Electron temperature fluctuation levels of the quasi-coherent mode across the plasma radius

. EDA H-mode is an ELM-free regime in which the edge quasi-coherent mode (QCM) replaces the ELMs. The estimated location of the quasi-coherent mode is in a partly optically thin region of steep gradients localized between ρ pol = 0.96 -1. Relative fluctuations of radiation temperature between 15 and 80kHz are about 7% with significant density contribution. In the electron cyclotron emission (ECE) channels with resonances in the plasma core, a mode with the same frequency as the quasi-coherent mode is measured. The peak amplitude of both core and edge modes matches the strongest electron temperature gradient in the core and the edge, respectively. The ECE core and edge signals are out of phase. The radiation transport forward model (ECRad) shows that the refraction explains the phase relation between the edge and the core ECE channels. The phase correlates with the sign of the core ∇ T e . The amplitude of the fluctuations in the core decreases with decreasing gradients, which is the trend seen in the experiment. The amplitude ratio of the core and edge fluctuation is a factor of five in the experiment; this ratio remains a factor of a hundred in the modeling.


Introduction
The EDA H-mode (Enhanced D α high confinement mode) regime is a regime free of edge localized modes (ELMs) with good energy confinement properties [1]. Recently it has been a significant focus of the ASDEX Upgrade experimental program and its main features are reported in [2]. At ASDEX Upgrade, the dominant external heating is the electron cyclotron resonance heating (ECRH) and the rotation profiles are hollow, similar to observations in some L-mode plasmas [3]. The ELMs are replaced by a quasi-coherent mode thought to regulate the transport and keep the pedestal stable against large type-I ELMs. The EDA H-mode regime is routinely obtained at ASDEX upgrade and the neutral beam injection NBI power window is extended with Ar seeding [4]. As mentioned, the prominent signature of EDA H-mode is the quasi-coherent mode measured at the plasma edge with different diagnostics; thermal He-beam emission spectroscopy (THB), electron cyclotron emission (ECE), and reflectometers. However, in some core ECE channels, a fluctuation appears with the same frequency as the quasi-coherent mode and is absent in the signals of other core diagnostics i.e., soft X-rays. The origins of the core ECE emission have been debated, and the main question remains whether it is a consequence of the strong refraction on the edge density or actual core fluctuations. * e-mail: vanovac@mit.edu The quasi-coherent mode (QCM) in the plasma edge is a feature of the EDA ELM-free regime, but it can also coexist with ELMs in ELMy H-modes, most likely appearing between ELMs. However, in the context of this work, we will refer only to the quasi-coherent mode where ELMs are absent and describe it in terms of its frequency and associated temperature fluctuation amplitudes.
The relative temperature fluctuation levels across the pedestal are assessed via the Correlation Electron Cyclotron Emission (CECE) instrument [5] covering the region of ρ pol = [0.85 − 1] while the standard ECE diagnostics is used for core-edge amplitude comparison and comparison to the modeling. EC Radiation transport is assessed with ECRad [6], a radiation transport code suitable for treating electron cyclotron emission with specifics of CECE and ECE diagnostics such as launching angles and IF bandwidth. Refraction is included in ECRad, allowing studies on the refractive effects on the core emission.

Frequency
The peak frequency of the quasi-coherent mode at ASDEX Upgrade during its stationary phase varies between 15 and 60 kHz. The calculated power spectral density from the ECE measurements at three different radial locations is displayed in figure 1. The peak frequency is determined from the spline fit to the data shown in gray. The black curve shows the power spectrum measured at the edge at ρ pol = 0.97, the purple one at ρ pol = 0.52 at the mid-radius, while the red curve corresponds to the measurement in the plasma core at ρ pol = 0.07. The peak frequency for both the edge and the core is identical at f = 22 kHz, indicating the same feature measured in both plasma regions. The power spectra broaden due to the changes in the frequency of the quasi-coherent mode during the integration time.

Localisation and amplitude
We use the CECE system for the localization and δT rad estimate. The CECE system at ASDEX Upgrade is a comb of 24 channels with fixed IF filters of 200 MHz bandwidth and 250 MHz spacing of the center frequencies, translating into approximately 2 mm of spatial resolution. Neighboring CECE channels measure correlated temperature fluctuations but uncorrelated thermal noise. By correlating neighbouring channels, coherency spectra γ c of turbulence are obtained. We obtain the fluctuation amplitude by integrating coherency in frequency space and subtracting the background noise. A dedicated experiment with two magnetic field strengths enables more accurate localization of the QCM. With changing magnetic field strength, the measurement position of the ECE & CECE channels changes while the mode location remains the same. Consequently, the mode amplitude moves from one channel to the next. In figure 2 we show the CECE measurements during discharge # 40703, for both field strengths. Figure 2 a) and 2 b) show the coherency spectra γ c against normalized radius. Figure 2 c) displays the relative temperature fluctuation levels versus normalized plasma radius ρ pol for Bt = 2.54 T in red and for Bt = 2.53 T in magenta. The mode affects the radial range between ρ pol = 0.96 and the sepa- Cross-coherence between subsequent correlation ECE channels for magnetic field strength of 2.53 T. c) Relative radiation temperature fluctuations integrated between 20 and 80 kHz from the CECE measurements for B t = 2.54 T in red and for B t = 2.53 T in magenta, respectively. Grey regions are marking peaks of strong noise in the channels. ratrix in both cases. Due to the low optical depth outside of ρ pol = 0.97, the fluctuation amplitudes of 7% can be a consequence of density perturbation in this region [7]. Profile ECE measurements integrated between 15 and 60 kHz are shown in figure 3 for the same discharge # 40703. Corresponding temperature profiles are shown in 3 a) and profile gradients in 3 b). For both magnetic field strengths, the maximum amplitude distribution (shown in 3 c)) matches the peak of the electron temperature gradients in the edge and the core of the plasma.
A typical feature of EDA H-mode is the high electron density, however, in our experiment ECE radiation is always below the cutoff and the ECE profile measurements are routinely obtained. The electron temperature and density profiles for two cases comparing two discharges are shown in figure 4. The discharge # 40647 had plasma current I p = 0.6 MA while the discharge # 40417 had I p = 0.7 MA and consequently higher density. Both discharges had the same magnetic field strength and the ECRH heating scheme. The higher current discharge had NBI blips applied for charge exchange measurements.
The corresponding temperature fluctuations across the pedestal for both cases averaged over 2 s of the discharges are shown in figure 5. The behavior of the radiation temperature fluctuations for two different density profiles differs. The T rad fluctuations for the low pedestal density case are increasing from 0.97 and peak just before the separatrix. The T rad fluctuations for the high pedestal density case are increased across an entire measurement region. This major difference in the shape of the radial ampli-  tude distribution of the temperature fluctuations suggests its density dependence. Figure 6 displays an EDA H-mode designed to study the effect of core temperature gradient on the quasi-coherent activity measured in the core and edge ECE channels. The temperature gradient during the discharge was changed by the ECRH deposition shifting from central to off-axis heating. The discharge has a plasma current of I p = 600 kA and a magnetic field B T = 2.5 T. Figure 6 a) illustrates the ECRH heating scheme. Between 2-4 s two central gyrotrons heat the plasma. The second phase, between 4-6 s combines one central gyrotron and one mid-radius  gyrotron. In the last phase, between 6-7.4 s, both gyrotrons deposit the power at mid-radius. The total power is about 1.4 MW throughout the discharge. The plasma had a fixed shape as represented by the upper triangularity δ u and the outer plasma boundary R aus as displayed in figure  6 b). The core and edge densities as well as the fueling are shown in figure 6 c) and remained constant throughout the discharge. Spectrograms of the edge and core ECE channels, displayed in figure 6 d) and 6 e) show the quasicoherent mode. Figure 6 f) displays the spectrogram of the magnetic coil measuring radial magnetic field fluctuations at the outer midplane. The strongest modes in the coil are around 200 kHz frequency, usually with toroidal mode numbers n = 5,6 and 7. The fundamental frequency of this harmonic structure has a frequency similar to the quasi-coherent mode in this example. The profile com- parison between on and off-axis ECRH heating during the discharge # 40647 is displayed in figure 7. The phase with on-axis heating is marked in blue, and the phase with offaxis heating is in orange. The average profiles measured with ECE are displayed as symbols, and corresponding fits as lines in figure 7 a). The estimated gradients of the measured and fitted profiles are shown in 7 b). The radial distribution of the ECE amplitude measurement integrated between 15 and 60 kHz is displayed in 7 c). The location of the peak amplitude and matching gradients is emphasized with a shaded region the core being in red and the edge marked in black.

Refraction effects
The edge quasi-coherent mode is the primary candidate for particle transport across the pedestal. However, the measurements of the quasi-coherent mode in the core ECE channels remain ambiguous. One hypothesis is that the mode measured in the core ECE channels is due to the refraction of the beams on a high-density perturbation at the edge. Another important ingredient is the steepness of the temperature profile. Density fluctuations are measured with a thermal He beam and reflectometers. Another supporting argument is the absence of the core mode in other core diagnostics, i.e. soft X-ray measurements. To account for the possible refraction from the significant density perturbation at the edge, we employ the radiation transport forward model ECRad [6] where the geometry of the ECE system is included. We model the steep and the flat temperature profile scenarios of the discharge shown in figure 7. In the modeling we use a single ray, hence the observation volume is neglected. As input to the ECRad we use a twodimensional T e and n e grid. Raytracing is then performed and the radiation transport equation is solved along the ray path for each time-point, resulting in time-resolved radiation temperature. The 2D data used for the modeling is the output of a recent JOREK simulation for a regime with small ELMs [8] regime, where a rotating mode at 20 kHz with n = 10 was observed. This set of data is, at present, suitable to treat the quasi-coherent mode as the perturbation structure of the small ELMs scenario has similar features as the quasi-coherent mode in terms of frequency, toroidal mode number and the extent across the pedestal. The JOREK simulation is performed for a different discharge than the one treated in this work. Therefore, JOREK data is further modified to be closer to the shape and magnitude of the background electron density and temperature profiles of the discharge # 40647.
The final modified profiles are fed separately into ECRad for the two cases. The modeling is performed for fifteen-time points to obtain time-resolved radiation temperatures. We then calculate the relative radiation temperature fluctuations (T rad − ⟨T rad ⟩)/⟨T rad ⟩ for each time point where ⟨T rad ⟩ is an equilibrium temperature without perturbation. The result for the case of the steep electron temperature profile is displayed in figure 8. We compare two different radial locations. The core channel is at ρ pol = 0.21 shown in red and the edge ECE channel at ρ pol = 0.98 in black. The edge and the core fluctuations are in anti- phase. The maximum amplitude of the core channel is about 0.15 %, while the radiation temperature fluctuations at the edge are 15 %, making it a factor of 100 difference between the edge and the core, in this modeling exercise. Now we compare this modeling result to the experimental measurements. The time-resolved ECE measurements (experiment) in the core and the edge of the plasma, for the on-axis heating scenario, are shown in figure 9. The channel at ρ pol = 0.2 is displayed in red while the edge channel at ρ pol = 0.98 is shown in black. The phase relation between the edge and the core changes over time. However, for the majority of the time, the two signals are close to anti-phase, similar to the modeling (see figure 8). Core and edge amplitude differ by a factor of 5. A modeling is then performed for the case with an off-axis  ECRH heating scheme in which case the flat core temperature profile is flat. A comparison between relative temperature fluctuations of the two different radial locations for the off-axis scenario is shown in figure 10. The core channel is at ρ pol = 0.21 in red and the edge ECE channel at ρ pol = 0.98 in black. The amplitude of the core fluctuation is about 0.06 %, which is 2.5 times smaller than in the case of the steep gradient. The edge fluctuation amplitude remains unchanged, which is expected since the only change to the modeling input is the temperature profile in the plasma core. The core and the edge channels are in phase. This is a consequence of the sign of the temperature gradient. In the case of the flat ∇T e , the core temperature leans towards the hollow core profile, allowing for the temperature gradient of the opposite sign if compared to the steep gradient case. This comparison is best seen in figure 7b).
For better clarity, figure 11 shows the ray path of one of the core ECE frequencies. The equilibrium ray path without perturbation is shown in black, while the red corresponds to the ray path with edge perturbation included. Corresponding resonances are marked with squared symbols. The bending of the ray path happens at the edge, which is seen in the zoomed edge region. As a consequence, the resonances are vertically displaced in the core. Figure 11. 2D density contour plot with density perturbation at the edge used in the forward model. The ECE ray is refracted at the edge which can be seen in the zoomed picture and the resonance (in red) is displaced with respect to the equilibrium (black) position.

Conclusion and Outlook
The correlation ECE instrument makes it possible to obtain the relative temperature fluctuation levels of the quasicoherent mode at the plasma edge. Estimated fluctuation T rad levels integrated between 20-80 kHz are around 7%. The location of the quasi-coherent mode is measured to be in the region of steep gradients between ρ pol = 0.96 -1 of insufficient optical depth, where density contributes to the measured radiation temperature fluctuations. Two scenarios with different plasma currents show differences in the trends when comparing the relative temperature fluctuations estimated with the correlation ECE instrument. With higher density, the fluctuations amplitude pattern seems to be flat across the gradient region. For the lower density case, they have a pronounced peaking close to the separatrix. This is further to be investigated. The profile ECE system at ASDEX Upgrade allows for comparing the fluctuation levels across the entire plasma radius. Channels in the core and edge measure oscillations at the frequency of the quasi-coherent mode. Maximum mode amplitudes from the core and edge ECE measurements match the location of the steepest T e gradient. The ECE instrument also enables phase measurements between the edge and core. With a steep gradient, the edgecore channels are anti-phase.