Multiband reflectometry system for density profile measurement with high temporal resolution on JET tokamak

Improved accuracy and robustness of electron density profiles from JET's X-mode frequency-modulated continuous-wave reflectometers

JET's frequency-modulated continuous wave (FMCW) reflectometers have been operating well with the current design since 2005, and density profiles have been automatically calculated intershot since then. However, the calculated profiles had long suffered from several shortcomings: poor agreement with other diagnostics, sometimes inappropriately moving radially by several centimeters, elevated levels of radial jitter, and persistent wriggles (strong unphysical oscillations). In this research, several techniques are applied to the reflectometry data analysis, and the shortcomings are significantly improved. Starting with improving the equilibrium reconstruction that estimates the background magnetic field, adding a ripple correction in the reconstructed magnetic field profile, and adding new inner-wall reflection positions estimated through ray-tracing, these changes not only improve the agreement of reconstructed profiles to other diagnostics but also solve density profile wriggles that were present during band transitions. Other smaller but also persistent wriggles were also suppressed by applying a localized correction to the measured beat frequency where persistent oscillations are present. Finally, the burst analysis method, as introduced by Varela et al. [Nucl. Fusion 46 S693 (2006)], has been implemented to extract the beat frequency from stacked spectrograms. Due to the strong suppression of spurious reflections, the radial jitter that sometimes would span several centimeters has been strongly reduced. The stacking of spectrograms has also been shown to be very useful for stacking recurring events, like small gas puff modulations, and extracting transport coefficients that would otherwise be below the noise level.

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev-Gauss quadrature

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev-Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. The method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

Application of random sample consensus method for parameter estimation of reflectometry density profile in toroidal plasma

Microwave reflectometry diagnostics have been widely used to measure density profiles in fusion plasma. However, the high sensitivity of the diagnostics to plasma turbulence often results in large radial deviations in the edge density profile and causes difficulty in profile evaluation. To improve the performance of profile evaluation, a modified RANdom SAmple Consensus (RANSAC) method has been applied to fit the density profiles measured by reflectometry on the experimental advanced superconducting tokamak. Compared with the traditional least-squares method, the modified RANSAC method is much more efficient and robust in fitting the experimental profiles. Furthermore, a combination of RANSAC and a genetic algorithm (GA-RANSAC) is used to further optimize the profile evaluation procedure. The results show that this GA-RANSAC method yields better performance and stabler convergence than the modified RANSAC alone.

New methodology for measuring electron density perturbations caused by plasma coherent modes using profile reflectometry: Magnitudes and radial profiles in DIII-D

New capabilities of fast-sweep frequency-modulated profile reflectometry are explored to measure electron density n_e perturbation magnitudes and radial profiles due to plasma coherent modes in DIII-D. The first approach is based on the frequency analysis of phase perturbations associated with high frequency (∼MHz) Alfvén eigenmodes (AEs). The measurement of ∼5.5 MHz fast-ion-driven global Alfvén eigenmodes (GAEs) is demonstrated in a neutral beam-heated DIII-D plasma. The GAE induced a broad radial distribution of phase perturbations in the profile reflectometer data. Analysis of these data determined the effective cutoff location displacement and the estimated n_e fluctuation profile. In the second approach, high resolution n_e profiles are used directly to determine the radial structure of n_e perturbations due to a neo-classical tearing mode. These new measurements broaden the application of profile reflectometry and advance the development of AE spectroscopy as a tool for non-invasive diagnosis of fast-ion-driven modes in DIII-D and burning plasmas such as ITER.

Microwave reflectometer for density profile and turbulence measurements on the COMPASS tokamak

The fast microwave reflectometer system on the COMPASS tokamak consists of an O-mode polarized K-band (18 GHz-26 GHz), Ka-band (26 GHz-40 GHz), and a part of U-band (40 GHz-54 GHz). The plasma density profile from the edge plasma area is measured using a fast sweeping rate up of to 6 µs of the probing wave. The processing of the reflected signal is realized by the heterodyne detection configuration based on the I/Q modulator. Two different methods of dynamic calibration of the required linear sweep frequency, together with static frequency and dispersion calibration, were used. The electron density profile was reconstructed by a spectrogram-based method with four sweeps on average. The system has the capability to measure the mid-plane low-field side electron density profile in the density range from 4 × 10¹⁸ m^-3 to 3.6 × 10¹⁹ m^-3. Experimental results obtained on COMPASS discharges are presented to demonstrate the performance of the diagnostics.

Evaluation of low-frequency operational limit of proposed ITER low-field-side reflectometer waveguide run including miter bends

The present design concept for the ITER low-field-side reflectometer transmission line (TL) consists of an ∼40 m long, 6.35 cm diameter helically corrugated waveguide (WG) together with ten 90° miter bends. This paper presents an evaluation of the TL performance at low frequencies (33-50 GHz) where the predicted HE₁₁ mode ohmic and mode conversion losses start to increase significantly. Quasi-optical techniques were used to form a near Gaussian beam to efficiently couple radiation in this frequency range into the WG. It was observed that the output beams from the guide remained linearly polarized with cross-polarization power levels of ∼1.5%-3%. The polarization rotation due to the helical corrugations was in the range ∼1°-3°. The radiated beam power profiles typically show excellent Gaussian propagation characteristics at distances >20 cm from the final exit aperture. The round trip propagation loss was found to be ∼2.5 dB at 50 GHz and ∼6.5 dB at 35 GHz, showing an inverse increase with frequency. This was consistent with updated calculations of miter bend and ohmic losses. At low frequencies (33-50 GHz), the mode purity remained very good at the exit of the waveguide, and the losses are perfectly acceptable for operation in ITER. The primary challenge may come from the future addition of a Gaussian telescope and other filter components within the corrugated guide, which will likely introduce additional perturbations to the beam profile and an increase in mode-conversion loss.

Front-end antenna system design for the ITER low-field-side reflectometer system using GENRAY ray tracing

A monostatic antenna array arrangement has been designed for the microwave front-end of the ITER low-field-side reflectometer (LFSR) system. This paper presents details of the antenna coupling coefficient analyses performed using GENRAY, a 3-D ray tracing code, to evaluate the plasma height accommodation capability of such an antenna array design. Utilizing modeled data for the plasma equilibrium and profiles for the ITER baseline and half-field scenarios, a design study was performed for measurement locations varying from the plasma edge to inside the top of the pedestal. A front-end antenna configuration is recommended for the ITER LFSR system based on the results of this coupling analysis.

Stationary Zonal Flows during the Formation of the Edge Transport Barrier in the JET Tokamak

High spatial resolution Doppler backscattering measurements in JET have enabled new insights into the development of the edge Er. We observe fine-scale spatial structures in the edge Er well with a wave number krρi≈0.4-0.8, consistent with stationary zonal flows, the characteristics of which vary with density. The zonal flow amplitude and wavelength both decrease with local collisionality, such that the zonal flow E×B shear increases. Above the minimum of the L-H transition power threshold dependence on density, the zonal flows are present during L mode and disappear following the H-mode transition, while below the minimum they are reduced below measurable amplitude during L mode, before the L-H transition.

Edge profile analysis of Joint European Torus (JET) Thomson scattering data: Quantifying the systematic error due to edge localised mode synchronisation

The Joint European Torus (JET) high resolution Thomson scattering (HRTS) system measures radial electron temperature and density profiles. One of the key capabilities of this diagnostic is measuring the steep pressure gradient, termed the pedestal, at the edge of JET plasmas. The pedestal is susceptible to limiting instabilities, such as Edge Localised Modes (ELMs), characterised by a periodic collapse of the steep gradient region. A common method to extract the pedestal width, gradient, and height, used on numerous machines, is by performing a modified hyperbolic tangent (mtanh) fit to overlaid profiles selected from the same region of the ELM cycle. This process of overlaying profiles, termed ELM synchronisation, maximises the number of data points defining the pedestal region for a given phase of the ELM cycle. When fitting to HRTS profiles, it is necessary to incorporate the diagnostic radial instrument function, particularly important when considering the pedestal width. A deconvolved fit is determined by a forward convolution method requiring knowledge of only the instrument function and profiles. The systematic error due to the deconvolution technique incorporated into the JET pedestal fitting tool has been documented by Frassinetti et al. [Rev. Sci. Instrum. 83, 013506 (2012)]. This paper seeks to understand and quantify the systematic error introduced to the pedestal width due to ELM synchronisation. Synthetic profiles, generated with error bars and point-to-point variation characteristic of real HRTS profiles, are used to evaluate the deviation from the underlying pedestal width. We find on JET that the ELM synchronisation systematic error is negligible in comparison to the statistical error when assuming ten overlaid profiles (typical for a pre-ELM fit to HRTS profiles). This confirms that fitting a mtanh to ELM synchronised profiles is a robust and practical technique for extracting the pedestal structure.

Robust regression with CUDA and its application to plasma reflectometry

In many applications, especially those involving scientific instrumentation data with a large experimental error, it is often necessary to carry out linear regression in the presence of severe outliers which may adversely affect the results. Robust regression methods do exist, but they are much more computationally intensive, making it difficult to apply them in real-time scenarios. In this work, we resort to graphics processing unit (GPU)-based computing to carry out robust regression in a time-sensitive application. We illustrate the results and the performance gains obtained by parallelizing one of the most common robust regression methods, namely, least median of squares. Although the method has a complexity of O(n(3)logn), with GPU computing, it is possible to accelerate it to the point that it becomes usable within the required time frame. In our experiments, the input data come from a plasma diagnostic system installed at Joint European Torus, the largest fusion experiment in Europe, but the approach can be easily transferred to other applications.