Design of a correlation reflectometer radiometer diagnostic and measurements of the electron density–temperature cross-phase angle in the H-mode pedestal with small edge localized modes at ASDEX Upgrade

Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi Design of a correlation reflectometer radiometer diagnostic and measurements of the electron density–temperature cross-phase angle in the H-mode pedestal with small edge localized modes at ASDEX Upgrade Cite as: Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 Submitted: 14 October 2024 •Accepted: 14 February 2025 • Published Online: 4 March 2025 C. Yoo,1,a) G. D. Conway,2W. Burke,1P. A. Molina Cabrera,1,b) B. Vanovac,1R. Bielajew,1 D. J. Cruz-Zabala,3A. Silva,4A. E. White,1and ASDEX Upgrade Teamc) AFFILIATIONS 1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany 3University of Seville, Seville, Spain 4Associação EURATOM/IST, Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal a)Author to whom correspondence should be addressed: [email protected] b)Present address: École Polytechnique Fédérale de-Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland. c)See authors list of H. Zohm et al., Nucl. Fusion 64, 112001 (2024), https://doi.org/10.1088/1741-4326/ad249d ABSTRACT This work presents the hardware design and first results from a newly commissioned correlation reflectometer radiometer diagnostic that measures the cross-phase angle between electron density and temperature fluctuations in ASDEX Upgrade plasmas. This diagnostic employscrosscorrelationsbetweensignalsmeasuredbyatunable,continuouswave,perpendicularincidence,fluctuationreflectometer,anda 24-channel radiometer sharing the same line of sight. Novel measurements in the pedestal of a helium H-mode plasma with small edge localized modes show changes in the cross-phase angle between the electron density and temperature fluctuations from ∼90○to 120○, suggesting changes in the properties of the turbulence driving transport in the plasma edge. ©2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0243894 I. INTRODUCTION Fluctuations due to drift-wave plasma turbulence generally dominatethe transport of energy,particles, and momentum inmagnetically confined plasmas, limiting their performance.1The experimental characterization of these fluctuations over a broad range of plasma conditions deepens our understanding of turbulence-driven transport and is important for improving our confidence in turbulent transport models used to predict the energy gain from future fusion devices. As shown in Eq. (1), the energy transport driven by electrostatic fluctuations, ˜ Q, depends on the saturated amplitudes, coherencies, and cross-phase angles between multiple fluctuating quantities, ˜ Q=3kθ 2Bϕ[n0˜ T˜ ϕγ˜ T˜ ϕsin(α˜ T˜ ϕ)+T0˜ n˜ ϕγ˜ n˜ ϕsin(α˜ n˜ ϕ)] (1) with the fluctuations in temperature, density, and electric potential given by ˜ T,˜ n, and ˜ ϕ, respectively; the coherencies between the fluctuating fields given by γ˜ T˜ ϕand γ˜ n˜ ϕ; the cross-phase angles between Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-1 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi the fluctuating fields given by α˜ T˜ ϕand α˜ n˜ ϕ; the wavenumber of the fluctuations given by kθ; the background toroidal magnetic field given by Bϕ; and the mean density and temperature given by n0 and T0, respectively.2While the fluctuating parameters driving turbulence can be measured together simultaneously on the edge of tokamak plasmas using Langmuir probes, similar measurements in the core are more challenging and performed less frequently.2,3 In this work, we present the design and first measurements from a newly commissioned correlation reflectometer radiometer (CRR) diagnostic, also commonly referred to as a density–temperature (nT)-phase diagnostic, that is used to measure the cross-phase angle (α˜ ne˜ Te)between turbulent fluctuations in electron density and temperature in ASDEX Upgrade (AUG) plasmas. The CRR diagnostic hardware, composed of a reflectometer and multi-channel radiometer measuring along the same line of sight, was designed to enable measurements in both the plasma core (ρpol =0.4–0.9)and edge (ρpol =0.9–1.0), furthering our ability to measure multiple turbulence parameters simultaneously and providing new capacity to characterize turbulence throughout the plasma volume. II. BACKGROUND The measurement of α˜ ne˜ Te, which was first carried out in the core of the W7-AS stellarator,4is important for informing our understanding of the turbulent fluctuations that drive plasma transport. A significant change in this cross-phase angle indicates that an important change has occurred in the physics underlying the electron density and temperature fluctuations. Previous work has found an association between changes in the value of α˜ ne˜ Teand changes to whether the turbulence is driven predominantly by long-wavelength ionorelectroninstabilities,i.e.,theIonTemperatureGradient(ITG) mode or the Trapped Electron Mode (TEM) (see, e.g., Refs. 2and 5–7). In addition, α˜ ne˜ Tecan be calculated from theory and simulation, including gyrokinetic and quasilinear codes, and therefore one canapplyexperimental measurements of α˜ ne˜ Tetowardthevalidation of computational models.2Furthermore, measurements of α˜ ne˜ Tecan beusedtoassesstheimpact ofdensityfluctuationson radiationtemperature fluctuation measurements in regimes of low optical depth, thereby aiding in the interpretation of measurements from diagnostics such as the correlation electron cyclotron emission (CECE) diagnostic.8 Previous measurements of α˜ ne˜ Teat AUG8–11 required pairing together components of an existing reflectometer and radiometer that were normally operated as entirely separate diagnostics. In this work, we report on the first dedicated CRR diagnostic at AUG that enables continuous α˜ ne˜ Temeasurement capability. This diagnostic was designed to maximize compatibility between the constituent reflectometer and radiometer in order to enable the measurement of long-wavelength fluctuations in electron temperature and density expected in the majority of AUG plasmas. The operation of the CRR diagnostic has enabled the first measurements of α˜ ne˜ TeassociatedwithfluctuationsinthepedestalofanH-modeplasmafeaturing small Edge Localized Modes (ELMs). Theremainderofthispaperisorganizedasfollows:Sec.IIIprovides background on the theory of α˜ ne˜ Temeasurements. Section IV details the CRR diagnostic hardware. Section Vpresents the data analysis methods for this diagnostic. Section VI gives an overview of the experiment. Section VII presents the CRR diagnostic experimental measurements. Section VIII gives a discussion of the results. Section IX concludes this paper. III. OVERVIEW OF α˜ ne˜ TeMEASUREMENT THEORY TheCRR diagnosticα˜ ne˜ Temeasurementspresented inthiswork employ correlations of reflectometer and radiometer signals measured along a common line of sight. Here, we describe the basic principles of this diagnostic. The fluctuation reflectometer component of the CRR diagnostic operates by transmitting X-mode-polarized microwaves in the W-band range of frequencies (75–103 GHz) into the plasma. The transmitted signal is reflected and modulated in phase and amplitude by fluctuations in the plasma density in the region where the transmitted signal’s frequency is equal to the right-hand cutoff frequency.12 Therefore, an analysis of these modulations can provide information on the behavior of the turbulence at the cutoff layer. However, depending on the strength of the density fluctuations, the response of the reflectometer signal to the density fluctuations can be linear or non-linear.12 For sufficiently small density fluctuations, corresponding to the linear regime, phase fluctuations have been found to be proportional to the density fluctuations at the cutoff region, although this proportionality breaks down for higher density fluctuation levels, corresponding to the non-linear regime.13 However, amplitude fluctuations have been found to retain their proportionality to density fluctuations better at high fluctuation levels.13 As reported in Ref. 14 and noted in Ref. 11, a finite phase anglemayexistbetweenthereflectometersignalfluctuations andthe density fluctuations, dependent on factors that include not only linearity but also the wavenumber range of the density perturbation and the effective curvature between the radiometer beam and the cutoff layer. This finite phase angle would yield a bias in the calculated reflectometer–ECE cross-phase angle compared to α˜ ne˜ Te.11,14 Evaluating the conditions under which each possible reflectometer signalmay be used as anappropriate measure of density fluctuations for α˜ ne˜ Temeasurements is an ongoing area of research and requires full-wave modeling. For further discussion, see p. 9 of Ref. 11, p. 5 of Ref. 2, and the references therein. The multi-channel radiometer component of the CRR diagnostic measures fluctuations in the intensity of X-mode-polarized second harmonic electron cyclotron emission (ECE) in the F-band range of frequencies (109–124 GHz). Under conditions in which the measured volume of the plasma is optically thick (τ≳2), the fluctuations in the ECE intensity can be interpreted as fluctuations in the electron temperature.15 The localization of the radiometer measurements is determined by the equilibrium magnetic field with finite-volume effects enhanced by Doppler broadening and the relativistic downshift.15,16 Cross correlation analysis of the signals measured by the reflectometer and radiometer components of the CRR diagnostic is performed to obtain α˜ ne˜ Te. Measurements of coherent α˜ ne˜ Tesignals require that the reflectometer and radiometer measure within the same turbulence correlation length in the radial direction along the line of sight of the diagnostic. The use of programmed reflectometer transmission frequency steps and a large array of radiometer Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-2 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi FIG. 1. Lines of sight for the CRR diagnostic’s transmitter (purple) and receiver (blue) antennas for a 110 GHz beam calculated using a vacuum-based Gaussian beam model for discharge 41455 during the interval 3.25–3.75 s over contours of ρpol, where ρpol is defined as the square root of the normalized poloidal magnetic flux. channels employed by the CRR diagnostic increases the likelihood of radially co-located reflectometer and radiometer measurements,thereby increasing opportunities for obtaining coherent α˜ ne˜ Te measurements. The CRR diagnostic has a poloidal spatial resolution set by the width of the microwave beam at the measurement location. Both the reflectometer and radiometer channels are sensitive to turbulent fluctuations with poloidal wavelengths longer than the poloidal beam width, defined here as the 1/e2beam power diameter or equivalently as the 1/eE-field beam diameter, but rapidly lose sensitivity when the wavelengths are shorter than the beam width.15,17 The application of a Gaussian beam model per Ref. 18 yields poloidal beam widths between ∼11 cm at the scrape-off layer (SOL) and 13.5 cm at ρpol =0.80, as shown in Fig. 1. The time resolution of the CRR diagnostic is affected by the need for ensemble averaging to obtain a level of coherence between the reflectometer and radiometer signals that is above the sensitivity limit. The equations for these parameters are shown in Sec. V. As will be shown in Sec. VII, half a second of ensemble averaging was required to obtain coherence levels above the sensitivity limit for the measurements presented in this work. IV. DESIGN OF THE CRR DIAGNOSTIC A schematic of the CRR diagnostic is shown in Fig. 2. Details of the antennas and components of the W-band heterodyne reflectometer and the F-band heterodyne 24-channel radiometer that together make up the CRR diagnostic are given in Secs. IV A–IV C. FIG. 2. Schematic of the CRR diagnostic hardware. Both the reflectometer and radiometer components of the overall diagnostic have their own radio frequency (RF) and intermediate frequency (IF) sections and share the same data acquisition system. The transmission path between the antennas and the DC breaks is simplified for clarity. Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-3 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi A. Antennas and diagnostic lines of sight The transmission and reception of the reflectometer and radiometer signals utilize a pair of bi-static, W/V-band pyramidal horn antennas. The antennas, installed on the low-field side of the tokamak,areseparated vertically by ∼56 mmasmeasured from their opticalaxes. The upper antenna isusedto transmit the reflectometer signal and features a downward vertical tilt of 3.6○, while the lower antenna is used to receive the reflectometer signal reflected by the plasma as well as the radiometer signals and features an upward vertical tilt of 3.6○. These small tilt angles lead to approximately normal incidence of the transmitted and measured beams with the contours ofconstant magneticfluxwithin theplasma.Figure1 showsthelines of sight of the microwave beams transmitted and received by the upper and lower antennas at 110 GHz, respectively. B. Reflectometer hardware 1. Transmitting hardware A tunable synthesizer in the transmission path outputs a pre-programmed, continuous-wave, fixed-frequency signal or a sequence of signals at selected frequencies within the range of 12.5–17.16 GHz. The oscillator that generates these output signals uses a fixed 10 MHz reference signal provided by a clock internal to the synthesizer. 6-m long low-loss Sub-Miniature version A (SMA) cables connect the reflectometer intermediate frequency (IF) and radio frequency (RF) sections. A frequency multiplier in the RF section increases the synthesizersignalfrequency byafactorof6,resultinginW-bandfrequency coverage in the range of 75–103 GHz. For standard AUG operation with an on-axis magnetic field of 2.5 T, this frequency range enables the reflectometer to measure density cutoffs between ∼2–6 ×1019 m−3. An amplifier in the multiplier module increases the reflectometer signal power up to 20 dBm. An attached isolator protects the transmitter components from reflected power. A W-band low-pass filter with a passband up to 103 GHz rejects frequencies 105 GHz and above in order to protect against stray radiation from electron cyclotron resonance heating (ECRH) gyrotron operation at 105 and 140 GHz. Between the W-band fundamental waveguide attached to the low-pass filter and the transmitting antenna are a pneumatic switch for optional diagnostic isolation, a DC break, two waveguide tapers, seven90○bends,avacuumfeed-throughGaussianperiscope, and an oversized waveguide. The 39 mm diameter circular oversized waveguide is used to minimize ohmic losses. The quasi-optical Gaussian periscope minimizes microwave mode conversion through the vacuumbreak.Mode conversion is also reduced throughtheuseof long waveguide tapers from the oversized to the fundamental circular waveguide. The desired X-mode microwave polarization is selected atthe fundamental circularto rectangular waveguide transition. Signal losses are reduced by keeping the fundamental waveguide as short as possible. 2. Receiving hardware The receiving optical transmission path, starting with the receiving antenna, is identical to the transmitting path up until a three-way waveguide coupler. One of the ports of the coupler connects to the reflectometer’s RF section. The signal then passes through a W-band low-pass filter identical to the one already described in the transmitting path. The incoming RF signal passes through a mixer, where it is mixed with a local oscillator signal generated by a second tunable synthesizer in the reflectometer’s IF section. The synthesizer in the receivingpath is identical to thesynthesizerinthetransmittingpath. It uses the same 10 MHz reference signal to avoid introducing systematic phase shifts into the received reflectometer signal during the demodulation process in the RF section mixer. However, the receiving path synthesizer is programmed such that the output frequency of the corresponding ×6 frequency multiplier is 500 MHz less than the frequency of the wave emitted by the transmitting antenna to facilitate proper demodulation in the I/Q mixer. The IF signal output by the RF section mixer is amplified, bandpass filtered (500 MHz center frequency with 2 MHz bandwidth), and fed into the RF port of an I/Q mixer. The I/Q mixer’s LO port receives a signal from a 500 MHz phase-locked oscillator, which itself uses the same 10 MHz reference signal to ensure it is phase-locked to the two synthesizers. The in-phase (I) and quadrature (Q) signals output by the I/Q mixer are then amplified and low-pass filtered at 1 MHz to prevent aliasing before digitization at 4 MHz. Special attention was given to the screening of reflectometer components and the avoidance of ground loops. C. Radiometer hardware The radiometer component of the CRR diagnostic measures electron cyclotron emission from the plasma using the same receiving antenna as the reflectometer. The design of the radiometer is based on the CECE diagnostic at AUG as described in Ref. 19. The third port of the three-way waveguide coupler connects to the radiometer signal’s W-band transmission path. After passing through a W-to-F-band waveguide coupler and the subsequent section of the F-band waveguide, the signal enters the radiometer RF section. The signal is first filtered using a side-band filter (109–124 GHz) before downconversion to intermediate frequencies in a mixer (107 GHz), although the selection of side-band filter and mixer can be reconfigured to enable access to different frequency ranges. During standard AUG operation with an on-axis magnetic fieldof2.5T,the109–124GHzfrequencyrangecorrespondstopositions within the range of ρpol =0.35–1.03. The radiometer measures over a subset of this radial range, depending on the configuration of the IF section, particularly the IF filter center frequencies. The set of IF filters installed at the time of this work corresponds to the narrower radial range ρpol =0.77–1.03. The IF output of the mixer is amplified before entering into the diagnostic’s IF section. TheIFsectionfeatures24fixedfrequencychannelsof200 MHz filter bandwidths split among three chassis, with 50 MHz spacing between adjacent filter bandwidths. After detection, amplification, and anti-aliasing at 1 MHz, the signals are sampled at 4 MHz using the same digitizer as the reflectometer signals. V. DATA ANALYSIS METHODS Within the receiver section of the reflectometer, the received signal is decomposed in a quadrature demodulator (I/Q mixer) into an in-phase (I) and quadrature (Q) signal. This demodulation Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-4 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi process enables estimates of the phase and amplitude modulations of the reflected signal relative to the transmitted signal as a result of the plasma fluctuations. The unwrapped phase, ϕ(t) =arctan(Q(t)/I(t)), amplitude, A(t)=√I(t)2+Q(t)2, homodyne I-phase, A(t)cos(ϕ(t)), homodyne Q-phase, A(t)sin(ϕ(t)), and the complex amplitude, A(t)eiϕ(t), can each be correlated with the radiometer signals.2,9,20 Ensemble-averaged estimates of the one-sided auto-powers (G˜ ne˜ ne,G˜ Te˜ Te) and cross-power (G˜ ne˜ Te)spectral densities are calculated per Ref. 21 using the chosen density signal (i.e., the phase, amplitude, homodyne, or complex amplitude reflectometer signal) and the temperature signal measured by an individual radiometer channel. The cross-power spectral density (PSD) calculation uses the convention of multiplying the complex conjugate of the Fourier transform of the density signal with the Fourier transform of the temperature signal. The density–temperature cross-phase angle, α˜ ne˜ Te, is calculated (per Ref. 21) as α˜ ne˜ Te(f)=arctan(Im(G˜ ne˜ Te(f)) Re(G˜ ne˜ Te(f))). (2) Thecoherencefunction,definedheretobereal-valued, canalso be calculated (per Ref. 21) as γ˜ ne˜ Te(f)=∣G˜ ne˜ Te(f)∣ √G˜ ne˜ ne(f)G˜ Te˜ Te(f). (3) The statistical uncertainty on the cross-phase angle is given by its standard deviation (per Refs. 21 and 22) as σα˜ ne˜ Te=¿ Á Á Á À1 2nd⎛ ⎝1−γ2 ˜ ne˜ Te(f) γ2 ˜ ne˜ Te(f)⎞ ⎠, (4) where ndis the number of data segments in the ensemble average. The one standard deviation uncertainty on the coherence is given (per Refs. 19 and 22) as σγ˜ ne˜ Te=√1 2nd(1−γ2 ˜ ne˜ Te(f)). (5) The sensitivity limit of the coherence function is defined as two standard deviations above zero, in line with Ref. 19. VI. EXPERIMENT OVERVIEW In this section, we give an overview of AUG discharge 41455, during which CRR diagnostic measurement results were obtained at the end of the 2022 experimental campaign. This was an auxiliaryheated [neutral beam injection (NBI) and ECRH], 0.8 MA, H-mode FIG. 3. (a) Core and edge line-averaged electron densities from interferometry. (b) Core (ρpol =0.20)and edge (ρpol =0.90)electron temperatures from the profile ECE diagnostic. (c) Input power levels. (d) ELM monitor. The shaded regions indicate the two time intervals of interest: 3.0–3.5 and 3.5–4.0 s. Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-5 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi discharge exhibiting marked changes in ELM characteristics over the course of the discharge. The plasma was majority helium with a minority of deuterium and nitrogen. Two time intervals are of interest to the α˜ ne˜ Temeasurements presented in this work: 3.0–3.5 and 3.5–4.0 s. As shown in Fig. 3, the core of the plasma featured a slight increase in the line-averaged electron density and a slight decrease in the electron temperature while the power was steady between the twointervals.ThefirsttimeintervalfeaturedafewsmallELMs,while the second time interval was ELM-free. The results in Sec. VII are averaged over the ELMs. Figure 4 shows the electron density and temperature edge profiles for both time intervals as calculated using integrated data analysis (IDA).23 Figure 5 shows the corresponding normalized logarithmicgradientscalelengths,definedasR/Lne=R×d/dr(ln(ne)) and R/LTe=R×d/dr(ln(Te)), respectively. The pedestal top can be identified just inside of ρpol =0.95. The neand Teprofiles and their gradients are not significantly changed between the two time intervals. The radiometer localization and IDA profile mappings were determined via magnetic equilibrium reconstruction using the integrated data analysis equilibrium (IDE).24 The reflectometer localization was determined from a right-hand cutoff frequency profile generated from the IDA neprofile and IDE magnetic equilibrium reconstruction. The reflectometer transmission frequency was increased from 75 to 99 GHz in steps of 6 GHz at each 1 s mark during this discharge. During both time intervals of interest, the transmission frequency was fixed at 93 GHz, yielding an approximately constant reflectometer localization during the two intervals.Thereflectometerandradiometerlocalizationswerefound to overlap at ρpol ≈0.98 during both time intervals. VII. RESULTS In this section, we first present measurements from the radiometer and reflectometer components of the CRR diagnostic, followed by α˜ ne˜ Temeasurements. The spectra shown in this section were calculated using fast Fourier transforms (FFTs) with 50% overlapping Hamming windows and 0.25 ms data segments, yielding ∼4 kHz frequency resolution. Figure 6 shows the coherence spectra between two neighboring radiometer (ECE) channels measuring in the plasma edge at FIG. 4. Edge (a) neprofiles and (b) Teprofiles from IDA for both time intervals. FIG. 5. Edge (a) R/Lneprofiles and (b) R/LTeprofiles from IDA for both time intervals. Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-6 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi FIG. 6. Coherence spectra for two radially adjacent radiometer channels for the two time intervals at the same radial location. A broadband feature exists at frequencies below 100 kHz in both spectra. The coherence is about 50%higher in the frequency range of 30–60 kHz during the second time interval. ρpol ≈0.98. The spectra were calculated by applying Eq. (3) to the two radiometer signals. The coherence level is about 50%–75% larger in the frequency range of 30–60 kHz during the second time interval. Turbulent electron temperature fluctuation amplitudes (δTe/Te)were calculated from the coherence spectra using Eq. (1) in Ref. 11 by integrating between 20 and 110 kHz and subtracting a background value taken as the mean coherence over the range of 150–200 kHz. For 3.0–3.5 s, δTe/Te=1.27% ±0.06%, while for 3.5–4.0 s, δTe/Te=1.66% ±0.05%. The optical depth (τ)at the measurement location was on the threshold of marginality, with τ≈2. Based on the poloidal beam width and temperature profile at the measurement location, the radiometer measurements were sensitiveto kθρs≲0.1, where kθisthe normalized poloidal wavenumber ofthemeasuredturbulenceandρsistheionLarmorradiusevaluated at the sound speed. Figure 7 shows the auto-power spectral densities (PSDs) of three reflectometer signals (amplitude, phase, and quadrature homodyne signals) for both time intervals. A threshold-based moving average filter was implemented per Ref. 25 to remove narrowband electronics noise peaks from the spectra. As with the radiometer, the reflectometer measurements were sensitive to kθρs≲0.1. Similar to the radiometer coherence spectra, the reflectometer autoPSD spectra all show a distinct broadband feature at frequencies less than ∼100 kHz. However, in contrast to the radiometer coherence spectra, the broadband features in the reflectometer spectra all exhibit a decrease in signal level from the first to the second time interval. A greater percentage decrease in the reflectometer phase and homodyne signals is observed between the two intervals compared to the amplitude signal. Given possible ambiguities regarding whether each of the reflectometer phase, amplitude, and homodyne signals are accurate proxies for the actual density fluctuations, rigorouscalculationsofthecorrespondingdensityfluctuationamplitudes require full-wave modeling and are beyond the scope of this paper. Figure 8 shows how the CRR diagnostic coherence and α˜ ne˜ Te spectra change between the two time intervals. An increase in the coherenceandα˜ ne˜ Teoccursfromthe first to the second timeinterval. Themaximumcoherence levelofthebroadbandfluctuations,within FIG. 7. Auto-power spectral densities (PSDs) for the reflectometer (a) amplitude, (b)phase,and(c)quadraturehomodynesignalsforbothtimeintervals.Eachspectrum shows a broadband feature at frequencies below 100 kHz. Note: y-axes are truncated. the frequency range of 20–80 kHz, increases ∼100% between the twotime intervals.Theincreasein thereflectometer–ECEcoherence spectra is correlated with an increase in the ECE–ECE coherence spectra but is inversely correlated with the change in the reflectometer signal spectra between the two time intervals. The signal bandwidths of the reflectometer–ECE coherence and α˜ ne˜ Tespectra are similar between the two time intervals, although the α˜ ne˜ Te Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-7 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi FIG. 8. Panels (a), (c), and (e) show the coherence spectra between the reflectometer amplitude, phase, and quadrature homodyne signal, respectively, and a radially co-located radiometer channel for the two time intervals. Panels (b), (d), and (f) show the cross-phase angle spectra using the same signals. The coherence spectra are larger, and the cross-phase angles are more out of phase during the second time interval. spectra display a more constant trend during the second time interval. The mean value of the cross-phase angle for 3.0–3.5 s is ∼90○ over the frequency range of 30–60 kHz, while the mean value of the cross-phase angle for 3.5–4.0 s is more out of phase, ∼120○, over the same range of frequencies. It is interesting to note the relatively large change in the coherence levels (≈100%)between the two time intervals compared to the relatively smaller change in the values of α˜ ne˜ Te(≈30%)within 30–60 kHz. In addition, the coherence spectra Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-8 © Author(s) 2025 05 March 2025 14:54:28 Review of Scientific Instruments ARTICLE pubs.aip.org/aip/rsi betweenthereflectometerandECEsignalsdropbelowthesensitivity limitby∼70kHz,whilethecoherencespectrabetweentheECE–ECE signals remain above the sensitivity limit beyond 100 kHz. Furthermore, the reflectometer–ECE coherence spectra exhibit a more pronounced dip at frequencies below 30 kHz, while the coherence spectra between the ECE–ECE signals do not. Another observation to note is that neither the magnitude of the reflectometer–ECE coherence nor the frequency bandwidth of the fluctuating signal nor the value of α˜ ne˜ Teappear to depend significantly on the choice of selected reflectometer signal during either time interval. It is important to address the question of whether density fluctuations in the plasma edge could influence the interpretation of the results of this work given the marginal optical depth in this plasma. We noted in Sec. II that α˜ ne˜ Tecan aid in assessing the impact of density fluctuations on radiation temperature fluctuations at low optical depth. Here, we conduct this assessment for the plasma conditions associated with discharge 41455. We follow the analysis conducted in Sec. 3B of Ref. 8. This analysis uses Eqs. (4) and (5) in Ref. 26, which model the radiation intensity fluctuation amplitude as a function of optical depth, δTe/Te,δne/ne,α˜ ne˜ Te, and wall reflectivity. For this model, we assume that δTe/Te=1.45%, as this is approximately representative of the reported values of δTe/Tefor the two time intervals in this discharge. We assume a conservative value of δne/ne=40%, as this is an upper limit for the δne/ne associated with the quasi-coherent mode (QCM) as measured using probes in the edge of the ELM-free discharge reported in Ref. 27. A wall reflectivity of 0.85 is used, in line with Ref. 8. Through this analysis, we find that the ratio of the radiation intensity fluctuation amplitudes to δTe/Tebecomes closer to 1, i.e., that marginal optical depth has less of an effect, as α˜ ne˜ Tebecomes more out-of-phase. We note that this qualitative trend holds regardless of the assumed values of δne/neand δTe/Tebut that it is more sensitive to the values of α˜ ne˜ Te. The results of this model predict that the measured radiation intensity fluctuation amplitude should decrease by ∼25%. Instead, the measured fluctuation amplitude was found to increase from 1.27% to 1.66%. In addition, there is a decrease in density fluctuationlevelsas indicated by the drop in thepowerspectral densities of the reflectometer signals from the first to the second time interval, as shown in Fig. 7. This suggests that any density fluctuation driven-pollution of the radiometer signals should decrease from the first to the second time interval, yielding a decrease in the measured temperature fluctuation amplitudes. This is counter to the observed increase in δTe/Te. Therefore, the reported increase in δTe/Tefrom the first to the second time interval does not appear to be explained by the impact of density fluctuations on the ECE measurements at marginal optical depth. It is also possible for marginal optical depth conditions to impact α˜ ne˜ Teitself. One possibility is that in low optical depth plasmas, an increase in density fluctuations would lead to a more inphase value of α˜ ne˜ Tesince the same underlying density fluctuations would be measured by both the reflectometer and the radiometer. A similar effect could play some role in the observed results, where a decrease in density fluctuation levels occurs concurrently with a more out-of-phase value of α˜ ne˜ Te. In order to evaluate this question more rigorously, future work will employ synthetic CRR measurements of non-linear gyrokinetic simulations, coupled with full-wave modeling, which is beyond the scope of the current paper. VIII. DISCUSSION ThenovelCRR diagnostic results presented inthiswork are the first such measurements in the pedestal region of a high density Hmode plasma across small ELM and ELM-free phases. Importantly, the broadband coherence spectra and cross-phase angles shown in this work exhibit coherence levels and signal bandwidths that are consistent with multiple previous measurements on AUG of drift-wave turbulence as per Refs. 9–11 as well as turbulent fluctuations associated with the edge weakly coherent mode per Ref. 8. The consistency of these new results with previous measurements indicates that this new diagnostic is functioning properly and demonstrates the compatibility between the constituent reflectometer and radiometer components for α˜ ne˜ Temeasurements. The results presented here are also consistent with previous work showing agreementinshapebetweenthereflectometeramplitude,phase,and homodyne signals in H-mode plasmas with low density fluctuation levels in the CCT tokamak.13 The agreement between each of the auto-power spectra shown in Fig. 7 and, separately, each of the α˜ ne˜ Te spectra shown in Fig. 8 as calculated using the reflectometer amplitude, phase, and homodyne signals suggests that the reflectometer response is in the linear regime and that each of these signals is proportional to the underlying density fluctuations. This result is also consistent with prior work reporting agreement between α˜ ne˜ Te as calculated using the reflectometer phase and amplitude signals.7 Future work employing non-linear gyrokinetic simulations, coupled with full-wave modeling, can confirm the linearity of these measurements. Such modeling can also be used to investigate the influence of factors that may lead to finite cross-phase angles between the reflectometer signals and the density fluctuations, as noted in Sec. III. Itisnoteworthythatthedischargefeaturedinthisworkwasnot specifically designed for commissioning measurements of the CRR diagnostic, in contrast to previous α˜ ne˜ Testudies at AUG in which the localizations of the reflectometer and radiometer were deliberately factored into the planning of the discharges to ensure radially colocatedmeasurements.Theabilitytoobtaincoherentmeasurements in this work nonetheless highlights the importance of stepping the reflectometer transmission frequency in order to increase the possibility of overlapping measurements. Furthermore, given the use of a shared receiver antenna and the use of adjacent microwave frequency bands, the W-band reflectometer and F-band radiometer are sensitive to very similar wavelengths of turbulent fluctuations. In addition, the chosen diagnostic frequency bands enable the colocation of the reflectometer and radiometer measurements across a wide range of plasma densities. An interesting point is that the measured CRR signals showed significant changes between the first and second time intervals while the profiles and their gradients exhibited only slight changes. The observed increases in the reflectometer–ECE coherence and α˜ ne˜ Te, the increase in δTe/Te, and the decrease in reflectometer auto-PSDs might be explained in part by the slight changes in the local gradients, which could affect the strength of the turbulence drive. On the other hand, there could be some additional physical mechanism leading to the measured changes in the characteristics of the turbulence. Future work will investigate additional possible sources of drive leading to these observed changes in the behavior of the turbulence. Another open question is for what physics reason the Rev. Sci. Instrum. 96, 033504 (2025); doi: 10.1063/5.0243894 96, 033504-9 © Author(s) 2025 05 March 2025 14:54:28