Nuclear Instruments and Methods in Physics Research A 720 (2013) 131–134

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Nuclear Instruments and Methods inPhysics Research A

0168-90

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journal homepage: www.elsevier.com/locate/nima

Effects of the input polarization on JET polarimeter horizontal channels

P. Gaudio a,n, M. Gelfusa a, A. Murari b, F. Orsitto c, A. Boboc d, JET–EFDA Contributors e,1

a Associazione EURATOM-ENEA, University of Rome ‘‘Tor Vergata’’, Roma Italyb Consorzio RFX Associazione, EURATOM-ENEA, per la Fusione, 4-35127 Padova, Italyc Associazione EURATOM-ENEA, CR Frascati, 00044 Frascati, Italyd Association EURATOM-CCFE, Culham Science Centre, Abingdon, OX14 3DB, UKe JET-EFDA, Culham Science Centre, OX14 3DB, Abingdon, UK

a r t i c l e i n f o

Available online 22 December 2012

Keywords:

Faraday angle

Phase shift

Polarimeter

02/$ - see front matter & 2013 EURATOM. Pu

x.doi.org/10.1016/j.nima.2012.12.017

esponding author.

ail address: gaudio@ing.uniroma2.it (P. Gaudi

e the appendix of F. Romanelli et al 2010 Pr

aejeon, Korea, October 2010).

a b s t r a c t

In the past, the analysis of JET polarimetry measurements were carried out only for the vertical

channels using a polarimetry propagation code based on the Stokes vector formalism [1,2]. A new

propagation code has been developed therefore for the horizontal chords to simulate and interpret the

measurements of the Faraday rotation and Cotton–Mouton phase shift in JET. The code has been used to

develop a theoretical study to the effect of the input polarization on the eventual quality of the

measurements. The results allow choosing the best polarization to optimize the polarimetric

measurements for the various experiments.

& 2013 EURATOM. Published by Elsevier B.V. All rights reserved.

1. Introduction

A magnetized plasma is an optically active and birifringentmedium. If a laser beam is sent into the plasma, the beamexperiences the Cotton–Mouton effect [3,4], proportional to themagnetic field perpendicular to the propagation direction, sincethis is the field which interacts with the birefringence of themedium. The polarization of the beam is subjected also to theFaraday effect, due to the magnetic field parallel to the directionof propagation. The principal interest of these measurements isgiven by fact that they allow to acquire information on the plasmamagnetic fields distribution using internal measurements. Thechange of the polarization state of an electromagnetic wave canindeed be used to provide indications about the magnetic fielddistribution, the plasma current and the electronic density. Theinterpretation of the Faraday rotation and Cotton–Mouton effectmeasurements is however not a simple task. Suitable propagationcodes are required to model the behavior of the electromagneticradiation inside the plasma. Such a propagation code has beenvalidated for JET polarimeter vertical channels [1]. The sameapproach is used in this paper to investigate the effects of theinput polarization on the measurements of the horizontal chan-nels of JET diagnostic. The initial polarization state of the laserbeam is indeed an important characteristic of the electromagneticradiation sent into the plasma to probe it. The results obtained

blished by Elsevier B.V. All rights

o).

oc. 23rd IAEA Fusion Energy

allow choosing the best polarization to optimize the polarimetricmeasurements for the various experiments. The analysis pre-sented in this paper is particularly relevant, since JET is the onlyexisting polarimeter with channels of a topology similar to ITERs.The present paper is organized as follows: in Section 2 a briefdescription of JET polarimeter is given; in Section 3 a briefdescription of the propagation code is presented; in Section 4the simulation of the change of polarization state and someresults for a significant shots are presented and the conclusionare made (Fig. 1).

2. A brief description of JET interferometer polarimeter

The system consists of eight channels, four vertical (1–4) andfour on equatorial port (5–8) denominated ‘horizontal’,which measure both the electron density by interferometryand the Faraday rotation angle and Cotton–Mouton effect bypolarimetry [5]. A Deuterium Cyanide laser at 195 mm is split intoa probing beam and a reference beam, which is modulatedby a rotating wheel at 100 kHz. In normal operation, to performmeasurements of the Cotton–Mouton angle, the initial linearpolarization of the input beam for vertical channels is fixed at451 with respect to the toroidal field direction. For the horizontalchannels the initial linear polarization state of the input laserbeam is parallel, with respect to the toroidal magnetic field.For these channels, a second laser, with wavelength of 119 mm,is also used as compensation laser. New algorithms have beenrecently developed to analyze the calibration data of thesystem [6].

reserved.

Fig. 1. Layout JET interferometer-polarimeter.

Bv

Br

Bx

By

Bz Bt

α

α

Fig. 2. Magnetic field decomposition expressed along the laser beam propagation

direction (Bx, By, Bz) and in toroidal cylindrical coordinates (Bt, Bv, Br).

P. Gaudio et al. / Nuclear Instruments and Methods in Physics Research A 720 (2013) 131–134132

3. The theoretical model implemented in the propagationcode based on Stokes formalism.

As is well known [7], the state of polarization of radiationpropagating in a magnetized plasma, in the absence of dissipa-tion, is described by the Stokes vector equation [5, 8]:

d s!

dz¼ O!� s!

ð1Þ

where the O-vector is expressed as:

O!¼ ka O1,O2,O3ð Þ ð2Þ

and the three components are equal to:

O1 ¼ C1ne B2x�B2

y

� �;

O2 ¼ 2C1neBxBy;

O3 ¼ C3neBz; ð3Þ

where Bx, By and Bz are the magnetic field components expressedalong the laser beam propagation direction (z) where Bx is alongthe toroidal direction, ne is the electronic density (m�3),C1¼1.74�10�22 and C3¼2�10�20 are constants calculated fora laser wavelength of 195 mm, k is the elongation and a the minorradius of the tokamak. Expressing the plasma magnetic field in acylindrical coordinate system (R,j,Z), where Z is parallel to thesymmetry axis of the tokamak, the beam direction lines in the(R,Z) plane, forming an angle a with the R-axis (Fig. 2). Assumingthe x axis parallel to the toroidal direction, the magnetic fieldalong the ray can be expressed in terms (Bt,Bv,Bt) Eq. (3) can thenbe rewritten as:

_s1 ¼ 2C1ne cos að ÞBvþBrsin að Þð ÞBts3�C3ne cos að ÞBr�Bvsin að Þð Þs2

_s2 ¼�C1ne B2t� cos að ÞBvþBrsin að Þð Þ

2� �

s3þC3ne cos að ÞBr�Bvsin að Þð Þs1

_s3 ¼ C1ne B2t� cos að ÞBvþBrsin að ÞÞð Þ

2� �

s2�2C1ne cosðað ÞBvþBrsin að ÞÞBts1

�

ð4Þ

where it has been assumed that the laser beam is sent into theTorus at an angle (a) with respect to radial magnetic fielddirection. In case of horizontal channel 7 of JET polarimeter thepropagation angle (a) can be neglected because it is introduce acorrection term inside the error limit.

The polarization angle (c) and the Cotton–Mouton phase shift(j) then can be expressed in terms of the components of theStokes vector by the following equations:

s2

s1¼ tan2c,

s3

s2¼ tanj ð5Þ

4. Results and conclusions

Starting from the propagation Eq. (1) and the geometry of thehorizontal channels, their output polarization after double passthrough the plasma has been found. In order to validate theoutput of the code, a comparison with the experimental Faradayangle has been performed. The effects of the change of inputpolarization on the polarimeter measurements have been eval-uated and the computed polarization has been compared with themeasurements for a relevant shot (Fig. 3). In the case of thehorizontal chords, the laser beam crosses the torus chamber of JETfacility with an initial linear polarization at 01 with respect to thetoroidal field direction.

The developed propagation code is used to simulate the effectsof the input polarization on the Faraday angle and the Cotton–Mouton phase shift for eight additional cases, simulating an initiallinear polarization state at 11, 151, 301, 451, 601, 751,851 and 911 with respect to the toroidal field. In our case,channel 7 has been simulated. In the plots of Figs. 3–6, the morerelevants simulated input polarization states for the Faradayangle (Figs. 3 and 4) and the Cotton–Mouton phase shift(Figs. 5 and 6) are compared with experimental data for steadystate phase of the discharge. The plots show two extremelyevident facts:

1)

a good agreement between Fadaday angle and numericalsimulation is found at polarization state equal to the experi-mental value (red line) and the recalibrated (for more detailsabout new calibration and current calibration see ref. [6]experimental data (blue line). The Faraday angle (FAR, Fig. 3)seems not to be much influenced by the change of inputpolarization of the laser beam up to 301. The polarization stateis plotted in Fig. 4 only between 301 and 60 1 because thisinterval contains the most significant results;

2)

the Cotton–Mouton phase shift (PH Figs. 5 and 6) shows ahigher dynamic range of variation (see Fig. 6) with the inputpolarization state of the laser beam. Only few degrees are

12 14 16 18 20 22 24 26 28 300

0.05

0.1

0.15

0.2

0.25

Time (s)

Rad

iant

s

Faraday angle ch# 7 for pulse # 76190

Measurements (New Calibration)Measurements (Current calibration)Simulated (15° polarisation)Simulated (45° polarisation)Simulated (60° polarisation)

Fig. 4. Faraday angle. Simulation of various polarization states of input laser beam

are plotted. (For Interpretation of the references to color in this figure legend, the

reader is referred to the web version of this article.)

12 14 16 18 20 22 24 26 28 300

2

4

6

8

10

12

14

16

18

20

Time (s)

Deg

ree

Phase Shift ch# 7 for pulse # 76160

Measurements (New Calibration)Simulated (0° polarisation)

Fig. 5. Phase shift. simulation of the relevant polarization state of input laser

beam are plotted. (For Interpretation of the references to color in this figure

legend, the reader is referred to the web version of this article.)

12 14 16 18 20 22 24 26 28 300

5

10

15

20

25

30

Time (s)

Deg

ree

Phase Shift ch# 7 for pulse # 76160

Measurements (New Calibration)Simulated (15° polarisation)Simulated (30° polarisation)Simulated (45° polarisation)Simulated (60° polarisation)

Fig. 6. Phase shift for several simulations of the input polarization state of the

laser beam are plotted at steady state. Comparison between the numerical

solutions and the experimental recalibrated data (blue line) is shown. (For

interpretation of the references to color in this figure legend, the reader is referred

to the web version of this article.)

12 14 16 18 20 22 24 26 28 300

0.05

0.1

0.15

0.2

0.25

Time (s)

Rad

iant

s

Faraday angle ch# 7 for pulse # 76190

Measurements (New Calibration)Measurements (Current calibration)Simulated (0° polarisation)

Fig. 3. Faraday angles for the steady state phase of the discharge 76190 are

plotted. A comparison between the numerical solution (red line) experimental

data (green line) and experimental recalibrated data (blue line) is shown. (For

interpretation of the references to color in this figure legend, the reader is referred

to the web version of this article.)

P. Gaudio et al. / Nuclear Instruments and Methods in Physics Research A 720 (2013) 131–134 133

enough to increase the simulated value of phase shift of4 times. The variation of PH shows a periodic dependence forevery quadrant (pH at 11 is equal to pH at 911) with amaximum value for polarization angle equal to 51. The bestagreement between simulations and experimental data (greenline) in this case coincides with the polarization state identicalto that of the experimental measurements of the recalibratedCotton–Mouton (blue line).

This change in dynamic range suggests the possibility to usedifferent input polarization states of the polarimeter laser beamin order to optimize the measurements depending on the experi-mental scenario. For example, in the case of high current experi-ments, where high variations of the refractive index of the plasmaare aspected, probably the best choice of input polarization is 01as currently done on JET. In other cases, where lower values of the

polarimetric signals are expected, a different input polarizationstate could be tested to optimize the signal to noise ratio of themeasurements. Further work are required to perform real mea-surements with different initial polarization angle as suggested inthis paper.

Acknowledgments

This work, supported by the European Communities under thecontract of Association between EURATOM/ENEA, was carried outwithin the framework of the European Fusion DevelopmentAgreement. The views and opinions expressed herein do notnecessarily reflect those of the European Commission.

P. Gaudio et al. / Nuclear Instruments and Methods in Physics Research A 720 (2013) 131–134134

References

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Oxford, 1971.

[4] S.E. Segre, PPCF 35 (1993) 1261.[5] K. Guenther, Plasma Physics and Controlled Fusion 46 (2004) 1423.[6] Gelfusa, et al., RSI 81 (2010) 053707.[7] S.E. Segre, PPCF 41 (1999) R57.[8] F. De Marco, S.E. Segre, Optics Communication 23 (1977) 125.