Implementing Faraday effect measurement constraints into the Grad-Shafranov equilibrium fitting code EFIT.

A new tool for the exploration and diagnosis of the internal magnetic field of plasmas in the DIII-D tokamak in the form of a constraint on the EFIT (Equilibrium Fitting) Grad-Shafranov code based on the Faraday-effect Radial Interferometer-Polarimeter (RIP) diagnostic is presented, including description, verification, and sample application. The physics underlying the diagnostic and its implementation into EFIT are discussed, and the results showing the verification of the model are given, and the model's limitations are discussed. The influence of the diagnostic's input on the resulting equilibrium parameters is characterized. The effect of electron density profile refinement is evaluated and found to be negligible. A sample application of the diagnostic is shown, indicating that the RIP constraint has similar effects on the equilibrium as motional Stark effect constraints do.

Non-inductive plasma vertical position measurement for the 1056 s discharge on EAST.

Vertical position stability plays a crucial role in maintaining safe and reliable plasma operation for long-pulse fusion devices. In general, the vertical position is measured by using inductive magnetic coils installed inside the vacuum vessel; however, the integration drift effects are inherent for steady-state or long-pulse plasma operation. Developing a non-magnetic approach provides a fusion reactor-relevant steady-state solution that avoids the negative impact of integration drift. In this paper, we compare the non-inductively determined vertical position achieved by line-integrated interferometer and polarimeter measurements to that employing an inductive flux loop for a 1056 s discharge recently achieved on EAST (Experimental Advanced Superconducting Tokamak). Experimental results show that the non-inductive measurement is more robust than flux loops after 300 s if the integrator is not reset to suppress integrator drift. Real-time vertical position control using the non-inductive system is proposed for the next EAST experimental campaign.

Faraday-effect polarimetry for current profile measurement in the tokamak plasma edge.

Toroidal current profile measurements in the tokamak plasma edge are critical for fusion plasma physics research and model validation. A three-wave Faraday-effect polarimeter-interferometer with a sub-centimeter spatial resolution is proposed on the DIII-D tokamak to determine the edge current profile via Abel inversion. By using probe beams with 316 µm wavelength, a low-field-side, vertical-view, single-pass optical layout covering the plasma edge region (R = 2.15-2.27 m) is assessed. Measurements with no greater than 0.1° polarimetric systematic uncertainty, no greater than 0.01° polarimetric root-mean-square noise (1 kHz bandwidth), and a 0.8 cm radial chord spacing are considered feasible based on the achieved performance of existing systems using similar wavelengths on fusion devices. Synthetic diagnostic calculations taking various factors into account, such as diagnostic uncertainty and quality of magnetic flux surfaces, find that the edge current profile can be determined with up to 0.12 MA/m2 uncertainty, or about 10% of the peak current density in the pedestal of an investigated high-confinement plasma.

Correlation polarimetry for broadband magnetic fluctuation measurements.

Correlation techniques have been successfully utilized for plasma diagnostics like electron cyclotron emission to reduce measurement noise. We present the first application of such a technique to Faraday-effect polarimetry measurements on the Madison Symmetric Torus (MST). The MST far infrared (FIR) interferometer-polarimeter diagnostic utilizes 11 vertical chords with a chord separation of 7-8 cm and a heterodyne detection system for fluctuation measurements up to several hundred kHz. The planar-diode mixers viewing each chord represent independent noise sources; modifying the optical setup so that two different mixers view the same chord allows cross correlation between the two independent signals to reduce the noise floor in fluctuation measurements. In this manner, the noise floor in both interferometry and polarimetry measurements in reversed-field pinch discharges has been reduced by a factor of 20-30. The correlation polarimeter provides a sensitive measurement of broadband magnetic fluctuations.

A heterodyne dispersion interferometer for wide bandwidth density measurements on DIII-D.

In order to improve both the density and particularly the temporal resolution beyond previous dispersion interferometers (DIs), a heterodyne technique based on an acousto-optic (AO) cell has been added to the DI. A 40 MHz drive frequency for the AO cell allows density fluctuation measurements into the MHz range. A CO2 laser-based heterodyne DI (HDI) installed on DIII-D has demonstrated that the HDI is capable of tracking the density evolution throughout DIII-D discharges, including disruption events and other rapid transient phenomena. The data also show good agreement with independent density measurements obtained with the existing DIII-D two-color interferometer. The HDI line-integrated density resolution sampled over a 1 s interval is ∼9 × 1017 m-2. Density fluctuations induced by MHD instabilities are also successfully measured by the HDI.

A Faraday-effect polarimeter for fast magnetic dynamics measurement on DIII-D.

A Faraday-effect-based radial-interferometer-polarimeter diagnostic has been developed to explore fast magnetic dynamics in high-performance DIII-D plasmas. The instrument measures radial magnetic field perturbations using three chords positioned near the magnetic axis. Newly developed solid-state sources operating at 650 GHz provide phase noise down to 0.01°/ k H z and tunable bandwidth up to 10 MHz. Various systematic errors which can contaminate the polarimetric measurement have been investigated in detail. Distortion of circular polarization due to non-ideal optical components is calibrated using a rotating quarter wave plate technique. The impact of perpendicular magnetic field, i.e., the Cotton-Mouton effect, is evaluated. The error due to non-collinearity of probe beams is minimized to less than 0.5° for electron density up to 7 × 1019 m-3 by alignment optimization. Optical feedback, due to multiple reflections induced by the double-pass configuration, is identified and reduced. Coherent and broadband high-frequency magnetic fluctuations for DIII-D H-mode plasmas are observed.

Tests of a full-scale ITER toroidal interferometer and polarimeter (TIP) prototype on the DIII-D tokamak (invited).

A full-scale ITER toroidal interferometer and polarimeter (TIP) prototype, including an active feedback alignment system, has been installed and tested on the DIII-D tokamak. In the TIP prototype, a two-color interferometry measurement of line-integrated density is carried out at 10.59 µm and 5.22 µm using a CO2 and quantum cascade laser, respectively, while a separate polarimetry measurement of the plasma-induced Faraday effect is made at 10.59 µm. The TIP prototype is equipped with a piezo tip/tilt stage active feedback alignment system that minimizes noise in the measurement and keeps the diagnostic aligned throughout DIII-D discharges. The measured phase resolution for the polarimeter and interferometer is 0.05° (100 Hz bandwidth) and 1.9° (1 kHz bandwidth), respectively. The corresponding line-integrated density resolution for the vibration-compensated interferometer is δnL = 1.5 × 1018 m-2, and the magnetic field-weighted line-integrated density from the polarimeter is δnBL = 1.5 × 1019 Tm-2. Both interferometer and polarimeter measurements during DIII-D discharges compare well with the expectations based on calculations using Thomson scattering measured density profiles and magnetic equilibrium reconstructions. Additionally, larger bandwidth interferometer measurements show that the diagnostic is a sensitive monitor of core density fluctuations with demonstrated measurements of Alfvén eigenmodes and tearing modes.

Non-inductive vertical position measurements by Faraday-effect polarimetry on EAST tokamak.

Vertical instability control in an elongated plasma is highly desirable for a tokamak reactor. A multi-channel 694 GHz far-infrared laser-based polarimeter-interferometer system has been used to provide a non-inductive vertical position measurement in the long-pulse EAST tokamak. A detailed comparison of vertical position measurements by polarimetry and external inductive flux loops has been used to validate Faraday-effect polarimetry as an accurate high-time response vertical position sensor.

Effects of stray lights on Faraday rotation measurement for polarimeter-interferometer system on EAST.

A double-pass radially view 11 chords polarimeter-interferometer system has been operated on the experimental advanced superconducting tokamak and provides important current profile information for plasma control. Stray light originating from spurious reflections along the optical path (unwanted reflections from various optical components/mounts and transmissive optical elements such as windows, waveplates, and lens as well as the detectors) and also direct feedback from the retro-reflector used to realize the double-pass configuration can both contribute to contamination of the Faraday rotation measurement accuracy. Modulation of the Faraday rotation signal due to the interference from multiple reflections is observable when the interferometer phase (plasma density) varies with time. Direct reflection from the detector itself can be suppressed by employing an optical isolator consisting of a λ/4-waveplate and polarizer positioned in front of the mixer. A Faraday angle oscillation during the density ramping up (or down) can be reduced from 5°-10° to 1°-2° by eliminating reflections from the detector. Residual modulation arising from misalignment and stray light from other sources must be minimized to achieve accurate measurements of Faraday rotation.

Initial measurements of plasma current and electron density profiles using a polarimeter/interferometer (POINT) for long pulse operation in EAST (invited).

A double-pass, radially viewing, far-infrared laser-based POlarimeter-INTerferometer (POINT) system utilizing the three-wave technique has been implemented for diagnosing the plasma current and electron density profiles in the Experimental Advanced Superconducting Tokamak (EAST). POINT has been operated routinely during the most recent experimental campaign and provides continuous 11 chord line-integrated Faraday effect and density measurement throughout the entire plasma discharge for all heating schemes and all plasma conditions (including ITER relevant scenario development). Reliability of both the polarimetric and interferometric measurements is demonstrated in 25 s plasmas with H-mode and 102 s long-pulse discharges. Current density, safety factor (q), and electron density profiles are reconstructed using equilibrium fitting code (EFIT) with POINT constraints for the plasma core.

Faraday-effect polarimeter diagnostic for internal magnetic field fluctuation measurements in DIII-D.

Motivated by the need to measure fast equilibrium temporal dynamics, non-axisymmetric structures, and core magnetic fluctuations (coherent and broadband), a three-chord Faraday-effect polarimeter-interferometer system with fast time response and high phase resolution has recently been installed on the DIII-D tokamak. A novel detection scheme utilizing two probe beams and two detectors for each chord results in reduced phase noise and increased time response [δb ∼ 1G with up to 3 MHz bandwidth]. First measurement results were obtained during the recent DIII-D experimental campaign. Simultaneous Faraday and density measurements have been successfully demonstrated and high-frequency, up to 100 kHz, Faraday-effect perturbations have been observed. Preliminary comparisons with EFIT are used to validate diagnostic performance. Principle of the diagnostic and first experimental results is presented.

An upgraded interferometer-polarimeter system for broadband fluctuation measurements.

Measuring high-frequency fluctuations (above tearing mode frequencies) is important for diagnosing instabilities and transport phenomena. The Madison Symmetric Torus interferometer-polarimeter system has been upgraded to utilize improved planar-diode mixer technology. The new mixers reduce phase noise and allow more sensitive measurements of fluctuations at high frequency. Typical polarimeter rms phase noise values of 0.05°-0.07° are obtained with 400 kHz bandwidth. The low phase noise enables the resolution of fluctuations up to 250 kHz for polarimetry and 600 kHz for interferometry. The importance of probe beam alignment for polarimetry is also verified; previously reported tolerances of ≤0.1 mm displacement for equilibrium and tearing mode measurements minimize contamination due to spatial misalignment to within acceptable levels for chords near the magnetic axis.

Bench testing of a heterodyne CO2 laser dispersion interferometer for high temporal resolution plasma density measurements.

A heterodyne detection scheme is combined with a 10.59 µm CO2 laser dispersion interferometer for the first time to allow large bandwidth measurements in the 10-100 MHz range. The approach employed utilizes a 40 MHz acousto-optic cell operating on the frequency doubled CO2 beam which is obtained using a high 2nd harmonic conversion efficiency orientation patterned gallium arsenide crystal. The measured standard deviation of the line integrated electron density equivalent phase resolution obtained with digital phase demodulation technique, is 4 × 1017 m-2. Air flow was found to significantly affect the baseline of the phase signal, which an optical table cover was able to reduce considerably. The heterodyne dispersion interferometer (DI) approach is found to be robustly insensitive to motion, with measured phase shifts below baseline drifts even in the presence of several centimeters of retroreflector induced path length variations. Plasma induced dispersion was simulated with a wedged ZnSe plate and the measured DI phase shifts are consistent with expectations.

Electron kinetic effects on interferometry, polarimetry and Thomson scattering measurements in burning plasmas (invited).

At anticipated high electron temperatures in ITER, the effects of electron thermal motion on Thomson scattering (TS), toroidal interferometer/polarimeter (TIP), and poloidal polarimeter (PoPola) diagnostics will be significant and must be accurately treated. The precision of the previous lowest order linear in τ = Te/mec(2) model may be insufficient; we present a more precise model with τ(2)-order corrections to satisfy the high accuracy required for ITER TIP and PoPola diagnostics. The linear model is extended from Maxwellian to a more general class of anisotropic electron distributions that allows us to take into account distortions caused by equilibrium current, ECRH, and RF current drive effects. The classical problem of the degree of polarization of incoherent Thomson scattered radiation is solved analytically exactly without any approximations for the full range of incident polarizations, scattering angles, and electron thermal motion from non-relativistic to ultra-relativistic. The results are discussed in the context of the possible use of the polarization properties of Thomson scattered light as a method of Te measurement relevant to ITER operational scenarios.

High resolution polarimeter-interferometer system for fast equilibrium dynamics and MHD instability studies on Joint-TEXT tokamak (invited).

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.

2D image of local density and magnetic fluctuations from line-integrated interferometry-polarimetry measurements.

Combined polarimetry-interferometry capability permits simultaneous measurement of line-integrated density and Faraday effect with fast time response (∼1 µs) and high sensitivity. Faraday effect fluctuations with phase shift of order 0.05° associated with global tearing modes are resolved with an uncertainty ∼0.01°. For physics investigations, local density fluctuations are obtained by inverting the line-integrated interferometry data. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of the polarimetry data. Reconstructed 2D images of density and magnetic field fluctuations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved.

Design of vibration compensation interferometer for Experimental Advanced Superconducting Tokamak.

A vibration compensation interferometer (wavelength at 0.532 µm) has been designed and tested for Experimental Advanced Superconducting Tokamak (EAST). It is designed as a sub-system for EAST far-infrared (wavelength at 432.5 µm) poloarimeter/interferometer system. Two Acoustic Optical Modulators have been applied to produce the 1 MHz intermediate frequency. The path length drift of the system is lower than 2 wavelengths within 10 min test, showing the system stability. The system sensitivity has been tested by applying a periodic vibration source on one mirror in the system. The vibration is measured and the result matches the source period. The system is expected to be installed on EAST by the end of 2014.

Faraday-effect polarimeter-interferometer system for current density measurement on EAST.

A multichannel far-infrared laser-based POlarimeter-INTerferometer (POINT) system utilizing the three-wave technique is under development for current density and electron density profile measurements in the EAST tokamak. Novel molybdenum retro-reflectors are mounted in the inside wall for the double-pass optical arrangement. A Digital Phase Detector with 250 kHz bandwidth, which will provide real-time Faraday rotation angle and density phase shift output, have been developed for use on the POINT system. Initial calibration indicates the electron line-integrated density resolution is less than 5 × 10(16) m(-2) (∼2°), and the Faraday rotation angle rms phase noise is <0.1°.

High-frequency fluctuation measurements by far-infrared laser Faraday-effect polarimetry-interferometry and forward scattering system on MST.

Magnetic fluctuation-induced transport driven by global tearing modes has been measured by Faraday-effect polarimetry and interferometry (phase measurements) in the MST reversed field pinch. However, the role of small-scale broadband magnetic and density turbulence in transport remains unknown. In order to investigate broadband magnetic turbulence, we plan to upgrade the existing detector system by using planar-diode fundamental waveguide mixers optimized for high sensitivity. Initial tests indicate these mixers have ×10 sensitivity improvement compared to currently employed corner-cube Schottky-diode mixers and ×5 lower noise. Compact mixer design will allow us to resolve the wavenumbers up to k ∼ 1-2 cm(-1) for beam width w = 1.5 cm and 15 cm(-1) for beam width w = 2 mm. The system can also be used to measure the scattered signal (amplitude measurement) induced by both plasma density and magnetic fluctuations.

Optical layout and mechanical structure of polarimeter-interferometer system for Experimental Advanced Superconducting Tokamak.

A Far-InfaRed (FIR) three-wave POlarimeter-INTerferometer (POINT) system for measurement current density profile and electron density profile is under development for the EAST tokamak. The FIR beams are transmitted from the laser room to the optical tower adjacent to EAST via ∼20 m overmoded dielectric waveguide and then divided into 5 horizontal chords. The optical arrangement was designed using ZEMAX, which provides information on the beam spot size and energy distribution throughout the optical system. ZEMAX calculations used to optimize the optical layout design are combined with the mechanical design from CATIA, providing a 3D visualization of the entire POINT system.