The radial localization of the transition from low to high confinement mode in the ASDEX Upgrade tokamak

A novel experimental method is applied to localize the initial suppression of turbulence, in the form of density fluctuations, at the transition from the low (L-) to the high (H-) confinement mode in toroidal magnetic fusion plasmas. The high radial and temporal resolution, combined with the unprecedented statistical significance, provided the awaited information on a possible dominant E×B shear layer in L-H transition physics. We show, for the first time, that the H-mode turbulence suppression is initiated at the inner E×B shear layer in the ASDEX Upgrade tokamak possibly shedding light on the causality behind the L-H transition process.


Introduction
The physics of the L-H transition in toroidal magnetically confined plasmas is a persisting enigma which has a critical implication for achieving efficient energy production in a fusion reactor that is to be operated in H-mode.The leading explanation for the L-H transition and the amount of heating power P thr required to access it is the E × B shear stabilization of turbulence at the plasma edge [1].The E × B velocity (v E×B = E r /B) in the confined region may result from any non-ambipolar transport mechanism, e.g.ion orbit losses [2], collisional (neoclassical) processes [3], or from turbulence Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
stresses [4].Here, E r is the radial electric field and B is the magnetic field strength.Outside the last closed flux surface (or separatrix), in the so-called Scrape-Off Layer (SOL), E r is mostly determined by the non-ambipolar parallel transport of ions and electrons defining the plasma potential via a sheath region in front of the targets [5].In the confined region inside the separatrix, the v E×B profile shape features two shear layers, hereafter referred to as the inner and outer layers.The knowledge of which shear layer is responsible for the L-H transition is crucial to tailor experimental strategies aimed to influence the dominant shear layer and, in turn, optimize the H-mode access.Several previous works have already shown the impact of the E × B flow shear on turbulence [6][7][8][9].In this Letter, we show, thanks to state-of-the-art diagnostics and advanced analysis, the possibility to identify at which shear layer the turbulence is firstly stabilized at the L-H transition.
In recent years, several experimental and modeling results pointed to the influence of the SOL and divertor conditions on the L-H power threshold.At the JET tokamak, it was observed that P thr increases with the X-point height and decreases with the divertor closure [10].Similar observations were obtained at the DIII-D and MAST tokamaks [11,12].Along the same lines, modeling results showed a correlation between P thr and v E×B just outside the last closed flux surface which could point to the importance of the nearby outer shear layer in the L-H transition physics [13].Moreover, in an interchangedrift-Alfvén turbulence model, the separatrix parameters well sort out the ASDEX Upgrade confinement [14].However, the model describes the H-mode sustainment but not its triggering.Finally, a theory based on the relative alignment of the E × B shear and the Reynold stress predicts a positive coupling to the outer shear due to the symmetry breaking of the magnetic shear at the X-point [15].All of these findings would suggest a dominant role of the outer shear layer.On the other hand, a correlation between the edge ion heat flux and the H-mode onset has been found in ASDEX Upgrade and ALCATOR Cmod [16,17] suggesting that the inner shear layer is the relevant one for the L-H transition.Finally, zonal flows can impact both the outer and the inner layer [18][19][20].These are, however, all indirect and not conclusive indications since outer and inner shear layers are strongly coupled.For instance, an increase of the E × B velocity at the inner shear would at the same time steepen the outer one while a change in the divertor conditions might also affect the density and temperature gradients within the separatrix and, in turn, the inner E × B shear.For these reasons, it is essential to directly measure the impact of the shear layer on the turbulence in the edge region.If the impact can be pinpointed temporally and locally, the shear region that plays the key role can be identified.The knowledge of the dominant shear layer for the L-H transition physics might help in validating any model of it.

Experiments
We present a novel method to radially localize the initial suppression of density fluctuations at the L-H transition.It exploits the Doppler reflectometry (DR) diagnostic, allowing to probe both the density fluctuation amplitude (in a limited wavenumber range), and the fluctuation propagation velocity, with a sub-µs time resolution and spatial sensitivity at the mm scale.Density fluctuations are a marker of the local turbulence and their reduction at the L-H transition has been a well-recognized and fundamental characteristic of this transition almost since its discovery [21].Furthermore, density fluctuations are frequently employed as indicators of the overall turbulence behavior, particularly when investigating the interplay between turbulence and flows as the L-H transition [9,18].Therefore, in the following, we will at times use the term 'turbulence' and 'density fluctuations' interchangeably.
The key of the method is the development of a discharge scenario where L-H-L dithers, typically at a frequency around 100 Hz [7,10,22], are present for a long time interval.To achieve this, the heating power has to be finely tuned just above P thr , while the electron density n e is in the range where P thr increases with density.This assures a fall back into L-mode after the rise of the density following the L-H transition [23].
Figure 1 shows such scenario with standard lower single null edge optimized shape, favorable B × ∇B drift, plasma current of I p = 0.8 MA, B t = −2.5 T, and safety factor q 95 = 5.3: the Neutral Beam Injection (NBI) power (figure 1(b)) is stepped by changing the NBI duty cycle, resulting in different phases, separated by the vertical lines, where the line averaged electron density (figure 1(a)) remains in the same range, while the L-H-L dithers frequency f LHL (figure 1(d)) is changed.Within one phase, two DR systems, one in X-mode and one in Omode, probe the plasma at frequencies scanned respectively in the range 76 GHz -94 GHz and 50 GHz -60.8 GHz four times (figure 1(c)).These frequencies corresponds to perpendicular wave number ranges of roughly 10 ÷ 14 cm −1 for the X-mode and 7 ÷ 9 cm −1 for the O-mode, which typically coincides with the transition between ion and electron modes (ITG-ETG) still below electron temperature gradient mode peak in the k-spectra [24].Here, we only show the analysis of the time window between 3.9 s and 4.9 s in which f LHL is mostly stable at around 200 Hz, however the same results were obtained also in the other phases.The frequency f LHL is calculated using the poloidal magnetic field fluctuation ( Ḃθ ) signal measured by a magnetic pick-up coil close to the X-point [25,26].An example of few L-H-L dithers as measured by the coil are shown in figure 2(a), where the H-and the L-mode parts are shaded in gray and green, respectively.Roughly 150 out of the total 200 L-H transitions within the reference phase have been selected and synchronized using an algorithm based on the running correlation of one reference L-H-L dither Ḃθ nature with the other dithers.A threshold in the correlation of 0.8 has been select only similar L-H transitions maximum correlation for a given transition as the synchronization time point.2(a) shows the reference L-H transition and other L-H-L dithers, in figure 2(b) the running correlation and in figure 2(c) the synchronized Ḃθ over the 150 L-H transitions.The exact definition of the L-H time point t LH is arbitrary and it has been defined by means of the turbulence measurement as shown later.Due to the large number of L-H transitions considered, the statistical significance of this analysis is much higher than in earlier L-H transition studies in which often only one or, in best cases, a few L-H transitions were investigated.

Results
Figure 3 shows the amplitude of n e fluctuation level, i.e. the amplitude of the DR signal A DR , for the X-mode (figure 3(a)) and the O-mode channel (figure 3(b)) synchronized to the one L-H-L dither and conditionally averaged as a function of the normalized plasma radius ρ pol and time.Red indicates high turbulence level while blue shows low turbulence level.Note that A DR is the measurement of the back-scattered microwave signal which can be used only as a qualitative monitor of the n e fluctuation, while a quantitative estimation of ñe is not possible [27].Nevertheless, in this work, we analyzed both the O-mode and X-mode systems to highlight the consistency and robustness of the results as they respond differently to the turbulence amplitude [24].The radial positions associated with the probing frequencies have been traced during the L-H-L cycle (in figure 3, see movement in time of the location of the measurements).The mapping was done by means of a ray-tracing code [28] with the density profiles obtained by synchronizing and conditionally averaging the of the electron density from the lithium beam emission spectroscopy diagnostic [29].The radial uncertainty in the density profile derived from the Li beam measurements is approximately 3 mm within the specified region.This uncertainty encompasses the effects of both the radial integration of the Li beam measurement channel and the finite lifetime of the Li2p excited state.The n e profile temporal resolution is the result of the binning the raw data, which is originally sampled at 1 microsecond intervals, and has been set to 200 µs to obtain a relatively accurate emission profile for the reconstruction of electron density.As for the equilibrium reconstruction, it is based on a pressure-constrained equilibrium with a time resolution of 100 microseconds [30].We do not expect significant changes on shorter time scales as these are prevented by the passive stabilizing loop structure present in AUG.
The synchronized DR data in figure 3 are binned to an equivalent temporal resolution of 10 µs which is the horizontal extension of the pixels, while the vertical one is the radial resolution from the ray-tracing code.Note that the turbulence level measured by DR for a certain frequency A DR is normalized to its mean value ⟨A DR ⟩ before the L-H transition (t ∈ [−0.5, 0] ms) to emphasize relative changes and to take into account the variation of the launched microwave power with the probing frequency.Both O-mode and X-mode channels show a localized initial turbulence decrease at ρ pol ≈ 0.98 at the L-H transition which extends towards the last close flux surface and the plasma center within few microseconds.To our knowledge, this is the first time that the L-H transition could be radially localized with this accuracy.
To determine at which E × B shear layer the initial turbulence reduction is triggered, the E × B velocity right before the transition needs to be determined.This can be done directly from the DR data.Thus uncertainties in the equilibrium reconstruction and in the relative alignment of different diagnostics are avoided.In principle, to localize the initial turbulence relative to the v E×B shear layers, it is not necessary to map the DR signals on ρ pol since we could just look at the probing frequencies.This is of crucial importance because we want to detect a phenomenon on the 1mm scale and the usual uncertainties of the equilibrium reconstruction are in the range of millimeters.The measurements are nevertheless shown mapped to help the reader understand the analysis method.Figure 4 shows the v E×B profiles from the X-mode (red) and O-mode (blue) channels, evaluated within the last 0.5 ms before the L-H transition.The v E×B minimum is roughly consistent with previous studies using the DR diagnostic [31].The absolute values are lower than the CXRS measurements in [32] while the position and the values of the gradients are compatible.The position of the initial turbulence suppression, i.e. ρ pol,shear ≈ 0.98 (see figure 3), is indicated by the black vertical line and it is clearly located within the inner shear layer for both X-and O-mode.

Conclusion and outlook
To conclude, we developed a new method to localize the L-H transition based on DR and on a plasma scenario with repetitive L-H-L dithers.The high statistical significance, combined with the high temporal and radial resolution allowed us to answer the long-standing question on a possible dominant shear layer in the L-H transition.In this Letter, we provide the evidence that the turbulence, in the form of density fluctuations, suppression at the L-H transition is initiated at inner E × B shear layer.Efforts in modeling and understanding the L-H transition shall therefore focus on the behavior of the inner E × B shear, or more in general, in reproducing this feature of the L-H transition phenomenology.Finally, the simplicity of the method to localize the L-H transition proposed in this Letter makes it well applicable to any fusion plasma device equipped with DR, allowing a direct comparison to the results shown here.
As an outlook, the newly installed Comb-Reflectometry at ASDEX Upgrade will offer the possibility to measure simultaneously at several different sampling frequencies providing time resolved A DR profiles without the need of repetitive L-H transitions [33].This will open the possibility to investigate many different scenarios and to test single step transitions against repetitive L-H-L dithers.

Figure 2 .
Figure 2. Synchronization procedure: (a) define a reference L-H transition (red) using the Ḃθ signal; calculate the running correlation (b) and set an acceptance threshold (in this case 0.8); use the maximum of the correlation for every L-H transition (in red in (b)) as synchronization time-point.Figure (c) shows the synchronized Ḃθ over 150 L-H dithers.

Figure 3 .
Figure 3. Synchronized turbulence level A DR normalized to the pre-L-H during an L-H-L transition from (a) X-mode DR and (b) O-mode DR.High to low turbulence levels are color coded from red to blue.The dashed horizontal line indicate roughly the initial turbulence suppression position and the vertical line the L-H transition time point.

Figure 4 .
Figure 4. Synchronized v E×B profiles over 150 L-H dithers, right before the L-H transition (t − t LH ∈ [−0.5, 0.0] ms): X-mode DR (red) and O-mode DR (blue).The vertical line indicates the radial position of the initial turbulence suppression.