Evelyne Salançon

Alain Degiovanni

Laurent Lapena

Roger Morin

From measuring electron charge to exploring particle-wave duality: a new didactic experimental approach

This paper points out the strong didactic potential of an experiment originally intended for electron source research. Using a dual stage micro-channel plate in a low-energy electron point projection microscope, electrons are spatially detected one by one. Field electron emission affords wide-ranging intensity enabling the electron charge to be determined by comparing counting and analog measurements. The same setup is used to illustrate buildup of an interference pattern from separate low-energy electron detection, thereby enabling the Planck constant to be determined.

Both granular and continuous signals are directly observable in this educational approach.

INTRODUCTION

Physics students obtain an understanding of electrons as particles through didactic experiments [START_REF] Paul | On thermionic emission and the use of vacuum tubes in the advanced physics laboratory[END_REF][START_REF] William | Determining e/m with a Bainbridge tube: Less data, more physics[END_REF][START_REF] Price | Electron trajectory in an e/m experiment[END_REF] . Examples include measuring the ratio (q/m) between the charge and the mass of the electron to confirm students' physical representation of electrons. When a Millikan experiment [START_REF] Müller-Hill | Control and stabilization: making Millikans oil drop experiment work[END_REF][START_REF] Ray | The Millikan oildrop experiment: Making it worthwhile[END_REF][START_REF] Mark | Millikan Oil-Drop Experiment in the Introductory Laboratory[END_REF][START_REF] Kapusta | Best measuring time for a Millikan oil drop experiment[END_REF] or shot noise analysis [START_REF] Kraftmakher | A shot-noise experiment with computer control and data acquisition[END_REF][START_REF] Earl | Undergraduate Experiment on Thermal and Shot Noise[END_REF][START_REF] Spiegel | Shotnoise measurements of the electron charge: An undergraduate experiment[END_REF] is added, they are also able to measure the electron's charge alone. While these experiments are very useful to confirm the particle behavior of the electron, they are necessarily based on the collective response because there is no individual signal from a single electron.

Electron diffraction experiments [START_REF] Jnsson | Electron Diffraction at Multiple Slits[END_REF][START_REF] Merli | On the statistical aspect of electron interference phenomena[END_REF][START_REF] Matteucci | Two further experiments on electron interference[END_REF][14][START_REF] Frabboni | Two and three slit electron interference and diffraction experiments[END_REF] allow students to approach wave mechanics too.

There is even a ready-made experimental setup available from a well-known educational company [START_REF]Electron Diffraction[END_REF] . In recent years, the particle-wave duality of matter [START_REF] Nairz | Diffraction of complex molecules by structures made of light[END_REF][START_REF] Carnal | Youngs double-slit experiment with atoms: A simple atom interferometer[END_REF] , and especially of electrons, was illustrated in different experiments based on the 1963 thought experiment of Richard Feynman [START_REF] Feynman | The Feynman Lectures on Physics[END_REF] . Carried out on a variety of particles (high energy electrons [START_REF] Tonomura | Demonstration of singleelectron buildup of an interference pattern[END_REF][START_REF] Frabboni | Elastic and inelastic electrons in the double-slit experiment: A variant of Feynmans which-way set-up[END_REF] , low energy electrons [START_REF] Chesnel | Young-type experiment using a singleelectron source and an independent atomic-size two-center interferometer[END_REF][START_REF] Bach | Controlled double-slit electron diffraction[END_REF] , photons [START_REF] Jacques | Single-photon wavefront-splitting interference[END_REF][START_REF] Dimitrova | The wave-particle duality of light: A demonstration experiment[END_REF][START_REF] Aspden | Video recording true single-photon double-slit interference[END_REF] ), these Feynman experiments are, however, too complex and costly for educational use.

Here, we use a low-energy electron point projection microscope [START_REF] Stocker | Low-energy electron and ion projection microscopy[END_REF][29][START_REF] Eisele | Nanometer resolution holography with the low energy electron point source microscope[END_REF][31] to independently determine certain particle and wave characteristics of the electron. First, its charge is determined by concurrently using an analog measurement method and a counting measurement method. Its mass can therefore be determined through the deflection in an electric or magnetic field. Then, its particle-wave behavior is observed and measured via the single-electron buildup of an interference pattern. This offers an experimental illustration of the de Broglie law, and the Planck constant can be deduced from these three measurements. In addition, the experiment allows students to directly observe the electron's ability to probe matter.

The granularity of electrons is observable and measurable only if the emission process gives access to several orders of magnitude of electron intensity. Field electron emission meets this condition, offering access to several orders of magnitude of emitted intensity described through the Fowler-Nordheim equation (1) [START_REF] Forbes | Physics of generalized Fowler-Nordheim-type equations[END_REF] .

I = A(Φ).F 2 .exp(-6.49 × 10 9 Φ 3 2 F ) (1)
with A(Φ), a pre-factor depending on the work function Φ, and F , the electric field applied to the emitter that is given by: F = V β.r for a metal tip of end-radius r supplied to the voltage V in front of a mass-connected extractor. β is a geometric pre-factor. In the case of a plane emitter/extractor setup, this electric field is simply F = V d , with d the distance between the emitter and the extractor. In practice, a decreasing linear plot ln I V 2 versus ( 1 V ) is the signature of a field emission process. In this experiment, linearity is observed for 10 orders of magnitude.

II. EXPERIMENTAL SETUP

The experiment uses a low-energy electron point projection microscope [START_REF] Fink | Holography with low-energy electrons[END_REF][START_REF] Daineche | Source of low-energy coherent electron beams[END_REF] which produces geometric projection shadows and in-line holograms of an object. This object needs to be partially opened in order to obtain a reference beam (Fig. 1). Here, the electron source relies on a field emission process. The source consists of a celadonite insulating crystal placed at the apex of a carbon wire [START_REF] Salançon | Single mineral particle makes an electron point source[END_REF] . The intensity is measured using a picoammeter (Keithley 485) floating between the power supply and the source. The object used here is a lacey carbon film (AGS166-3H from AgarScientific): a copper grid covered by a random-holed carbon layer. It is grounded. To increase microscope magnification, the grounded object is moved towards the source (from 2.5 cm to 100 nm) with a piezoelectric actuator (MS30 from Mechonics). This piezoelectric actuator is mounted on the same mechanical system as the source. Rotation of the system makes it possible to turn the beam towards the detector.

A dual stage micro-channel plate fluorescent screen assembly (F2225-21P from Hamamatsu) detects single low-energy electrons from 10 to 1000 eV. We recently showed that in counting mode, this apparatus enhances the resolution of a low-energy electron microscope [START_REF] Salançon | High spatial resolution detection of low-energy electrons using an event-counting method, application to point projection microscopy[END_REF] . In the present experiment, this mode is used both to determine the electron charge and to show the particle-wave duality. This detector is placed 86 cm away from the source. Images and films of the fluorescent screen are recorded using a cooled CCD camera (Model C4742-95 from Hamamatsu). Here, a counting mode record is directly obtained from the integrated software HiPic from Hamamatsu: the stain produced by the impact of one electron is reduced to one pixel, and each impact counts as 1.

In this experiment, electron energy is directly determined by the emission voltage V e . The emission process being a Fowler-Nordheim type, intensity increases exponentially with voltage. For teaching purposes, two adjustments to this experiment setup can be envisaged:

• First, the source could be changed, employing a tungsten tip field emitter or any field electron emitter. However, the advantage of using a celadonite source is that the pressure can be 3 orders of magnitude higher, up to about 10 -6 mbar , than with a tungsten tip.

• Second, a cheaper camera could be used and the counting mode treatment performed with a free external plugin like QuickPalm 37 . However, this would mean recording and treating every single event's analog image, which would require significantly increased computer memory, from 225Mo to 3Go.

III. ELECTRON CHARGE MEASUREMENT

To perform the electron charge measurement, the shadow of the lacey carbon film is recorded both in analog and in counting mode (Fig. 2) thanks to the greatly increased electron velocity in the circuit. The velocity of electrons after the grounded object in the experiment is given by the emission voltage as: v = 2eVe me ∼ 10 7 m.s -1 with m e the electron mass and e, the electron charge. Electrons are detectable one by one as they hit the detector with a high enough energy (or momentum). The electron charge is first determined from measurements at a given emitted current, i.e. at a given voltage V e . Then measurements for different V e are plotted via a Fowler-Nordheim plot for statistical analysis leading to more precise determination of the electron charge.

A. Measurements at a given voltage

The electrical intensity is the emitted charge q in a time t:

I e = q t = N e e t (2)
with N e the number of emitted electrons in a time t and e the electron charge.

To enable the electrons to be counted, the measurement has to be performed at very low intensity, as low as 1 pA. This is possible with our setup, since only a fraction of the electron beam is detected. To determine the electron charge from Eq. 2, we apply the following procedure:

• First, determine the analog emitted intensity (I e );

• Second, count the detected hits(n d );

• Third, determine the ratio of detected hits (n d ) to emitted electrons (N e ), which gives the number of electrons emitted.

Determining analog emitted intensity

As its name implies, the picoammeter cannot measure intensity below picoamps, which is why the first step is required. We exploit the fact that, in continuous mode, analog intensity I e is related to gray level gl(t) of the image of an illuminated part of the detector for exposure time t.

For example, here (Fig. 2a), the intensity measured for V e = -440 V corresponds to I e = I 440 = 10 pA, the average gray level measured on the illuminated part on Fig. 2a is gl 440 = 2030 for an image composed of 10 frames of 10 s (t 440 = 100 s) and a channel plate applied voltage of about 1.2 kV. Thus, the analog calibration of the gray level for this channel plate amplification is:

I e = gl t × t 440 gl 440 × I 440 (3)
The following factors require particular attention:

• image noise: each image needs to be corrected with a long exposure time noise image,

• image saturation: amplification of the channel plate and frame time need to be tuned to prevent saturation,

• channel plate amplification: if the amplification is changed, recalibration of Eq. 3 is required, using measurements made before and after the change,

• area used to find the gl on each image (size of rectangles in Fig. 2), which has to be virtually identical between any two measurements.

Counting detected hits

For low intensity 10 -3 < I e < 10 -1 pA an image can be recorded in analog mode and in counting mode in the highest-intensity region detected. For V e = -350V , Fig. 2b gives an analog intensity deduced from gray level analysis of about I 350V = (3.51 ± 0.05) × 10 -3 pA.

Determining ratio of detected hits to emitted electrons

To determine this ratio, we need to know the angular distribution of emission and the electron detection efficiency of the detector.

The electron's angular distribution in the cone angle is measured by rotating the source/sample assembly with respect to the detector. It is here assumed that the solid angle is the same whatever the emission voltage. Fig. 3 shows 3 meshes of the copper grid (900 pixels). The shadow actually extends along 12 meshes, but the detector is not large enough to detect the entire angular distribution. On the accessible signal, intensity is almost normally distributed (plot in in Fig. 3b) with a standard deviation σ = (300 ± 50) pxls, determined by fitting the experimental curve. Assuming that the intensity distribution is isotropic, the emission area in the plane of the detector is obtained by integrating the normal distribution determined over the area, S = 2πσ 2 . However, this yields major uncertainty:

S = (6 ± 2) × 10 5 pxls
The manufacturer of the channel-plate specifies 60% for the open area ratio, with a detection efficiency η that varies from 50 to 85% depending on the electron energy, open area ratio and electron angle incidence [START_REF] Galanti | A High Resolution, High Sensitivity Channel Plate Image Intensifier for Use in Particle Spectrographs[END_REF] . This means that the actual number of electrons is about (1.4 ± 0.4) times the number of hits. Therefore, the number of emitted electrons is given by:

N e = 1.4 × S × n d (4)
with n d the number of detected hits per pixel measured at the highest signal intensity and S the emission area in pixels. From this direct analysis of the data obtained in the above three steps, the electron charge was here determined at V e = -350 V:

e = I e 1.4×S×n d t = 3.51 × 10 -3 × 10 -12 1.4×6×10 5 ×19.4 555 = 1.2 × 10 -19 C (5)
Given the accumulation of uncertainties here, result is highly satisfactory:

• the pre-factor in analog mode is determined for each amplification change;

• the distribution in the detector plane is approximated to a normal law and is not measured everywhere (which would be possible with a more precise angular distribution measurement);

• the number of detected hits depends on the threshold used. For example, with Fig. 2d at V e = -300 V, the highest-intensity region is still visible but the signal-to-noise ratio is clearly lower than in other cases ((S/N ) = 10). If the threshold used for the counting mode is too low, false hits are detected; if it is too high, hits are lost. For the highest-intensity measurements, the threshold is fixed with reference to the gray level distribution without a signal: the threshold is fixed at the upper limit of this measurement, giving a signal-to-noise ratio of up to 4000. For the lowest-intensity measurements, the threshold is fixed so as to obtain a signal-to-noise ratio of about 10.

We then used this method to perform electron charge measurement for different power supplies. The values in Tab.I clearly illustrate the accumulated errors: for the highest intensity levels measured (about 0.1 pA), the number of detected hits seems overestimated and for the lowest intensity levels (under 0.0001 pA), the number of hits is underestimated.

This is due in one case to false hits and in the other case to the poor signal-to-noise ratio.

To obtain a more representative value, measurements were performed subsequently over a large voltage range.

B. Measurements over a large voltage range

The objective here was to provide more robust results by decreasing uncertainty on analog and counting measurements. These measurements are not defined by their actual value but rather by their value on the Fowler-Nordheim fit obtained in each mode. A statistical study was performed over a large intensity range. Fig. 4a is the I(1/V ) semi-log plot in analog mode and (N e /t)(1/V ) in counting mode with Ne t = 1.4×S×n d t . Right (N e /t) and left (I e ) scales have the same magnitude and we can pass from one to the other by multiplying the right scale by the charge of the electron. To determine this charge in Fig. 4b, the right scale is shifted so that the data fits from analog and counting modes are perfectly aligned. Here, the different experimental data fitted with the same slope, V 0 = -5461 V, and gave an R squared of about 98%. Note that the actual measurements at -330 V, -350 V, -400 V in analog and in counting modes are not exactly on their respective fits. The emitted intensity is now directly comparable to the electron emission rate (i.e. 10 -6 pA = e × 8 e -/s). From this procedure, the electron charge is found to be e = 1.3 × 10 -19 C. Clearly, here, the error that most impacts electron charge measurements is the error on the angular distribution of electron emission and on dual micro-channel plate efficiency. Given the uncertainties on these values, the calculated uncertainty on the determined electron charge is particularly large. Thus, the electron charge found here is:

e = (1.3 ± 0.8) × 10 -19 C
To approach the actual SI base units e = 1.602 × 10 -19 C, channel-plate efficiency should be clarified and angular distribution should be measured more precisely. One way of doing this would be to place the detector closer to the source, enabling the whole signal to be measured.

Note that the Fowler-Nordheim curve for these intensity measurements plotted in Fig. 4c confirms the process involved here as field electron emission. For the highest intensities (I e > 1 µA), the plot changes and shows a level of saturation previously observed for this kind of source [START_REF] Salançon | Single mineral particle makes an electron point source[END_REF] . Field emission is observed for more than 10 orders of magnitude.

IV. DETERMINING PLANCK CONSTANT

The electron charge was measured with object far away from the source and a minimum emission voltage of -300 V to obtain a reasonable signal-to-noise ratio. At this voltage, the average electron emission rate is 100 electrons per second. The velocity of electrons after the grounded object is about v = 10 7 m.s -1 . The experimental apparatus being almost one meter long, electrons are in the experiment for about 0.1 µs. Although the source is not yet known to be a single electron source, it is possible to perform a kind of Feynman thought experiment involving particle-by-particle double slit interference pattern recording.

To perform such a double slit experiment, two "virtual sources" can be obtained by using an electrostatic biprism [START_REF] Donati | An Experiment on Electron Interference[END_REF] . In the lacey carbon film, some carbon filaments are very small and a cylindrical attractive field often appears surrounding them. This results either from the electrostatic influence of the source when the hole around the filament is large compared to the source-to-filament distance, or from positive charging under the electron beam when the secondary electron coefficient is larger than 1. This field deflects the electron beam which, after crossing the object, seems to come from two virtual sources placed in the real source plane 29 (Fig. 5a).

For example, the interference pattern shown in Fig. 6 was obtained for a source-object distance d = (19 ± 1) µm and the filament observed had a diameter about φ = (118 ± 9) nm (see Fig. 5c: the scanning electron micrograph of the lacey carbon film). The experiment is carried out at V e = -227 V. The electrical intensity is about 10 pA, corresponding to an average distance l = 14 cm between 2 electrons. Images are recorded every t f = 10 × 111 ms.

At this rate, an average number of 100 electrons are detected per frame on the whole detector. Fig. 6 corresponds to (1.5 × 1.5) mm 2 on the detector; the interference pattern appears clearly after one minute (see Fig. 6g).

The measured distance between fringes is i = λD a = 0.24 mm. The inter-source distance a, found by geometrical analysis from Fig. 5a, is: a = wd+φ(d+D) D . Fig. 5b shows a full view of the detector and gives: w = (0.72 ± 0.05) mm, then a = (280 ± 30) nm, the object-detector distance D = 86 cm, giving a wavelength λ = (0.08 ± 0.01) nm.

By using the deBroglie relationship, λ = h

FIG. 1 .

 1 FIG. 1. Low-energy electron microscope. A field emission source, biased to some V e = -100 V through a picoammeter, illuminates a lacey carbon film. The physical shadow of the film is observed on a dual stage micro-channel plate fluorescent screen assembly. Example of electron velocities are given for V e = -1000 V and I e = 1 µA.

Fig. 2c ,

 2c Fig.2c, the counting mode image for an exposure time t = 555 sec, gives an average number of hits n d = 19.4 hits/pxl. Because the number of hits in the shadow of the grid should be null, the signal-to-noise ratio (S/N ) is measured directly on the image. (S/N ) is the ratio between the gray level in the illuminated part and in the shadow of the grid. In Fig.2c(S/N ) = 500 and in Fig.2d(S/N ) = 10. Fig.2dshows the lowest signal-tonoise ratio measured in this work, with the uncertainty on the number of detected hits n d = (0.060 ± 0.006) hits/pxl.

FIG. 2 .

 2 FIG. 2. Depending on electron detection, continuous intensity or granularity of electrons are illustrated (a) For a few picoamps, picoammeter and gray level detection are required; gray level gives the intensity calibration; (b) For a few femtoamps, analog intensity is measured through the gray level when (c) the counting mode gives the number of detected hits; (d) For a few attoamps, the number of detected hits is given for the highest-intensity zone. Measurements are performed in rectangles.

FIG. 3 .

 3 FIG. 3. Measurement of the intensity distribution in the cone angle (a) counting mode imaging of the sample shadow (V = -360 V, I = 0.012 pA); (b) in blue: intensity profile along the white rectangle in (a) and in red: normal distribution with a standard deviation σ = (300 ± 50) pxls.

FIG. 4 .

 4 FIG. 4. (a) Black and green dots: Intensity versus inverse voltage for analog measurements (picoammeter and gray level measurements); Orange: electron emission rate deduced from counting mode imaging; (b) Alignment of data fits from picoammeter, analog mode and counting mode measurements; these fits are exponential decays with a constant of V 0 = -5461 V; blue circles: single measurements at V e = -330 V,-350 V and-400 V; (c) Fowler-Nordheim plot observable below 10 orders of magnitude using the full dataset.

FIG. 5 .FIG. 6 .

 56 FIG. 5. (a) Geometrical representation of the experiment where s is the real source and φ, the biprism diameter; s 1 and s 2 are the "virtual sources" (b) Analog recording of the electron projection of the biprism: interference pattern from s 1 and s 2 in the plane of the detector appears in w; (c) Scanning electron microscope view of the filament used as biprism in the experiment, width about φ = 118 nm.

√

  2meE , the Planck constant is deduced from the wavelength measurement λ = (0.08 ± 0.01) nm, the electron mass m e = 9.31 × 10 -31 kg and the electron energy E = eV e = 227 eV: h = (6.5 ± 0.8) × 10 -34 kg.m 2 .s -1 V. CONCLUSION This paper describes an experiment originally intended for electron source research but which has strong didactic potential. Using a low-energy electron projection microscope, students can observe electron signals in two modes: continuous signals resembling a closed circuit and granular signals indicating individual electrons. This second mode enables an interference pattern buildup, which allows scope for Feynman thought experiments and meaof the Planck constant. A physical law, the Fowler-Nordheim law describing the emission of electrons by a field effect, makes it possible via statistical treatment to enhance the precision of charge measurement. The advantage of using a projection microscope is that important notions like source, object, imaging, magnification become easily accessible to any student using a simple light point source. Such experiments also provide opportunities to raise more subtle questions, like the role of the detection process in image formation, the trajectory of a particle or the diffraction of a wave. This experiment is used in highlevel university courses like masters' degrees in physics, as well as in vocational training for secondary school teachers. A teachers' group is already using experimental data from this training to prepare movies for young students in France, where particle-wave duality concepts are on the secondary school curriculum.

TABLE I .

 I Measurements for t = 555 sec and corresponding calculated electron charge for 3 power

	supply conditions
	V e (V)	-330	-350	-400
	I e (pA)	4.7 × 10 -4	3.51 × 10 -3	3.8147 × 10 -1
	n d (hits/pxl)	1.4	19.4	3336.4
	e (C)	2.2 × 10 -19	1.2 × 10 -19	0.8 × 10 -19

S. Frabboni, G.C. Gazzadi and G. Pozzi, Youngs double-slit interference experiment with electrons, Am. J. Phys. 75 (11), 1053-1056 (2007).

J. Bardon, A. Degiovanni, V. Georges, and R. Morin, Conducting, semiconducting and insulating objects observed by low-energy electron holography, Ultramicroscopy 92, 133-142 (2002).

ACKNOWLEDGMENTS

The authors would like to thank Marjorie Sweetko for improving the English of this article and IRES (institute of research in science education) teachers' group for its filming work


Evelyne Salançon

Alain Degiovanni

Laurent Lapena

Mehdi Lagaize

Roger Morin

A low-energy electron point-source projection microscope not using a sharp metal tip performs well in long-range imaging

come

A low-energy electron point-source projection microscope not using a sharp metal tip performs well in long-range imaging

1-Introduction

The normal low-energy electron point-source projection microscope [1,2,3,4] is a lensless system where an electron point source illuminates a perforated object, and the "physical shadow" of the object is recorded on a more distant fluorescent screen. The so-called physical shadow corresponds to the interference between the reference wave that comes directly from the source and the object wave that results from object scattering. This Fresnel interference pattern is an electronic hologram of the object. Numerical reconstruction yields an image of the object in its position during the recording [5,6,7].The projection microscope is known to reach a magnification of about 10 5 with an experimental spatial resolution of about 1nm [8,9,10]. These characteristics are obtained using electron sources that consist of ultra-sharp metal tips with a tip radius of about 10nm [11,12]. The magnification of the microscope, G, directly depends on the distances between point source and object , and between point source and screen + :

= (1.1)
For ultra-sharp tips, the source-to-object distance can be decreased down to sub-micrometer level while retaining point-source behavior and large enough magnifications, without running the risk of the tip crashing into the object. We recently introduced an electron source [13,14,15] based on emissions from a single insulator crystal of celadonite deposited at the apex of a 10µm-diameter carbon fiber. In terms of the wave, this provides a point-source although, physically-speaking, the source is wide. The term wide-point-source can be used, since the source optically corresponds to a point-source but its geometry is wide. The wide-point-source cannot get closer than about 50µm from an object without any risk of crashing into it. Despite the weak projection magnification resulting from this limitation and some negative features described below, this source also presents major advantages compared to sharp metal tips. For example, it can operate in a relatively poor ultra-high vacuum or emit with wide emission angles, a crucial parameter for high-resolution imaging. To compensate for the weak magnification, a setup consisting of two Einzel lenses is added to the imaging system to provide images of any plane between the source and the entrance of the first lens. At electron energy of 100eV, a lens setup magnification of x70 was measured [16]. Combining projection and electronic lenses should therefore lead to magnification greater than × 10,000. This enables projection microscopy to work at high source-object distances while keeping the field on the object stable and limiting image distortions [17,18,19,20,21].

A microchannel-plate/fluorescent-screen assembly with a spatial resolution of about 100µm is the typical detection system used in low-energy electron projection microscopy. Recently, we showed that the resolution of the detection is 15µm [22,23] when a counting technique is used with a dual-stage microchannel plate (MCP), allowing this detection technique to deliver a resolution of some nanometers.

In this paper, we provide details of the source's construction, the microscope setup and the method used to record holograms. Various aspects of resolution on the images after reconstruction are also discussed, assuming normal working conditions with a source-to-object distance of 600µm.

2-Experimental setup

The design of the electron point-source projection microscope is described in figure 1 and an industrial drawing is provided in figure 2. The microscope operates under vacuum maintained with an ionic pump.

The electron source is a 10µm-diameter carbon fiber with a celadonite crystal at its apex [15].

This source and its characteristics are described in section 2.1. The source-to-object distance d, is controlled by a piezoelectric actuator (MS30 from Mechonics) providing distance control from 100nm to 2.5cm. Because of the source diameter, the minimum reachable source-to-object distance is about ≳ 50μ . The perforated object commonly used is a holey or lacey carbon film sufficiently perforated to obtain scattered-object and reference waves to the rear of the object. The object is generally connected to the electrical ground through a picoammeter. The source is mounted on an axis fixed on a rotating flange to orient the beam either towards a fluorescent screen alone or towards the lens. The object is fixed on the same axis and rotates with the source.

The entrance to the lens is approximately 30mm from the source depending on the source size and on the translation position. At this stage, the pure projection magnification is about x300.

The lens consists of two Einzel lenses. It is described in section 2.2, together with the methods used to enlarge the projection image and to improve lens performance in our configuration .

Finally, the detector is composed of a dual-stage MCP / fluorescent screen assembly from Hamamatsu (F2225-21P). It has a diameter of 4cm and it is placed 6cm from the lens exit fixed around a mu-metal cylinder. A window flange is 4cm from the screen. A camera Hamamatsu Orca flash 4.0 films the fluorescent screen through a Canon optical lens, with a 16-bit dynamic range. In analog imaging mode, which allows continuous image acquisition, the spatial resolution of the detector is about 150µm. In counting imaging mode, each electron impact is translated as '1' and their accumulation yields a detector resolution of about 15µm [23]. This system and its operation are described in section 2.3.

2.1-Electron point-source: preparation and characteristics

The electron source is composed of one celadonite crystal at the apex of a 10µm diameter carbon fiber. For ease of manipulation, 2 or 3mm of the fiber are left projecting from a 90μm inner diameter stainless steel tube where it has been inserted, as carbon fiber breaks very easily. The fiber is glued to the tube with silver lacquer. The larger tube is inserted into a Macor® support fixed on a rotating flange (see figure 3). The celadonite crystal is deposited at the apex of the carbon fiber (figure 4a) when all elements have been glued together and are in contact. The mineral celadonite is an insulator crystallized in the monoclinic system (figure 4b). When celadonite is ground, the overall crystal shape is a rectangular slab (1000 nm x 500 nm x 50 nm).

The celadonite crystal is deposited using a glass capillary with a tip aperture diameter of 10µm minimum (figure 4c). The crystal's powder is first dispersed under ultra-sound in deionized water. The capillary is filled with dispersed celadonite water and slight pressure is applied to the wide end of the capillary to form a small drop to buffer the apex of the carbon fiber. To obtain at least one crystal in the deposited water drop, dissolution requires about 0.2mg of celadonite powder in 10mL deionized water. Tens of electron sources were prepared in this way, all of them emitting. This electron point-source follows a Fowler-Nordheim regime over a 10 orders-of-magnitude current range with a saturation regime at the highest currents (typically 100nA and 500V applied voltage). Thus, the process observed is electric field emission. Yet the applied electric field is only some V/µm. Since field emission requires an electric field of some V/nm this means that there is an electric field enhancement at the metal/insulator interface [15].

Typically, when the object (the perforated carbon layer) is 1mm from the source, several hundred volts are applied to trigger the emission. Figure 5 shows three typical ( ) curves. The green curve corresponds to the electrical characterization of the source used in this article.

Electrical measurements were made with a source-to-object distance of about = 600μ .

Intensity is measured between the object and the electrical ground.

The experiments presented here were performed with the same source-to-object distance of 600µm. According to the imaging mode chosen, electron intensity is tuned through the voltage applied to the source. However, emission intensity could also be tuned through the source-toobject distance chosen. Moving the object closer to the source increases the electric field; emission intensity increases even if the voltage is constant. This tuning mode is not used here, due to a possible emission site change discussed in Results and discussion. The brightness of a particle source is given by:

( , ∆ ) = ( ∆ ) ×!
(2.1), with ( ∆ ) the emission intensity of the source at energy with a given relative energy dispersion ∆ / . $ is the surface of the emission site and Ω the solid angle of the emission.

Here, the brightness is about = 10 & '. () . *+ (& , comparable to field emission tips but with a larger emission angle 2, ≃ 60° (Ω~1*+), double that of the tips. This high solid angle improves spatial resolution [7] of the microscope, theoretically given by the Abbe diffraction

limits 0 = 1 ).2.3.
where λ is the wavelength and 4. '. = sin ,, the numerical aperture of a projector with , the half emission angle.

The source can even operate under a relatively poor vacuum: it still works at 8 = 10 () 9:+.

However, its life-time and its stability increase with good vacuum conditions, so pressure is maintained at 8 = 10 (; 9:+ for microscopy. The robustness of the source and its ability to work in poor vacuum conditions are great advantages in terms of experimental time and the risk of damage to the source.

Results shown here are from experiments performed at 8 = 10 (; 9:+ maintaining the same source-to-object distance = 600μ ; the emitted intensity is tuned by changing the voltage applied to the emitter.

2.2-Einzel lens magnification

The two Einzel lenses are illustrated in figure 6: the length of the system is 54.5cm; the entrance aperture is a diaphragm of 1mm and the exit has a diameter of 3cm. Because of the large number of voltages involved in the electron optical system, we fixed 3 voltages at zero ( <& , <= , <> ) and varied 2 voltages ( <) , <? ). In this experimental approach, two successive inversions of images were observed. Figure 7 schematically shows how the projection image is magnified, with 8 the pure projection plane and 8 ) the detector plane. The focal lengths, and therefore plane 8 , are unknown. However we know that 8 stands between the source and the entrance to the lens and that Einzel lenses are convergent with a focal length that decreases with the central voltage. First, projection is magnified by the first lens and the image is reversed; then the second lens reverses the image once again. Microscope magnification is given by the ratio: @ = × < between a pure projection magnification , where $ E , $ F B , $ F D are the sizes of the object and its images in planes 8 and 8 ) . A typical magnification obtained with the lenses of our experimental setup is shown in figure 8.

The lens potentials of this specific image are indicated in the caption as an example. For figure 8c, with an emission voltage of H = I634 : V L2 =-632V and V L4 =-590V to reach a magnification of @ = 25400. This is almost 20 times the direct projection image obtained for figure 8b, a classic result for this setup. Here, the source-to-object distance is about = 600μ : this is deduced from the magnification given on the short projection in figure 8a. The carbon grid lattice corresponds to At this source-to-object distance, the part of the projection of the object seen on the lens screen is shown in figure 8b, where the magnification is

P = [[.& \D [ .& \] ≈ 1100.
The magnification measured on the image is 1104, so the source-to-object distance is found with a good confidence level.

2.3-Dual-stage microchannel-plate/fluorescent screen assembly detector

The detector-resolution of the classic point-source projection electron microscope is about 100µm. This is equivalent to the Point-Spread-Function of a microchannel plate [24] or to the single-event answer of one pitch of the microchannel plate. One way to improve spatial detector-resolution is to record images in counting mode [23]. In this mode, the position of each electron's impact on the detector is determined. The complete detection system is presented in figure 9. The amplification ratio of the dual-stage microchannel plate depends on QRF = ( _`a I bW ). Here, the detector entrance is connected to the electrical ground bW = 0 . The starting amplification given by the manufacturer of the MCP is from about 10 = at 1 Sc to some 10 [ at 2 Sc . The analog imaging mode operates at an amplification of about 10 = ( QRF ≤ 1.2S ) and the counting imaging mode at a higher amplification (1.5 ≤ QRF ≤ 2S ). To detect every single event, a dual-stage microchannel plate must be used but the electron flux must also be sufficiently low: if events follow each other too closely, they cannot be counted. There are almost 1.8 million channels on the first microchannel plate, which has a diameter of 4cm.

Impacted by one electron, each can produce a micrometric stain. The electron is counted at the stain's center of mass. Increasing video frequency would substantially reduce imaging time.

Here, the minimum exposure time for the camera is (X efg ) hbW = 3.02 *. For the counting imaging mode, the maximum dose acceptable is about 10,000 hits per frame: TUVHHW = 1.6 × 10 (&i & j =. )×& \k = 0.5l'. and the isolated fluorescent screen connected to TUVHHW (c) camera and its optical lens.

3-Results and discussion

The detector-resolution is known to be about η=15µm in counting imaging mode and η=150µm in analog imaging mode [23,2425]. Under microscope magnification, G, this detector-resolution should lead to a microscope-resolution of η/G. In our example, the magnification is about x25.400, which should give a microscope-resolution of 6nm in analog mode and 0.6nm in counting mode. To see whether this is the case, the microscoperesolution is estimated by plotting the profile of gray-level intensity along a line placed at the edge of the object in the reconstruction of the hologram (figure 10). The microscoperesolution is equivalent to the width of this edge.

To compare the microscope-resolutions obtained in analog and in counting mode, the same image is recorded in both modes. However, the (2048 × 2048)pixel CMOS device of the camera does not allow every channel of the entire microchannel plate to be resolved. The answer is to zoom onto one part of the screen. The counting image is then incorporated into the analog image, as shown in figure 10. An analog image is first recorded (figure 10a) in 25sec

(mean of 50 frames of X HYP = 500 *). Then, the image of the object is positioned at the center of the screen. The focal length of the camera lens and the camera position are changed to zoom on the object. A (7 × 7) ² area of the screen is then filmed at a high imaging rate: here, 42,000 images of X = 3.02 * every 30ms form the counting image obtained in figure 10b.

At H = I500 , the emission intensity is about 10nA (figure 5), yielding 10pA after the diaphragm. Just a small part represented by the white circle in figure 8b illuminates the whole screen: the intensity arriving on the screen is about 0.1pA: 80 hits per frame ((7 × 7) ² of the screen). This counting imaging mode is time-consuming: it took 34min to record figure 10b.

The image in figure 10c Holograms are reconstructed by re-propagating a modeled reference wave modulated with the hologram to find the object wave in the plane of the object [6,19]. Figure 10d results from the analog imaging and figure 10e from a mix of the analog and the counting imaging shown in figure 10c.

The contrast, Γ = •Ž• ( ••' •Ž• ••'
, of the reconstruction is better where the counting image is incorporated. Profiles obtained on figure 10f give Γ = 0.33 for the analog image and 0.66 for the counting image. The microscope-resolution found on this image is about 40nm in analog mode and 30nm in counting mode (see figure 10f). We can conclude that due to mechanical drift, the analog image achieved in 25s leads to a microscope-resolution of about 40nm and the counting image achieved in 34min leads to a microscope-resolution of about 30nm.

Alignment and the first analog images take only a few minutes, but there are still some practical challenges. First, to capture the best counting image, the object has to be stable. Second, monitoring an object during approach can be difficult because the emission can sometimes show two sources under the same crystal. During the source-to-object approach, either both sources emit or one dominates the other. Figure 11 shows two sources working at the same time. Different image centers are observed from the two sources: images are drifted and superimposed. The distance between sources is about 5μm, corresponding to the drift between images. This inter-source distance is particularly high compared to distances previously measured [14]. Here, two closed crystals seem to emit at the same time. However, when the electric field is stable, the source doesn't change. Several point-sources can emit from one crystal, but under a given electric field condition, one of them emits preferentially. Therefore the co-existence of two sources means that the counting image obtained can be different from the image chosen before the source-to-object approach when the electric field shape changes.

It is hard to anticipate how the image will change before beginning the lengthy counting procedure. To overcome this problem, an image is first recorded in analog mode with low lens magnification and without changing the source-to-object distance before moving to counting imaging mode.

4-Conclusion

This paper describes a new design for a low-energy electron point-projection microscope with an insulator crystal as source instead of a sharp metal needle, an electron optical system, and a high-spatial-resolution detector.

The source used is an insulator/metal interface emitter formed by a celadonite crystal deposited on the apex of a 10μm diameter carbon fiber. The robustness and the great brightness of this source, combined with an accessible high-intensity range, make it a good candidate for electron microscopy. However its shape is a limitation to its use for classic projection microscopy, because it is difficult to manipulate at less than some tens of micrometers from an object. The projection is thus combined with electrostatic lenses to reach magnification of about 10 5 . High electron spatial detector-resolution is achieved using a dual-stage microchannelplate/fluorescent-screen assembly. This technique affords spatial detector-resolution close to 15µm, the lattice parameter of the microchannel plate, but requires a long imaging time. An example combining analog imaging on a large field with counting imaging on a smaller field is shown. In the example given in this article, the source-to-object distance is 600μm, magnification reaches x25,000 and the resolution of the microscope is about 30nm. Both emission site changes and object drifts are observed during the lengthy imaging.

In conclusion, the celadonite source emitter combined with Einzel lens performs comparably to a point projection microscope. Moreover, its source can work under poor vacuum conditions, its robustness reduces risk during manipulation and contributes to its long life-time, and its high cone angle promises better resolution for the microscope. All of these advantages open new horizons for projection electron microscopy. With its potential for long-range imaging, the celadonite-source projection microscope holds promise for charge reduction and ease of manipulation during imaging.

Figure 1 :

 1 Figure 1: Experimental design. The electron source provides an electron energy range from 100

Figure 2 :

 2 Figure 2: Industrial drawing of the point-source projection microscope; (a) source support, (b)

Figure 3 :

 3 Figure 3: Photograph and industrial drawing of the electron source in front of the object, a holey

Figure 4 :

 4 Figure 4: a-Scanning electron microscopy images of the 10µm diameter carbon fiber; b-

Figure 5 :

 5 Figure 5: Typical ( ) curves obtained for three different structures. The green curve represents

Figure 6 :

 6 Figure 6: The two-Einzel-lens scheme. The scale bar indicates 10mm. The entire length is about

Figure 7 :

 7 Figure 7: Electrostatic optical rays from the source to the screen with s: the source, O: the

Figure 8 :

 8 Figure 8: Physical projection images of the same object in analog mode. White scale bars

( 1 . 7 0. 1 )

 171 on the screen placed at a distance = 12 from the source, the grid lattice measures 84.7µm, so the magnification = (200 10) and ≃ B Z B = (600 30)μ .

Figure 9 :

 9 Figure 9: Technical drawing of the complete detection system. (a) Electrostatic lens; (b) dual

  is realized by incorporating the figure 10b (7 × 7) ² counting image into the figure 10a (4 × 4) ² analog image.The detector-resolution on the counting image is not 15µm here because it is blurred by a mechanical drift of the object towards the source position. The measurements performed on 10b give a recording detector-resolution of about 48μm, which corresponds to a mean drift of 16nm/sec between the source and the object.

Figure 10 :

 10 Figure 10: (a) Analog image of a carbon membrane physical shadow. Projection distance

Figure 11 :

 11 Figure 11: Projection image from two sources.

Acknowledgment

The authors would like to thank Marjorie Sweetko for improving the English of this article.


J Gaspar

Y Corre

M Firdaouss

J L Gardarein

J Gerardin

J P Gunn

M Houry

G Laffont

T Loarer

M Missirlian

J Morales

P Moreau

C Pocheau

E Tsitrone

First heat flux estimation in the lower divertor of WEST with embedded thermal measurements

Keywords: heat flux estimation, heat flux decay length, embedded thermal measurement, inverse method

The present paper deals with the surface heat flux estimation with thermocouples (TC) and fiber Bragg grating (FBG) embedded in the plasma facing components (PFC) of the WEST tokamak. A 2D heat transfer model combined with the conjugate gradient method (CGM) and the adjoint state is used to estimate the plasma heat flux deposited on the PFC. The plasma heat flux is characterized by the time evolution of its amplitude and spatial shape on the target (heat flux decay length 𝜆 𝑞 𝑡 , power spreading in the private flux region 𝑆 𝑡 and the strike point location 𝑥 0 ). As a first step, five ohmic pulses have been investigated with different magnetic configuration and divertor X-point height varying from 44 to 68 mm from the surface. Despite an outboard shift, the relative displacements of the outer strike point as well as the heat flux decay length derived from the TC/FBG systems are consistent with the magnetic equilibrium reconstruction.

Introduction

The main objective of WEST is to study the behavior of ITER like Plasma Facing Components (PFCs) and to test the resistance and ageing of these components under high heat loads [START_REF] Bourdelle | WEST Physics Basis[END_REF]2]. To achieve these objectives, measurement of the distribution and the amplitude of the heat flux on the divertor PFC is necessary. The divertor X-point configuration allows access to a wide range of heat flux shapes on the PFC by changing the X-point height to the target: the magnetic flux surfaces can be compressed or expanded, as soon as the X-point moves away or gets closer to the target respectively [3].

Plasma breakdown, plasma current ramp-up and diverted plasma have been successfully achieved during two WEST experimental campaigns (C2 and C3a). To derive the heat flux from temperature measurements, the plasma must be in steady state, without sweeping, and the plasma current flat top should last for at least a couple of seconds. A series of ohmic pulses meeting these requirements has been performed with X-point height varying from 44 mm up to 68 mm. During ohmic experiments, the power reaching the divertor is too small, so that the PFC surface temperature is below the threshold for IR thermography measurements on tungsten components [START_REF] Courtois | Full coverage infrared thermography diagnostic for WEST machine protection[END_REF]. Therefore, we propose here to use embedded thermal sensors in order to characterize the heat load pattern in the lower divertor.

The paper is organized as follows. The thermocouple (TC) and fiber Bragg grating (FBG) diagnostics as well as the heat flux estimation methodology are presented in section 2. A detailed description of the heat flux calculation applied to one ohmic pulse is given in section 3. The heat flux decay length on the targets as well as the positions of the maximum heat flux derived from embedded thermal sensors are compared to the magnetic equilibrium reconstruction, as a function of the X-point height, in section 4.

Diagnostic set-up: TC and FBG systems 2.1 WEST lower divertor

The role of the WEST lower divertor target is to sustain the power conducted through the last closed flux surface to the strike points. The WEST divertor consists of 12 independent toroidal sectors of 30° each composed of 38 plasma facing units. During the WEST phase 1 a mix of ITER-like actively cooled components (bulk W) [START_REF] Missirlian | [END_REF] and non-actively cooled W-coated graphite components is used [3]. The W-coated graphite is divided in two separate components, one in the low field side (LFS/outer) and one in the high field side (HFS/inner).

A total of 20 TCs are in the W-coated graphite components in order to study the heat load pattern on the divertor. Here we present the use of the two series of 4 TCs embedded in the outer PFCs. The TCs are 1mm sheathed type N TC embedded at 7.5mm from the surface in a 1.3mm diameter hole and 10mm depth from the PFC side. The TCS are bonded in the hole with graphite adhesive. The graphite adhesive is attempted to sustain 1370°C much higher than 1200°C which is the maximum temperature admissible for both TC type N and W coating. The use of graphite adhesive with thermocouple have been successfully tested in high heat flux facility up to 900°C.

In WEST, 4 optical fiber temperature sensing probes, each of them including 11 regenerated fiber Bragg gratings equally spaced by 12.5 mm, have been specifically designed and installed in the outer PFCs [6]. The FBGs are temperature transducer based on a diffraction gratings photowritten by laser into the core of an optical fiber. The FBGs are monitored in reflection by a spectrometer. The spectrometer spectral range is 120 nm between 1500 and 1620 nm with spectral resolution of 8mm. The Bragg wavelengths of the gratings have been spectrally spaced to avoid spectral overlapping during temperature gradient measurement up to 540°C. The 4 FBGs are embedded at 3.5 and 7 mm from the surface, 2 at each depth, in a side groove of 1.2mm height and 4mm depth, in outer PFCs of the divertor only [6]. The regenerated FBG installed have a long-term use above 900°C (>9000h). The advantages of FBG with respect to a single TC are to be immune to electromagnetic interference and to allow the measurement of temperature at different locations on a single fiber. Each sensing line includes 11 spot temperature measurements equally spaced by 12.5 mm in the poloidal direction. The data acquisition rate is 10 and 20 Hz for the FBG and the TC, respectively.

The time response of the TC and FBG have been evaluated about 𝜏=250𝑚𝑠 in a dedicated set-up. In the heat flux calculation we take into account the sensors time-response by convoluting the temperature calculated at the TC location with the sensor step response. Nevertheless the estimation cannot resolve time evolution faster than 250ms, only a time-averaged value can be extracted.

Inverse heat conduction problem and heat flux distribution assumptions

Over the years several techniques have been developed for the heat flux estimation with embedded measurement, some of them with a forward approach [7,8] or with an inverse approach [9,10]. Here we extend the inverse approach described in [10] by using multiple sensors in order to estimate the different parameters which characterize the heat flux spatial distribution.

The inverse heat conduction problem consists in the determination of the surface heat flux (ϕ) minimizing the discrepancy between the output of a heat conduction problem giving the PFC bulk temperature and the temperature measurements provided by the 4 TCs or the 11 Bragg gratings. The conjugate gradient method combined with the adjoint state is the optimization process used to solve the inverse problem [11,12]. Eich et al. showed for JET and ASDEX-Upgrade divertors [11] that the spatial distribution of the heat flux can be expressed by a heuristic formulation, built with IR thermography during carbon-wall operations, defined by:

𝜙(𝑥, 𝑡) = 𝜙 𝑀 (𝑡)𝑒𝑥𝑝 [( 𝑆 𝑡 2𝜆 𝑞 𝑡 ) 2 - 𝑥-𝑥 0 𝜆 𝑞 𝑡 ] × 𝑒𝑟𝑓𝑐 ( 𝑆 𝑡 2𝜆 𝑞 𝑡 - 𝑥-𝑥 0 𝑆 𝑡 ) + 𝜙 𝐵𝐺 (𝑡) ( 1
)
where 𝑥 is the target coordinate, 𝑥 0 is the strike point location, 𝜆 𝑞 𝑡 is the local heat flux decay length on the target (i.e. not mapped to the outboard midplane), 𝑆 𝑡 is the heat flux spreading factor on the target, 𝜙 𝑀 (𝑡) the time evolution of the maximal heat flux and 𝜙 𝐵𝐺 (𝑡) the background heat flux radiated by the plasma.

Using this expression as a priori in the IHCP we can estimate simultaneously the unknowns 𝜙 𝑀 (𝑡), 𝜆 𝑞 𝑡 , 𝑥 0 and 𝜙 𝐵𝐺 (𝑡) from the TC and FBG measurements. 𝑆 𝑡 can also be estimated with the FBG measurements thanks to the high number of spot measurements (11 versus 4 for FBG and TC, respectively).

The uncertainties on the estimates using this approach for each diagnostic have been studied in previous work [12,13] with numerical data. These works have shown uncertainties of 8% for 𝜆 𝑞 𝑡 , 10% for 𝑆 𝑡 and less than 1mm

for 𝑥 0 (but due to the Bragg grating size we will consider an uncertainty of 2mm).

TC, FBG data and estimated heat flux ( pulse)

Fig. 1. Temporal evolution of the heating as measured by 2 series of 4 TC and one FBG for the pulse #53237. Figure 1 shows the heating of the lower divertor as measured with the different embedded measurements during WEST ohmic plasma with plasma current of Ip = 500kA and toroidal magnetic field Bt = 3.7 T (#53237). From the left to the right, the plots show the two series of the 4 outer TC and one FBG (sensors locations in figure 5). The two diagnostics have good performance in terms of noise with a standard deviation of 0.3 and 0.2°C for the TC and FBG, respectively. The signal noise ratio remains good even for the low heating reported during ohmic experiment. The comparison of the TC and FBG at same poloidal location (blue, red, green and magenta correspond to the FBG N°10, 7, 4 and 1, respectively) shows equivalent heating for the two diagnostics. From these data we can compute the heat flux deposited by the plasma on targets. Figure 2 shows the time evolution of the estimated heat fluxes for the different embedded diagnostics. The time evolution of the heat flux is consistent with the ohmic power and the Xpoint diverted phase as illustrated in figure 3. The mean amplitude of the estimated heat fluxes during the plasma current flat top phase is found to be 100 kW/m². The heat flux is small which is consistent with highly radiative ohmic plasma discharges studied here, the radiated power fraction is about 76%.

LFS TC LFS FBG LFS TC

Heat flux distribution as function of the magnetic configuration

Table 1 summarizes the plasma parameters of the 5 ohmic pulses studied, the values have been average during the plasma current flat top phase. The pulses have been selected due to the different X point height achieved during these discharges. Based on the magnetic equilibrium reconstruction with the EQUINOX code [10], the variation goes from 44.2mm for the pulse #52665 to 68.5mm for the pulse #53237. Figure 4 shows the magnetic reconstructions of EQUINOX near the divertor for the two extreme cases. The increase of the X-point height can be seen as well as the two strike point of the separatrix on the inner and outer PFCs, at the HFS and LFS, respectively.

a) b)

Figure 5 shows the estimated heat fluxes distribution on PFC for the series of 5 pulses with X-point height varying from 44mm up to 68mm. In order to keep only the heat flux coming from the scrape-off layer, the normalized heat fluxes have been computed by:

𝜙 ̅ ′ = 𝜙 ̅ -𝜙 ̅ 𝐵𝐺 𝑚𝑎𝑥 (𝜙 ̅ -𝜙 ̅ 𝐵𝐺 )
mean values during Ip flat top [START_REF] Bourdelle | WEST Physics Basis[END_REF] The change of the heat flux distribution with respect to the magnetic configuration is clearly seen in the figure 5 b). Both parameters, 𝜆 𝑞 𝑡 and 𝑆 𝑡 , decrease when the Xpoint height increases and the magnetic flux expansion decreases simultaneously. Figure 6 a) plots the estimated 𝜆 𝑞 𝑡 and 𝑆 𝑡 as function of the X-point height. The magnetic expansion, fx, is computed with respect to the outboard mid-plane: it varies from 5.3 down to 3.7 (at the separatrix) when X-point height is 68mm. This confirms that for similar plasma conditions we can compress or expand the heat flux on the target by tuning the X-point height [3]. the FBG/TC measurements and with the two magnetic reconstruction codes used for WEST (EQUINOX [14] and VACTH [15]). The displacement of the strike point is consistent with the evolution of the X-point height. The SP is moving toward the outer side linearly when the Xpoint is moved away from the target (see figure 4). However, a mean shift of 23mm towards the baffle (outer side) is observed between EQUINOX and thermal measurements. On the same time, VACTH estimates a lower X-point height than EQUINOX. The discrepancies between the two magnetic reconstruction codes and also with the TC/FBG observations is under investigation. Errors on the passive currents in the structure used in the magnetic reconstructions could be a part of the explanation. Looking at the peak heat flux, the shift is less pronounced (figure 5 a)) due to the simultaneous reduction of 𝜆 𝑞 𝑡 and 𝑆 𝑡 (consequence of the equation 1).

As a result, the shift of the peak heat flux is about 2 cm on the LFS.

Conclusion

The WEST embedded PFC diagnostics (TC and FBG) have allowed to estimate heat fluxes on the divertor target for ohmic plasmas with low temperature heating, where no IR measurements are available. The heat load pattern has been investigated in terms of peak heat flux position and broadening as a function of the X-point height. The displacement of the peak heat flux is consistent with the magnetic equilibrium reconstruction. This demonstrates that although the input power is modest, both the TC and the FBG diagnostics are very sensitive to the location of the strike points. This shows that these diagnostics will be very complementary to the IR monitoring system that will be available for surface temperature and heat flux analsyis on the surface of the divertor target for larger input power.

The next experimental campaign will be the opportunity to investigate higher X-point height (up to 90mm) and consolidate these observations with optimized plasma parameters (same plasma current, magnetic field and divertor density) and additional heating power (Lmode experiments).

Fig. 2 .

 2 Fig. 2. Time evolution of the estimated heat fluxes with embedded measurements (#53237).

Fig. 3 .

 3 Fig. 3. Estimated heat flux (blue), plasma current (Ip), ohmic and radiated power as function of time (#53237).

Fig. 4 .

 4 Fig. 4. Magnetic reconstruction (EQUINOX) for the two extreme X-point height.

Fig. 5 .

 5 Fig. 5. a) Normalized heat flux as function of space for the 5 investigated ohmic pulses and sensor localization, b) Maximal heat fluxes transposed at the same location.

Figure 6 b

 6 Figure 6 b) shows the outer strike point location (x0) versus the X-point height. The values are estimated with

Fig. 6 .

 6 Fig. 6. a) 𝜆 𝑞 𝑡 and 𝑆 𝑡 as function of X-point height, b) strike point location (x0) as function of X-point height for LFS.

Table . 1

 . . Plasma parameters and estimated values for the 5 ohmic pulses.

										𝜆 𝑞 𝑡	𝑆 𝑡
										LFS	LFS
										(mm)	(mm)
	52655	700	3.7	44.2	1	86	0.1	1.6	63.5	55.3	28.5
	53073	600	3.3	55.8	0.84	77.2	0.1	2.45	76	44.2	22
	53027	600	3.6	60.8	0.79	84.2	0.125	1.2	72	42.5	22.1
	52980	594	3.7	62.9	0.825	79.1	0.125	1.25	66	42.9	23
	53237	500	3.7	68.5	0.56	76.4	0.3	3	100	39	19.5

Acknowledgments

This work has been carried out thanks to the support of the A*MIDEX project (n°ANR-11-IDEX-0001-02) funded by the "Investissements d'Avenir" French a) b)

Government program, managed by the French National Research Agency (ANR). This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission and ITER Organization


Felix Pino
email: felixpino@gmail.com

Cristiano Fontana

Marcello Lunardon

Luca Stevanato

Cinzia Sada

Alberto Carnera

Francesca Soramel

Sandra Moretto

Giancarlo Nebbia

Alix Sardet

Lino Cristiano

Marcello Fontana

Luca Lunardon

Cinzia Stevanato

Alberto Sada

Francesca Carnera

Sandra Soramel

Moretto

Cedric Carasco

Bertrand Perot

Guillaume Sannie

Alessandro Iovene

Carlo Tintori

Pawel Sibczynski

Lukasz Swiderski

Krystian Grodzicki

Marek Moszynski

Advances on the development of the detection system of C-BORD's rapidly relocatable tagged neutron inspection

Keywords: Tagged neutron inspection system, non-intrusive inspection, C-BORD PACS numbers: 89.20.-a, 29.40.Mc

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

Introduction

The mission of C-BORD 1 is to develop and test a comprehensive cost-effective solution for the generalized inspection of container and large-volume freight. To protect European Union (EU) borders, the project copes with a large range of container non-intrusive inspection (NII) targets, including explosives, chemical warfare agents, illicit drugs, tobacco, and special nuclear materials. In comparison with the technologies currently used (mainly imaging system based on X or gamma rays), C-BORD is expected to increase interdiction of illicit material in containerized freight and deliver new capabilities against critical operational requirements and constraints by: increasing throughput of containers per time unit; reducing need for costly, time-consuming, and dangerous manual container inspections; and lowering false negative and false positive alarm ratios. The main technical objective of C-BORD is to develop a toolbox of TRL-7 first-line and second-line devices employing different non-destructive passive and active techniques: advanced radiation management, next-generation cargo X-ray, tagged neutron inspection, photo-fission and evaporation-based detection. The idea is to develop a unique graphical user interface (GUI) for all systems: a data-fusion display, decisionsupport software, and a common data format. At the end of the project, recommendations and tools for standardized tests for the different C-BORD NII technologies will be elaborated. In this work we present the progress on the development of the C-BORD's rapidly re-locatable tagged neutron inspection system (RRTNIS). In particular, we give the results concerning the comprehensive characterization of the gamma scintillator detectors. We studied the response of three different photomultipliers, to be coupled to large-sized NaI:Tl crystals, to find the one that satisfies all the requirements of our system. Moreover, we assembled two new LaBr 3 :Ce detectors that were completely characterized.

C-BORD's Tagged Neutron Inspection System

The concept of the C-BORD's tagged neutron inspection technique can be explained simply as follows. Fast neutrons (E n = 14 MeV), produced using the D-T fusion reaction (D + T  n + α), are tagged in time and direction by detecting the associated alpha particles using a position-sensitive detector (YAP:Ce scintillator coupled to a multi-anode photomultiplier). Characteristic de-excitation gamma rays are emitted in all directions when these neutrons interact, mostly by inelastic scattering, with some nucleus belonging to a large target (for example a cargo container). Using a gamma detector array, one can record the neutron-gamma time-of-flight (ToF) spectrum and the gamma energy spectrum of the emitted photons. By selecting only a window of the ToF spectrum and a 1860125-3 particular tagged neutron incident direction, one can inspect a small voxel of the entire target. The analysis of the selected gamma energy spectra is performed by comparing those with a database of elementary gamma signatures. A simple scheme of the C-BORD's Tagged Neutron Inspection System (TNIS) is shown in Fig. 1. The detection module of C-BORD's TNIS consists of a gamma detector array composed of twenty large-sized 5 in  5 in  10 in NaI:Tl and four 3 in  3 in LaBr 3 :Ce scintillators (see Fig. 2). The electronics chain for signal processing is based on fast digitizers, and the custom-made data acquisition software denominated ABCD 2 complete the system. The nuclear electronics chain is composed of two CAEN V1730 VME Digitizers, 16 ch, 14 bit, 500 MS/s (Samples/second); five CAEN V6533 VME HV supplies, 6 ch (NEG), 4 kV/3 mA; and one CAEN V2718 VME-PCI Optical Link Bridge. The NaI:Tl detectors that will be used to assemble the C-BORD's TNIS were also used in a previous project, called EURITRACK. [3][4][5] These detectors must satisfy the C-BORD project requirements. The main requirements are good energy resolution (~7-8% 1860125-4 at 662 keV), good time resolution (< 3 ns, thresh. ~500 keV), linearity, and gain stability for counting rates up to ~200 kcps (counts-per-second). In the case of LaBr 3 :Ce detectors, the requirements for the linearity and gain stability were for counting rates up to ~20 kcps, as well as for energy and time resolutions approximately 2 the NaI:Tl detectors.

Experimental Set Up

After a preliminary assessment of the energy resolution, time resolution, and gain stability of the NaI:Tl, it was determined that not all the detectors satisfy the requirements of the C-BORD's TNIS. 2 Therefore, it was necessary to refurbish at least 10 of the 20 NaI:Tl detectors. In particular, the photomultipliers (PMTs) and voltage dividers had to be replaced. The physical integrity of all crystals was checked as well. The crystal/PMT optical couplings were tested with several optical interfaces (optical greases with different viscosities and silicon pads). The best results were obtained using optical grease with high viscosity.

In this work we present a comparative study of three different PMTs to select the best match for the project's requirements. Table 1 shows the main technical characteristics of the PMTs under study. Active voltage dividers (VD), delivered by Hamamatsu and ETEL, were used respectively. We give the results of only two of the four LaBr 3 :Ce detectors. These two crystals were coupled, using an EJ-560 silicon pad, to two Hamamatsu R10233-100-01 photomultipliers, which is a model especially designed for this kind of crystal, with very high light outputs. Two experimental set ups were used to perform a comprehensive characterization of the gamma detectors. With the first set up, the energy resolution, the linearity, and the gain stability of the detectors were tested. With the second set up, the time resolution of the detectors was measured. The electronic chain and the DAQ used to perform these measurements were the same that are going to be used in the final integration of the TNIS (described in Sec. 2).

Energy resolution, linearity and gain stability

The energy resolution, the linearity, and gain stability of the detectors were measured as a function of the counting rate. To perform such tests, a set of calibration gamma sources ( 137 Cs, 22 Na, 60 Co, 54 Mn and 88 Y) was used; each source had activities ~370 kBq. All the sources were used at the same time to reach a counting rate between 250 kcps and 300 kcps when the sources were placed very close to the NaI:Tl detectors. Two detectors were evaluated in one run (we performed several runs). A run consisted of moving all the sources from a position far away from the detectors (~2.5 m, having a counting rate ~2.5 kcps in the case of NaI:Tl detectors) to a very close position. When moving the sources, the energy spectra of both detectors were continuously acquired. For each event, the digitizer saved the timestamp and the long integration of the corresponding analog pulses. Therefore, this information let us reconstruct the energy spectra at some instant t ± Δt (corresponding to some counting rate value, C R ± ΔC R ).

Time resolution

Coincidence measurements using 22 Na and 60 Co sources were performed to get the time resolution of the detectors at different energy thresholds. A 2 in  2 in EJ-228 fast plastic scintillator was used as the start detector in the case of the NaI:Tl scintillator study. Regarding the LaBr 3 :Ce scintillators, being fast and identical detectors, the coincidence measurements were done using just the two detectors under study. For all time measurements, a new firmware, developed for the V1730 digitizer, containing a digital constant-fraction discriminator was employed. In this way, the reconstruction of the coincidences and the time spectrum were done on-line without any off-line postprocessing.

Results

NaI(Tl) detectors: energy resolution and linearity

Figure 3 shows the energy calibration and resolution curves of the NaI:Tl detectors coupled to the three PMTs under evaluation. All detectors exhibit a very linear behavior, at least up to 2.734 MeV, which is the most energetic gamma photon of our calibration set ( 88 Y). The energy resolution curves are very similar; the small differences could be explained because we used three different crystals to perform the measurements. The energy resolution obtained at 662 keV was ~8%.

NaI(Tl) detectors: high counting rates

Figure 4 presents the energy resolution and the relative peak position (at 662 keV) as a function of the counting rate for the three NaI:Tl detectors under study. The energy resolution increases as the counting rate gets higher; however, at 200 kcps the Hamamatsu photomultipliers show an increase less than 5% of the energy resolution value at low counting rates. Concerning the gain stability of the detectors, we explored the relative peak positions (at 662 keV) as a function of the counting rate, and we concluded that the ET9390 and the Hamamatsu R11833-100HA are the best PMTs. Those detectors exhibited a very stable behavior up to 200 kcps. In fact, the R11833-100HA is able to work properly even at more than 260 kcps. On the other hand, the R877-100 PMT showed a very large gain shift (around 50% at 200 kcps) and was consequently discarded to refurbish our NaI:Tl detectors.

LaBr3(Ce) detectors: energy resolution and linearity

Figure 5 shows the energy calibration and resolution curves (up to 2.7 MeV) of the two LaBr 3 :Ce detectors. Both PMTs working at -1200 V show very good linearity. Concerning the energy resolution, we obtained similar results for both detectors, having an average resolution value of ~3.5% at 662 keV being acceptable according to the literature. 6,7

LaBr3(Ce) detectors: high counting rates

Figure 6 presents the energy-resolution values and the relative peak position (at 662 keV) as a function of the counting rate for both detectors under study. The energy resolution is very stable even up to 120 kcps, the variations are estimated to be lower than 5% with respect to the values at low counting rates for both detectors. Concerning the gain stability, we observed that LaBr -A is more stable than LaBr -B; however, the gain shift exhibited by the latter is very small (~1% at 120 kcps).

Time resolution

The on-line digital constant fraction discrimination (DCFD), embedded in the firmware of the digitizer V1730, has to be properly configured to achieve an optimal performance. The parameters delay (D) and fraction (F), which are used to determine the fine timestamp of the event, were studied for both types of detectors (NaI:Tl and LaBr 3 :Ce). As an example, Fig. 7 presents the time-resolution values of the LaBr 3 :Ce detector's system for different possible values of D and F, coming from the 22 Na coincidence measurement (using the two 511 keV annihilation photons). In this case, using D = 40 ns and F = 25%, we obtained the best timing performance of the LaBr 3 :Ce detectors. The time resolution is represented by the full width at half maximum value (FWHM) of the time-coincidence spectrum. Using the 22 Na coincidence measurements, we obtained 0.50 ± 0.01 ns of time resolution (thresh. 500 keV) for each LaBr 3 :Ce detector. With the 60 Co, 1173 keV and 1332 keV correlated photons, (thresh. 1 MeV) the result was 0.40 ± 0.01 ns. Concerning the NaI:Tl detectors, Table 2 shows the time-resolution values for the three different PMTs under study. From our tests, we found out that Hamamatsu R11833-100HA PMT shows the best performance, with a time resolution lower than 3 ns using an energy threshold ~500 keV. The others PMTs do not comply with the requirements of the C-BORD's TNIS.

Fig. 1 .

 1 Fig. 1. General scheme of the C-BORD's tagged neutron inspection system (TNIS).

Fig. 2 .

 2 Fig. 2. View of NaI:Tl (left) and LaBr 3 :Ce (right) scintillators.

  Int. J. Mod. Phys. Conf. Ser. 2018.48. Downloaded from www.worldscientific.com by CEA CEA/SACLAY on 02/22/19. Re-use and distribution is strictly not permitted, except for Open Access articles. F. Pino et al.

  Int. J. Mod. Phys. Conf. Ser. 2018.48. Downloaded from www.worldscientific.com by CEA CEA/SACLAY on 02/22/19. Re-use and distribution is strictly not permitted, except for Open Access articles.Detection-system development for CBORD's tagged neutron inspection 1860125-5

6 Fig. 3 .

 63 Fig. 3. (left) Energy calibration and (right) resolution curves for the three PMTs under study.

Fig. 4 .

 4 Fig. 4. (left) Energy resolution and (right) relative peak position at 662 keV as a function of the counting rate for the three PMTs under study.

  Int. J. Mod. Phys. Conf. Ser. 2018.48. Downloaded from www.worldscientific.com by CEA CEA/SACLAY on 02/22/19. Re-use and distribution is strictly not permitted, except for Open Access articles. Detection-system development for CBORD's tagged neutron inspection 1860125-7

Fig. 5 .

 5 Fig. 5. (left) Energy calibrations and (right) energy resolution curves for the two 3 in  3 in LaBr 3 :Ce scintillators.

Fig. 6 .

 6 Fig. 6. (left) Energy resolution and (right) relative peak position at 662 keV as a function of the counting rate of the two 3 in  3 in LaBr 3 :Ce scintillators.

  Int. J. Mod. Phys. Conf. Ser. 2018.48. Downloaded from www.worldscientific.com by CEA CEA/SACLAY on 02/22/19. Re-use and distribution is strictly not permitted, except for Open Access articles.

Fig. 7 .

 7 Fig. 7. Time resolution (FWHM) of the LaBr 3 :Ce system as a function of the DCFD delay for different values of fraction.

Table 1 .

 1 Comparison of the main technical characteristics of the three PMTs under study.

			Hamamatsu	Hamamatsu
		ET9390	R877-100	R11833-100HA	XP4512*
	Photocathode			bialkali
	Spectral range (nm)	300-630	300-650	290-630
	Active diameter (mm)	115	111		110
	Luminous sensitivity (muA/Im)	75	90	105	70
	QE (%)	28		35	24
	Nominal anode sensitivity (A/Im)	50	40	50	70
	Gain at nominal	7  10 5	4.4  10 5	2  10 5	2  10 7
	Dark current typ (nA)	1	10	8	90
	Rise time (ns)	13	20	4	2.5
	Transit time (ns)	60	115	49
	* Legacy Photonis PMT from the former project. No longer commercially available.

Table 2 .

 2 Time resolution results for the NaI:Tl detectors. Int. J. Mod. Phys. Conf. Ser. 2018.48. Downloaded from www.worldscientific.com by CEA CEA/SACLAY on 02/22/19. Re-use and distribution is strictly not permitted, except for Open Access articles.

	PMT	Time Resolution ( 22 Na), ns	Time Resolution ( 60 Co), ns
	ET9390	3.9 ± 0.2	3.0 ± 0.1
	R877-100	3.5 ± 0.1	2.5 ± 0.1
	R11833-100HA	2.5 ± 0.1	1.8 ± 0.1

Acknowledgments

This work has received funding from the European Union's Horizon 2020 research and innovation programme, under grant agreement No. 653323. This text reflects only the author's views, and the Commission is not liable for any use that may be made of the information contained therein.

1860125-9

Conclusions

In this work we presented the advances on the development of the detection module of the C-BORD's TNIS compared to our previous work in Ref. 2. In particular we performed a complete characterization of a part of the gamma detectors set. We studied the energy resolution, linearity, time resolution, and gain stability at high counting rates of different crystal/PMT combinations. We evaluated three different PMTs to be coupled to the large-sized NaI:Tl crystals, and we assembled and characterized two new 3 in  3 in LaBr 3 :Ce detectors.

The LaBr 3 :Ce scintillators (coupled to a Hamamatsu R10233-100-01 PMT) exhibited an energy resolution around 3.5% at 662 keV and a time resolution (FWHM) around 0.5 ns (with a threshold of 500 keV). These values are in good agreement with the literature. Concerning the refurbishment of the NaI:Tl detectors, we found that the Hamamatsu R11833-100 PMT exhibits the best performance. The detector assembled with this PMT shows an energy resolution ~8% at 662 keV, a time resolution ~2.5 ns ( 22 Na coincidence measurements), a very good linearity, and finally, a very good stability at high counting rates (no gain shift up to 260 kcps).