Filipe Da Silva

Stéphane Heuraux

Evgeniy Z Gusakov

Alexei Popov

A Numerical Study of Forward-and Backscattering Signatures on Doppler-Reflectometry Signals

Keywords: FDTD, microwave Doppler reflectometry, wave propagation in plasmas, wave scattering

In Doppler reflectometry, two scattering processes may be involved, Bragg backscattering and forward scattering. In this paper, a numerical study of both processes is undertaken using a finite-difference time-domain full-wave code with plasma parameters compatible with Tore Supra or Asdex Upgrade Doppler reflectometers. The spectra modeling the plasma turbulence were chosen to isolate forward-and backscattering events, allowing the segregation of the two different signatures and bring forth the different mechanisms intervening in each of the cases. Some numerical precautions needed for this type of simulations are presented. The results obtained are compared with the theoretical models.

I. INTRODUCTION

A N IMPORTANT development of reflectometry diagnos- tics is Doppler reflectometry, a technique that is able to convey information on the plasma turbulence rotation from the spectral shift of the return scattered signal [START_REF] Conway | Plasma rotation profile measurements using Doppler reflectometry[END_REF]- [START_REF] Hirsch | Doppler reflectometry with optimized temporal resolution for the measurement of turbulence and its propagation velocity[END_REF]. Two different scattering processes may be involved in Doppler reflectometry. Bragg backscattering, occurring when the turbulence wavenumber k f and the local wavenumber of the injected wave k(r) are resonant: k f = 2k(r), and forward scattering, which becomes dominant for k f < 2k A , where k A is the Airy wavenumber [START_REF] Fanack | Ordinary-mode reflectometry: Modification of the scattering and cutoff responses due to the shape of localized density fluctuations[END_REF]. In small and midsize devices with low levels of turbulence, scattering is accepted to be caused by Bragg backscattering in the vicinity of the oblique cutoff [START_REF] Conway | Plasma rotation profile measurements using Doppler reflectometry[END_REF]- [START_REF] Hirsch | Doppler reflectometry with optimized temporal resolution for the measurement of turbulence and its propagation velocity[END_REF]. Nevertheless, under high turbulence conditions or long plasma paths, as occurring in larger machines such as JET, JT 60, or ITER, a distinct process of cumulative forward scattering is expected to appear, contributing to the Doppler frequency shift of the signal, and spread out the probing beam, reducing the wavenumber resolution [START_REF] Gusakov | Multiple scattering effect in Doppler reflectometry[END_REF]. The need to understand scattering phenomena in Doppler reflectometry is the origin of several studies. Spatial and wavenumber resolutions have been evaluated analytically and numerically under Born or paraxial approximation [START_REF] Bulanin | Spatial and spectral resolution of the plasma Doppler reflectometry[END_REF], [START_REF] Gusakov | Spatial and wavenumber resolution of Doppler reflectometry[END_REF]. Spatial distribution of the scattering phenomena, which are usually assumed to occur in the cutoff vicinity, is a key issue for diagnostic applications. In case of low turbulence level, when only single scattering is significant, this problem was investigated in the framework of linear theory numerically in [START_REF] Hirsch | Doppler reflectometry for the investigation of propagating density perturbations[END_REF] and analytically in [START_REF] Gusakov | Spatial and wavenumber resolution of Doppler reflectometry[END_REF] and [START_REF] Gusakov | Two dimensional theory of fluctuation reflectometry diagnostics[END_REF]. Those studies assumed a small amplitude of the fluctuations, which allows neglecting multiple-scattering contributions to the received signal. However, this approximation can be incorrect in the plasma periphery, where the turbulence amplitude is usually high, or in large plasma devices, where the probingray trajectory is long [START_REF] Gusakov | Spatial and wavenumber resolution of Doppler reflectometry[END_REF]. This situation of high turbulent density perturbation level, when the multiple forward scattering is dominant, has been investigated analytically [START_REF] Gusakov | Multiple scattering effect in Doppler reflectometry[END_REF]. In this paper, a numerical study of both processes is undertaken using a finite-difference time-domain (FDTD) full-wave code. The spectra modeling the plasma turbulence were chosen to isolate forward-and backscattering events allowing the segregation of the two different signatures. The numerical constraints needed to simulate forward scattering, more demanding than those needed for backscattering, are also underlined.

II. CODE AND SIMULATION SETUP

The code used in this work is an ordinary-mode 2-D FDTD full-wave code, which solves Maxwell equations using a Yee scheme

μ 0 ε 0 (∂ t E z ) n i,j = (∂ x B y -∂ y B x -μ 0 J z ) n i,j (∂ t B x ) n+1/2 i,j+1/2 = -(∂ y E z ) n+1/2 i,j+1/2 (∂ t B y ) n+1/2 i+1/2,j = (∂ x E z ) n+1/2 i+1/2,j . ( 1
)
The plasma is modeled through the definition of the electron density n e (r, t) and coupled to the code-propagation kernel (1) by the equation of the density current

(∂ t J z ) n+1/2 i,j = e 2 /m e (n e E z ) n+1/2 i,j
.

(

Here, we will use a slab base plasma with radial linear density profile n e 0 . A matrix of turbulence δn e is calculated and added to n e 0 n e (r, t) = n e 0 (r, t) + δn e (r, t).

(

The total density n e (r, t) (profile plus turbulence) is fed into (2). The turbulence matrix is defined using an internal model.

Usually, we use a model of sum of modes, with δn e being defined by

δn e T RB = i M i=i m j M j=j m A(i, j) cos [k x (i)x + k y (j)y + ϕ(i, j)] (4)
where A(i, j) is a chosen amplitude spectrum and ϕ(i, j) is a random generated phase, combining all possible wavenumbers. Simulations were performed using a rectangular grid with dimensions of L x = 150 λ 40 GHz by L y = 150 λ 40 GHz , which correspond to 3000 × 3000 grid points (112 × 112 cm), where the Cartesian coordinate dimensions L x and L y correspond to the radial and poloidal dimensions in a tokamak. Part of the box comprises the emission setup (antenna and optical system) and a vacuum distance between the antenna and the plasma. In this work, a monostatic 2-D H-plane horn antenna with a total flare angle of 2ψ = 43.6 • has a half-power beamwidth of 22 • . A lens with an effective focal length of 15.7 λ 40 GHz (11.8 cm), placed at a distance of 4 λ 40 GHz (3 cm) from the antenna mouth, focuses the antenna beam into a low divergence beam with a planar wavefront. The -3-dB width of the radiation diagram taken at a radius of 50 λ 40 GHz is 18 • . Through the use of a prism, the beam is deflected into the plasma with an injection angle α = 7 • [START_REF] Silva | Unidirectional transparent signal injection in finite-difference time-domain electromagnetic codes-Application to reflectometry simulations[END_REF]. The antenna and the optical system (lens plus prism) appear on Figs. 2 and5. The plasma measures L xp = 66 λ 40 GHz by L yp = 150 λ 40 GHz or 1353 × 3000 grid points (50 cm × 112 cm). The probing frequency is f = 40 GHz, corresponding to a vacuum wavelength of λ 0 = 0.75 cm and to a critical density n c ≈ 2 • 10 19 m -3 . Turbulence is homogeneous, and its rms level is defined referring to the critical density for 35 GHz as δn RMS e T RB /n e (x c 35 GHz ) × 100%. Calculations have been made for values of 0.1%, 0.25%, 1.0%, 2.5%, 3.0%, 5.0%, 7.5%, and 10.0%. The plasma flows in the y-direction, corresponding to the poloidal direction in a tokamak, with constant velocity v y = 22.5 × 10 6 m • s -1 , i.e., v y /c = 7.5%.

III. MODEL FOR TURBULENCE

In these simulations, a Kolmogorov-like amplitude kspectrum A(i, j) was used as defined by a flat top up to a chosen wavenumber from where it decays according to a k 3 rule; in concrete terms

S amp (k) = b (k -a) 3 (5)
where the constants a and b adjust the shape of the decay. We have chosen this amplitude spectrum shape to have a behavior similar to Analyse Localisee du Transport Anormal par diffusion dune lumiere IR (ALTAIR)-French acronym for local analysis of anomalous transport using infrared light)-experimental data, where the amplitude of the fluctuation wavenumber is assumed to have a constant top followed by a decay according to a power law k 3 f (f ) (both along radial and poloidal directions). ALTAIR was an experiment installed at Tore Supra to measure density fluctuations throughout the whole plasma with collective infrared laser scattering [START_REF] Devynck | Localized measurements of turbulence in the TORE SUPRA tokamak[END_REF].

IV. SIMULATION CONSIDERATIONS

One vital aspect to take into account in reflectometry simulations in general, and in Doppler reflectometry in particular, is the injection of the signal. The injection method used defines a radiation diagram which determines the wavenumber vectors injected in the plasma. Ideally, a single wavenumber (a plane wavefront) from a narrow nondivergent beam should be used, assuring that a narrow zone within the plasma is probed with a unique wavenumber. The antenna setup described in Section II guarantees this requirements. Another point to take into consideration is the fact that the received scattered signal has a much lower amplitude than the injected one, implying the need for a proper signal decoupling. Without it, the minute received signal will have its characteristics masked by the main emission. It is important that the technique used in the code does not lose the connection with reality; otherwise, the significance of the results will be compromised. For instance, the existence of sidelobes in a radiation diagram and the effect of mode selection in a waveguide are important aspects that influence the response of a reflectometer and must be kept in the simulation setup. Our code addresses the problem of signal injection using a unidirectional transparent source (UTS) associated with an optical system [START_REF] Silva | Studies on O-mode reflectometry spectra simulations with velocity shear layer[END_REF], [START_REF] Silva | Unidirectional transparent signal injection in finite-difference time-domain electromagnetic codes-Application to reflectometry simulations[END_REF]. The UTS allows the injection of the probing wave only in the forward direction and effectively separates the weaker received signal from the main emission. Full-size spatial dimensions can be simulated with the code, but full temporal simulations, due to the small time step discretization dictated by Courant-Friedrichs-Lewy (CFL) conditions, impose the need to scale down the duration of the events simulated and, consequently, to scale up the velocities involved. Let R t be the ratio between t real , the duration of a reflectometry probing (either fixed or swept frequency), and the time simulated

t siml R t = t real t siml . (6)
A plasma feature, with some characteristic dimension L p , moving with velocity v real will take a time T real to pass a given point. In the simulation, this event will be reproduced taking a time

T siml = T real R t ( 7
)
with a corresponding increase in velocity

v siml = L p T siml = R t L p T real = R t v real . ( 8
)
This will also affect the frequency shift due to Doppler effect

Δf siml = 1 2π k p • v siml = 1 2π R t k p • v real = 1 2π R t Δf real . ( 9
)
These effects can be fully compensated, the correct real values regained, and the deformation of the shape of the signal spectra recovered, as verified in [START_REF] Silva | Studies on O-mode reflectometry spectra simulations with velocity shear layer[END_REF].

Preliminary studies indicate that in the presence of significant forward scattering, to obtain the long time evolution of the system and to give statistical meaning to the results, long time series must be used. This implies the use of large turbulence matrices and, consequently, a large number of iterations. The turbulence matrices used in these simulations have a poloidal dimension of L m = 1500 λ 40 GHz (1.12 m), corresponding to 30 000 grid points. The number of iterations performed was N iter = 800 000, a value considerably larger than usually observed in reflectometry simulations, a situation due to the very long wavelength associated with forward scattering, which implies a large number of points to obtain significant averages.

V. FORWARD-SCATTERING SIMULATION RESULTS

A snapshot of the electric-field structure obtained is shown in Fig. 2 for a turbulence level of 10%. Under this strong turbulence level, the beam is split into several subbeams with a loss of coherence and resolution. Near the oblique cutoff, wave trapping can be observed together with multireflections.

The evolution of the scattering process can observed, analyzing the temporal behavior of the signals, for a given turbulence matrix at three levels of turbulence of 0.1%, 1%, and 10%. In Fig. 3, the results obtained are summarized. At the top, the scattered signals are shown, and one can notice their intermittent nature and an increase in the amplitude of the bursts with turbulence, which is confirmed by the curves of the windowed rms amplitude of the scattered signals, shown at the bottom, obtained with a sliding window of ∼2.5 T 0 .

The previous analysis has shown how the behavior of the scattered signals evolves during the simulation, while the following results have been calculated globally on the whole signal, and averages are obtained using eight runs with different realizations of the narrow low-wavenumber k-spectrum according to (4). The average rms value of the amplitude of the scattered signals appears in Fig. 4-top (in red) via the turbulence level. Individual rms curves (for each of the runs) are shown in dots. There is an initial linear response of up to 2.5% followed by a nonlinear saturation. As the turbulence level increases, the dispersion of the individual curve values around the average curve increases. At the bottom of Fig. 4, the eight-run average spectra of the signals are shown. As the turbulence level increases, changes in the behavior of the spectra are observable. There is both an enlargement of the width of the spectra and a displacement of the maxima clearly seen in the 0.1%-2.5% curves, until the limit values are reached for both the enlargement and the maxima. The width of the spectra (at -3 dB) rises from 0.1 up to 0.5 GHz. The limit for the maximum deviation from the carrier is the theoretical value for the Bragg backscattering deviation at the oblique cutoff Δf = k f v y /2π = -0.76 GHz, and it is marked in the figure by a black vertical line. In addition to the spectral broadening, for higher turbulence values of 5%-10.0%, a nonlinear response appears in the interval of 37-39 GHz. Notice that, for the lowest value of turbulence (0.1%), one can still see the very narrow mark of the carrier at 40 GHz.

VI. BACKSCATTERING SIMULATION RESULTS

A snapshot of the electric-field structure obtained is shown in Fig. 5 for a turbulence level of 10%. When compared with the field structure shown in Fig. 2, we notice a completely different field structure. The power is being scattered in a much finer structure. The structures showing wave trapping are not present.

With the same procedure used in the former section, the results for the wide Kolmogorov spectrum were processed. The same temporal-analysis procedure was repeated, and the results are shown in Fig. 6. The signals show a more continuous nature than the one observed in the previous case. The oscillations in the windowed rms curves have a much higher frequency than the one from the forward-scattering case and show a noneruptive nature of the signal.

The average global behavior was obtained as before for eight runs with different matrix realizations, and the results are shown in Fig. 7. The average rms signal-amplitude curve shows an initial linear response of up to ∼1%, reaching a maximum around 2.5%, from where it starts to decay. The maximum dispersion of the individual rms curves (lesser than the forwardscattering case) is also reached at 2.5%. The average spectrum curves show also a behavior distinct from the former case. All the curves are centered around the Bragg deviation Δf = k f v y /2π, independent of the level of turbulence. The progressive increase of the width of the spectra seen on the former case is not observed here. The half-power widths are more or less the same, which are ≈0.5 GHz. For higher levels of turbulence, strong nonlinear effects appear in the interval of 37-39 GHz.

VII. DISCUSSION

The simulations performed illustrate quite clearly the different mechanisms intervening in Bragg backscattering and forward-scattering processes. Forward scattering appears as a process of intermittent nature, resulting from multiple scattering contributions, while the Bragg backscattering has a faster and more continuous character, resulting essentially from a single scattering event in the vicinity of the oblique cutoff. Simulations indicate than the slower nature of forward scattering requires longer simulation time series than the one needed to study backscattering, which is at least ten times longer. The longer is the time series obtained, the closer we will be to the theory which is formulated in an asymptotic limit [START_REF] Gusakov | Multiple scattering effect in Doppler reflectometry[END_REF], [START_REF] Surkov | Nonlinear regime of Doppler reflectometry in cylindrical plasmas[END_REF]. The spectral behavior of the scattered signals is distinct in the two situations. For Bragg backscattering, the spectra suffer for all levels of turbulence; the maximum linear Bragg deviation allowed in the system, which is given by Δf = k f v y /2π occurs at the oblique cutoff where the wave radial wavenumber k r = 0 and k f = 2k p , with k p being the poloidal wavenumber of the wave. This confirms Bragg backscattering as a phenomenon occurring mainly at the vicinity of the oblique cutoff. The results for forward scattering show an evolution of the Doppler deviation from the carrier to the maximum Bragg deviation together with an enlargement of the peak as the turbulence level increases. This is in agreement with the theoretical models for forward scattering proposed [START_REF] Gusakov | Multiple scattering effect in Doppler reflectometry[END_REF], [START_REF] Surkov | Nonlinear regime of Doppler reflectometry in cylindrical plasmas[END_REF]. These models use Gaussian amplitude spectra to model the fluctuations instead of the Kolmogorov-like spectra, which is closer to the experiments used in our model. This, nevertheless, does not seem to play a larger role since the predictions of the model and the results of the simulations are in close agreement. One exception is on the amplitude of the returned forward-scattered signals, which is higher in the simulations for turbulence levels that are higher than 5%. This, we believe, is due to the fact that in the simulation, there are additional effects that are not included in theory, namely, the appearance of hill-hole zones which trap the wave. These cavities have a fill-relax time that trap the waves over periods much longer than the time of flight. When relaxing, the additional release of electric field contributes to the signal in sudden bursts. Another additional factor outside the domain of the theory, verified in simulations, is the emergence of secondary cutoff surfaces, sometimes detached from the location of the main cutoff surfaces. For the same levels of turbulence > 5%, the beam, in the case of Bragg backscattering near the oblique cutoff, dispersed in all directions, justifying the reduction of the rms power observed. Also observed in the simulations is the appearance of nonlinear secondary responses for turbulence above 5%, which is of lower power than the main, having a Doppler displacement higher than the one given by the Bragg rule and which can be justified by a the nonlinear Bragg response, as described by the second unstable zone of Mathieu's equation.

Fig. 1 .

 1 Fig. 1. Representation of the two amplitude spectra used. The Bragg resonant wavenumber k Bragg = 211.11 rad • m -1 is marked with the broken line.

Fig. 2 .

 2 Fig. 2. Snapshot of the electric field obtained with the narrow Kolmogorov spectrum for a level of turbulence of 10%.

Fig. 3 .

 3 Fig. 3. Results from the narrow Kolmogorov spectrum for three levels of turbulence (0.1%, 1%, and 10%). (Top) multiscattered returned signal. (Bottom) Windowed rms amplitude of the scattered signals.

Fig. 4 .

 4 Fig. 4. (Top) RMS amplitude values of the multiscattered returned signals for eight different realizations of narrow Kolmogorov turbulence matrices for several turbulence levels. The continuous curve is the average rms value. (Bottom) Average spectra of the returned signals for different levels of turbulence. Each curve is an average of eight individual spectra.

Fig. 5 .

 5 Fig. 5. Snapshot of the electric field obtained with the wide bandpass Kolmogorov spectrum for a level of turbulence of 10%.

Fig. 6 .

 6 Fig. 6. Results from the wide bandpass Kolmogorov spectrum for three levels of turbulence (0.1%, 1%, and 10%). (Top) Multiscattered returned signal. (Bottom) Windowed rms amplitude.

Fig. 7 .

 7 Fig. 7. (Top) RMS amplitude values of the backscattered returned signals for eight different realizations of wide bandpass Kolmogorov turbulence matrices for several turbulence levels. The continuous curve is the average rms value. (Bottom) Average spectra of the returned signals for different levels of turbulence. Each curve is an average of eight individual spectra.

Filipe

  da Silva received the B.S. degree in electrical and computer engineering from Technical Superior Institute (IST), Lisbon, Portugal, in 1991, the M.S. degree in management of science and technology from the Superior Institute of Economy and Management, Lisbon, and the Ph.D. degree in physics from IST in 2007. He is currently with the Institute of Plasmas and Nuclear Fusion, IST. Dr. da Silva is a member of the Portuguese Engineers Association (Ordem dos Engenheiros). Stéphane Heuraux was born in Epinal, France on May 24, 1958. He received the Ph.D. degree in plasma physics and the "Habilitation à Diriger les Recherches" from the Henri Poincaré University, Nancy, France, in 1986 and 1999, respectively. In 1983, he was with LPMIA, Henri Poincaré University. He was invited by the CEA Cadarache in 2003-2004 to work on antenna-plasma coupling and reflectometry diagnostic. Since 2007, he has been a Full Professor with the Henri Poincaré University. His scientific interest mainly involves wave in plasma physics, theory, simulation and applications, particularly regarding ponderomotive force, propagation in fluctuating plasmas, whether magnetized or not, reflectometry diagnostics for characterization of density fluctuations in fusion plasmas, antenna-plasma coupling for fusion plasma heating, and RF sheath physics to explain and look ahead of hot spots in fusion devices during RF heating. Evgeniy Z. Gusakov is with the Division of Plasma Physics, Atomic Physics, and Astrophysics, IOFFE Physical Technical Institute, St. Petersburg, Russia, where he is the Head of the High Temperature Plasma Physics Laboratory. His interests include wave propagation in inhomogeneous turbulent plasmas, nonlinear wave-plasma interaction, RF heating, and microwave plasma diagnostics. Alexei Popov is with the Division of Plasma Physics, Atomic Physics, and Astrophysics, IOFFE Physical Technical Institute, St. Petersburg, Russia, where he is a Member of the High Temperature Plasma Physics Laboratory. His interests include plasma reflectometry and ECE emission.

ACKNOWLEDGMENT

The views and opinions expressed herein do not necessarily reflect those of the European Commission, IST, and FCT.

This work was supported in part by the European Communities and Instituto Superior Técnico, carried out within the Contract of Association between EURATOM and IST, and in part by the Fundação para a Ciência e Tecnologia in the frame of the Contract of Associated Laboratory. F. da Silva is with the Associação EURATOM/IST, Técnico, 1049-001 Lisboa,


R F Lang

G Angloher

M Bauer

I Bavykina

A Bento

A Brown

C Bucci

C Ciemniak

C Coppi

G Deuter

F Von Feilitzsch

D Hauff

S Henry

P Huff

J Imber

S Ingleby

C Isaila

J Jochum

M Kiefer

M Kimmerle

H Kraus

J.-C Lanfranchi

M Malek

R Mcgowan

V B Mikhailik

E Pantic

F Petricca

S Pfister

W Potzel

F Pröbst

S Roth

K Rottler

C Sailer

K Schäffner

J Schmaler

S Scholl

W Seidel

L Stodolsky

A J B Tolhurst

I Usherov

W Westphal

Discrimination of recoil backgrounds in scintillating calorimeters

Keywords: CRESST, 210 Po, Low Background, Dark Matter PACS: 29.40.Mc, 29.40.Vj, 95.35.+d

The alpha decay of 210 Po is a dangerous background to rare event searches. Here, we describe observations related to this alpha decay in the Cryogenic Rare Event Search with Superconducting Thermometers (CRESST). We find that lead nuclei show a scintillation light yield in our CaWO 4 crystals of 0.0142 ± 0.0013 relative to electrons of the same energy. We describe a way to discriminate this source of nuclear recoil background by means of a scintillating foil, and demonstrate its effectiveness. This leads to an observable difference in the pulse shape of the light detector, which can be used to tag these events. Differences in pulse shape of the phonon detector between lead and electron recoils are also extracted, opening the window to future additional background suppression techniques based on pulse shape discrimination in such experiments.

Introduction

Experiments that search for rare processes such as neutrinoless double-beta decay [1] or elastic scattering of Dark Matter particles [2] require a strong reduction of ambient radioactive backgrounds. One important source of radioactivity is radon gas, a member of the natural decay chain of 238 U [START_REF] Firestone | Table of Isotopes (CD ROM Edition)[END_REF]. 222 Rn decays under emission of an alpha particle with a half-life of 3.8 days. This is long lived enough to plate out on materials in the vicinity of the detectors. In these alpha decays, recoiling nuclei can be implanted in surfaces. Eventually, the daughter nucleus 210 Po alpha decays into 206 Pb with a half-life of 138 days and a total energy of 5407 keV Email address: rafael.lang@mpp.mpg.de (R. F. Lang) available in the decay. On the one hand, this results in the ejection of a 5304 keV alpha particle which can be a background to neutrinoless doublebeta decay searches. On the other hand, the lead nucleus recoils with an energy of 103 keV. This can be a dangerous background in Dark Matter searches that needs to be dealt with, as we describe in the following.

CRESST-II Detector Module

For the CRESST-II experiment, we use scintillating CaWO 4 crystals as a target for a Dark Matter search. The crystals are cut in cylindrical shape of 4 cm diameter and similar height, and weigh about 300 g each. We expect Dark Matter to induce tungsten recoils in the target with energies below a few tens of keV. To enable a calorimetric measurement of these low energies, the crystals are cooled to ∼ 15 mK where heat capacities are low. Tungsten films, evaporated on the crystals, are thermally stabilized in their transition to the superconducting state. This allows measurement of the rising film resistance caused by the temperature rise following a particle interaction in the crystal. CaWO 4 is a good scintillator even at the cryogenic temperatures relevant here [START_REF] Mikhailik | [END_REF]. To measure the scintillation light following a particle interaction, a separate light detector is used. This allows discrimination of the dominant electron and gamma background from nuclear recoils which are expected from Dark Matter interactions, since the light output of these backgrounds is significantly higher than that of nuclear recoils. The light detector consists of a light absorbing wafer and another tungsten thermometer evaporated onto it. The scintillation light is absorbed in the wafer and results in a small but measurable temperature rise of the thermometer. Only about one percent of the total energy of a particle interaction is detected by the light channel [5,[START_REF] Frank | Proceedings of the 7th International Conference on Advanced Technology and Particle Physics[END_REF]6].

Figure 1 shows one such detector module. It consists of the target crystal with the tungsten thermometer, which we refer to as the phonon detector, and the light absorbing wafer with its thermometer, the light detector. To improve the light collection, both detectors are enclosed in a reflective housing. On the right, the CaWO 4 crystal can be seen in its reflective housing, and with the thermometer evaporated on top of it. On the left, the light absorbing wafer is shown (silicon on sapphire) with its thermometer barely visible.

To obtain the energy from the observed pulses, we use a template fit procedure. A template pulse is built from a large set of pulses with similar en-ergy. This template is then fitted to each observed pulse, with three free parameters: the level of the baseline, the onset of the pulse, and its amplitude as the measure of interaction energy. Energy calibration is performed in a dedicated calibration run. Heater structures on the thermometer are used to inject large pulses in order to drive the thermometer into the normal conducting state. The thermometer response is then used to stabilize the operating temperature of the detector over many weeks. In addition, smaller pulses with fixed energies can also be injected to calibrate the thermometer at low energies where no external calibration source is available. Details of these procedures are laid out in [START_REF] Angloher | The CRESST Collaboration)[END_REF][START_REF] Angloher | accepted for publication in Astroparticle Physics[END_REF].

Po-210 Decay Observed with Silver Reflectors

Figure 2 shows a scatter plot of events recorded by one crystal enclosed in a silver reflector. The exposure is 12.31 kg d; no calibration source was present during this data taking. The horizontal axis shows the energy deposited in the phonon channel. The vertical axis shows energy measured by the light detector in units of keV electron equivalent (keV ee ), defined such that for 122 keV gamma events (from a 57 Co calibration source) in the CaWO 4 crystal we register 122 keV ee in the light detector. The diagonal band consists of electron recoils and gamma induced events. Nuclear recoil events yield significantly less light than electron or gamma 2 events. Here, we define nuclear recoils to mean events below a slope of 25 keV ee /200 keV. Particles hitting the light detector directly show up along the vertical axis. The spectrum of nuclear recoil events is shown in figure 3. The continuum of events in this band is dominated by neutron induced events, since at the time of data taking, the detector was not yet surrounded with a neutron shield. In addition, a population around ∼ 100 keV is visible which we attribute to recoiling 206 Pb nuclei following the decay of 210 Po in the vicinity of the crystals. If the 210 Po decay happens on a nearby surface, decays can result in lead nuclei impinging on the target crystal. From simple momentum conservation the energy of these nuclei is fixed to 103 keV. Furthermore, if 210 Po is implanted in the crystal very close to its surface, the alpha particle may also deposit part of its energy in the target. Then our calorimetric measurement results in an energy higher than 103 keV. Finally, a more relevant possibility occurs if the polonium is implanted in nearby surfaces such as the reflective foil. Then the lead nucleus loses energy on its way to the crystal, resulting in an event with less than 103 keV. This can be a dangerous background to direct Dark Matter searches. With our CaWO 4 crystals in particular, such lead recoils mimic Dark Matter induced tungsten recoils, which are expected in the energy region below a few tens of keV [START_REF][END_REF][START_REF] Angloher | accepted for publication in Astroparticle Physics[END_REF]. It is therefore indispensable to be able to distinguish this background from tungsten recoils.

Having identified the population as being due to recoiling lead nuclei allows us to measure the amount of light emitted by these events. This quantity is also relevant to the search for Dark Matter due to the similarity of recoiling lead nuclei and the tungsten recoils that are expected from Dark Matter. We define the light yield as energy in the light detector (in keV ee ) over energy in the phonon detector (in keV). To measure its value for lead recoils, one has to exclude events above 103 keV which possibly have a light contribution from the alpha particle. As a lower limit we use 93 keV to keep the influence of neutrons small. Figure 4 shows the light yield of these events. From a Gaussian fit the light yield of ∼ 100 keV lead recoils at cryogenic temperatures of about 15 mK in CaWO 4 crystals is found to be (0.0142 ± 0.0013) compared to that of electrons of the same energy. This value is robust within the stated errors when small variations of the chosen energy interval are included.

Po-210 Decay Observed with Scintillating Reflectors

To distinguish this polonium induced background from Dark Matter induced tungsten recoils, we surround our detectors with a VM2000 class polymeric foil (from 3M), which is highly reflective and in addition also scintillates. Then the alpha particle from the polonium decay produces some additional scintillation light in the foil, shifting those events out of the region of nuclear recoils. Indeed, once this was done, the class of events observed in figure 2 disappeared from the nuclear recoil band. Figure 5 shows the corresponding scatter plot. The data shown is from another detector and a later data taking period, in which a neutron shield was present [START_REF] Angloher | accepted for publication in Astroparticle Physics[END_REF], thus also eliminating the continuous neutron induced background in the nuclear recoil band.

The foil is highly efficient, and no events are seen in the nuclear recoil band around 100 keV. Comparing this scatter plot to figure 2, we note that the scintillating foil causes a population of excess light events above the main gamma/electron band, dominantly at low energies in the phonon detector. Incidentally, the polonium events are shifted to the gamma/electron recoil band. This can be illustrated by examination of the pulse shapes in the light detector. CaWO 4 is a rather slow scintillator in contrast to common plastic scintillators at millikelvin temperatures [6]. Hence pulses with an additional contribution from the scintillating foil are faster than pulses that are only due to an interaction in the crystal. This can be seen even by eye, comparing polonium events to crystal events in figure 6.

Events from direct interactions in the light detector deposit no energy in the phonon detector and hence show up along the vertical axis in figure 5. Such events deposit their energy instantaneously in the light detector and allow us to measure the detector response. This represents the fastest pulses possible, with much faster rise times than the usual events originating in the crystal, as can be seen in figure 6.

A second template pulse is built from such directhit events, and all events are fitted with both the standard template and this second template pulse. The fastest pulse is a direct hit in the light detector which takes only τ rise = 0.16 ms from 10 to 90% peak height. A usual pulse from electron/gamma interactions in the crystal takes τ rise = 0.54 ms. A template of events from the 210 Po surface decays is also shown, seen to be in between the two other templates, with τ rise = 0.28 ms (uncertainties are less than 0.01 ms).

The qualities of the two individual template fits (their RMS values) are plotted against each other as in figure 7. Events where the fast (direct hit) template pulse fits better are tagged as events which potentially have an additional light contribution from the scintillating foil. In the scatter plot of figure 5 these events are highlighted, and their spectrum is shown in figure 8. Events of various origins are extracted by this tagging procedure: Particles hitting the light detector directly (they appear along the vertical axis in figure 5) are recognized as such. As can be expected from pulse shape discrimination, the tagging pro-4 cedure fails towards low energies in the light detector. This results in many mis-tagged events below ∼ 40 keV ee , where only less than a few 100 eV are deposited in the light detector. Events leaking from the gamma/electron band form a continuous background in figure 8. Excess light events are also tagged, supporting our idea of their origin involving the faster scintillating foil. Finally, the polonium decay events are clearly identified and can be recovered from the gamma/electron band by this procedure. 3, the detector was surrounded by a neutron shield, and the continuous background here is not due to neutrons, but due to leakage from the main gamma/electron band when applying the tagging procedure.

Pulse Shape of Lead Recoils

Having extracted the events from the polonium decay based on the pulse shape in the light detector, we can examine the pulse shape in the phonon detector as well. By eye or based on simple parameters like the rise or decay times, no difference between the individual pulses can be seen. Yet a second template is built from these events around 103 keV (figure 8). This again gives an additional fit quality parameter (the fit RMS), this time for the phonon detector. The ratio of this value and of the corresponding value of the standard template fit quality is plotted in figure 9, for events in the energy interval [100, 120] keV, both for the population of lead recoils from the polonium decay, and for standard electron or gamma events. The two populations clearly separate in this parameter on a level better than 1σ. Hence the ratio of the quality of two standard event fits in the phonon detector can act as an additional discrimination parameter between electron and nuclear recoils. 9: Difference in phonon detector pulse shape for electron and nuclear recoils of about 100 keV. This difference is characterized by the ratio of the fit-RMS values obtained from lead template and standard template fits. Lead recoils were tagged by the different pulse shape in the light detector, which is possible in this particular case due to the additional light from the scintillating foil. Both distributions are normalized to unity to ease the comparison.

Conclusion

The decay 210 Po → 206 Pb + α results in recoiling lead nuclei, a potentially dangerous background in the search for Dark Matter. We find that in CaWO 4 at millikelvin temperatures, 100 keV lead recoils have a light yield of (0.0142 ± 0.0013) compared to electrons of the same energy. In the case of scintillators as Dark Matter targets, we have shown a way to discriminate these lead recoils by surrounding the target with a scintillating foil, which leads to an enhanced light output for events from this background. Using the pulse shape of events in the light detector allows tagging of events which have a contribution from the scintillating foil for energies above ∼ 40 keV ee . Thus the polonium induced lead recoils can be identified, and in addition, excess light events are tagged, revealing their origin as being due to the scintillating foil. Furthermore, we have shown that a difference exists in the pulse shape of the phonon-detector events for heavy nuclear recoils with respect to electron or gamma induced events at energies around 100 keV. This can be utilized to cross-check the origin of events in the phonon channel.

Acknowledgments

This work was partially supported by funds of the DFG (SFB 375, Transregio 27 "Neutrinos and Beyond"), the Munich Cluster of Excellence ("Origin and Structure of the Universe"), the EU networks for Cryogenic Detectors (ERB-FMRXCT980167) and for Applied Cryogenic De-

Figure 1 :

 1 Figure 1: Picture of an opened CRESST-II detector module.On the right, the CaWO 4 crystal can be seen in its reflective housing, and with the thermometer evaporated on top of it. On the left, the light absorbing wafer is shown (silicon on sapphire) with its thermometer barely visible.

Figure 2 :

 2 Figure2: Events observed in one crystal encapsulated within a silver reflector, over a period of about one month (12.31 kg d, detector Daisy/run 27). We consider events below the line as nuclear recoils.

Figure 3 :

 3 Figure 3: Spectrum of events in the nuclear recoil band of figure 2. The prominent feature around 103 keV is attributed to the decay of 210 Po on and below nearby surfaces. The continuous background is attributed to neutrons, since at the time of data taking no neutron shield was present yet.

Figure 4 :

 4 Figure 4: Light Yield of events between 93 keV and 103 keV.The right population is a cross section of the gamma and electron recoil band with a light yield of unity. The left population comes from 206 Pb nuclei hitting the crystal. A Gaussian fit gives the light yield of these events as (0.0142 ± 0.0013) keVee/keV.

Figure 5 :

 5 Figure 5: Events observed in one detector module enclosed within a scintillating reflector (light dots, detector Zora/run 30). The exposure is 21.94 kg d, about two months of data taking. Events tagged by the selection criterion based on the pulse shape of the light detector are marked as heavy dots (see text for details).

Figure 6 :

 6 Figure6: Template events from the light detector, built from a few events of each class with energies of about 100 keVee: The fastest pulse is a direct hit in the light detector which takes only τ rise = 0.16 ms from 10 to 90% peak height. A usual pulse from electron/gamma interactions in the crystal takes τ rise = 0.54 ms. A template of events from the 210 Po surface decays is also shown, seen to be in between the two other templates, with τ rise = 0.28 ms (uncertainties are less than 0.01 ms).

Figure 7 :

 7 Figure 7: Histogram of events in figure 5 in the plane spanned by the two fit quality parameters. Entries per bin are color coded according to the logarithmic scale on the right. Events where the direct-hit template fits better (below the angle bisector) are tagged and shown as dark points in figure 5.

Figure 8 :

 8 Figure8: Spectrum of events which are tagged based on the quality of the two template fits of the light detector. These events are shown as dark points in figure5. In contrast to figure 3, the detector was surrounded by a neutron shield, and the continuous background here is not due to neutrons, but due to leakage from the main gamma/electron band when applying the tagging procedure.

tectors (HPRN-CT2002-00322), and the Maier-Leibnitz-Laboratorium (Garching). Support was provided by the Science and Technology Facilities Council.


Olivier Lopez

Adil Haboucha

Fabien Kéfélian

Haifeng Jiang

Bruno Chanteau

Vincent Roncin

Christian Chardonnet

Anne Amy-Klein
email: anne.amy-klein@univ-paris13.fr

Giorgio Santarelli

Cascaded multiplexed optical link on a telecommunication network for frequency dissemination

Keywords:

We demonstrate a cascaded optical link for ultrastable frequency dissemination comprised of two compensated links of 150 km and a repeater station. Each link includes 114 km of Internet fiber simultaneously carrying data traffic through a dense wavelength division multiplexing technology, and passes through two routing centers of the telecommunication network. The optical reference signal is inserted in and extracted from the communication network using bidirectional optical adddrop multiplexers. The repeater station operates autonomously ensuring noise compensation on the two links and the ultra-stable signal optical regeneration. The compensated link shows a fractional frequency instability of 3×10 -15 at one second measurement time and 5×10 -20 at 20 hours. This work paves the way to a wide dissemination of ultra-stable optical clock signals between distant laboratories via the Internet network.

Introduction

The transfer of ultra-stable frequency signals between distant laboratories is required by many applications in time and frequency metrology, fundamental physics, particle accelerators, and astrophysics [START_REF] Foreman | Remote transfer of ultrastable frequency references via fiber networks[END_REF][START_REF] Daussy | Long-distance frequency dissemination with a resolution of 10 -17[END_REF][START_REF] Calhoun | Stable Photonic Links for Frequency and Time Transfer in the Deep-Space Network and Antenna Arrays[END_REF][START_REF] Shillue | Transmission of low phase noise, low phase drift millimeterwavelength references by a stabilized fiber distribution system[END_REF][START_REF] Wilcox | Stable transmission of radio frequency signals on fiber links using interferometric delay sensing[END_REF][START_REF] Karshenboim | Fundamental physical constants: looking from different angles[END_REF][START_REF] Flambaum | Enhanced effect of temporal variation of the fine-structure constant in diatomic molecules[END_REF][START_REF] Uzan | The fundamental constants and their variation: observational and theoretical status[END_REF]. Stable radio and microwave frequency transmission over an optical link has already been demonstrated [START_REF] Daussy | Long-distance frequency dissemination with a resolution of 10 -17[END_REF][START_REF] Calhoun | Stable Photonic Links for Frequency and Time Transfer in the Deep-Space Network and Antenna Arrays[END_REF][START_REF] Shillue | Transmission of low phase noise, low phase drift millimeterwavelength references by a stabilized fiber distribution system[END_REF][START_REF] Wilcox | Stable transmission of radio frequency signals on fiber links using interferometric delay sensing[END_REF][START_REF] Lopez | 86-km optical link with a resolution of 2×10 -18 for RF frequency transfer[END_REF][START_REF] Fujieda | Coherent Microwave Transfer Over a 204-km Telecom Fiber Link by a Cascaded System[END_REF][START_REF] Kumagai | Stable radio frequency transfer in 114 km urban optical fiber link[END_REF][START_REF] Lopez | High-resolution microwave frequency dissemination on an 86-km urban optical link[END_REF]. Frequency transfer using the optical phase of an ultra-stable laser over a dedicated fiber link was reported on distances up to about 200 km by several groups [START_REF] Newbury | Coherent transfer of an optical carrier over 251 km[END_REF][START_REF] Williams | High-stability transfer of an optical frequency over long fiber-optic links[END_REF][START_REF] Musha | Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network[END_REF][START_REF] Jiang | Long-distance frequency transfer over an urban fiber link using optical phase stabilization[END_REF][START_REF] Grosche | Optical frequency transfer via 146 km fiber link with 10 -19 relative accuracy[END_REF][START_REF] Terra | Phasecoherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link[END_REF][START_REF] Schnatz | Phase-Coherent Frequency Comparison of Optical Clocks Using a Telecommunication Fiber Link[END_REF]. The current challenge is to extend this technique of frequency dissemination on longer distances in order to connect laboratories of different countries.

Scalability of the roundtrip noise compensation to long-haul optical link is not straightforward: attenuation and phase noise increase with the fiber length whereas correction bandwidth and noise rejection decrease with it [START_REF] Newbury | Coherent transfer of an optical carrier over 251 km[END_REF]. The geographic situation of the link has also a strong impact since uncompensated link phase noise power spectral density per unit of length can vary over 3 orders of magnitude [START_REF] Schnatz | Phase-Coherent Frequency Comparison of Optical Clocks Using a Telecommunication Fiber Link[END_REF][START_REF] Kéfélian | Long-distance ultrastable frequency transfer over urban fiber link: toward a European network[END_REF]. A 900 km dedicated optical link has been demonstrated very recently with a very good resolution thanks to the intrinsic low-noise of the link [START_REF] Grosche | 1,5 µm Fiber Network for Long-Distance Metrology[END_REF]. For a noisier link, a multiple segments approach can be implemented [START_REF] Musha | Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network[END_REF]. The number and length of each segment can be optimized depending on the noise distribution along the link.

We have recently developed a frequency dissemination approach which takes advantage of the existing Internet fiber network already connecting research facilities and universities via the National Research Networks (NRENs) [START_REF] Kéfélian | High-resolution optical frequency dissemination on a telecommunication network with data traffic[END_REF]. With this approach, the ultra-stable signal propagates directly on a telecommunication fiber simultaneously transmitting digital data, using dense wavelength division multiplexing (DWDM) technology.

Internet fibers present a higher number of connectors and additional specific WDM equipment, as compared to dedicated fibers, which leads to an increased attenuation and propagation noise. The multiple sub-link approach allows for an increased correction bandwidth and robustness regarding attenuation, but requires the development of a repeater station between each segment.

In this paper, we present the first demonstration of a cascaded optical link for frequency transfer including two segments of internet network fibers and one repeater station. A major part of the link uses telecommunication fibers simultaneously transmitting digital data of the Internet network. In a first part we will describe the repeater station which has to work autonomously in a telecommunication network node. Then we will present the architecture of the cascaded link we have implemented. Finally results will be presented and discussed.

Repeater station for multi-segment link

Principle of operation

With a multiple segments approach, intermediate stations are required where a low-noise optical oscillator is phase locked to the incoming signal in order to regenerate a spectrally pure signal seeding the next segment. The purpose of the N th station along the link is threefold as depicted in Figure 1. First it sends back part of the incoming optical signal to the previous station (N-1), after amplification and frequency shift, in order to stabilize the incoming link (named link N). Second, the station regenerates the incoming optical signal thanks to a cleanup optical tracking oscillator based on a low-noise Bragg grating fiber laser phase-locked on the incoming signal. The regenerated signal then feeds the link departing to the next station (N+1). Third, it processes the signal sent back from station N+1, allowing for noise compensation of the following link segment (link N+1). The compensation is based on the assumption that the laser phase fluctuations due to propagation are identical in both directions. This usual assumption is valid for symmetrical propagation characteristics (frequency and polarisation state). The use of a Faraday mirror imposes polarisation state retrace of the return beam. The forward and backward signals have a frequency difference of 2x35 MHz. Since the phase is, at first order, proportional to the frequency, it induces different forward and backward phase fluctuations. This leads to an imperfect determination of the phase correction of the link which is proportional to the free running link phase fluctuations multiplied by the ratio between the frequency offset and the optical frequency (3x10 -7 ). In principle this error can be compensated by digital frequency processing. However if we assume a long term free running instability of a few 10 -14 , this gives an upper limit for the link resolution below 10 -20 . Finally the Sagnac effect, which is intrinsically asymmetric, is an ultimate limit for frequency resolution.

To implement this approach, repeater stations are designed to be installed in remote telecommunication sites which are noisier and have greater temperature fluctuations than the laboratory environment. Consequently, a highly robust and reliable system is required. Each station consists of two modules, one for the electronics package and the other for the optical part.

Optical set-up

The optical set-up of each station consists of a laser, an optical module, three acousto-optic modulators (AOM) and two photodiodes (PD). For the local optical oscillator we use a fiber laser system based on a distributed-feedback technique (Koheras Basik OEM). Its freerunning linewidth is about 1kHz. Its frequency can be tuned over a range of ~ 2 GHz, which is sufficient for compensating the long term noise of this laser by controlling the PZT port. Indeed a ± 1 K fluctuation of the room temperature corresponds to a variation of the optical frequency smaller than 500 MHz.

The compact optical module has been realized by splicing off-the-shelf fiber-optic components. This module contains all the critical components of the station in term of phase stability : 2 Faraday mirrors, 2 isolators (in front of the photodiodes) and a few couplers. Consequently, the fiber pigtail lengths have been minimized and finely matched in order to reduce the effect of the residual thermal fluctuation of the non-common paths' lengths. The whole optical circuit is housed in an aluminum box (dimensions 30x100x180 mm) covered by a thick polyurethane foam layer (50mm) for acoustic noise and temperature shielding. Moreover the temperature is actively stabilized around 298 K using a Peltier element. The temperature varies less than 20 mK when the ambient temperature fluctuates about 1 K.

The optical set-up is designed to generate two beat-note signals (see Fig. 1). The first one, detected by photodiode 1 (PD1), is used to lock the local laser on the incoming signal from link N using the laser PZT and AOM3. The second beat-note signal on PD2 quantifies the roundtrip phase fluctuations caused by acoustical, mechanical, and thermal delay propagation fluctuations along link N+1. AOM1 is then used to compensate for this fiber induced noise. AOM2 shifts the frequency of the return signal to station N-1 in order to distinguish it from parasitic reflections.

Electronic set-up

The electronic system can be seen on Fig. 1. The beatnote signal for the laser lock is first filtered with a 75 MHz band pass filter to reduce the noise bandwidth to about 10 MHz. In order to make the control system insensitive to amplitude fluctuations, we use a logarithmic amplifier. A digital phase-frequency detector generates the phase-error signal processed by a loop filter (PLL1). Fast corrections (100 kHz bandwidth) are applied through the voltage controlled oscillator driving AOM3. Slow corrections are applied to the laser PZT input with a few tens of Hz bandwidth.

The beatnote signal for the N+1 link stabilization is filtered with a narrow 150 MHz band pass filter (5 MHz bandwidth) to reject the parasitic reflections and amplified with a logarithmic amplifier. A tracking oscillator is then used to filter the signal in an ultra-narrow bandwidth of 100 kHz. The tracking oscillator signal, after a digital division by 960, is mixed with the local RF oscillator signal at 75MHz, itself divided by 480. This signal is processed by PLL2 and applied to AOM1. The division is necessary since the link phase noise is very high and it enables increasing dynamic compensation control, hence improving the robustness of PLL2.

The station automatic operation

The station is automatically operated by microcontrollers in order to achieve autonomous operation. First of all, one microcontroller manages the local laser phase-lock acquisition. The laser frequency is scanned until the beatnote signal at the logarithmic amplifier exceeds a pre-defined power level. This ensures that it is inside the capture range of the phase lock loop. Consequently the loop is closed by the microcontroller, and the laser frequency is locked at the frequency n-75 MHz, where n is the received laser frequency. At a second step, the tracking oscillator loop is closed, and finally PLL2 is closed.

All RF signals are synthesized from a single local RF reference (see Fig. 1). Thanks to the optimized choice of the beat-note frequencies at 75 and 150 MHz, any possible drift of the local oscillator has no influence on the N to N+1 frequency transfer. The local laser is locked to the input signal (after AOM2) with a -75 MHz shift. The transferred signal to the next station is shifted to this local laser by +75 MHz, since the return signal from the next station is locked to the local laser signal with a 150 MHz shift. Both frequency shifts are synthesized by the same RF local oscillator of the station. Since they are opposite in sign, their sum is exactly zero, whatever the drift of the local oscillator.

Cascaded Link

Station testbed

To characterize the stability performance of the repeater station, we have used fiber spools in order to mimic the installed fiber span. The testbed link is comprised of two segments of 150 km length cascaded with the repeater station, as described in section 2. Each segment includes 4 optical add drop multiplexers (OADM) and 2 bidirectional Erbium-doped fiber amplifiers (EDFA) as in a real multiplexed link (see below). At the link input, an identical station, denoted as input station, is fed with a cavity-stabilized laser [START_REF] Jiang | Long-distance frequency transfer over an urban fiber link using optical phase stabilization[END_REF]. The link performance is evaluated by measuring the end-to-end beatnote signal between the local laser of the input station and the end of the link. For instability measurements, we use a multichannel zero deadtime counter which operates with a -type window. Two channels simultaneously record the frequency of the compensated link with a bandwidth of 100 kHz and 10 Hz respectively. A third channel is used to record the AOM1 frequency, which represents the free-running frequency noise of the first link of 150 km. The fractional Allan deviation is then calculated from the frequency samples and is shown in Fig. 2. The stability of the testbed link for a 10 Hz bandwidth (black squares) is 3x10 -16 at 1 s averaging time, averaging down with a 1/ slope to the mid 10 -20 range at 30000 s. This very good stability arises from the lower noise of the spools (red circles) compared to an installed fiber. On the same graph is plotted the system noise floor of the frequency transfer obtained with a zero-length link (green up-triangles), which reaches the 10 -20 level at 10 4 s.

Cascaded link using the telecommunication network

Using this station, we have demonstrated a first implementation of a 300-km cascaded optical link on the French academic and research network (RENATER).

The overall scheme of the 300 km-long optical link (LPL-Nogent l'Artaud-LPL) with an intermediate repeater station located at Nogent l'Artaud (100 km east of Paris) is depicted in Fig. 3. This link starts and ends at LPL laboratory (at Université Paris 13, in the north surroundings of Paris), and is composed of three different fiber spans. In each span, there are two identical parallel fibers labeled as UL and DL. UL is used for the uplink consisting of 114 km of fiber carrying internet traffic and 36 km of dedicated dark fiber. DL is used for the downlink with the same characteristics. The first span is composed of two 11 km-long fibers connecting the information service and technology center of Université Paris 13 to a Data Centre Facility (DCF) located in Aubervilliers (Interxion1). The digital stream between Université Paris 13 and Aubervilliers is encoded over an optical carrier on channel #34 (1550.12 nm) of the International Telecommunication Union (ITU) grid whereas the ultrastable signal is carried by the channel #44, at 1542.14 nm. The second span is composed of two 36 km-long urban dark fibers which connect the two DCFs of Interxion 1 and TeleHouse 2, downtown Paris. The third span is composed of two 103 km long-haul intercity fibers simultaneously carrying internet data traffic. In this part the digital data signals are transferred over channels #42 and #43, only 0.8 nm and 1.6 nm away from the ultrastable signal. At Nogent l'Artaud the ultra-stable signal arriving from UL is processed in the repeater station and sent into the other 150 km-long fiber (DL) back to Université Paris 13. Eight OADM are used to insert and extract the ultrastable signal from the Internet fibers. These three-port components can insert or extract the 1542.14 nm wavelength into or out of the other wavelengths with isolation better than 25 dB for an adjacent channel (100 GHz) and better than 40 dB for other channels. Attenuation is an issue since the round-trip propagation of the optical signal is required over the same fiber for noise compensation. Total roundtrip attenuation for each 150 km link is more than 100 dB due to fiber losses, OADMs and the large number of connectors. In order to overcome these losses, we used two bidirectional EDFA for each link. Better amplification performance could be obtained with Fiber Brillouin Amplifiers as demonstrated in [START_REF] Terra | Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber[END_REF].

Results and discussions

Fig. 4 shows the temporal behavior of the link propagation delay over 3.5 days. The (a) curve displays the 300-km free-running propagation delay measured by replacing the Nogent l'Artaud station with an optical amplifier and using fixed AOM frequency shifts. It gives the free-running fiber propagation delay fluctuation, which spans over a few ns. This corresponds Figure 5 shows the phase noise spectral density of the various segments composing the link. The phase noise is evaluated by analyzing the end-to-end beatnote signal of a very narrow linewidth laser. This measurements show that the Interxion1-Telehouse2 link segment is the noisiest one. The optical phase noise power spectral density of the cascaded optical link of 2 x 150 km is shown in Fig. 6, without and with compensation. The phase noise reduction is around 50 dB at 1 Hz, which is very close to the theoretical limit of 51 dB [START_REF] Newbury | Coherent transfer of an optical carrier over 251 km[END_REF]. For Fourier frequencies below 5 Hz, both spectra exhibit some peaks which are likely to be due to seismic noise since optical fibers on the long-haul span are buried along the railway tracks. Fig. 7 shows the fractional frequency instability (Allan deviation) of the 2150 km link for four days of continuous operation, measured with a -type frequency counter. The freerunning fiber frequency noise of the UL (red circles) is measured simultaneously using the compensation signal applied to the AOM located in the LPL. The Allan deviation is 310 -15 at 1 s averaging time and scales down as 1/ from 1 s to 70000 s reaching 510 -20 in a measurement bandwidth of 10 Hz (black squares). With the full bandwidth (about 100 kHz), the Allan deviation is 6 times larger (blue up-triangles). A crucial aspect of frequency dissemination is robustness and reliability. In our case, the optical fibers are located in an uncontrolled environment without any particular protection against thermal changes and acoustic noise. As a consequence the noise behavior is non stationary, as can be seen from the comparison between the red curves in Fig. 5 and6, which are displaying the phase noise PSD of the 300-km link and twice the 150-km link respectively. They were recorded at different times. However the control system can easily handle these fluctuations and the link remains locked for several days. When the human activity effect, mainly in the DCF, exceeds the maximum control dynamics, phase jumps can occur with maximum amplitude of a few hundreds of ps. Those events are quite rare, at most a few per days, and induce several cycles slips without any severe unlock of the system. With longdistance propagation, the polarization state fluctuation is also a crucial point. After a few days, we had to adjust the polarization state in order to optimize the beatnote signal amplitude of the local laser phase-lock. The repeater station is not designed for an automatic adjustment of the polarization. With a single remote station, it is always possible to manually tune the polarization at the other ends of both link segments. With a multiple station link, this approach becomes impossible and the automatic polarization control is an issue.

Renater Data transponder

Conclusion

We show the ultra stable transfer of an optical frequency over 300 km of installed optical fibers of an optical telecommunication network simultaneously carrying Internet data. The optical link goes through two Data Center Facilities using multiplexers and bidirectional erbium-doped fiber amplifiers. We obtained an instability of 310 -15 at 1 s which averages down to around 510 -20 after about 20 hours. This result demonstrates that non-dedicated fiber links are a valuable alternative to dark fiber links. With such Internet links, high performance frequency dissemination could be foreseen for a large ensemble of scientific users using NRENs dense fiber network facilities. In conjunction with the recently proposed PTB technique [START_REF] Grosche | Method for making available a reference frequency[END_REF] to provide several users with one single optical link, optical links are now very attractive for widescale frequency dissemination. This will enable a broad range of highsensitivity measurements, including the search for fundamental constants variation [START_REF] Karshenboim | Fundamental physical constants: looking from different angles[END_REF][START_REF] Flambaum | Enhanced effect of temporal variation of the fine-structure constant in diatomic molecules[END_REF][START_REF] Uzan | The fundamental constants and their variation: observational and theoretical status[END_REF][START_REF] Shelkovnikov | Stability of the proton-to-electron mass ratio[END_REF] and gravitational mapping.

Fig. 1 .

 1 Fig. 1. Scheme of the N th repeater station, FM : Faraday mirror, PD : photodiode, LO : local RF oscillator, AOM : acousto-optic modulator, Log : logarithmic amplifier, µC : microcontroller, PLL : phase-lock loop

Fig . 2 .

 2 Fig .2. End-to-end fractional frequency instability of a 2x150 km cascaded testbed link: 150km free running up-link (red circles), 2x150 km compensated link measured with a 10 Hz filter (black squares), system floor with zero-length link (green up-triangles)

Fig. 3 .

 3 Fig. 3. Scheme of the 2 x 150 km cascaded optical link.

Fig. 4 .

 4 Fig. 4. Temporal behavior (sampled every 10s) of the optical link propagation delay: (a) endto-end propagation delay of the 300 km free-running optical link recorded without repeater station at Nogent l'Artaud (red trace); (b) end-to-end propagation delay of the 300-km cascaded compensated link (black trace), (c) correction signal (applied to the input AOM at LPL) of the 150-km up-link (red dashed trace). Curves (b) and (c) were recorded simultaneously.

Fig. 5 .

 5 Fig. 5. Phase noise power spectral density of the different subsections of the link. Black line: first subsection LPL-Interxion1-LPL of 22 km. Blue line: LPL-Telehouse2-LPL link of 94 km. Red line: LPL-Nogent l'Artaud-LPL link of 300-km.

Fig. 6 .

 6 Fig.6. Phase noise power spectral density (PSD) of the compensated 2150 km link (black line) and twice the phase noise PSD of the free running 150 km up-link (red line).

  time  [s] End to end stability 10 Hz BW End to end stability full BW Up-link stability open loop

Fig. 7 .

 7 Fig.7. End-to-end fractional frequency instability of the 150 km free running up-link (red circles), and 2x150 km compensated link measured without filter (blue up-triangles) and with a 10 Hz filter (black squares)

Acknowledgments

The authors are deeply grateful to D. Vandromme, T. Bono and E. Camisard from GIP RENATER and J. F. Florence from Université Paris 13 for their support in using the Renater network, and to F. Wiotte and A. Kaladjian for technical support. We acknowledge funding support from the Agence Nationale de la Recherche (ANR BLAN06-3_144016) and Université Paris 13.


Isabelle Niedhammer

Eve Bourgkard

Nearkasen Chau

Occupational and behavioural factors in the explanation of social inequalities in premature and total mortality: a 12.5-year follow-up in the Lorhandicap study

Keywords: Adult, Body Mass Index, Chi-Square Distribution, Female, France, epidemiology, Health Behavior, Health Status Disparities, Humans, Life Style, Longevity, Male, Middle Aged, Mortality, Occupational Exposure, Occupations, statistics & numerical data, Proportional Hazards Models, Sex Factors, Social Class occupational groups, mortality, occupational exposures, health behaviours

Occupational and behavioural factors in the explanation of social inequalities in premature and total mortality: a 12.5-year follow-up in the Lorhandicap study.

Introduction

Social inequalities in health have been reported for a long time. They refer to differences in morbidity and mortality between social groups, i.e. the lower the social position, the poorer the health status, and the measures of morbidity and mortality. These inequalities have been demonstrated for various chronic diseases such as cardiovascular diseases, and general measures of morbidity and mortality .

[ 1 -4 ] Several indicators may be used to measure social position or socioeconomic status (SES), education, occupation, and income being the most widely used of these indicators , . Besides the report of social inequalities in health, it appears crucial to better understand the [5 6 ] mechanisms linking social position and health. Consequently, identifying mediating factors that may contribute to explain social inequalities in health may be helpful to reduce the exposure to these factors in specific social groups, and thus to reduce social inequalities in health.

Various theories have been developed to explain the pathways and mechanisms underlying these inequalities . These theories [7 -9 ] include the materialist explanation, that put the emphasis on material conditions (access to goods/services, and exposures to material risk factors in the living and working environment), the psychosocial explanation, that focuses on psychosocial and stress related influences with a plethora of risk factors such as social support or sense of control, and the behavioural explanation, that emphasizes the importance of behavioural risk factors in explaining social inequalities in health. As mediating factors probably are interrelated, some authors have suggested simplified causal models to disentangle the direct (independent) effect of mediating factors, and their indirect effect through other factors , . [10 11 ] Social inequalities in all-cause mortality have been described extensively. Studies showed strong and persistent social inequalities in mortality in various countries, such as France , and other European countries , but the studies that attempted to explain these [START_REF] Saurel-Cubizolles | Social inequalities in mortality by cause among men and women in France[END_REF] [ [START_REF] Mackenbach | Widening socioeconomic inequalities in mortality in six Western European countries[END_REF] inequalities are still sparse. Most of them focused on behavioural factors, such as smoking, alcohol consumption, physical activity, body mass index, etc., and biologic factors (fibrinogen, cholesterol, triglycerides, blood pressure, etc.) as potential mediating factors .

[ 14 -19 ] These studies, in general, found that these factors, and especially smoking, explained a part (that may be small in some studies) of social inequalities in mortality, suggesting that a wider range of factors need to be considered to explain these inequalities.

Occupational factors, that included both material and psychosocial factors, such as physico-chemical, biomechanical, and psychosocial exposures, are considered as major determinants of health, and they may be socially graded (the lower the social position, the higher the exposures). Consequently, they may be pertinent candidates to explain social inequalities in health, as underlined in a recent commentary [

. Some studies have already mentioned the contribution of occupational factors, especially psychosocial work factors, in explaining at 20 ] least partly social differences in various measures of morbidity . To our knowledge, no previous study has attempted to evaluate [21 -28 ] the impact of both occupational and behavioural factors on social inequalities in all-cause mortality.

The objectives of this study were to analyse the association between SES as measured using occupation, and two measures of all-cause mortality, premature and total mortality, and to evaluate the contribution of occupational and behavioural factors in explaining social differences in mortality among a sample of men and women of the French working population.

Materials and methods

This study was based on the data from the Lorhandicap survey set up in 1996 in the nord-east of France. Several studies have already been published using this survey . The initial sample consisted of everyone aged 15 years or more living in 8000 randomly [29 -31 ] selected households in the Lorraine region of the north-east of France. Only households with a telephone were eligible. The investigation was approved by the Commission Nationale de l Informatique et des Libert s (CNIL), and written informed consent was obtained from the

' é
respondents. The study protocol included: an application to participate to ascertain the number of persons in the household, and three self-administered questionnaires with a covering letter and a pre-paid envelope for the reply, were mailed at 1-month interval. When the number of individuals was unknown, two questionnaires were sent first, and a complementary one was sent later. The questionnaire included various sections covering socio-demographic characteristics, job characteristics, working conditions, health status, and behavioural factors. If people were retired, they were asked about their main job during working life.

SES was measured using occupational groups. Four occupational categories were considered following the international classification of occupation (ISCO): professionals/managers, associate professionals/technicians, service workers/clerks, and manual workers.

Professionals/managers were used as reference category. Occupation was studied as a marker of SES because it characterises adult SES, is available for all working people, and may reflect occupational exposures better than education , .

[

Occupational factors were assessed by: biomechanical exposure (exposure to vibrations -manual handling of vibrating tools or vibration from a fixed machine-, manual materials handling, postural and articular constraints such as standing/walking, awkward posture, handling objects or tools, working on a production line, or other constraints), physical exposure (exposure to noise, cold or hot temperatures, or outdoor work), work status (temporary versus permanent job) as a marker of job insecurity, psychological demands (exposure to high work pace, or mental load), and social support from colleagues (very unsatisfied, or unsatisfied versus neither satisfied nor unsatisfied, satisfied, or very satisfied). Exposure to biomechanical and physical factors, and to psychological demands was defined by the presence of at least one item. Details on the formulation of the question and items, as well as the number and percentage of exposed people for each item separately may be found in the . The factors that were the most prevalent were standing/walking, awkward appendix posture, and manual materials handling for biomechanical factors, and noise, and hot and cold temperatures for physical factors. The study of the associations between the 5 occupational exposures studied (biomechanical and physical exposures, work status, psychological demands, and social support) showed three significant positive associations (p<0.001) between biomechanical exposure and physical exposure, between biomechanical exposure and psychological demands, and between temporary contract and low social support, as well as two significant negative associations between psychological demands and temporary contract (p<0.001) and between psychological demands and low social support (p<0.01) i.e. that people with high levels of psychological demands were less likely to have a temporary work contract and low levels of social support.

Behavioural factors included: smoking status (smoker, ex-smoker or non-smoker), body mass index (BMI) in kg/m , and alcohol 2 abuse measured using the French version of the Cut/Annoyed/Guilty/Eye-opener (CAGE) questionnaire and defined by at least two [START_REF] Beresford | Comparison of CAGE questionnaire and computer-assisted laboratory profiles in screening for covert alcoholism[END_REF] positive responses to four items: consumption considered excessive by the subject, consumption considered excessive by people around the subject, subject wishes to reduce consumption, and consumption on waking.

The cohort was followed up for mortality from 1st July 1996 to 31th December 2008. The vital status of all subjects was assessed by searching using the national computerised database listing all deceased subjects in France, contacting the registry offices of the birth places for people born in France, and the registry office devoted to foreign born French people (Ministry of Foreign Affairs). Two measures of mortality were considered: death, and premature death before the age of 70. Premature death focusses on deaths occurring at younger ages, and may be considered as a useful public health measure providing information on preventable deaths. In addition, this outcome was retained because, as reported by Krieger et al.

, unlike life expectancy and years of personlives lost, it is easy to understand, easy to [START_REF] Krieger | The fall and rise of US inequities in premature mortality: 1960 2002[END_REF] compare, methodologically transparent, and a sensitive indicator of inequities in health.

The associations between SES (i.e. occupation) and occupational and behavioural factors were tested using the Chi-Square test to determine the significance and direction of these associations. Cox proportional hazard model, which yields hazard ratios (HRs), was used to examine the association between SES and mortality. The duration of follow-up for each subject was calculated for each subject from 1st

July 1996 to 31th December 2008, or earlier in the case of death, or 70 birthday for premature mortality. The associations between th occupational and behavioural factors and mortality were also examined using Cox regression models. Occupational and behavioural factors that displayed inverse social gradients were excluded in subsequent analyses. Several models were performed: a basic model Almost all behavioural and occupational factors displayed strong and significant associations with SES, except alcohol abuse for men and women, and smoking for women ( ). A trend towards increasing alcohol abuse with lower SES was observed for men. Table 1 Biomechanical and physical exposures, temporary contract, and low social support were strongly socially graded, the lower the occupational group, the higher the exposure. High psychological demands displayed a significant inverse social gradient, managers/professionals being more likely to be exposed. Psychological demands were consequently omitted from subsequent analyses.

(
A significant association was found between SES and premature mortality ( ), which was confirmed after adjustment for age Table 2 and sex (model 1), manual workers being at increased risk of mortality. This association was observed for men and women separately, although non significant for women. Male gender and all behavioural and occupational factors displayed significant crude associations with premature mortality (not all significant for each gender separately). Adding behavioural factors to model 1 did not change the HRs for manual workers very much (model 2). Additional analyses (not shown) exploring the separate effects of each behavioural factor showed that the biggest contribution was found for alcohol abuse [START_REF] Goldman | Social inequalities in health disentangling the underlying mechanisms[END_REF] in the total sample. The inclusion of occupational factors to model 1 led to a % substantial decrease in the HRs for manual workers, by 72 for the total sample, 74 for men, and 61 for women. The HRs for manual % % % workers were no longer significant after adjustment for occupational factors. The occupational factors that contributed to decrease the social difference in premature mortality were in the total sample (not shown): biomechanical exposure [START_REF] Monden | Current or lifetime smoking? Consequences for explaining educational inequalities in self-reported health[END_REF], job insecurity (28 ), % % physical exposure [START_REF] Hemstrom | Health inequalities by wage income in Sweden: the role of work environment[END_REF], and social support [START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]. Model 4 that included behavioural and occupational factors simultaneously provided a % % similar explanation of social differences in premature mortality than model 3.

Significant social differences for total mortality were observed ( ). Manual workers were at higher risk for mortality, a similar Table 3 trend was observed for service workers/clerks after adjustment for age and sex (model 1). Social differences were also found for men and women separately, manual workers being at significant higher risk of mortality for men. Male gender and almost all behavioural and occupational factors were found to be predictive factors of mortality in crude associations. The inclusion of behavioural factors to model 1 did not modify the HRs for manual workers very much (model 2). Studying each factor separately showed that the biggest contributions were found for BMI [START_REF] Galobardes | Indicators of socioeconomic position (part 2)[END_REF] and alcohol abuse (4 ) in the total sample. Adding occupational factors to model 1 contributed to decrease the % % social differences between manual workers and managers/professionals by 41 for the total sample, 44 for men, and 31 for women % % %

(model 3). The HRs for manual workers were no longer significant after adjustment for occupational factors. The contributions of each occupational factor separately were as follows in the total sample: job insecurity [START_REF] Borrell | Social class and self-reported health status among men and women: what is the role of work organisation, household material standards and household labour?[END_REF], social support [START_REF] Van Oort | Material, psychosocial, and behavioural factors in the explanation of educational inequalities in mortality in The Netherlands[END_REF], biomechanical exposure (10 % %

), and physical exposure [START_REF] Mackenbach | Health inequalities: Europe in profile[END_REF]. Adding behavioural and occupational factors simultaneously increased only slightly the explained % % fractions (model 4) compared to model 3.

Discussion

Significant social differences were observed for premature and total mortality in this 12.5-year follow-up study among the French working population. Manual workers were at increased risk of total and premature mortality compared to managers/professionals with HRs reaching almost 2. Occupational factors played a substantial role in explaining social differences in mortality. Their contributions were 31-74 , and were more pronounced for men and for premature mortality. The contribution of behavioural factors was very low.

%

Manual workers were the occupational group that displayed a significant excess of mortality compared to managers/professionals.

Other previous studies showed social disparities in mortality in France and in other countries, using various SES markers , . Our [12 13 ] study also underlined social inequalities in occupational exposures, with the lowest occupational groups, especially manual workers, being more likely to be exposed to negative working conditions. Other previous studies reported the accumulation of unfavourable working conditions in the lowest occupational categories , , . One major exception was psychological demands, that displayed a [22 23 25 -27 ] strong inverse social gradient, managers/professionals being more likely to be exposed, something already reported , , , . [22 [START_REF] Borrell | Social class and self-reported health status among men and women: what is the role of work organisation, household material standards and household labour?[END_REF] 25 26 ] Although there were a number of studies describing social inequalities in mortality in various populations, studies that tried to explain these inequalities were less numerous. This study is one of the seldom studies evaluating the contribution of occupational factors to social inequalities in all-cause mortality, and suggested that these factors may play a substantial role.

Other studies explored the contribution of occupational factors to social inequalities in several measures of morbidity. Our study is in agreement with some previous studies underlying the role ] occupational factors, that were the most prevalent, may play a substantial role in explaining social differences in mortality, i.e. standing/walking, awkward posture, and manual materials handling among the biomechanical factors, and noise, and hot and cold temperatures among the physical factors, supporting previous results on the explanation of social inequalities in morbidity outcomes in

France

. Our results are also in agreement with another study showing that the role of occupational factors in explaining social [START_REF] Niedhammer | The contribution of occupational factors to social inequalities in health: findings from the national French SUMER survey[END_REF] inequalities in health was not modified very much when behavioural factors were taken into account . The issue of independent [START_REF] Borg | Social class and self-rated health: can the gradient be explained by differences in life style or work environment?[END_REF] (direct) and indirect (through behavioural factors) effects of occupational factors is consequently less important in our study as we did not observe any major role of behavioural factors. Consequently, the contribution of occupational factors remained almost the same with or without adjusting for behavioural factors.

Behavioural factors did not play an important role in explaining social inequalities in mortality in our study. Other authors demonstrated that behavioural factors may explain only a modest proportion of social inequalities in mortality , , . Several [10 11 15 ] hypotheses may be assumed to explain this. Behavioural factors were evaluated only at baseline, and as the follow-up was long, people might change their behaviours, which is likely to lead to misclassification and dilution of their effects. Behavioural factors were based on self-reported data, that may lead to an underreporting bias of the most negative health behaviours. For example, the heaviest drinkers may be underrepresented in our sample, because of both selection and underreporting bias. Evaluation of alcohol consumption was done using the CAGE instrument that may be adequate to measure alcohol-related problems, but may neglect some specific ones that may be more strongly related to SES, such as binge drinking.

Gender differences were also of interest in our study, this was why genders were studied separately. Women were more likely to be service workers/clerks, and men manual workers. The prevalence of occupational and behavioural factors was found to be different between genders. Men were more likely to be exposed to physical exposure, and women to job insecurity. Men were more likely to be smokers and overweight, and to have alcohol-related problems. The risk of mortality was also higher for men than for women. These results confirm the different patterns of occupation and occupational exposures between genders, related to the strong sexual division of labour, as well as the differences in health behaviours and mortality between genders. Similar social inequalities in mortality were observed for men and women, but the contribution of occupational factors was found to be higher in men than in women. This result is in agreement with other studies . Strong gender differences were observed for the associations between behavioural factors and [START_REF] Niedhammer | The contribution of occupational factors to social inequalities in health: findings from the national French SUMER survey[END_REF] mortality; smoking and alcohol abuse were found to be strong predictors of premature and total mortality for men, but not for women.

Nevertheless, the contribution of behavioural factors was very modest and appeared to be similar in explaining social inequalities in mortality in both genders.

Limitations of our study may be mentioned. A selection bias may have occurred, as the response rate was about 44 . However, this % response rate is similar to those of other studies using postal self-administered questionnaires in France . Furthermore, the gender and

[34 ]
age distributions of the initial sample were close to those of the census population. Nevertheless, previous studies showed that non-respondents may be more likely to have lower SES, poorer health-related and behavioural factors . Consequently, it is likely that

[34 ]
such a bias may lead to underestimate social inequalities in health. A limitation was related to sample size especially for women, and led to more uncertainty in the estimation of HRs and explained fractions for this group. Another limitation was that behavioural and occupational factors were not based on lifetime exposures. Other authors demonstrated that this may lead to underestimate the contributions of behavioural and occupational factors to social inequalities in health , . The contribution of these factors may also be underestimated [35 36 ] because some behavioural and occupational factors were not explored, such as diet or physical activity, as well as chemical/biological exposures, decision latitude at work, reward, or workplace violence. Thus, inclusion of more mediators might result in different estimates of the contributions of mediators. Finally, the generalisation of our results to other populations should be made with caution because of cultural and socioeconomic differences between countries.

Strengths of the study also deserve to be mentioned. The sample was derived from the general population, making generalisation possible for the population in the nord-east of France. Sample size allowed us to study men and women separately, which may be crucial in occupational epidemiology . The study was based on a 12.5-year follow-up, i.e. a rather long period. Mortality was measured using [START_REF] Niedhammer | How is sex considered in recent epidemiological publications on occupational risks?[END_REF] national database (an exhaustive and independent source of data). Mortality is also an objective outcome measure, consequently no reporting bias may be suspected. Occupational groups were used in this study as a marker of social position, and are a well-known measure of social position in the working population. Although results may differ somewhat using other measures of social position (such as education or income) , , relatively similar conclusions have been provided by others , . We performed additional analyses that [5 6 ]

[ 24 36 ] included the presence of chronic disease at baseline in our models to make sure that no previous chronic disease may introduce a confounding effect in our results. These results confirmed the robustness of our findings. We also performed the analyses for premature mortality before 65 and found similar results, but statistical power was lower because of a smaller number of premature deaths.

To conclude, occupational factors may play a substantial role in explaining social inequalities in mortality, especially premature mortality. Preventive actions focusing on these factors and specific social groups may be useful to reduce social inequalities in mortality.

More research is needed to better understand the role of these factors, over the life course, on social inequalities in various health outcomes.

Exposure

No

  model 1) measuring the association between SES and mortality after adjustment for age (and sex), behavioural factors added to model 1 (model 2), occupational factors added to model 1 (model 3), and behavioural and occupational factors added simultaneously to model 1 (model 4). The contribution of behavioural and/or occupational factors to the explanation of the social differences in mortality was estimated by the change in the HRs for occupational groups after inclusion of the variable(s) in the model, i.e. explained fraction values increases in HRs. The contribution was calculated only if the HR for a given occupational group was significant in model 1. The proportional hazard assumption was checked based on Schoenfeld residuals for the global model and for each covariate. Analyses were also done with additional adjustment for chronic disease at baseline, the results were unchanged. Results are presented for men and women separately, and for the total sample for Cox regression models. The statistical analyses were performed using STATA software.

	calculated by the formula: (HR	model 1 -	HR	extended model	)/(HR	model 1 -	1)	[16 ]	. Positive values indicate reductions in HRs, and negative %	%

Results

Of the 8000 households included in the sample, mailings to 193

[START_REF] Huisman | Educational inequalities in cause-specific mortality in middle-aged and older men and women in eight western European populations[END_REF]

were lost (due to addressing error or death). Of the 7807 % households contacted, 3460 (44.3 ) participated (all eligible members of the family took part in 86 of those). In total, 6235 subjects % % filled in the questionnaire, 19 were of unknown sex or age, leaving 6216 subjects who were similar in age and sex distribution to the overall population of the north-east of France . During the follow-up, 143 subjects (2.3 ) were lost and excluded. The subjects with [30 ] % unknown smoking habit or alcohol abuse were excluded (296 subjects, i.e. 4.8 ). Only the subjects who had been working, were alive, % and aged 70 years or less at baseline (1st July 1996) were retained for this study i.e. 4118 subjects, 2189 men and 1929 women. In total, 291 deaths (206 and 85 among men and women) occurred, and 165 deaths before age 70 (115 and 50 among men and women).

Table 1

 1 Associations between SES (occupation) and age, behavioural and occupational factorsChi-Square test to test the association between SES (occupation) and each mediator, * p<0.05, ** p<0.01, *** p<0.001

	. of exposed (N)	% exposed

Table 2

 2 Contribution of behavioural and occupational factors to social differences in premature mortality (<70y)

	TOTAL SAMPLE N 4118 =	Crude HR 95 CI %	Adjusted HR (1)	95 CI %	Adjusted HR (2)	95 CI %	% Adjusted HR (3)	95 CI %	% Adjusted HR (4)	95 CI %	%
	SES (occupation)
	Managers, professionals	1		1		1			1			1
	Associate professionals, technicians	1.25	0.70 2.22 -	1.02	0.57 1.82 -	1.02	0.57 1.82 -		0.78	0.43 1.43 -		0.78	0.43 1.45 -
	Service workers, clerks	0.96	0.59 1.57 -	1.40	0.84 2.32 -	1.37	0.82 2.28 -		1.13	0.67 1.90 -		1.12	0.66 1.88 -
	Manual workers	1.92 **	1.20 3.08 -	1.88 **	1.17 3.01 -	1.88 **	1.17 3.03 -	0	1.25	0.74 2.12 -	72	1.27	0.75 2.17 -	69
	Men	2.08 ***	1.49 2.90 -	1.96 ***	1.38 2.82 -	1.59 *	1.08 2.33 -		2.08 ***	1.44 3.00 -		1.68 **	1.13 2.49 -
	Smoking
	Non-smoker	1				1						1
	Ex-smoker	2.14 ***	1.46 3.13 -			1.52 *	1.02 2.28 -					1.49 *	1.00 2.23 -
	Smoker	1.40	0.93 2.12 -			1.57 *	1.01 2.43 -					1.57 *	1.01 2.44 -
	Alcohol abuse	2.63 ***	1.80 3.85 -			2.01 ***	1.35 2.98 -					1.90 **	1.28 2.83 -
	BMI (kg/m ) 2
	<25	1				1						1
	25 30 -	1.71 **	1.22 2.41 -			0.90	0.63 1.28 -					0.91	0.63 1.31 -
	>30	1.58 *	1.04 2.39 -			0.90	0.59 1.38 -					0.91	0.60 1.40 -
	Biomechanical exposure	1.52 **	1.12 2.06 -						1.35 §	0.96 1.90 -		1.31	0.93 1.84 -
	Physical exposure	1.59 **	1.17 2.15 -						1.19	0.83 1.70 -		1.18	0.82 1.68 -
	Temporary contract	2.81 ***	2.05 3.85

-1.86 *** 1.28 2.70 -1.80 ** 1.24 2.63 -Low social support 2.21 *** 1.62 2.99 -1.39 * 1.00 1.94 -1.39 * 1.00 1.93 -

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

[START_REF] Laaksonen | Health behaviours as explanations for educational level differences in cardiovascular and all-cause mortality: a follow-up of 60 000 men and women over 23 years[END_REF]

Acknowledgements:

Lorhandicap study group: N Chau, F Guillemin, JF Ravaud, J Sanchez, S Guillaume, JP Michaely, C Otero Sierra, B Legras, A Dazord, M Choquet, L M jean, N Tubiana-Rufi, JP Meyer, Y Schl ret, and JM Mur. The question was: please indicate the occupational exposures you have (had) been highly exposed during your working life