width toa few micrometers [13]. We were able to overcome thislimitation and fabricate wires with a width down to 1 µmemploying innovative nanofabrication techniques.

MethodsAccelerator setup. Our goal was the generation of elec-tron beams with rms vertical size below one micrometer atthe interaction point with the wire scanner. The rms trans-verse size of the beam at position s along the acceleratoris

σ(s) =√

εn

γβ (s) , (1)

where β (s) is the β -function of the magnetic lattice at po-sition s, εn is the normalized emittance and γ is the elec-tron Lorentz factor. The beam size can be minimized byreducing the normalized emittance, increasing the beamenergy, and reducing the β -function at the interactionpoint. The final energy E of the SwissFEL injector is 330MeV, so we focused our efforts in minimizing the emit-tance and the β -function at the WSC location.

In RF photoinjectors, the emittance is determined bythree different contributions: intrinsic or thermal emit-tance, space charge, and RF fields [27]. To minimizethe space-charge contribution to the emittance increase,we operated at a very low charge, below 1 pC. The RF

5

gun was set to its maximum accelerating gradient, whilethe gun phase was empirically adjusted to minimize thebeam energy spread. In these conditions, the emittancewas practically determined by the intrinsic or thermal con-tribution, which is proportional to the laser beam size onthe cathode. We therefore reduced the laser iris to thesmallest possible diameter, corresponding to an rms laserspot size on the cathode of about 80 µm. The electronbeam emittance was measured in both transverse planesdownstream of the bunch compressor using the symmet-ric single-quadrupole-scan technique [28]. The measurednormalized emittances are εn,x = 42 nm and εn,y = 53 nmin the horizontal and vertical planes respectively, with es-timated uncertainties of ∼ 10%. The different transverseemittances derive from a slight asymmetry of the laserspot on the cathode.

Concerning the optics, the strengths of five quadrupolemagnets between the bunch compressor and the chamberwere calculated to minimize the vertical β -function at theinteraction point, while keeping the horizontal β -functionto a reasonable value. This optimization was performedusing the code ELEGANT [29]. Figure 4 shows the evo-lution of the β -functions from the bunch compressor tothe interaction point for the calculated optics. During theexperiment, the optics at the exit of the bunch compres-sor were iteratively matched to their design values usingseveral quadrupole magnets upstream of the bunch com-pressor. Then, the five quadrupole magnets were set tothe pre-calculated settings. Finally, the last quadrupolemagnet upstream of the chamber was empirically adjustedto minimize the beam size at the wire-scanner. This ad-justment compensated any possible errors in the incomingbeam optics at the bunch compressor, the electron beamenergy, the quadrupole field, and the exact position of thewire scanner.

The computed β -functions at the chamber location areβx = 0.273 m in the horizontal plane and βy = 2.61 mmin the vertical one. According to Eq. (1), the rms verticalbeam size is 460±20 nm for the considered experimentalparameters E, εn,y and βy (cf. Table 2).

Design and fabrication of sub-micrometer resolutionwire-scanner on-a-chip. Figure 5(a) shows the sketch ofa sub-µm resolution WSC on-a-chip. It consists of a 6x6mm2 Si chip having a 2x2 mm2 silicon nitride (Si3N4)

Figure 4: Evolution of the β -functions. Horizontal andvertical β -function evolution between the bunch compres-sor and the experimental chamber location at the Swiss-FEL injector. The blue rectangles and the magenta dotin the lower plot indicate the location of the quadrupolemagnets and the wire scanner, respectively. The magnetsare set to obtain a vertical β -function of 2.61 mm at thewire scanner position.

membrane at its center. On the membrane two metalstripes of different widths w1 = 1 µm and w2 = 2 µm,are electroplated. The separation between the two stripesis 0.67 mm. This distance has been chosen such that eachstripe can be separately scanned through the beam. Thestripe material selected is gold. This heavy metal pro-vides a strong scattering cross section for a good signal-to-noise ratio of the loss signal, as well as sufficient resis-tance against heating from the beam interaction.

The implemented fabrication procedure is an applica-tion of the nanofabrication technique described in [30,31]. The prototype fabrication starts with the evaporationof a Cr-Au-Cr metal layer sequence (5-20-5 nm) on a 250nm thick Si3N4 membrane. Then a 3.2 µm thick layer ofpoly-methyl-methacrylate (PMMA) resist is spin-coated(cf. Fig. 6(a)). The two Cr layers ensure better adhe-sion between Au and the membrane as well as the resist[30]. In a second step, applying electron beam lithogra-phy we wrote two parallel stripes into the resist, expos-ing it to a 100 keV electron beam at 5 nA beam currentand a dose of 1900 µC/cm2. The electron beam changes

6

(a) (b)

Figure 5: Sub-micrometer resolution wire scanners on-a-chip. Panel (a) Sketch of a sub-µm resolution WSC on-a-chip: 6x6 mm2 Si chip with a central 2x2 mm2 Si3N4 250 nm thick membrane. Two gold stripes of widths w1 = 1µm and w2 = 2 µm are electroplated on the membrane. The stripes thickness is 3 µm. Panel (b) Sub-micrometerresolution wire scanners on-a-chip (center and left) and a conventional 5 µm tungsten wire scanner (right), mountedon sample holders.

the chemical and physical properties of the PMMA resist,making it soluble in the developer solution. In particular,the exposed regions were developed by immersing the re-sist in a solution of isopropanol and water (7:3 by volume)and then rinsing the sample in de-ionized water and blow-drying it in a N2 gas jet. The development time was 45s, and as a result the exposed parts of the membrane havebeen completely removed (cf. Fig. 6(b)). After the devel-opment, we etched the sample by Cl2/CO2 plasma for 45s, to remove the top Cr layer and reveal the underlying Ausheet. The developed resist trenches were subsequentlyfilled with Au by electroplating in a cyanide-based plat-ing bath at a plating current density of 2.5 mA cm−2 for14 minutes. After the electroplating, the PMMA resistwas completely removed by ashing in an oxygen plasmafor 15 minutes. In this way, only the Au stripes remainedon top of the membrane (cf. Fig. 6(c)). The manufacturedsamples were inspected and characterized with a Scan-ning Electron Microscope (SEM). Figure 7 shows SEMimages of a 2 µm and a 1 µm wide Au stripe on the Si3N4membrane. The measured stripe thickness is 3 µm.

Detection setup. Figure 8(a) shows a schematic draw-ing of the experimental chamber in the SwissFEL in-jector, employed to perform the wire scanner measure-ments. The chamber is equipped with an in-vacuummanipulator operated by a 2-phase stepper motor via afeed-through. Four sample holders are mounted on themanipulator where four different samples can be settled.The stepper motor translates vertically the manipulator sothat a sample can be inserted into the SwissFEL vacuumchamber along this direction and brought to the interac-tion point with the electron beam. By using a load-lockpre-chamber, the samples can be installed on the sampleholders without breaking the vacuum employing a manu-ally controllable manipulator. [19].

In the chamber we installed the sub-µm resolutionWSC on-a-chip as well as a reference WSC consisting ofa 5 µm tungsten wire. The wire in this case is mountedusing the conventional technique of stretching it onto thesample holder and fixing it between two pins (cf. Fig.5(b)). Fig. 8(b) shows the prototypes installed in theSwissFEL injector beamline.

During a WSC beam profile measurement, the wire isscanned through the beam along the vertical direction at

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E (MeV) Q (pC) β -functions Emittancesβx (m) βy (mm) εn,x (nm) εn,y (nm)

330 < 1 0.273 2.61 42 53

Table 2: Beam parameters. First and second column show the electron energy and the beam charge. εn,x and εn,y arethe measured normalized emittances in the vertical and horizontal plane. βx and βy are the computed horizontal andvertical β -function at the interaction point.

(a)

(b) (c)

Figure 6: Block diagram of the WSC on-a-chip fab-rication process (not to scale). Panel (a) Si3N4 mem-brane deposited on a Si chip. The membrane is coatedwith a Cr-Au-Cr layer. A 3.2 µm thick layer of PMMAresist is spin-coated on this Cr-Au-Cr layer. Panel (b) ThePMMA resist is exposed by electron beam lithography towrite in it two parallel stripes. Exposed resist regions arethen developed by immersion in a mixture of isopropanoland water. Panel (c) The developed membrane trenchesare filled with Au by electroplating. The PMMA resist isremoved by ashing in an O2 plasma.

(a)

(b)

Figure 7: Scanning electron microscope pictures ofnanofabricated stripes. The gold stripes are electro-plated onto a Si3N4 membrane. Panel (a) Tilted view ofthe 2 µm wide gold stripe edge. The viewing angle is 50◦.The stripe thickness was measured from the SEM imageto be 3 µm. Panel (b) Tilted view of the 1 µm wide goldstripe.

8

(a)

(b)

Figure 8: SwissFEL Injector experimental chamberand WSC prototypes installed in the beamline. Panel(a) Schematic drawing of the experimental chamber. Anin-vacuum manipulator, operated by a 2-phase steppermotor, is equipped with four different sample holders toharbor samples. A load-lock pre-chamber allows the in-sertion of samples in the beam pipe without breaking theaccelerator vacuum using a manually controllable manip-ulator. Panel (b) Wire scanners installed in the SwissFELInjector beamline: (1) conventional 5 µm tungsten wire,(2) wire scanner on-a-chip.

a constant velocity. The wire position is acquired by anabsolute optical encoder (0.1 µm resolution). When theelectron beam intercepts the wire a shower of primaryscattered electrons and secondary emitted e+ e− γ is pro-duced. The shower intensity is proportional to the fractionof the beam intercepted by the wire and represents the sig-nal of interest (loss signal). The loss signal is detectedoutside of the vacuum chamber by a beam loss monitor(BLM) installed 4.5 m downstream of the experimentalchamber. SwissFEL BLMs consist of a scintillator fiber(Saint Gobain BCF-20) wrapped around the beam pipe.This scintillator fiber is connected via a plastic opticalfiber to a photomultiplier tube, which has remotely ad-justable gain in the range [5 · 103, 4 · 106]. The signal isfinally sent to an ADC unit for digitization and processing[32]. The BLM gain was set to 9 ·104. This value guaran-teed a suitable signal quality and amplification during thebeam profile measurement with the three wires.

For every wire position along the beam we measuredthe loss signal for one second at a beam repetition rate of10 Hz. Every point in the beam profiles presented in Fig.3 is the average of these acquired values.

Data processing. Every infinitesimal element of the wirewidth induces on the beam a loss that is proportional to theproduct of the wire thickness and the beam distribution[33]. Under the assumption of a Gaussian beam shape themeasured loss signal is given by

f (y; ∆,α,σ ,γ) =∫

∞

−∞

t(u)[

∆+α e−(u−y−γ)2

2σ2

]du , (2)

where y is the wire position along the measurement direc-tion and t(·) is a function describing the wire thicknessshape. α , γ are the Gaussian function amplitude and cen-troid respectively; ∆ is an offset and σ is the Gaussianfunction standard deviation. The data were fitted throughthis function, with free parameters ∆,α,σ ,γ .

The conventional 5µm tungsten wire is cylindrical,hence to describe the wire shape we choose the function

t(u) =

{2√(D

2

)2−u2 for u ∈[−D

2 ,D2

]0 otherwise ,

(3)

where D = 5 µm is the wire diameter.

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Instead, the 2 and 1 µm gold stripes are rectangularso the proper function to describe their shape is the stepfunction

t(u) =

{tw for u ∈

[−w

2 ,w2

]0 otherwise ,

(4)

where tw = 3 µm is the stripe thickness and w is the stripewidth.

Since the tungsten wire radius and the widths of thegold stripes are known from measurements, it is not nec-essary to consider them free parameters in the fit.

Wire scanner geometrical resolution. The geometricalresolution r of a wire is defined by its rms size [13, 15].The square rms size of a wire whose thickness is describedby the function t(·) is

σ2rms =

∫ +∞

−∞t(u)(u−< u >)2 du∫ +∞

−∞t(u) du

, (5)

where

< u >=

∫ +∞

−∞t(u)u du∫ +∞

−∞t(u) du

. (6)

A wire that is round in cross-section has an rms size equalto D/4 [34], since its thickness is described by the func-tion t(u) in Eq. 3. As a result, the 5 µm W wire geomet-rical resolution is equal to r = 1.25 µm. For a rectangularstripe we have r = w/

√12 (cf. Eq. 4). Therefore, the

geometrical resolutions of the 1 and 2 µm Au stripes areequal to 0.3 and 0.6 µm, respectively.

Data availability. The data that support the findings ofthis study are available from the corresponding authorupon request.

Competing Interests. The authors declare that they haveno competing financial interests.

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AcknowledgementsThe authors would like to express their sincere thanksto Thomas Schietinger for his careful proof-reading ofthe manuscript and to Beat Rippstein for his help dur-ing the mounting of the wire scanner on-a-chip. Weare furthermore grateful to the SwissFEL vacuum, oper-ation and laser groups for their support. This researchis supported by the Gordon and Betty Moore Foundationthrough Grant GBMF4744 to Stanford.

Author ContributionsM.B., S.B., C.D., R.I., G.L.O. designed the wire scan-ner on-a-chip. V.G. nanofabricated the devices and withS.B. characterized them. S.B., R.I., G.L.O. designed theexperimental set-up. E. P. calculated the optics and min-imized the beam size at the wire-scanner location duringthe experiment. E. F. and E. P. set up and transportedthe electron beam through the accelerator. S.B., E.F. andR.I. installed the wire scanners. R.I. and E.P. wrote thedata acquisition codes. S.B., E.F., R.I., G.L.O., C.O.L.,E.P. performed the beam profile measurements. S.B., R.I.and G.L.O. performed the data analysis. S.B. wrote themanuscript, which was enriched by all the co-authors sug-gestions.

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