Interfero-polarimetry diagnostics developments for ITER

1. Interfero-polarimetry diagnostics developments for ITER Francesco Paolo Orsitto CREATE CONSORTIUM, Naples(Italy) ENEA CR Frascati (Italy) INTERNATIONAL SCHOOL OF FUSION REACTORS TECHNOLOGY 16th Course: Diagnostics and Technology Developments in view of ITER and DEMO ERICE-SICILY: 28 April - 4 May 2017 F P Orsitto ENEA

2. Lectures Plan first lecture . 1.1.the theme of interferometry/polarimetry is treated in general . System operating on JET is described . 1.2.Recent results of Analysis of JET polarimetry measurements will be presented in detail showing what can be extracted from these measurements.  1.3.The use of measurements of interferometry/polarimetry for the evaluation of the MHD equilibrium is introduced:The analysis of the results briefly discussed. the new direction of improvements of equilibrium calculations using interfero/polarimetry is outlined. 1.4..the polarimetry /interferometry  for  a fusion reactor is discussed: it is possible a 'complete polarimetry' for ITER/DEMO? 2nd lecture . the novel application of polarimetric Thomson Scattering for electron temperature measurements in high temperature plasmas will be presented : the main characteristics of the project for FTU outlined . 2

3. Main Theoretical references • S E Segre and F De Marco – Plasma Phys 14(1972)245 • S E Segre – Plasma Phys Controlled Fusion 41(1999)R57 • A A Fuki , Yu A Kratsov and O N Naida – Geometrical Optics of weakly anisotropic media – ed. Gordon and Breach Science Publ(1998) F P Orsitto ENEA

4. Some References on interfero-polarimetry systems ( JET and FTU) and analysis of JET polarimetry measurements • ref for JET • [1] D. Veron, “Submillimeter interferometry of high-density plasmas,” in Infrared and Millimeter Waves (Academic Press, 1979), Vol. 2, pp. 67–135. • [2] Braithwaite G, Gottardi N, Magyar G, O’Rourke J, Ryan J and Veron D (1989) Rev. Sci. Instrum.60 2825 • [3] Guenther K et al. (2004) Plasma Phys. Control. Fusion46 1423 • [4] F P Orsitto et al (2008) Plasma Phys Contr Fusion50 115009 • [5] F P Orsitto et al Rev Sci Instr 81(2010) 10D533 • [6] F P Orsitto et al (2011) Plasma Phys Contr Fusion53 035001 • [7] P Gaudio et al. IEEE Trans on Plasma Science 41(2013)1575 • [8] A Boboc et al Rev Sci Instr 86(2015) 091301 • ref for FTU • [9] A Canton, P Innocente, O Tudisco , Applied Optics 45(2006) 9105 F P Orsitto ENEA 4

5. First Lecture

6. Outline • Brief introduction to physics and modelling of polarimetry measurements • Information that can be extracted from polarimetry measurements • Main results of the analysis of JET polarimetric measurements • Conclusions F P Orsitto ENEA 6

7. interferometry/polarimetrybasic physics • the plasma in a magneticfieldis a dielectric medium withdifferentindexofrefractionalong the magneticfieldcomponents • the plasma issimilarto a crystalwithsymmetryaxis: • the plasma isbirefringent • since the processofrefractionisessentially a re-emissionof the light by the plasma electrons, the birefringencedependsupon: • the electron density , • magneticfield (vector) and • alsoupon the electron temperature ( or in general the electron velocitydistributionfunction). 7

8. Polarimetry : what for? • The measurementsofpolarimetry in tokamakplasmas can giveimportant information on plasma current and density ( and possibly temperature) • In a plasma, in presenceof a magneticfield, the polarizationplaneof a laser beampropagatingalong the magneticfieldrotates (Faraday effect). • Whereas, if the laser beamispropagatingperpendicularto the magneticfieldthereis a change in the ellipticityof the polarization (Cotton-Moutoneffect). • In a beampropagatingverticallyalong a line in a poloidalplaneof a tokamak , botheffects are presents : the polarizationbecomeselliptical and the planeof the polarizationrotates. • In first approximation • Faraday rotation angle = electron density * plasma current • Cotton-MoutonPhaseshift = electron density * toroidalmagneticfieldsquared. F P Orsitto ENEA 88

9. interferometry/polarimetrybasic concepts • a linearlypolarisedwaveentering a plasma and propagatingalong a magneticfieldsplits in twocircularly ( in generalelliptical ) polarisedwaveswithtwodifferentphasesbeing the indexofrefractiondifferentforbothwaves • toget some quantitative evaluationstwoparameters are important • X=( ωP/ωL )2=1.6 10-3. and Y=(ωc/ωL)=0.073. • ωP/ωL=plasmafrequency / laser frequency • ωc/ωL=electroncyclotronfrequency / laser frequency • laser wavelengthλL=195micron; electron density =0.510 20 m-3. magneticfield B=4T. 9

10. interferometry/polarimetry basic concepts The wavesplitsintotwocircularly( in general elliptical) coounterpropagatingpolarizedwaves with differentphasevelocitiesasdetermined by the refractiveindices (  = angle between K and B ) μ+=1-X/2 +XY (cos )/2 [ordinarywave ] and μ-=1-X/2 -XY (cos ) /2 [extraordinarywave] X/2=8 10-4 ; XY/2= 5.84 10-5. laser wavelengthλL=195micron; electron density =0.510 20 m-3. magneticfield B=4T. Faraday rotation (1/2) cos  X Y  z /c Ellipticityε X Y2 (sin)2 sin 2  z /c (  angle betweenelectricfieldof the wave and the magneticfield)

11. what we need to measure • the phase difference between the input and output electric field of the light wave • the rotation of the polarisation plane • the phase shift between the two components of the output electric field

12. Introduction to Stokes vector formalism to determine the polarization of a light beam Removing τ from the equations the equation of an ellipse is obtained

13. the ellipse of propagation The presence of the crossed term ExEy reveals that the ellipse is rotated by an Angle ψ. Tan2ψ=(2E0xE0y)/(E0x2-E0y2) Tan α= E0y/E 0x. Tan χ = ±b/a =minor radius of ellipse /major radius of ellipse ; sin 2χ=(sin2α)sinδ

14. Ellipse of propagation and the Stokes vector

15. Examples of polarizations states vs Stokes vectors • Right (left)Circularly polarized light Ex=Ey;δ=±90°. • Linearly horizontal (vertical) polarized light Ey(Ex)=0

16. Ellipticity and ellipse rotation vs Stokes vector components Stokes vector and Poincare’ sphere

17. MULLER MATRIX of a polarizer In general The MULLER MATRIX determines the transformation of polarization of a light beam ( i.e. the Stokes vector) when passing through an optical element . Given the attenuations along two hortogonal axis px and py

18. MULLER MATRIX of an ideal polarizer An ideal linear polarizer has trasmission along only one axis say px=1 and py=0

19. MULLER MATRIX of a phase shifter The phase shifter ( or retarder) introduces a total phase shift φ between the two hortogonal components of the electric field of a wave. This can be done causing a phase shift of + φ/2 on the x-component and -φ/2 on the y-component. Inserting these equations in the definition of the Stokes vectors The Muller Matrix of a phase shifter can be deduced.

20. Measurement of the components of the Stokes vector

21. Physics of polarimeter Usual paradigm of polarimetry Faraday rotation Cotton-Mouton The present talk is about 1.the limits of this physical scheme and 2. how polarimetry can be useful in giving directly correction to the Calculation of the magnetic equilibrium F P Orsitto ENEA 2121

22. Propagation of polarization Along a vertical line By = B toroidal Bx = B radial Bz = B poloidal Cold plasma approximation F P Orsitto ENEA 2222

23. Plasma Mueller Matrix • The Stokes eq can be written also M is the Mueller-likematrix of the plasma

24. Dependence of polarimetry /interferoetry upon the electron temperature • [V V Mirnov et al Nuclear Fusion 53 (2013)113005 ] For Te=25keV =0.05 and /≈11% ψ/ψ≈-10%

25. Relation between Stokes vector and Faraday / Cotton-Mouton F P Orsitto ENEA

26. Input to the Stokes equations (Bx,By,Br ) are given by EFIT ( only magnetic measurements) or EFTM( when available, magnetic equilibrium obtained using MSE + pressure profile constraints) Ne(z,t) , Te(z,t) given by LIDAR Thomson Scattering ( and when available ) by HRTS ( High Resolution TS) projected on the vertical line of sight using equilibrium. F P Orsitto ENEA

27. Type I approx W12 and W32<<1 F P Orsitto ENEA

28. Outline Brief introduction to physics and modelling of polarimetry measurements Information that can be extracted from polarimetry measurements Main results of the analysis of JET polarimetric measurements Short summary of Experience on JET and Proposals for JET Ideas for JET in support for ITER Conclusions F P Orsitto ENEA

29. JET polarimeter Primary measurements by the polarimeter are : Amplitudes of Wave components Ex,Ey, phase shift between Ex and Ey F P Orsitto ENEA

30. JET Interfero - Polarimeter =Ey/Ex F P Orsitto ENEA

31. Scheme measurements( A Boboc,M Gelfusa,K Guenther) Definition of parameters that describe the polarization state of ellptically polarized light. Amplitude ratio =Ey/Ex Phase shift angle InSb He-cooled Detectors Phase sensitive Electronics Polarization state Ellipticity Stokes vector Faraday rotation angle F P Orsitto ENEA

32. Characteristics of the JET apparatus The relative intensities devoted to the interferometry and polarimetry is related to relative importance given to the two measurements Then the accuracy and the calibration of the measurements ( in particular of Cotton-Mouton) depends upon the relative intensity used. The so-called ‘residual birefringence’ due to the effect of the output optical system must be modelled in order to compensate its effect. F P Orsitto ENEA

33. Outline Brief introduction to physics and modelling of polarimetry measurements Information that can be extracted from polarimetry measurements Main results of the analysis of JET polarimetric measurements Short summary of Experience on JET and Proposals for JET Ideas for JET in support for ITER Conclusions F P Orsitto ENEA

34. Summary of results of the analysis i) It turns out that the Faraday rotation[6] measurements on JET can be reproduced in any condition only by the numerical solution of Stokes equations and ii) a rigorous approach to the interaction between Faraday and Cotton-Mouton, ( studied in recent papers, see ref [7] for details): it is demonstrated that at high density and current, the Cotton-Mouton must be calculated including the dependence by Faraday rotation. [6] F P Orsitto et al (2011) Plasma Phys Contr Fusion53 035001 [7] F P Orsitto et al Rev Sci Instr 81(2010) 10D533 [8] P Gaudio et al. IEEE Trans on Plasma Science 41(2013)1575 F P Orsitto ENEA

35. Modelling of Faraday rotation angle: low density shot ne19<4 Faraday rotation. comparison between the models(symbols + ad o) and measurements( blue lines) is presented for the shot #60980, channel #3. From the top the comparison of measurements with the Type II approximation, the 'linear' W3 approximation, and the Guenther Model A. Faraday rotation measurement (blue — continuous line, shot #60980, channel #3) is plotted together with the calculated values ( ' * ' symbol ) using the numerical solution of Stokes equations. F P Orsitto ENEA

36. Faraday calculations using EFTM: a smaller DR=0.02m needed Faraday rotation evaluation depends upon the accuracy of the Equilibrium calculations: i.e. Bz,Br,BT evaluation vs z F P Orsitto ENEA

37. Type II approx Stokes eqs. In a tokamak : F P Orsitto ENEA

38. Meaning of the results of type II approx The Type II solution can be interpreted saying : in a tokamak , the Faraday and Cotton-Mouton effects cannot be treated separately when W3 is large. I.In practice for Faraday rotation angles ψ≤12o, 1≥cos (W3)≥0.9 and tanφ≈W1, within an approximation of 10%. ( cotton-mouton is independent upon the faraday). II.For Faraday angles (ψ≥12o,) higher than 12°. the Cotton-Mouton increases due to the enhancement linked with Faraday rotation( W3≥π/15=0.2). F P Orsitto ENEA

39. Interaction between Faraday and Cotton-Mouton(I) the Faraday interact with Cotton-Mouton effect : i) for large Faraday effects (W3≈1) the Cotton-Mouton increases strongly with respect to the ‘linear ‘ form ( tan φ = W1) ( see figure where W1 is not enough for the estimation of Cotton-Mouton); ii) the Faraday is not depending from Cotton-Mouton at this level of approximation. Some hints can be extracted from Type II approximation : F P Orsitto ENEA

40. Non-linear coupling between Faraday and Cotton-Mouton(shot#75238 IP=3.4MA,BT=2.75T) F P Orsitto ENEA

41. Departure from linearity of cotton-mouton for high density shot 67777, nmax=1.2 1020m-3 . Plot of tanφ(Cotton-Mouton)/W1 versus W3 Ch#4 demonstrates that already for W3>0.4 the ratio of cotton-mouton and W1 ( the linear evaluation) exceeds 1.2. F P Orsitto ENEA

42. Main results(I) detailed analysis of Faraday measurements at JET and comparison with available models: It turns out that the Faraday rotation measurements on JET can be reproduced in any condition only by the numerical solution of Stokes equations; this means that the linear formula used presently in EFIT is of limited range of application , Being valid only for W32<<1. F P Orsitto ENEA

43. Main results(II) ii) in a rigorous approach to the interaction between Faraday and Cotton-Mouton,it is demonstrated that at high density and current, the Cotton-Mouton must be calculated including the dependence upon the Faraday rotation. This means that if a new constraint using Cotton-Mouton phase shift measurements is introduced in EFIT the formula for the constraint must include the effect of the Faraday rotation on Cotton-Mouton. F P Orsitto ENEA

44. The constraint for Faraday in EFIT Type I approximation is used into EFIT throughout the calculations : rigorously this restricts the validity of EFIT calculations Since Type I formulas are valid only for low –medium density and low plasma current, and not for all channels. A clear example is the analysis carrried out for channel #4. The analysis shows that in general the Stokes model is more suitable to be used in any plasma conditions and all the channels Alternatively the Type II approximation could be used F P Orsitto ENEA

45. Conclusions from analysis A complete analysis of the polarimetry data for all the KG4R channels leads to the conclusion that Stokes model is suitable to predict the measurements. In this context( modelling of polarimetry measurements) the tools for the validation of data for all the polarimetry channels are available. The present version of EFIT has built- in a constraint i) on Faraday rotation angle measurements Ii) using Type I approximation which has been tested as not valid for all the plasma conditions and polarimetry channels. The introduction into EFIT of the Stokes model could remove the limitation related to the plasma parameters and in addition It could be used to introduce a new constraint on Cotton-Mouton phase shift which lead to improvement of evaluation of electron density The possibility of using all the channels into EFIT constraints can be very helpful. F P Orsitto ENEA

46. Ellipticity 1.the ellipticity is a small parameter in JET plasmas And has only linear dependences from plasma parameters different from Faraday and Cotton-Mouton A first principle approach allows for the derivation of the plasma density from the measurements of the ellipticity of the wave emerging from plasma. 2.An EMPIRICAL MODEL (K Guenther PPCF2004) was USED by B Bieg and A Boboc (ECPD 2015) TO DERIVE A FORMULA which GIVES WITH FURTHER ADJUSTEMENTS THE LINE AVERAGE ELECTRON DENSITY FROM ELLIPTICITY MEASUREMENT with a precision of 1.5 fringes

47. Advantages of using ellipticity tan2χ=sin φ sin2ψ=2ε/(1-ε2) ≈ 2ε ( for ε<<1) ε=tanχ= ellipticity For small χ and ε , s3≈2χ=W1 . Plasma density can be Determined directly from ellipticity measurement F P Orsitto ENEA

48. Pulses analyzed The polarimetry measurements used in this talk are KG4R ( real time polarimetry) and the DDA is ELLI3 : the ellipticity measured on the vertical channel 3 of the polarimeter

49. Stokes terms for propag. Of Ellipticity F P Orsitto ENEA

50. The plots show the difference between the line integral of plasma density extracted from ellipticity and the line integral meas by the interferometer