Investigation of the effect of divertor geometry on the L-H

transition using reflectometry diagnostics

Luıs Manuel Cerdeira Gilluis.gil@tecnico.ulisboa.pt

Instituto Superior Tecnico, Lisboa, Portugal

October 2015

Abstract

The effect of divertor geometry on the L-H transition at ASDEX Upgrade has been investigated,revealing that the power threshold to access H-mode is inversely correlated to the magnetic X-pointheight at high density. Microwave reflectometry diagnostics were used to measure edge electron densityprofiles and fluctuations across the L-H transition in order to improve the physics understanding of thephenomenon. A steepening of the edge density gradients, a reduction of low frequency fluctuations andthe appearance of a quasi-coherent mode were observed following the L-H transition. A fluctuationincrease at high frequencies was also found, being consistent with turbulence suppression by shearedflow. The dependence of the L-H power threshold on the divertor configuration may be partly relatedto divertor detachment, which is deduced from the observation of a high field side high density front.Density gradients before the transition were found to be identical, so new experiments must be conductedto evaluate the importance of other key quantities, such as the ion temperature.Keywords: Nuclear fusion, L-H transition, Power threshold, Divertor, Microwave reflectometry

1. Introduction

In the absence of instabilities, the confinement ofa tokamak plasma is determined by Coulomb col-lisions and a theory for the transport of particlesand energy which would occur under these circum-stances has been developed [1]. Unfortunately, thereal plasma losses often exceed the calculated valuesby an order of magnitude or more, due to turbulencedriven by instabilities [2], making the achievementof high temperatures and pressures required for adesirable fusion reactor very difficult.

It was found, however, that under certain condi-tions there is a discontinuous improvement in con-finement as the heating power is increased [3]. Theregime of higher confinement is called the H-modeand the previous lower level is called the L-mode.The H-mode has been responsible for important ac-complishments in the quest for fusion energy [4], butthe physics of the L-H transition is not yet fully un-derstood, despite numerous proposed theories [5].

One important aspect of the H-mode is that theconfinement improvement is caused by a region ofreduced transport at the edge of the plasma [6]. Theappearance of this edge transport barrier is linkedto the development of a radial electric field well [7],which is believed to decorrelate turbulent eddies bysheared E × B flow [8, 9]. However, the origin of

the edge radial electric field remains a current topicof investigation.

The critical requirement to access H-mode in a fu-sion plasma is the application of a sufficiently highheating power, known as the L-H power thresh-old. Because auxiliary heating systems are expen-sive and constitute a technological challenge for fu-ture large scale experiments, such as ITER, reliablypredicting and controlling the power threshold isessential for the development of high performancefusion devices. To take into account transient ef-fects, it is defined as the loss power to the plasmaboundary at the L-H transition [10], given by

PLH = Pohm + Pheat −dW

dt, (1)

where Pohm is the ohmic power, Pheat is the ab-sorbed auxiliary heating power, and dW/dt is therate of change of the stored plasma energy. Theradiated power from the bulk plasma may also besubtracted in the definition, as the net heat powerloss across the separatrix is more likely to be the rel-evant global physics parameter to characterize theH-mode threshold [11].

A widely used law for the power threshold, uponwhich current extrapolations for ITER are based,is the 2008 ITPA multi-machine scaling [10], which

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for deuterium is given by

PLH = 0.0488ne0.717BT

0.803 S0.941 , (2)

where PLH is the power threshold in MW withoutsubtracting radiation losses, ne is the line-averageddensity in 1020 m=3, BT is the magnetic field in T,and S the plasma surface area in m2. While it is wellknown that the power threshold strongly dependson these quantities, there is a considerable scatteraround the scaling law, which is caused by unin-cluded hidden parameters, such as divertor config-uration, triangularity and X-point position [12].

Studies at JET [11, 12], DIII-D [13] and MAST[14] have shown that the position of the X-pointcan vary the power threshold by up to a factor of2 and may therefore have a large impact on futuredevices. These studies have demonstrated a sig-nificant decrease of the L-H power threshold withreduced X-point height. However, experiments atAlcator C-mod have shown the inverse dependence[15]. The involved physics in not fully understoodbecause these geometric effects modify the diver-tor neutral recycling, plasma parameters around theX-point, pumping efficiency, scrape-off layer (SOL)flows and the aspects related with atomic physicsare complex and may be relevant.

The L-H transition of the ASDEX Upgrade(AUG) tokamak is studied in this work using mainlyreflectometry diagnostics, with focus on the effect ofdivertor geometry on the L-H power threshold. Thenext section briefly describes the machine and itsmain diagnostics, with emphasis on microwave re-flectometry. Section 3 presents the developed meth-ods of reflectometry data calibration and analysis toprovide useful information about the plasma. Theexperiment conducted at AUG and its results re-garding the L-H power threshold and evolution ofdensity profiles and fluctuations are discussed insection 4, followed by a concluding section.

2. Experimental apparatus

ASDEX Upgrade is a divertor tokamak of majorradius R = 1.6 m and minor radii a = 0.5/0.8 mwhose overall goal is to prepare the physics base forITER. It is equipped with neutral beam injection(NBI), ion cyclotron resonance heating (ICRH) andelectron cyclotron resonance heating (ECRH). AUGpossesses an extensive set of diagnostics for machineoperation and scientific investigation. Some of thesystems used in this work were the DCN interferom-eter to measure the line-averaged electron densityalong lines of sight through the core and edge of theplasma, Thomson scattering to measure the overallevolution of the electron temperature in the plasmacore and edge, Dα radiation and divertor currentsat the inner and outer divertor regions to monitor

edge localized modes (ELMs) and help the identifi-cation of L-H transitions. Unfortunately, the chargeexchange diagnostic could not be used to provideedge radial electric field and ion temperature databecause the boron spectrum was perturbed by resid-ual nitrogen.

Microwave reflectometry has been used as themain diagnostic for measurement of edge electrondensity profiles and fluctuations. Reflectometryhas a modest requirement for plasma accessibilityand the capacity of conveying microwaves to a re-mote location, making it an ideal method for a fu-sion reactor, finding extensive use in tokamak re-search [16, 17]. Its operating principle is the follow-ing: microwave radiation with a given frequency islaunched into the plasma along the density gradientand reflected at the layer where a critical electrondensity is achieved. The reflected wave is receivedat an antenna and phase changes due to propa-gation and reflection in the plasma are measuredby mixing the reflected radiation with a referencebeam. The relative positions of the density layersin the density profile are determined by making themeasurement with a range of different probing fre-quencies. Alternatively, movements of a single layercan be studied by using a fixed probing frequency.

The current reflectometry system for density pro-file measurement at AUG [18] is based on O-mode frequency-modulated continuous-wave (FM-CW) probing. It has the unique capability of si-multaneously measuring the high field side (HFS)and low field side (LFS) of the machine, allow-ing an extensive range of comparative studies thatotherwise would be impossible to make. In theHFS, four channels are used to cover the densityrange 0.3–6× 1019 m=3, corresponding to probingfrequencies in the range 17–70 GHz, divided in thefrequency bands K(17–25 GHz), Ka(25–37 GHz),Q(37–50 GHz) and V(50–70 GHz). In the LFS, anextra channel with the W frequency band (70–100 GHz) complements these four to cover densitiesup to 1.24× 1020 m=3. The reflectometer was builtso that the plasma is probed in the equatorial plane,close to the magnetic axis. An automatic procedurehas been developed over the years to minimize pos-sible errors in the reconstruction of density profiles[19], resulting in a time resolution of 1 ms.

The AUG reflectometer for fluctuation measure-ments [20] consists of Q band (33–49.2 GHz) and Vband (49.4–72 GHz) channels with heterodyne I/Qdetection and 2 MHz sampling frequency. The sys-tem is designed to allow a fast frequency change foran arbitrary frequency step and therefore is calledfast frequency hopping reflectometer . Its antennasare located inside the tokamak vessel to minimizespurious signals, as shown in figure 1. The lines ofsight are aligned to be perpendicular to the density

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cutoff layers in the plasma edge region.

Figure 1: Cross-sectional view of AUG showingthe antennas of the hopping reflectometry system.The FM-CW antennas (not shown) are located at aheight similar to the FLQ antenna but at differenttoroidal positions.

The heterodyne system allows separate measure-ments of amplitude and phase through the use of anI/Q detector. The reference and reflected signal aredirectly mixed and filtered to obtain the in-phase (I)signal. For the quadrature (Q) signal, the referenceis 90◦ phase shifted by a delay line prior to mix-ing and filtering. The output of the I/Q detector istherefore given by

I = A1A2 cos (φ) , (3a)

Q = A1A2 sin (φ) . (3b)

where A1 and A2 are the amplitude of the referenceand reflected signal and φ is the phase difference be-tween them. The reflectometry amplitude, A, andphase, φ, are then computed with the expressions

A =√I2 +Q2 , (4a)

φ = atan2 (Q, I) , (4b)

where atan2 is the two-argument inverse tangentfunction with values from −π to π.

3. Methods of data analysis and validation

The outputs of the AUG microwave reflectometrysystems need post processing mainly for calibration

purposes, mitigation of deleterious turbulence ef-fects and data interpretation, in order to providerobust and useful information about the plasma.

The FM-CW data undergoes a sophisticated pro-cedure for the reconstruction of density profiles, butit is far from perfect in the presence of turbulence orfast events. To reduce the nonphysical features inthe profiles due to these causes, several consecutiveprofiles are averaged. This is a trade-off betweentime resolution and accuracy, such that averaging 5to 10 profiles is usually worthwhile.

The hopping reflectometer outputs I/Q data withno calibration, needing post processing to provideinformation about density fluctuations. I and Qoffsets must be removed to separate reflectometryphase and amplitude, so an automatic algorithmbased on iterative circular fitting for determiningthe offsets was developed. Its overall scheme issummed up in the following steps:

1. Average the 0.1 % lowest and highest I and Qvalues for an initial estimate of the center andradius of the circle;

2. Choose all points whose distance from the cen-ter is above 90 % of the estimated radius;

3. Fit a circle to the chosen points with an unnor-malized orthogonal distance regression to getimproved estimates of the center and radius;

4. Repeat from step 2 using the improved esti-mates until the variation of the center coordi-nates is less than 1 %;

5. The coordinates of the circle center obtainedwith the last fit are the I and Q offsets.

This is an effective and robust way of determin-ing the I/Q offsets, as can be seen from the finalfit example of figure 2. The method works in caseswhere simple averages are not able to correctly de-termine the offsets and also in cases where a simpleaverage or a single fit would suffice.

Figure 2: Final circle fit to determine I/Q offsets.

The offset algorithm was applied to each probingfrequency step of the shots analyzed in this work.It was found that there are no drifts in the offsets,

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which are approximately constant for all frequen-cies. The average I and Q offsets were computedand subtracted from the signals, allowing the sep-aration of reflectometry amplitude and phase. Theunconstrained unwrapped phase was computed byadding ±2π to all phase values after a phase differ-ence between successive samples exceeded ∓π.

There are 1D analytical models relating the re-flectometry phase to density fluctuations, valid forlow density fluctuation levels and long wavelengths[17, 21, 22]. However, the phase of reflectometrysignals alone rarely contains easily available infor-mation about density fluctuations. Figure 3 showsan example of the unwrapped phase time evolutionof a single hopping frequency step. There are threephase jumps of 2π which are not linearly related todensity fluctuations. At first one may think this isjust a problem of the unwrapping algorithm, pos-sibly due to a low sampling frequency. Howeverthis has been investigated and is not the case. Infact, phase jumps have been reported in many re-flectometer systems [22–25] and reproduced in full-wave simulations [26] for high fluctuation levels.

Figure 3: Unwrapped phase of a frequency step.

Often the unwrapped phase presents a continu-ously increasing behavior which is inconsistent witha realistic motion of the reflecting layer. This phasedrift or runaway has been observed in many de-vices [24, 27, 28]. The required condition for phasejumps and drifts is the existence of turbulence withlarge amplitude, which originates interference ef-fects due to 2D density fluctuations in the cutofflayer [23, 28].

For the shots analyzed in this work, phase jumpsand drifts are an almost ubiquitous phenomenon, soit is important to study the validity of reflectometrysignals in high fluctuation regimes. Two extremeexamples were chosen as a basis for this study. Oneis a frequency step without phase jumps from anH-mode with low fluctuation level whose I/Q plotis shown in figure 4a. The other is a frequency stepwith strong phase runaway from an L-mode withhigh fluctuation level whose I/Q plot is shown in

figure 4b.

(a) low fluctuation level

(b) high fluctuation level

Figure 4: I/Q plots of frequency steps with low andhigh fluctuation levels.

A statistical analysis of these examples showedthat the low fluctuation level phase distribution ispeaked, while the high fluctuation level distribu-tion is almost uniform. The amplitude distributionis also very different, being almost Gaussian in thefirst case, but becoming very skewed in the highfluctuation regime due to a heavy tail at low am-plitudes. Similar results have been obtained in full-wave simulations coupled to turbulence codes [26].

Power spectra of the unwrapped phase, highpassfiltered at 5 kHz, and wrapped phase are shown infigure 5b. In the low fluctuation level case, the spec-tra are identical up to 200 kHz, above which thereare wrapping artifacts. For high fluctuation levels,they are very different. The unwrapped phase spec-trum is approximately inversely proportional to thesquared frequency, while the wrapped phase spec-trum is much flatter. This frequency dependenceof the unwrapped phase has been observed in manyreflectometer systems in cases of high turbulence[16] and also in full wave simulations, bearing nosimilarity with the turbulence spectrum generatedby the used turbulence codes [26].

Since the reflectometry phase alone is not ade-quate to describe density fluctuations in a highly

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(a) low fluctuation level

(b) high fluctuation level

Figure 5: In-phase, amplitude, wrapped phaseand filtered unwrapped phase power spectra of fre-quency steps with low and high fluctuation levels.

turbulent plasma, power spectra of in-phase andamplitude signals are also shown in figure 5. Inboth fluctuation regimes the amplitude and in-phase power spectra are similar up to 200 kHz, afterwhich the in-phase spectrum decays more rapidlywith frequency. In the case of low fluctuation level,the in-phase spectrum is similar to the phase spec-tra, but in the case of high fluctuations levels theyare very different. This behavior has also been ob-served in the CCT tokamak [29]. The wrappedphase spectrum is similar to the amplitude spec-trum for high fluctuation. It was also found thatthe coherence between reflectometry amplitude andphase signals is generally very low, which meansthat they are not linearly related. The observedsimilarities and differences between phase, ampli-tude and in-phase signals indicate that amplitude infact contains important information about densityfluctuations in the plasma and must not be ignored.

One way of combining amplitude and phase sig-nals is to define the complex signal Aejφ or equiva-lently I + jQ. Besides containing information fromboth quantities, the complex signal also has the ad-vantage that no phase unwrap is needed and itspower spectrum can be used to identify Doppler

shifts. However, its interpretation is not as intuitiveas that of phase signals and its relation to densityfluctuations is not well investigated, especially withregard to full-wave simulations, so the informationwhich can be retrieved from the complex signal is atthe moment mostly qualitative. Double-sided com-plex power spectra and spectrograms are used in therest of this work as the main method to study edgeelectron density fluctuations from fixed frequencyhopping reflectometry data.

4. Evolution of density profiles and fluctua-tions

4.1. Experiment

To investigate the influence of the X-point positionon the L-H transition, an experiment was performedat AUG in 2014 with deuterium plasmas, lower sin-gle null configuration and favorable ion ∇B drifttowards the X-point. Figure 6 shows the magneticconfigurations used in the experiment, which will behereafter referred to as low, mid and high X-pointconfigurations, according to their relative X-pointheights. Besides having different distances betweenX-point and strike points, it must be noted that theouter strike point of the high X-point configurationis located on the vertical target, contrary to the lowand mid cases, whose outer strike points are locatedon the horizontal target. This affects the pumpingcapability and may also have an impact on the L-Htransition dynamics [30]. Several geometric param-eters are also inevitably changed, such as upper andlower triangularity, δU and δL, elongation, κ, andarea of the last closed flux surface, S. Table 1 showsthe main geometric parameters of the magnetic con-figurations before the L-H transition. There is noknown influence of κ on the L-H transition and itdoes not vary dramatically, so it should not affectthis experiment. δU is very low on all configurationsso its effect should also be negligible. δL is reducedin the high X-point configuration and may influencethe L-H transition [11]. Finally, S also varies, butits effect on the power threshold can be removed bynormalization with the ITPA scaling law.

Table 1: Main geometric parameters of the mag-netic configurations before the L-H transition.

Shot X-point κ δU δL S (m2)

30533 low 1.60 0.028 0.43 43.730534 mid 1.59 0.088 0.44 44.730545 high 1.54 0.068 0.39 41.7

Due to the limited number of available shots, thestrategy for the experiment was to have two L-Htransitions per discharge, the first one at a low den-sity and the second one at a higher density. This

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Figure 6: Poloidal cross section of AUG showingthe magnetic configurations of the experiment.

was achieved by puffing a large amount of gas be-tween the two transitions. All shots were conductedat toroidal magnetic field BT = −2.4 T and plasmacurrent IP = 0.83 MA. At these conditions the L-Hpower threshold is expected to lie between 0.7 MWand 1.8 MW, so 0.3 MW of ECRH followed by anNBI power ramp up to 3.5 MW was applied in eachdensity step. Ideally the power ramp would be aslow and continuously increasing function of time,but, due to the discrete nature of the NBI powersteps, the power ramp had to be achieved by mod-ulating the NBI sources and pulse widths.

4.2. Identification of transitions and power thresh-old

The typical time evolution of the main parametersused to identify the L-H transition in shown in fig-ure 7. The time derivative of the line-averagedelectron density suffers two significant increaseswhich correspond to the transitions from L-modeto dithering H-mode and then to full H-mode, here-after called L-D and D-H transitions, respectively.The outer and inner Dα and divertor current sig-nals decrease at both transitions and exhibit ELMsafter the D-H transition. The electron temperaturedoes not show a sudden increase in either transi-tion, just slowly increasing after the L-D transitionin the edge and after the D-H transition in the core.

Not all transitions are as clear as the one justshown one and the Dα and divertor current sig-

Figure 7: Time evolution of the main parametersused to identify the L-H transition. The transitiontime intervals are delimited by vertical dashed lines.

nals often do not show easily detectable decreases atthe transitions, especially when their values are al-ready low in L-mode. Therefore the following crite-ria were used to systematically identify the L-D andD-H transitions of the experiment: there must bean increase in the time derivative of the density ateach transition; between the transitions there mustbe fluctuations with few kHz in the Dα or divertorcurrent which are reduced at the D-H transition,possibly with the emergence of ELMs; if there is asingle density increase, only a single L-H transitionis considered. The L-H power threshold was calcu-lated with equation 1 after smoothing the absorbedNBI power and plasma energy signals to account forthe slow energy transfer from the NBI to the bulkplasma. A boxcar window of 40 ms was used basedon simple estimations of the typical fast ion slowingdown time. Since the absorbed heating power needstime to reach the plasma edge, the power thresholdwas averaged over 60 ms to take into account theenergy transport. This corresponds to about halfof the energy confinement time and ensures thatthe maximum power loss is always included in theaveraging procedure. The standard deviation of thepower loss in this period was taken as an estimateof the uncertainty in the power threshold.

The power threshold for the D-H transition as afunction of line-averaged electron density is shownin the top plot of figure 8. At low density thereis only a small difference between the divertor con-figurations but the transitions at high density havevery different power thresholds. The low X-pointconfiguration has the highest power threshold, fol-

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lowed by the mid X-point configuration. The highX-point configuration appears to be insensitive todensity variations, having the lowest power thresh-old at high density. To allow the comparison oftransitions at different densities, the power thresh-olds were normalized to the ITPA scaling (eq. 2)and are shown in the bottom plot of figure 8. Thisscaling is only valid for the high density branch ofthe power threshold and does not account for therollover usually observed at low densities. There-fore the density region below the typical minimizingdensity for the power threshold at AUG is markedas yellow and the normalization of points insidethis region is in principle invalid. The high densitypoints of the three configurations have significantlydifferent power thresholds.

Figure 8: D-H power threshold for all divertorconfigurations. The bottom plot shows the powerthreshold normalized to the ITPA scaling.

It has been shown that there is an increase of theL-H power threshold with X-point height at highdensity in AUG for the divertor configurations ofthis experiment. This result is similar to the oneobtained at Alcator C-Mod [15] if it is interpreted interms of outer divertor leg length instead of X-pointheight. However, this trend is contrary to what isobserved in JET [12], DIII-D [13] and MAST [14]with both interpretations, since in these machinesthere a clear increase in power threshold with X-point height and outer divertor leg length, whichare covariant in the experiments.

4.3. L-H transition

The typical evolution of reflectometry density pro-files for a low density transition is shown in figure 9.The LFS SOL is identical at the different phases ofthe discharge, having a shoulder and a steep gradi-ent around 2.155 m, due to the shadowing effect of a

limiter. During the ohmic phase, there are no othersharp gradients and the plasma density increasestowards the core. With the application of ECRH,a transport barrier is formed just inside the separa-trix, causing a higher core density, but the gradientsoutside this region remain unchanged. NBI heatingdoes not alter the profile noticeably until the L-Dtransition, after which the transport barrier gradi-ent increases, leading to a clear edge pedestal andincrease in core density. The fully developed H-mode profiles between ELMs have a much steeperedge gradient and higher densities from the trans-port barrier inwards. The L-H transition thus ap-pears to be a phenomenon which directly affectsonly a small edge region inside the separatrix, buthas a significant impact on the whole plasma. TheLFS and HFS behaviors are similar, with the differ-ence that the separatrix position at the HFS is nottightly controlled. It must be noted that for highdensity transitions the overall evolution of densityprofiles is the same, but there is a clear pedestaleven in L-mode and the difference between L-modeand H-mode profiles is not as marked as in the lowdensity transitions.

Figure 9: Typical evolution of reflectometry densityprofiles for a low density transition. The separatrixis indicated by vertical dashed lines.

Edge density fluctuations were studied with thefast frequency hopping reflectometer and the typ-ical double-sided complex reflectometry spectro-gram across a low density L-H transition is shown infigure 10. This is not a continuous spectrogram, butinstead a sequence of Welch periodograms of 6 msof continuous data from the same probing frequencyseparated by 64 ms of void time periods. During theohmic phase, which lasts until 1.8 s, the spectrum issymmetric and the power decreases with frequency.After the application of ECRH heating at 1.8 s, thespectrum widens and there is a power increase athigh frequencies. After the L-D transition, which istriggered by the application of NBI heating, there isa slight power decrease for frequencies below 50 kHzand a wide peak at about 70 kHz begins to develop.

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With the D-H transition, there is a further powerreduction at low frequencies, the peak is intensified,its frequency increases and its harmonics becomemore evident. This is the quasi-coherent mode of-ten observed in H-mode, which is associated withsteep edge gradients and is thought to play a keyrole in limiting the pedestal gradient [31].

Figure 10: Hopping reflectometry complex spectro-gram across a low density L-H transition. The tran-sition time intervals are indicated by dashed lines.

Discrete reflectometry complex spectra of severalphases of a low density transition are shown in fig-ure 11. The ohmic L-mode spectral power decreaseswith frequency, as expected from a spectrum of tur-bulence. With the application of ECRH the powerincreases for all frequencies and the spectrum be-comes wider. This is also expected since ECRHincreases plasma density and temperature, therebyleading to stronger turbulent fluctuations. Thedithering H-mode spectrum exhibits higher powerfor frequencies above 50 kHz and a slight power re-duction in frequencies below 50 kHz. The quasi-coherent mode is present in this spectrum, with apeak frequency of about 70 kHz and a total withof about 60 kHz. In the fully developed H-modespectrum between ELMs, the quasi-coherent modebecomes more intense, its peak frequency increasesto about 90 kHz and its harmonics become moreevident. There is a further reduction in low fre-quency power, along with an increase at high fre-quencies, above 160 kHz. To explain these results, itis noted that cross-field turbulent transport is cor-related with the radial size of turbulent structuresand there is a general tendency in physics for largestructures to associated with low frequencies andvice versa. Plasma turbulent structures seem toobey this rule [32, 33] and it is known that low fre-quencies are the most relevant for transport [32, 34].Therefore a reduction of density fluctuations in thelow frequency range, as suggested by reflectometry,may be sufficient for a confinement improvement inspite of the fluctuation increase at high frequen-cies. In fact, this observation is consistent with

the breaking up of large turbulent structures intosmaller ones, as suggested by the theory of reducedtransport due to decorrelation of turbulent eddiesby radially sheared E ×B flow [8].

Figure 11: Reflectometry complex spectra of differ-ent phases of a low density transition. The totalpower of each spectrum in arbitrary units is indi-cated in the legend after the time interval.

The total power of each complex spectrum in ar-bitrary units is also indicated in the plot legend offigure 11 after each time interval. The ECRH L-mode spectrum has a higher power than the ohmicspectrum and a lower power than the dithering H-mode spectrum. For some transitions, however, thetotal power of the dithering H-mode spectrum islower than the L-mode one. The total power of thefully developed H-mode spectrum between ELMsis lower than the dithering H-mode and ERCH L-mode powers, as expected. This is what usuallyhappens, but a few exceptions were encountered inthe transitions of this experiment and the temporalevolution of the total power presents large fluctua-tions. This may be due to the often overwhelmingcontribution of very low frequencies, below 5 kHz. Itshould also be noted that part of the difference be-tween L-mode and H-mode complex spectra may becaused by different density gradients, as simple 1Dreflectometry models predict a dependence of thephase fluctuations on the square root of the densitygradient length scale in case of low fluctuation levels[21]. For these reasons, the total power of complexreflectometry spectra may not be the best quantityto characterize overall density fluctuation levels andthe subject needs further investigation.

4.4. Influence of divertor configuration

Average electron density profiles before each L-D transition for the three divertor geometries areshown in figure 12. The low and high X-point con-figurations have very similar LFS and HFS profiles,while the mid X-point configuration has a broaderSOL at the LFS and a very different profile at the

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HFS. There is a clear high density region in the SOLwhich ends abruptly at 1.55 m due to the HFS lim-iter. The development of a HFS high density frontassociated with the inner divertor detachment hasbeen reported at AUG [35] and it has recently beenshown that there is a relation between the midplanedensity profiles and divertor detachment [36]. It hasalso been suggested that the inner divertor detach-ment state plays an important role in the L-H tran-sition, possibly facilitating access to H-mode due toa higher SOL radial electric field [37]. This mayexplain the observed difference in power thresholdbetween the low and mid X-point configurations,since the mid X-point configuration is closer to theinner divertor and HFS wall than the low X-pointconfiguration. This could ease the detachment ofthe inner divertor at high density, contributing tothe lower power threshold observed in the mid X-point configuration. The even lower power thresh-old of the high X-point case cannot, however, be ex-plained by this hypothesis, since this configurationis farther from the divertor than the other two. Theprofile similarity of the low and high X-point con-figurations before the transition excludes the pos-sibility of different critical density gradients to ex-plain the power threshold dependence. This depen-dence is not a simple consequence of different par-ticle confinement properties either, as it was foundthat the density profiles are also very similar for thesame heating power. Therefore there must be othereffects in play, possibly related to plasma-wall in-teraction and the ion temperature gradient, as hasbeen suggested by other experiments [38].

Figure 12: Reflectometry density profiles of LFSand HFS before the L-D transition for different con-figurations. The separatrix is indicated by verticaldashed lines.

A comparison of L-mode and H-mode complexspectra between the low and high X-point config-urations at a reflectometry probing frequency of36 GHz is shown in figure 13. The L-mode spec-tra are both asymmetric, but skewed towards op-posite directions. This is consistent with antenna

misalignment, since the flux surfaces of the twoconfigurations are tilted in opposite directions withrespect to the antenna. The H-mode spectrum ofthe high X-point configuration exhibits a power re-duction at low frequencies along with the 60 kHzwide quasi-coherent mode with 90 kHz peak fre-quency. However, the quasi-coherent mode is ab-sent in the low X-point spectrum, which has just aslight power reduction in the low frequency range.The quasi-coherent mode has been associated withedge temperature gradients [31], which may dependon the divertor configuration, but cannot be mea-sured with reflectometry. The reduction in low fre-quency fluctuations is usually more evident whenthe quasi-coherent mode is present, but it is notclear if this reduction is affected by the quasi-coherent mode or if it just a consequence of anincreased radial electric field associated with steepedge gradients, which also happen to be the drivingmechanism of the quasi-coherent mode.

Figure 13: Reflectometry complex spectra of L-mode and H-mode for low and high X-point con-figurations.

5. Conclusions and future work

An automatic I/Q calibration algorithm has beendeveloped, revealing that reflectometry signals suf-fer from numerous phase jumps and considerablephase drift for high fluctuation levels. In such casesthe reflectometry phase is not linearly related todensity fluctuations and should be used togetherwith the amplitude signal to best infer the charac-teristics of turbulence. The double-sided complexspectrum of reflectometry signals has been proposedand tested as a method of combining amplitude andphase measurements. Qualitatively, it is sensitiveto the plasma conditions, but full-wave simulationscoupled to turbulence codes and comparison withother diagnostics are needed to unlock its full po-tential and allow more quantitative measurementsof density fluctuations with high turbulence levels.

A set of criteria for identifying transitions to

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dithering H-mode and to full H-mode on AUG hasbeen proposed. Robust methods were used to com-pute the L-H power threshold, revealing that it issensitive to the divertor configuration only at highdensities, exhibiting an inverse correlation with X-point height. Although this is consistent with re-sults from C-Mod, the behavior is contrary to whatis observed in most machines and cannot be at-tributed to overall plasma shaping parameters, soit should be related to more subtle edge physics.

The evolution of edge density profiles and fluc-tuations across the L-H transition has been stud-ied with reflectometry. The profiles were found tosteepen during the H-mode, leading to higher coredensity, which is expected. H-mode reflectometryspectra revealed a quasi-coherent mode that hasbeen observed in other machines, where it is be-lieved to play a role in limiting the pedestal gradi-ents. The fluctuations after the L-H transition werefound to decrease at low frequencies and increaseat high frequencies. This may indicate turbulencemodification at different scales, as predicted by thetheory of turbulence suppression due to breakingup of large eddies into smaller ones by sheared flow.Experimental evidence of this phenomenon is lim-ited and valuable, as it contributes to confirmingthe theory and improving knowledge on the subject.Reflectometry may therefore play an important rolein understanding the L-H transition.

A comparison of density profiles at the L-H tran-sition for different divertor geometries revealed thatthe mid X-point configuration, which is closer tothe inner divertor and HFS wall, has a high densityfront in the HFS. This is associated with divertordetachment, which may influence the L-H transi-tion, but it cannot explain the significant differencein power threshold between the low and high X-point configurations, where no high density front isobserved. Nevertheless, the relation between diver-tor detachment and the L-H transition in this exper-iment should be further investigated by analyzingdata from bolometry and Langmuir probes at thedivertor. No significant differences in density gradi-ents were found between the low and high X-pointconfigurations, indicating that the ion temperaturegradient may be the more relevant parameter forthe L-H transition in these cases. New experimentsmust be conducted to evaluate the importance ofthis quantity and other key measurements not avail-able in this experiment, such as the electric fieldand plasma flow. Hopping reflectometry revealedthat the existence of the quasi-coherent mode de-pends on the divertor geometry, although this de-pendence may be a consequence of different tem-perature gradients. The reduction in low frequencyfluctuations seen by reflectometry is more evidentwhen the quasi-coherent mode is present, but this

may be due to a stronger radial electric field asso-ciated with steep edge gradients, which also drivethe quasi-coherent mode. Future experiments per-formed with adequate hopping settings may allowthe measurement of the radial amplitude profile ofthe quasi-coherent mode and the investigation of itsrelation to edge gradients and fluctuations.

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