A novel method for thermal noise reduction, enabling measurements of broadband, low-amplitude electron temperature fluctuations using individual radiometer channels

TL;DR

This work tackles the challenge of measuring broadband, low-amplitude electron temperature fluctuations with single-channel CECE radiometry, where thermal noise typically swamps the signal. It introduces Time Alternating Self-Correlation (TASC), a downsampling-based method that creates two temporally separated streams from the same channel to exploit the difference between noise and plasma fluctuation correlation times, enabling noise reduction without multi-channel hardware. Validation against conventional dual-channel spectral decorrelation on ASDEX Upgrade data across L-, I-, and H-modes demonstrates comparable SNR improvements and accurate recovery of $\delta T_e/T_e$ values, such as $4.6\%$ (I-mode WCM) and $0.75\%$ (L-mode core). The method offers broader diagnostic coverage and potential applicability to other domains where small signals are buried in white noise, while highlighting the need to minimize broadband electronics noise to prevent aliasing during downsampling.

Abstract

A new analysis method has been developed for measurements of broadband, low-amplitude turbulent electron temperature fluctuations in fusion plasmas using individual radiometer channels of a Correlation Electron Cyclotron Emission (CECE) diagnostic. This method takes advantage of differences in the correlation time of thermal noise compared to the correlation time of plasma fluctuations in fusion reactors. The validation of this single-channel method is demonstrated using comparisons with the standard dual-channel radiometer spectral decorrelation method for measurements of turbulent electron temperature fluctuations in the core and edge of low confinement (L), improved confinement (I), and high confinement (H)-mode plasmas at the ASDEX Upgrade tokamak.

Figures (8)

• Figure 1: Overview of the Time Alternating Self-Correlation (TASC) method. In this example, the original time series from a single radiometer channel with sample rate $f_{s}$ is downsampled into six data streams (without anti-aliasing), each with sample rate $f_{s}^{'} = f_{s}/6$ and half-period $\Delta t$. The amount of downsampling is chosen so that $\Delta t$ is much longer than the correlation time of the thermal noise but much shorter than the correlation time of the plasma fluctuations. The first and fourth data streams are then correlated to produce a cross-power spectral density. A TASC-based coherence spectrum is calculated using the downsampled auto-power and cross-power spectral densities.
• Figure 2: The auto-power spectral density calculated from the original time series from a single radiometer channel can be multiplied by the magnitude of the coherence spectrum calculated using the TASC method. This operation results in the denoised auto-power spectral density, in which the thermal noise floor is reduced and which is therefore characterized by an enhanced SNR compared to the auto-power spectral density of the original time series.
• Figure 3: The magnitudes of the TASC-based coherence spectra of the I-mode WCM at $\rho_{\rm pol} = 0.98$ for downsample factors 2, 4, 6, and 8, where $\rho_{\rm pol}$ is defined as the square root of the normalized poloidal magnetic flux. At high frequency (above 200 kHz, corresponding to the upper end of the frequency range of the plasma fluctuations), the coherence drops to the sensitivity limit as the downsample factor is increased to 6. The sensitivity limit is calculated the same way as for dual-channel CECE. Narrowband peaks are the result of electronics noise.
• Figure 4: The denoised auto-power spectral density exhibits a greater SNR compared to the auto-power spectral density of the original time series for measurements of the I-mode WCM at $\rho_{\rm pol} = 0.98$. The denoised auto-power is produced using the workflow shown in Figure \ref{['fig:TASC_flowchart']} and uses the TASC-based coherence calculated with a downsample factor of 6 as shown in Figure \ref{['fig:Figure_downsample_factor_scan']}. The increase in SNR is shown to be equivalent to that obtained using dual-channel spectral decorrelation CECE at $\rho_{\rm pol} = 0.976$. Narrowband peaks are the result of electronics noise.
• Figure 5: The magnitude of the TASC-based coherence spectra of the QCM compared to the dual-channel CECE spectrum in a small-ELM H-mode at $\rho_{\rm pol} \approx 0.98$. Narrowband peaks are the result of electronics noise.