Dynamic edge transport investigations at ASDEX Upgrade using gas puff modulation

Gas puff modulation experiments are performed at ASDEX Upgrade in L-mode, EDA H-mode and quasi-continuous exhaust discharges. Plasma density and temperatures are measured and their temporal development is analyzed simultaneously, revealing that both heat and particle transport are strongly influenced by the modulation. As a consequence, the particle transport coefficients are underdetermined. In the transport modelling, the pedestal cannot be treated as a single region, but the pedestal foot must be allowed to increase its transport with gas puff modulation independently. The analysis of the temporal behaviours of the heat and particle diffusivities shows that they are strongly correlated. Considering the heat diffusivity as a proxy for the particle diffusivity, allows interpretation of the density evolution: a pinch is not required for any of the discharges. An analysis with the gyrokinetic turbulence code GENE identifies dominant instabilities and reproduces several experimentally found trends. Despite all uncertainties concerning particle transport, one can expect a future reactor featuring a weak edge density gradient even with purely diffusive transport.


Introduction
Transport in the pedestal region determines the edge profiles, together with sources and sinks. These profiles give the boundary condition for the core plasma and influence various a See Stroth et al 2022 (https://doi.org/10.1088/1741-4326/ac207f) for the ASDEX Upgrade Team. * Author to whom any correspondence should be addressed.
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. phenomena such as the L-H transition power [1] or the ELM stability [2]. The understanding of the transport processes is still lacking, especially for particle transport. Heat transport is considerably easier to quantify than particle transport: Besides the heat sources, which are usually known or directly measurable, only the geometry of the flux surfaces and the temperature and density profiles are necessary for obtaining the heat diffusivities χ e and χ i . For particle transport, there is the possibility for additional convective transport, making the determination of particle diffusivity D and convection velocity v from the measured profiles alone impossible. Furthermore, the particle source S e due to ionized neutrals is far less accurately determined than power sources. Dynamic plasma states offer additional insights into the transport behavior compared to the steady state. This is true for heat transport [3,4], where transient states show how transport changes with altered conditions, but also, and especially, for particle transport [5][6][7][8][9][10][11][12][13], where convective and diffusive transport contributions can, in principle, be separated.
In this work, transient states are caused by modulating the fuelling gas flux. The evolution of temperature and density profiles is measured and modelled simultaneously with the ASTRA transport code [14]. It is found that both heat and particle diffusivity react sensitively to fuelling, even on the short times scales considered in this publication. While presenting an additional complication for particle transport studies, several conclusions can be drawn regarding the transport behaviour at the pedestal top and the pedestal foot and the relative evolution of heat and particle transport.
The paper is structured as follows: In section 2, after a presentation of the experimental data, the analysis method using the ASTRA code is described. The results of the analysis are discussed in section 3. Section 4 compares the transport behavior of the experiment to corresponding GENE [15,16] simulations. Finally, before the conclusions, section 5 discusses the edge density profile of future reactors.
Parts of this work were published in the first author's PhD thesis [17] and presented at the 18th H-Mode Workshop in Princeton, USA 2022; and the 29th T&C and 40th PEP ITPA meetings in Cadarache, France 2022.

Experiments
All experiments were performed at the ASDEX Upgrade tokamak. The experimental setup is similar, or identical, to the one described previously [18]. The fuelling gas flux of 8 × 10 21 electrons per second is modulated using fast-acting invessel piezo valves, located at the low field side (LFS) [19] or high field side (HFS) [20] midplane. The valve is closed 22 ms after it was opened, and reopened 18 ms after it was closed. The period of the modulation is therefore 40 ms and the modulation frequency is 25 Hz. In some discharges additional, temporally constant fuelling from the lower divertor is employed.
Using the above described method, data for ten different cases was obtained and subsequently analyzed: • three L-mode plasmas at different densities • two quasi-continuous exhaust (QCE) [21,22] discharges, one fuelled from the HFS midplane and one from the LFS midplane • five (other) H-mode plasmas: one with low heating power, and four with different densities where the lowest density case features a quasicoherent mode and is classified as EDA H-mode [23] Table 1 gives the numbers, times and key parameters of all discharges. Note that the EDA H-mode features several ELMs, whose time intervals are removed from the analysis as they are for the other H-modes.
To improve the readability of the text and to avoid overloading the figures, we only discuss three representative discharges for three groups, in which the discharges show similar behavior and transport properties. The selected discharges are marked in gray in table 1. The time period of the L-mode discharge was selected to allow a direct comparison to the previous publication. All other time periods show a similar behaviour. The QCE discharges receive their name from the property of quasi-continuous exhaust, meaning those are discharge without type-I ELMs. The configuration is close to double-null and the separatrix density is high, a combination that allows the pedestal foot to become ballooning unstable [21,22,24]. The selected QCE discharge is the one with HFS fuelling, as it shows a much clearer response in the measured densities, probably because the SOL density shoulder, found in these discharges [25] on the LFS, is responsible for neutral screening. In the H-mode discharge, the time period that could be identified as EDA H-mode was chosen as representative for the other time periods, as there are only very few ELMs, while its edge transport behaves very similarly. Note that the investigated H-mode is heated with rather low power. With higher heating power the ELM frequency increases and the experimental data are not suitable for our analysis method. Figure 1 shows the equilibria of the selected discharges together with the lines of sight of the DCN interferometer. In our analysis we use the electron cyclotron emission (ECE) diagnostic (not shown in figure 1), situated at the outboard midplane, for electron temperature measurements, and a combination of the Lithium beam diagnostic and interferometry, which has 5 integration paths (see figure 1 for density measurements). The alignment of the diagnostics to the separatrix position of the IDE equilibrium [26] has been done using the usual procedure [27] that relies on the 2-point model for an estimate of the separatrix temperature and the edge Thomson scattering diagnostic that measures density and temperature in the same plasma volume. For all the discharges analysed, no shift was applied to the used diagnostics ECE, Lithium beam and DCN.
During the selected time periods all other plasma parameters are kept constant, so that the effect of the gas puff modulation can be investigated. Figure 2 shows the effect of gas puff modulation (gas puff 'on' is shaded in gray) on the electron temperature, where the ECE signal is averaged for 0.8 < ρ pol < 0.9, and on the H5 interferometer channel. The H5 interferometer channel is tangential to ρ pol = 0.88 for the L-mode and EDA H-mode cases and to ρ pol = 0.85 for the QCE case. It can clearly be seen that the individual gas puffs cause very reproducible effects and that the average absolute values of electron density and temperature stay constant during these phases. Figure 3 shows the temporal changes of the edge density, as measured by edge interferometry, for the three exemplary cases. The data are timesynchronized to the gas puff and averaged. In all cases, the  density rises after the valve is opened at t = 0. The strongest increase occurs for the QCE, where the density change climbs by 2.7 × 10 18 m −2 until the valve closes at 22 ms. The L-mode shows a similar behavior, albeit the total increase is less pronounced with 2.0 × 10 18 m −2 . For the EDA H-mode, the density does not drop as rapidly after the valve is closed, and the total increase is merely ≈1 × 10 18 m −2 . Figure 4 shows the reconstructed density profiles for the three cases, at a time when the valve has been closed for a comparably long time of 17 ms (black dashed lines) and when the valve has been open for 19 ms (red solid lines). When opening the valve, the separatrix density rises in L-mode (figure 4(a)) and EDA H-mode (figure 4(c)), and sinks in the QCE discharges. In the steep gradient region, the density increases slightly for the L-mode case, increases stronger for the EDA H-mode case, and sinks for the QCE case. In the outer core, at ρ pol = 0.90, the density in L-mode increases slightly, increases strongly in the QCE case, and remains unaltered in the EDA H-mode.

Temperature response.
Increasing the fuelling not only alters the density profile, but also cools the plasma. For each radius, a sine is fitted to the temperature evolution to obtain amplitude and phase of the perturbation The mean value χ e,0 , the absolute amplitude A and phase delay τ are determined by a least-square fit to the experimental data. The relative amplitude is defined as Because we talk about cold pulses and not heat pulses, the definition above would yield a delay τ = 20 ms if the plasma cools immediately after the valve opening. For temperatures we subtract 20 ms from τ to preserve the simple interpretation of τ as delay compared to the valve opening.   the maximum temperature difference is therefore twice the amplitude. Figure 5(b) shows the phase of the temperature change, where a phase of 0 would refer to a maximum cooling rate directly when the valve opens, and positive phases refer to a delayed cooling. The sine fits to the experimental data are shown as symbols, while the lines are fits of the amplitudes and phases used for the analysis. We only consider temperatures at and inside of ρ pol = 0.98 to avoid interpreting (ECE) measurements from regions with optically non-opaque plasma.
Considering the amplitude (figure 5(a)), one finds that the plasma cools the strongest in the QCE discharge, with an amplitude of ±15 eV between ρ pol = 0.70 and ρ pol = 0.98. In Lmode and EDA H-mode, T e reacts more weakly, with a maximal amplitude of 10 eV at ρ pol = 0.95 (L-mode) and ρ pol = 0.90 (EDA). The amplitude decays to 5 eV (L-mode) and 7 eV (EDA) at ρ pol = 0.70. The phase (figure 5(b)) shows that the plasma does not cool uniformly, but that the cooling propagates as cold pulse from the edge into the core. The QCE plasma reacts the quickest, with a phase delay compared to the valve of 4 ms at ρ pol = 0.98, growing to a delay of 12 ms at ρ pol = 0.70. The propagation speed is comparable for all three cases, with the L-mode being delayed ≈2 ms compared to the QCE case, and the EDA H-mode being delayed ≈4 ms compared to the QCE case.

ASTRA analysis
The presented experimental data is analyzed using the 1.5 dimensional transport code ASTRA [14] and the workflow described in detail previously [18]: The IDE equilibrium [28], the power sources, the separatrix density and the electron temperature are set to the evolving experimental values. Then, unknown parameters such as the particle source, diffusivity and convection are initialized at random values, and are fitted such that the experimental interferometry time traces are recovered. The recovered density profile and transport coefficients then allow interpreting the experiment. To judge the uncertainties of the reconstructed quantities, the fit is repeated several times with different initial values for the  fitted quantities. In our fitting procedure, only the electron temperatures are predetermined, the experimental densities are fitted within their uncertainties. The workflow presented previously [18] is extended in two aspects: For the QCE discharge, where ion temperatures are available, they are prescribed directly. And the separatrix density gradient is fitted in addition to the interferometry time traces.

Transport behavior
The ASTRA analysis shows that transport changes on fast time scales when the fuelling is altered. From previous work it is known that neutrals can directly interact with turbulence, an effect which was discussed and studied for the scrape-off layer [29,30]. But in the confined region, a more indirect cause for the changes in transport is suspected: An increased particle source, due to the fuelling, increases the local plasma density and cools the plasma because ionization and heating of the ion-electron pair requires energy. As a point of reference, the fuelled particle flux of 8 × 10 21 s −1 requires 200 kW to be heated to 50 eV. These initial changes to the kinetic profiles influence turbulence. One example of this is the collisionality ν * ∝ n e /T 2 e , which correlates with the found χ e close to the separatrix [18].

Heat diffusivity
The heat flux across flux surfaces can be calculated from the applied heating power and the measured radiated power. In general, the radiation profiles at the edge could introduce uncertainties, but this is only of little influence here because all investigated cases are unseeded, i.e. without adding impurities for radiative cooling. The heat diffusivity profile can then be determined for each point in time, using the heat flux together with the measured temperature gradient, the reconstructed density, and the known geometry of the plasma. Without knowledge of T i , it is unclear how the heat flux is shared between electrons and ions, but the relative changes of χ e that this publication discusses are a robust result: An analysis of the QCE case with and without prescribed ion temperatures reveals that replacing the experimental ion temperature with χ i ∝ χ e only slightly influences the relative changes.
At each time point, the χ e profile was determined from the power balance using the ASTRA code. Figure 6(a) shows the resulting relative amplitude of the χ e modulation, as function of radius. At ρ pol = 0.98, the heat diffusivity changes by ±16% in all three cases. Moving inward, the modulation amplitude of χ e drops rapidly to ±7% at ρ pol = 0.94 for the L-mode (blue solid line). Further in, the relative amplitude remains unchanged. For QCE (dashed orange line) and EDA H-mode (dotted red line), χ e reacts sensitively not only in the pedestal but also at the pedestal top and outer core: Until ρ pol = 0.88 χ e modulates by ±10%.
The timing of the transport changes is shown in figure 6(b). A phase of 0 refers to the strongest increase in χ e exactly when the valve opens, and positive phases refer to a delayed increase in χ e . Starting again with the L-mode, one finds that the χ e increase in the pedestal is delayed by 8 ms compared to the valve opening. At inner radii, the phase is between 2 ms and 5 ms. In the EDA H-mode case, transport increases both in the pedestal and the outer core ≈5 ms after the valve has been opened. The behavior of the QCE case strongly deviates: Heat transport in the pedestal increases 12 ms after the valve opening, and inward of ρ pol = 0.95 the phase delay is even larger than 15 ms.
When the phase shift between valve and χ e is in the range of π/4 and 3π/4, i.e. between 10 ms and 30 ms, transport is lower when the valve is open than when it is closed. Other phase shifts correspond to increased transport with an open valve. In L-mode and EDA H-mode, transport increases with the open valve: in L-mode mainly in the steep gradient region, in EDA H-mode both in the pedestal and the outer core. The QCE discharge behaves differently: Already in the pedestal, χ e reacts delayed to the increased fuelling. And in the outer core, transport is clearly stronger at times without additional fuelling.

Flattening of the density gradient at the separatrix
In all cases, the edge density as measured by the H-5 interferometer increases when fuelling is increased. Simultaneously, a flattening of the separatrix density gradient is observed in the L-mode and QCE cases. Intuitively, an increase in fuelling would coincide with an increase in the number of neutral atoms crossing the separatrix. An increased particle source also agrees well with the measured increase in pedestal top density. The developed ASTRA models, in which heat and particle transport are consistent with the measured data, also agree that the neutral flux is higher when the valve is open.
It will now be shown that the flattening of the density suggests an increase in particle diffusivity D. This, however, does not mean that D remains constant or is reduced in the cases where the separatrix density does not flatten: Increased particle flux due to additional fuelling could cause steeper gradients even if D increases.
The density in the steep gradient region reaches steady state after a few millisecond. The particle transport equation then becomes The necessary increase in D for flattening is more severe the stronger the source S e grows with additional fuelling. To arrive at the minimally necessary change in D, a change of the source with valve opening ∆S e = 0 is assumed. A particle diffusivity behaving analogously to χ e in the steep gradient region matches the experiment well: If we set v = 0, equation ( For the opened valve the gradient is flatter, therefore the particle diffusivity has to be larger. For an alternative explanation with temporally constant coefficients, one could envision outwards convection for the Lmode where the separatrix density increases and inward convection for the QCE discharge. However, as will be discussed shortly, a D at the separatrix which increases with fuelling forms a coherent picture with the other transport channels, and a temporally constant D could not reproduce the dynamic behavior.

ASTRA modelling of the particle transport
With the ASTRA model described in section 2.2, the flattening of the separatrix density was reproduced. As discussed above, either D has to increase significantly or convective contributions are necessary. Previously [18], it was assumed that the particle transport coefficients are uniform outside of ρ pol = 0.95. To reproduce the flattening of n e , the transport coefficients are then restricted to values that are incompatible with the requirement of reproducing the density evolution further inside: To flatten the density gradient at the separatrix, the increase of D has to overcome the additional fuelling. But if the same increase in D is prescribed between ρ pol = 0.95 and the separatrix, the additional diffusivity overcomes the additional fuelling in the whole source region. Then, the density would not increase at all, contradicting the interferometry measurements.
In the following, we split the pedestal region in two parts, with different transport behaviour, the steep gradient region and the pedestal foot, just inside the separatrix or equivalently outside of ρ pol = 0.99. Restricting the region in which D and v modulate to outside of ρ pol = 0.99, the experiment can be reproduced • if D is allowed to modulate, • if D and v are allowed to modulate proportional to each other, • not if only v modulates.
We therefore conclude that D does not remain constant. It modulates more strongly close to the separatrix than inside, otherwise either the pedestal density cannot increase sufficiently or the separatrix density does not flatten. To reproduce the evolution of the separatrix density gradient, the modulation of D was treated as a free parameter that is fitted to the experimental data. v is set to be proportional to D, meaning both modulate and are in phase. Figure 8 shows the fitted phase of D close to the separatrix (at the pedestal foot) and the phase of χ e at ρ pol = 0.97 for all discharges which feature a flattening of the density at the separatrix. In this way we can compare the temporal modulation of D with the temporal evolution of χ e .
For the L-mode case with no background fuelling (Γ b = 0 × 10 21 s −1 ) the phase of χ e is determined to be in the range 6 ms to 9 ms. The predicted phase of D lies within a 10 ms window centered at 7 ms. To conclude, D modulates, and it does so in phase with χ e . With intermediate background fuelling (Γ b = 5 × 10 21 s −1 ), the phases of D and especially χ e are less accurately determined. The median phase shift is less than for the case with no additional fuelling, meaning the increase of transport after the opening of the valve occurs more rapidly. The phases of D and χ e are again identical within the uncertainties. For the two QCE cases, the phases of both χ e and D are very accurately determined with uncertainties of 5 ms to 8 ms. The different fuelling location does not influence the phases of χ e and D. The modelled phase of D is 4 ms smaller than the phase of χ e , corresponding to a slightly earlier increase in particle transport than in electron heat diffusivity. This comparably small difference could be physical and for example show that transport at the separatrix reacts slightly faster than transport at ρ pol = 0.97.
In conclusion, D and χ e at the pedestal foot modulate in phase.

Implications of modulating particle transport coefficients
In the previous sections, the change of transport coefficients on fast time scales as response to a change in fuelling was discovered and quantified. This interesting phenomenon allows studying properties of turbulence in the edge, but also makes the disentanglement of D and v vastly more difficult. It will be shown how the altered transport conditions fit together with the measurements under the assumption D ≈ χ e , resolving the issue of the unexpectedly weak density modulation in the Hmode cases.
Before discussing the behaviour of the three groups qualitatively, it will be shown from a mathematical point of view that a temporally evolving D can justify most density evolutions even without a pinch. Starting with the density equation, we obtain ∂ t n e = ∂ ρ (D∂ ρ n e − vn e ) + S e (6) Equation (7) is interpreted as ordinary differential equation for D(ρ, t) for given n e (ρ, t), v(ρ, t) and S e (ρ, t). For every combination of those parameters and for every time t it is possible to solve the differential equation. The method to determine D and v with the aid of modulation experiments, as it is usually used, assumes D and v to be independent of time; these D and v then have to solve equation (7) for all t. From the previous section it is known, however, that D is not identical for all points in time. This means a D(ρ, t) can be determined for each t and each choice of v, and there is no information left to determine the physical v. From a technical point of view, we have to take care of the integration constant, which can be used to set the particle flux at the magnetic axis to zero, and the division by the density gradient which can be 0. D will also be negative in some occasions, but in general these restrictions will not be enough to decide if a pinch is present.
With the knowledge of the χ e modulation, additional information about the transport behavior is available. Figure 8 shows that both particle and heat transport are closely linked, agreeing with the physical picture that both quantities are transported with the same mechanisms. In the following, χ e will be treated as proxy for D, allowing a qualitative interpretation of the measured density evolution.
The response of the density profile to increased fuelling is a competition between an increased particle source and altered transport conditions. In L-mode, the increased particle source increases the electron density inwards of ρ pol = 0.98 because transport increases only slightly. Even though the particle source also increases in the steep gradient region, the strong increase in transport, especially close to the separatrix, leads to only a minor density rise and a flattening at the separatrix. In the QCE case, the density rises strongly in the outer core (ρ pol = 0.90): The reduction of transport in this region, when the valve is open, and the increased particle source, both increase the density. In the pedestal, the density is reduced: The particle flux from the outer core is reduced due to weaker transport, and the increased transport in the pedestal region flattens the density gradient. For the EDA H-mode, the behavior is completely different, mainly because of the different conditions at the pedestal top and in the outer core. A strong and rapid increase in transport at both these locations flushes out the additionally fuelled particles, leaving the density at ρ pol = 0.90 unaltered. The resulting particle flux across the pedestal leads to an increase in density, despite the increased transport in the pedestal. Although the players influencing transport in the pedestal are the same in all 3 cases, namely neutral source increase due to the gas puff, increased transport at the pedestal foot and change in transport in the outer core region (both directions, slightly weaker in L-mode, weaker in QCE and stronger in EDA H-mode), it is the balance of all these effects that determines the resulting density profile.

Gyrokinetic analysis with GENE
A numerical analysis with the gyrokinetic turbulence code GENE [15,16] was performed for the three discussed cases. Due to the enormous costs of nonlinear edge simulations, the analysis is restricted to linear instability investigations in a flux-tube simulation domain to obtain first insights in a reasonable time span. Obviously, such simulations would not capture the relevant transport mechanisms in highly nonlinear strong turbulence regimes. However, recent results from GENE, where linear and non-linear gyro-kinetic modelling results were compared [31][32][33], indicate that in some cases the linear results give already a good indication of the dominant turbulent transport mechanisms. We use the linear approach to obtain a pre-characterisation of the plasma turbulent state. The input profiles, i.e. density and temperatures, come from the ASTRA modelling. The radial positions ρ pol = 0.90 and ρ pol = 0.98 were selected, to characterise the outer core region and the steep gradient region. The GENE simulations were performed at different time points during the modulation period. For the QCE discharge at ρ pol = 0.90, the times 0 ms, 10 ms, 20 ms and 30 ms with respect to the valve opening were chosen to resolve the temporal behavior seen in the experimental analysis. All other cases are analyzed at 0 ms and 20 ms, i.e. when the valve has been closed and opened for as long as the modulation allows. The real frequencies of the modes are shown in figure 9, and figure 10 shows the obtained dominant growth rates at large scales, as function of turbulent structure size for the three modelled discharges. The small scales at ρ pol = 0.90 show the same trends as the large scales, and are not shown. At ρ pol = 0.98, the large scales dominate strongly. The real frequencies help to identify the character of the dominant instability. If the sign changes at a certain wavenumber, this is a clear indication that here the instability changes its type. In the GENE convention, positive/negative frequencies correspond to ion/electron diamagnetic drift direction. Other features like the amplitude or the dispersion relation can also help the characterisation. Additional scans in beta or the driving gradient (ion temperature for ITG) are carried out. We have scanned the gradients of density by 60% and temperature by 30%, and the character of the dominant turbulence is robust with respect to these gradient changes. In the first row of figure 9 we show the frequencies in the outer core region. In all cases the signature corresponds to ITG at large scales switching to ETG at small scales. Differences can be observed in the steep gradient region, at ρ pol = 0.98, depicted in the second row. In L-mode we determine a dominant TEM at low k. In EDA H-mode we identify a KBM-like instability at low k. This could be a remnant of the flux-tube approach and KBM could become subdominant in global simulations [34]. Especially for the EDA H-mode case, the transition from KBM to TEM is within the experimental error bars. In the QCE case the gradient region is dominated by KBM-like turbulence, which is confirmed by a beta scan. The found ballooning modes for QCE agree well with the general understanding of this scenario [21,22].
In L-mode at ρ pol = 0.90 ( figure 10(a)), the growth rates are larger when the valve is open for all structure sizes. The behavior at ρ pol = 0.98 ( figure 10(b)) is not as uniform. Very large structures, i.e. values of k y ρ s smaller than 0.3, grow slightly faster when the valve is open, while smaller structures grow faster when the valve is closed. The expected transport from turbulent structures is approximated by combining the growth rate with the structure size as γ/ (k y ρ s ) 2 [35]. Weighting the growth rates accordingly reveals that structures with k y ρ s < 0.3 contribute more to transport than smaller structures. The measured transport increase can only be explained if the higher growth at very low k contributes significantly, which can only be determined in non-linear simulations. Figures 10(c) and (d), depicting results for the EDA Hmode, yield the reverse behavior: The dominant modes, at small k y ρ s , grow more weakly when the valve is open. In the experiment, transport in the whole edge region increased promptly when the valve was opened. A possible explanation can be found when considering the spectrograms shown in figure 11. The EDA H-mode is the only case where a highfrequency mode between 180 kHz and 190 kHz is visible in the magnetics, in addition to the lower-frequency mode characteristic for the EDA H-mode regime [23]. Whenever the highfrequency mode is present, the low-frequency components  below 30 kHz, originating from turbulence, are absent. This suggests that the high-frequency mode causes sufficient transport to suppress these other instabilities. The linear flux-tube simulations with GENE presented here appear to not capture the transport of this mode.
The QCE pedestal (figure 10( f )) is once again dominated by large structures, which exhibit an increased growth rate for the fuelled case. This increase by ≈30% is far larger than what was seen for the other cases. Also the experiment finds an increase in transport when opening the valve. The found KBM is the proposed instability for the QCE pedestal foot [21,22]. At ρ pol = 0.90 (figure 10(e)), the agreement between GENE and the ASTRA analysis is imperfect. According to GENE, transport is indeed comparably small at t = 0 ms, but, already at t = 10 ms, GENE finds transport comparable to the later points in time. A clear increase in transport can be deduced in agreement with the experiment. All in all, the linear flux-tube instability analysis with GENE reproduces and identifies some of the underlying trends. A more complete picture would, however, require nonlinear and possibly radially global simulations considering the various experimental input parameter uncertainties. This tremendous task is left for future work.

Edge density profile in future reactors
Finally, we turn to the prediction of transport and profiles for future reactors. The two effects which can lead to a density gradient are a pinch and a finite particle flux across the separatrix. A pinch is not apparent in present experiments, but cannot be excluded. Additionally, it is not clear how edge particle transport will differ between present machines and future devices.
Also the particle flux across the separatrix is not known, but a lower bound can be estimated [36]: A reactor utilizing D-T fuel will produce 3.6 × 10 20 helium ions per second for each gigawatt of fusion power; in steady state the helium flux across the separatrix therefore has to be 3.6 × 10 20 s −1 for a 1 GW reactor. A high concentration of helium would dilute the fuel. Assuming equal transport for helium and hydrogen isotopes, the D-T flux across the separatrix has to be more than 20 times the flux of helium to maintain a helium concentration below 5% [36]. For ITER, with 500 MW of fusion power, this results in a deuterium flux F across the separatrix of 3.6 × 10 21 s −1 . As a consequence, there is a density gradient at the edge, even if transport is purely diffusive: with A being the area of the flux surface. D in the ITER pedestal is unknown, therefore one cannot predict the associated density gradient. With D = 0.2 m 2 s −1 one obtains 1 × 10 20 m −4 , approximately 5% of the density gradient at ρ pol = 0.985 in the AUG QCE discharge #37774 at 6.8 s which was discussed in this publication. Such a density gradient is very 'flat' compared to present-day devices, and a convective transport process, which has been ignored in the consideration so far, would lead to an increase of the gradient if its sign is negative and a reduction of the gradient if positive.
In large devices, such as ITER and DEMO, a high SOL density is expected to shield neutrals efficiently [36]. This is also shown by the two QCE cases discussed here, which feature a high density in the LFS SOL known as density shoulder [37,38]. When fuelling from the LFS, the response of the plasma is similar but small compared to the HFS case, where the neutrals can travel undisturbed across the SOL into the confined region.
The neutral flux across the separatrix originating from recycling and gas fuelling is therefore expected to be small in future reactors, smaller than the 3.6 × 10 21 s −1 deemed necessary to keep the helium concentration low [36]. Pellet fuelling can increase the particle source in the confined region. For the EU-DEMO power plant, pellet fluxes of ≈7 × 10 21 s −1 are expected [39].
In conclusion, ITER and DEMO will feature a density gradient at the edge, except if particles are convected outward. But it likely will be smaller than in present devices because the large gas fuelling and recycling particle source in the pedestal region is strongly reduced. The particle flux across the separatrix, and with it the density gradient in the pedestal, however has to be kept high enough to facilitate helium exhaust. This requires sufficient pellet fuelling.

Conclusions
In this work, successful gas puff modulation experiments in several L-mode, EDA H-mode, H-mode and QCE discharges were performed. Accurate time-dependent edge data both for n e and T e , and in the QCE case also for T i , were obtained. For the extensive analysis, all discharges were modelled using the ASTRA code. Fits of the unknown, randomly initialized parameters yield accurate diffusivities for heat transport and a set of solutions for the particle transport. The analysis shows that transport in heat and particle channels change with the modulation. This makes a determination of particle diffusivity and convection impossible, but allows to determine the nature of the underlying dominant transport mechanisms. It was not only shown that the pedestal top, or outer core, behaves differently than the steep gradient region, but also that the pedestal foot close to the separatrix has to be treated independently. The evolution of the density profile can always be understood as a result of increased particle source due to fuelling and a particle diffusivity which evolves similar to χ e ; a pinch is never necessary.
An analysis with GENE finds that in L-mode, TEM modes are dominant at ρ pol = 0.98, while ITG and ETG dominate at ρ pol = 0.90. For the QCE discharges, transport at the pedestal foot increases, in agreement with dominant KBM (GENE) and as suggested by Harrer et al [21] and Radovanović et al [22]. Transport at the pedestal top is reduced, or increases strongly delayed, by the additional fuelling, an effect which is not fully captured by GENE. In the EDA H-mode and ELMy H-modes, transport increases in the whole edge region, until ρ pol ≈ 0.85, only few milliseconds after fuelling is increased. GENE does not reproduce this behavior. The magnetics show mode activity in the investigated case, whose transport behavior is not captured in the linear flux-tube limit of the performed GENE simulations.
The edge density profile in next generation devices, such as ITER or DEMO, will show a density gradient, even if no pinch is present: Sufficient helium exhaust requires a particle flux on the order of 1 × 10 22 s −1 per gigawatt of fusion power. Diffusive transport requires a density gradient to cause this flux of particles.