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statistically independent intensity measurements σI α   ∂D 2 σD2 = σI2 , α ∂Iα α

day effect cancels out while rotation of the polarization plane ) still takes place due to birefringence described by (U 3 term with cos 2α = −1.

where the intensity measurement errors are determined by Poisson statistics such that σI2 ∝ Iα . The relative α error in the electron temperature measurement, σT /Te e √ = σD (Te ∂D/∂Te )−1 = W/( QTe ∂D/∂Te ), is presented by a product of two universal functions W (ψ, χ ,√ θ, Te ) and (∂D/∂Te )−1 (ψ, χ , θ , Te ) with a scaling factor 1/ Q which does not depend on the polarization variables (Q is effectively proportional to the total number of scattered photons). The factorization allows us to perform minimization of σT anae lytically for the full range of incident polarizations, scattering angles, and electron temperatures. Although Fig. 4 shows that at θ = 90◦ and θ = 120◦ , the derivative ∂D/∂Te is the largest for circular polarization, fast growth of W in this parameter range determines the overall minimum of the error bars at linear incident polarization with χ = ψ = 0. This proves that the regime of linear polarization with ψ = 0 is optimal not only because of the convenience of two-channel measurements but due to intrinsic polarization properties of Thomson scattered radiation. More detailed analysis is presented in Ref. 20. At θ ∼ 90◦ and Te > 9 keV, the error bars are less than 5%, and less than 2% above 23 keV making polarizationbased diagnostics competitive with standard spectrum-based measurements. For ITER polarimetry (FR and CM) and interferometry measurements, it is proposed to use retroreflection of the I/P probing laser beams so that the beam enters and exits through the same port. With retroreflection, the FR and CM effects on the input and return paths are additive if the retroreflection is performed through an odd number of reflections and subtractive if the number of reflections is even.21 Evolution of polarization resulting from the mean electron velocity and described by (U) exhibits an opposite response and is additive in the case of an even number of reflections. If polarization effects are small enough, using the roof-top reflector (RTR) allows us to eliminate contributions from magnetic FR and CM effects described by the (B) vector and detect the signal determined by the pure (U) effect. Using FIR laser wavelength λ = 432μm with parallel propagation (α = 0) along the central viewing cord of ITER TIP system and double-passed retro-reflection from RTR, yields the angle of rotation of polarization ψ U ∼ 15◦ at Ue /c ∼5 × 10−4 . Another effect is predicted in the case of quasiperpendicular propagation α = 90◦ . Then, the magnetic Fara-

ACKNOWLEDGMENTS

This material is based on work supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences under Award Nos. DE-FC02-05ER54814, DEFG02-01ER54615, the U.S. NSF Cooperative Agreement No. PHY-0821899 Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas and the U.S. ITER Project Office. 1 I. H. Hutchinson, Principles of Plasma Diagnostics (Cambridge University

Press, 2002), p. 440. V. Mirnov, W. X. Ding, D. L. Brower, M. A. Van Zeeland, and T. N. Carlstrom, Phys. Plasmas 14, 102105 (2007). 3 M. A. Van Zeeland, R. L. Boivin, D. L. Brower, T. N. Carlstrom, J. A. Chavez, W. X. Ding, R. Feder, D. Johnson, L. Lin, R. C. O’Neill, and C. Watts, Rev. Sci. Instrum. 84, 043501 (2013). 4 R. Imazawa, Y. Kawano, and Y. Kusama, Nucl. Fusion 51, 113022 (2011). 5 F. Orsitto and N. Tartoni, Rev. Sci. Instrum. 70, 798 (1999). 6 J. Sheffield, D. H. Froula, S. H. Glenzer, and N. C. Luhmann, Plasma Scattering of Electromagnetic Radiation, 2nd ed. (Academic Press, 2011), p. 520. 7 S. E. Segre and V. Zanza, Phys. Plasmas 7, 2677 (2000). 8 R. E. Pechacek and A. W. Trivelpiece, Phys. Fluids 10, 1688 (1967). 9 V. V. Mirnov, D. L. Brower, D. J. Den Hartog, W. X. Ding, J. Duff, and E. Parke, Proceedings of 24th International Conference on Fusion Energy, ITR/P5-32, San Diego, CA (IAEA, Vienna, 2012). 10 M. Born and E. Wolf, Principles of Optics, 3nd ed. (Pergamon Press, 1965), p. 808. 11 S. E. Segre and V. Zanza, Phys. Plasmas 9, 2919 (2002). 12 A. P. Smirnov, R. W. Harvey, and K. Kupfer, Bull. Am. Phys. Soc. 39, 1626 (1994). 13 O. P. Ford, J. Svensson, A. Boboc, D. C. McDonald, and JET EFDA Contributors, Plasma Phys. Controlled Fusion 51, 065004 (2009). 14 S. E. Segre, Plasma Phys. Controlled Fusion 41, R57 (1999). 15 V. V. Mirnov, D. L. Brower, D. J. Den Hartog, W. X. Ding, J. Duff, and E. Parke, Nucl. Fusion 53, 113005 (2013). 16 D. L. Brower, W. X. Ding, B. H. Deng, M. A. Mahdavi, V. Mirnov, and S. C. Prager, Rev. Sci. Instrum. 75, 3399 (2004). 17 V. V. Mirnov, D. L. Brower, and W. X. Ding, Collection of Abstracts of International Sherwood Fusion Energy Conference, Boulder, CO (2008) (http://sherwood.colorado.edu/Uploads/MIRNOV__onpossib3101 _10.pdf). 18 I. Lerche, Am. J. Phys. 43, 910 (1975). 19 V. V. Mirnov, D. L. Brower, D. J. Den Hartog, W. X. Ding, J. Duff, and E. Parke, submitted to AIP Proceedings of International Conference on Fusion Reactor Diagnostics, Varenna, Italy (AIP Publishing, 2014), vol. 1609. 20 E. Parke, V. V. Mirnov, and D. J. Den Hartog, Proceedings of the 16th International Symposium on Laser-Aided Plasma Diagnostics (Madison, WI, 2013) ; J. Instrum. 9, C02030 (2014). 21 S. E. Segre and V. Zanza, Plasma Phys. Controlled Fusion 50, 105006 (2008). 2 V.

REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D303 (2014)

High resolution polarimeter-interferometer system for fast equilibrium dynamics and MHD instability studies on Joint-TEXT tokamak (invited)a) J. Chen,1 G. Zhuang,1,b) Q. Li,1 Y. Liu,1 L. Gao,1 Y. N. Zhou,1 X. Jian,1 C. Y. Xiong,1 Z. J. Wang,1 D. L. Brower,2 and W. X. Ding2 1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China 2 Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095, USA

(Presented 2 June 2014; received 29 May 2014; accepted 17 July 2014; published online 5 August 2014) A high-performance Faraday-effect polarimeter-interferometer system has been developed for the J-TEXT tokamak. This system has time response up to 1 μs, phase resolution < 0.1◦ and minimum spatial resolution ∼15 mm. High resolution permits investigation of fast equilibrium dynamics as well as magnetic and density perturbations associated with intrinsic Magneto-Hydro-Dynamic (MHD) instabilities and external coil-induced Resonant Magnetic Perturbations (RMP). The 3-wave technique, in which the line-integrated Faraday angle and electron density are measured simultaneously by three laser beams with specific polarizations and frequency offsets, is used. In order to achieve optimum resolution, three frequency-stabilized HCOOH lasers (694 GHz, >35 mW per cavity) and sensitive Planar Schottky Diode mixers are used, providing stable intermediate-frequency signals (0.5–3 MHz) with S/N > 50. The collinear R- and L-wave probe beams, which propagate through the plasma poloidal cross section (a = 0.25–0.27 m) vertically, are expanded using parabolic mirrors to cover the entire plasma column. Sources of systematic errors, e.g., stemming from mechanical vibration, beam non-collinearity, and beam polarization distortion are individually examined and minimized to ensure measurement accuracy. Simultaneous density and Faraday measurements have been successfully achieved for 14 chords. Based on measurements, temporal evolution of safety factor profile, current density profile, and electron density profile are resolved. Core magnetic and density perturbations associated with MHD tearing instabilities are clearly detected. Effects of non-axisymmetric 3D RMP in ohmically heated plasmas are directly observed by polarimetry for the first time. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4891603] I. INTRODUCTION

Tokamak plasma is confined by magnetic field generated by external magnetic coils and self-carrying plasma current. The profile of magnetic field, or equivalently the safety factor profile, is closely related to the equilibrium and stability of the plasma and has critical importance in tokamak physics research as well as advanced operation. Consequently the measurement of core magnetic field and its temporal dynamics is considered as one of those indispensable diagnostics for modern tokamak study.1 In addition, as the development of diagnostic technology advances, measurement of core plasma magnetic field perturbations related to intrinsic instabilities and externally imposed non-axisymmetric effects have become an important area of plasma control and physics studies. After several decades of exploration, laser-based Faraday-effect polarimetry is now a promising candidate for measurement of equilibrium magnetic field and its perturbation in the core plasma. The principle of polarimetry as a plasma diagnostic was first proposed in 1972.2 The intrinsic a) Invited paper, published as part of the Proceedings of the 20th Topical

Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0034-6748/2014/85(11)/11D303/8/$30.00

similarity between polarimetry and interferometry makes them possible to be combined for multi-field measurement. Since 1970, several different techniques have been proposed for polarimetric measurement and one of those techniques, the three-wave technique, a variation of which was first proposed by Dodel and Kunz in 1976,3 has been largely developed in recent years. This technique has intrinsic high time response and phase resolution. The applications of this technique on MST and Alcator C-Mod have successfully lead to observation of magnetic field perturbation during Magneto-Hydro-Dynamic (MHD) activity and even high frequency fluctuation, along with electron density perturbation and fluctuation if the third wave is utilized.4, 5 To explore the equilibrium and perturbation of magnetic field and electron density, especially the fine structure of perturbation during MHD activity, a high resolution polarimeterinterferometer system (POLARIS) based on three-wave technique has been developed on J-TEXT tokamak.6–8 To achieve this goal, J-TEXT POLARIS is intentionally developed with high phase resolution (less than 0.1◦ for Faraday angle and less than 1◦ for line-integrated density at 50 kHz bandwidth), high temporal resolution (

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