Analysis and expansion of the quasi-continuous exhaust (QCE) regime in ASDEX Upgrade

The quasi-continuous exhaust (QCE) regime, formerly known as either type-II ELM or small ELM regime is studied in ASDEX Upgrade. The regime is a natural type-I ELM-free H-mode. The operational space of QCE discharges in ASDEX Upgrade with respect to their separatrix conditions and their power exhaust capabilities are presented. A significant broadening of the power fall-off length is observed, correlating to an increased separatrix density and pressure. Moreover, the possible reactor relevance of this regime is demonstrated by expanding the operational space to low edge safety factor and demonstrating the benign tungsten impurity behaviour. A discharge without any type-I ELM from start to end reaching a partially detached divertor at high normalised energy confinement time is presented.


Introduction
Two main challenges of power exhaust for future tokamak power plants are the avoidance of transients, like type-I ELMs, * 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. and access to a (partially) detached divertor. These two constraints are often studied independently of each other. Many type-I ELM avoidance schemes focus on a low pedestal top collisionality which will be present in a future reactor due to the high temperature. The access to a detached regime requires a high pedestal foot-or separatrix-collisionality due to the required high density. While present day tokamak experiments can approach reactor-like values for either independently, the combination of both is only possible with a reactorsized experiment.
A promising regime in which the absence of type-I ELMs is linked to the tailoring of the pedestal profile at the foot is the so-called quasi-continuous exhaust (QCE) regime. The regime is a natural type-I ELM-free H-mode that was previously identified with type-II ELMs [1][2][3][4][5] or small ELMs [6,7] and is now named QCE [8] due to enhanced filamentary transport at the plasma edge compared to inter-type-I ELM phases. While in ASDEX Upgrade this regime is achieved with high normalised energy confinement time when using highly shaped plasma discharges at high separatrix density [6], also plasmas with low plasma shaping and high separatrix density can be type-I ELM-free. The EDA H-mode [9] is another ELMfree regime observed at ASDEX Upgrade with high plasma shaping [10]. The EDA H-mode is situated at lower powers and separatrix densities, with generally better energy confinement compared to QCE, but with re-occurrence of ELMs above a separatrix power threshold. At lower fuelling and separatrix density a transition from the QCE to the EDA H-mode regime is observed. The conditions at the separatrix seem to be important as access condition to a small ELM regime.
The high separatrix density, together with an observed broadening of the power fall-off length [8] is believed to be beneficial for detachment [11,12]. However, these considerations assume steady-state conditions, while the QCE has temporarily changing heat and particle fluxes caused by the filamentary transport. Future experiments and modelling have to show if these filaments can be detached/buffered in order to achieve time-integrated low particle erosion at the divertor. While it was shown that low amplitude type-III ELMs can be buffered in JET [13], the same was not yet studied for the filaments in the QCE regime.
A theoretical description of the QCE regime is given by ballooning modes being unstable at the pedestal foot, close to the separatrix. These ballooning modes are thought to cause transport, limit the radial extend of the steep gradient region and thereby prevent the occurrence of type-I ELMs [6,14,15].
The QCE regime exhibits a density shoulder, likely linked to the filamentary transport across the separatrix [8,16]. A density shoulder is associated with enhanced particle and heat fluxes to plasma facing components outside the divertor region [17]. Future studies have to show if this will cause an unacceptable heat load and erosion and if so investigate measures to suppress these.
Recent works in ASDEX Upgrade showed that turbulence considerations, similar in nature to the work by [18], outline the separatrix operational space of the H-mode by successfully describing the H-L transition, the L-mode density limit as well as an ideal ballooning limit [19,20].
In this work we analyse the operational space of QCE discharges in ASDEX Upgrade with respect to their separatrix conditions and their power exhaust capabilities. Moreover, we show the possible reactor relevance of this regime by expanding the operational space to low edge safety factor q 95 , demonstrating the benign tungsten impurity behaviour, and develop a discharge without any type-I ELM from start to end.
The article is organised as follows: section 2 defines an automatic qualifier to distinguish between type-I ELMs and QCE filaments. Section 3 provides an experimental approach to access the QCE regime by a correlation with engineering as well as physics parameters. The achievable electron temperature and density range at the separatrix is presented in section 4. In section 5 a scaling of the pressure fall-off length as well as the broadening of the power fall-off length with increasing separatrix density and pressure is discussed. A correlation between edge quantities and confinement is presented in section 6. Section 7 highlights the route to low safety factor and the low tungsten core concentration in QCE. Section 8 presents a discharge avoiding type-I ELMs from start to end. A discussion on ITER-like plasma parameters and the open questions regarding detachment are presented in section 9. Section 10 contains a summary and conclusions.

Qualifier for absence of ELMs
For the automated analysis of the operational space of H-mode discharges without type-I ELMs we searched for a qualifier for the absence of ELMs. We inspected many different signals that could act as qualifier in ASDEX Upgrade. The most reliable one proved to be the scrape-off layer current measured via shunts in the divertor tiles I SOL . Type-I ELMs show up as large peaks on a signal that is dominated by thermo currents [21]. Our ELM proxy is defined by the shunt current measured at the outer divertor target. The current is multiplied by the edge safety factor to account for the resistivity varying with connection length. The edge safety factor is defined as [20] Here, B tor is the toroidal magnetic field on axis, a geo and R geo are the minor and major radii, κ is the elongation, δ the averaged triangularity, µ 0 the vacuum permeability and I p the plasma current. We normalise this quantity by dividing it by 21 kA and define it as With this normalisation, E prox is a dimensionless quantity. For a value below 1 the plasma is in the QCE regime, above 2 type-I ELMs are present and in between 1 and 2 the ELM behaviour is ambiguous. Note here, also discharge phases in EDA H-mode are ELM-free and have E prox < 1.
In order to show that E prox correlates with the power load on the outer divertor we chose a type-I ELMy discharge and compared E prox with the infrared thermography (IR, [22]) measurements. Figure 1 shows the relation between divertor power load P IR div and E prox . The divertor power load is the spatially integrated heat flux measured by IR. E prox = 1.0 corresponds roughly to 2-2.5 MW divertor power load. At higher values, Figure 1. Integrated power load on the outer divertor measured by infrared thermography P IR div compared to the ELM proxy Eprox. Data is taken from # 32291 in the time interval between 3.4 s and 5.0 s where the discharge was in a clear type-I ELMy H-mode with constant plasma shape. The blue solid (dashed) line represents the upper (lower) limit used for detecting ELM-free (type-I ELMs) time points. e.g. during type-I ELMs, no strict linear correlation between divertor power load and shunt current exists, however, a larger shunt current still corresponds to larger divertor power load.
In the remainder of this article we distinguish between time windows with type-I ELMs from those with QCE filaments only. For this, the maximum (99.9% percentile) of E prox in an interval is taken. As an example, figure 2 shows three 150 ms time slices of integrated divertor power load and normalised divertor shunt current of a discharge with type-I ELMy and QCE phases. They represent (a) a type-I ELM phase with max(E prox ) = 4.1, (b) a mixed phase with some ELMs with max(E prox ) = 2.7 and (c) a QCE phase with max(E prox ) = 0.6. For the last window, no IR measurements are available due to volume radiation.
We assembled a data set covering a wide range of plasma quantities in ASDEX Upgrade. The main parameters are summarised in table 1. P heat is the applied power corrected for neutral beam shine-through losses and changes in stored energy. The data set is concentrated at high plasma shaping (high upper triangularity of δ up ≈ 0.3, close to double-null). This high plasma shaping is a key ingredient for realising the QCE regime whilst maintaining a high normalised confinement time [1,14,15]. Each data point represents an average of around 150 ms. This ensures steady state values and allows the separatrix analysis of Thomson scattering (TS, [23]) data as described in [19,20] using the sub-script edge for the reference point 1 mm (poloidally averaged) inside the separatrix (ρ pol ≈ 0.999). This TS analysis provides edge temperature T e,edge , density n e,edge and pressure p e,edge as well as the exponential fall-off lengths of these. The data processing is sketched in the following paragraph.
The TS profiles are mapped to the outer mid-plane by the magnetic equilibrium reconstruction. Due to the strong gradients, the location of the separatrix is chosen by a power balance assuming Spitzer-Härm electron heat conduction being the dominant transport mechanism in the scrape-off layer setting the electron temperature at the separatrix. The temperature is estimated following [24]: with aspect ratio A and Spitzer-Härm electron heat conduction coefficient κ e 0 . Typically a ratio of λ q = 2 7 λ Te is used. At low separatrix density the validity of this assumption was shown in ASDEX Upgrade [25][26][27]. In our QCE data set we account for a change in the electron temperature gradient between inside and outside the separatrix as reported in [8]. Here, we use λ q = 2 5 λ Te , in line with the measurements shown in section 5. Note, this does not mean we do not follow Spitzer-Härm electron heat conduction, but rather that the gradient just inside, which dominates the estimate of λ Te in our approach, is steeper than in the near scrape-off layer. We are interested in the gradients and absolute values just inside the separatrix. Figure 3 shows a comparison between two approaches to extract the edge density for the full data set. The edge density from the integrated data analysis (IDA, [28]) is very similar to the values obtained by the technique applied here (using Spitzer-Härm electron heat conduction, SH). On the other hand, the IDA edge temperature scatters significantly making the SH approach necessary.
A manual classification between type-I ELMy and QCE phases is compared to the ELM proxy E prox to validate the automatic sorting for the full data set.
Z eff = 1.24 is assumed for all data points (no discharges with impurity seeding are included). The marker type is a binary classification by hand. It is observed that nearly no type-I ELM phase has max(E prox ) < 1 and nearly no QCE phase has max(E prox ) > 2, while phases in both regimes exist in the space between. The manual classification is less strict than the automatic sorting in the sense that single ELMs within a QCE time window are not marked as ELMy. This is seen in figure 4 with points marked as QCE but having max(E prox ) > 2. In the remainder of the paper, we use the automatic sorting and only phases with max(E prox ) < 1 as QCE and max(E prox ) > 2 as type-I ELMy and discard the phases in between. This binary sorting has two main drawbacks: (i) the drive of the filaments exists already in phases where occasional type-I ELMs are present [6] and (ii) the transition can be a smooth process, with the type-I ELM amplitude reducing continuously until the type-I ELMs vanish completely [8]. Hence, we are not searching the onset point of the filaments but the absence point of type-I ELMs.

Access conditions to QCE
For type-I ELMs to be suppressed, transport across the separatrix must be increased so that the pedestal pressure profile cannot reach the global peeling-ballooning stability threshold. Here, we are looking for the conditions that provide the necessary high transport level. The access conditions to the QCE regime are investigated in two ways. First, we look at engineering parameters, namely edge density n e,edge and the power crossing the separatrix P SOL . Then, we investigate the access dependence on edge collisionality ν * e,edge and turbulence control parameter α t , both parameters associated with increased transport [29,30]. Additionally, we investigate the closeness of the separatrix pressure profile to the ideal ballooning limit.
The two engineering parameters for the scrape-off layer of a tokamak, edge density n e,edge and power crossing the Open blue symbols represent QCE phases, filled red symbols represent type-I ELMy phases as sorted by hand. The black lines represent the threshold for the automatic sorting, with the solid line being the upper limit for QCE and the dashed line the lower limit for type-I ELMy.
separatrix P SOL , are shown in figure 5. The power crossing the separatrix is calculated using P heat and subtracting the radiated power inside the confined region as calculated from a bolometric reconstruction [31]. For both parameters, there is a considerable overlap of QCE and type-I ELMy phases. However, it is noted that only QCE phases exist below a ratio of P SOL (MW)/n e,edge (10 19 m −3 ) = 1 and/or above n e,edge = 5.4 · 10 19 m −3 . The power dependence is consistent with findings from non-linear MHD simulations performed with JOREK [32]. These simulations find a transition to type-I ELMs when increasing P SOL starting from a small ELM phase.
Two physics quantities, α t and α MHD (normalised to the ideal ballooning limit α crit ), are shown in figure 6. They are defined as in [19]: with the poloidally averaged pressure fall-off length ⟨λ pe ⟩. The normalised pressure gradient α MHD /α crit corresponds to the closeness to the ideal ballooning limit with larger values indicating that electromagnetic effects are becoming more important for the turbulence. The parameter α t is linked to the α d parameter of [33] and corresponds to transport by turbulence and is correlated with the strength of resistive ballooning modes [29]. It was shown in previous works that in QCE phases the pedestal foot, close to the separatrix but further inside than the analysis here, is ideal ballooning unstable in HELENA calculations [14,15]. Here, however, both QCE as well as type-I ELMy phases exist for the full range of α MHD /α crit covered in the data set. It is noted that a finite α MHD is associated with H-mode conditions [20,33,34]. With the exception of a handful of outliers, all values in this data set are above α MHD /α crit = 0.15. This is consistent with the minimum values observed for type-I ELMy H-modes as presented in figure  1 of [19].
The α t parameter sorts QCE and type-I ELMy phases remarkably well. Two boundaries are shown in figure 6 with vertical lines. For α t < 0.45 almost all data points show type-I ELMs while for α t > 0.55 almost all data points are in the QCE regime. In the range 0.45 < α t < 0.55 we find signatures for both regimes. We note that the edge collisionality ν * e,edge sorts the data similarly well, with the boundary being ν * e,edge > 14 for the absence of type-I ELMy data points. This can be seen in the absence of ELMy data points, max(E prox ) > 2, above ν * e,edge > 14 in figure 4. Summarising the separatrix access conditions to QCE, we can state that engineering parameters are not sufficient, but both α t > 0.55 and ν * e,edge > 14 provide a reliable description for the suppression of type-I ELMs.

Separatrix operational space of QCE
The operational space in the edge (1 mm inside separatrix) parameters temperature T e,edge and density n e,edge is a concept to qualify the power exhaust capability of a regime as well as the limits in terms of ideal ballooning stability and nature of turbulence. Furthermore, also the operational window of the H-mode was shown to be well correlated with the separatrix parameters [20]. As indicated in figure 6 in the previous section, this concept could also be useful to distinguish between QCE and type-I ELMy phases.
The present data set covers the vast majority of the accessible H-mode separatrix operational space in ASDEX Upgrade. In this section the data set is limited to a fixed plasma current and toroidal magnetic field strength at which the majority of data points are taken. Table 2 presents the key parameters of this data set. The closeness to double-null is measured by the distance of the two X-points mapped to the outer mid-plane d R,XP . This set is a sub-set of the set presented in section 2. Edge electron temperature and density measured by TS for this data set is shown in figure 7. The set consists of density (by fuelling with gas valves as well as pellets) and heating power variations, filling the high density part of the achievable H-mode space. The black and blue lines represent the ideal ballooning limit α MHD = α crit and the H-L back transition criterion by Eich et al (equation (8) of [20]), respectively. The  average α crit = 2.88 and equation (13), shown in section 5, is chosen to estimate the pressure fall-off length in order to infer the boundary lines. The error-bars for the black line represent the minimum and maximum of α crit for the experimental data points close to the boundary. It is found that the data set reaches both boundaries. Figure 8 shows four discharges with an H-L back-transition. The transition is provoked by a heating power ramp-down (# 39388 and # 39541) and fuelling ramp-up (# 40068 and # 40069). For all four discharges the transition is close to the blue line, confirming the validity of this limit also at very high edge densities and for high plasma shaping.
In fact, this data set includes the highest edge density points in ASDEX Upgrade ever observed. The Greenwald density [35] for the discharge parameters is n GW = 1.0 · 10 20 m −3 , thus, the edge density spans a range of n e,edge = (0.2 − 0.7) n GW .
We reach here a higher value than the upper limit described in [36]. This can be explained by (i) a broadening of the pressure fall-off length compared to the scaling law taken in [36], leading to a lower α MHD at similar edge electron density n e,edge , and (ii) by the higher α crit due to the higher plasma shaping. The ideal ballooning limit can be seen as a soft limit, rather leading to a broadening of the pressure fall-off length due to increased radial transport than an abrupt termination as expected in [36]. Indeed, the H-mode density limit was later  [20].
An additional limit in the separatrix operational space is introduced here. In section 2 a criterion for the absence of type-I ELM was found using the turbulence control parameter α t in line with the concept of the separatrix operational space. The green line in figure 7 represents α t = 0.55 which separates QCE and type-I ELMy phases. The QCE phases are between the green, black and blue lines and cover a substantial part of the operational space.

Pressure and power fall-off lengths
The loss of type-I ELMs is attributed to a change of turbulence near the separatrix as characterised by the turbulence control parameter α t and an increase of the edge collisionality ν * e,edge . The impact of this change on transport is studied in this section by looking at the fall-off lengths in the vicinity of the separatrix. Eich et al [19] found a broadening of the pressure falloff length with increasing α t for a data set excluding highly shaped plasma discharges; we apply the same analysis to our highly shaped plasma discharges.  (11)) as well as a regression with the same function parameterisation for the presented data set equation (12). The line in (c) represents equation (13).

Electron pressure fall-off length in the vicinity of the separatrix
We discuss the electron pressure fall-off length just inside the separatrix (−1 mm ± 1.2 · ⟨λ pe ⟩). In the work by Eich et al [19], the poloidally averaged pressure fall-off length ⟨λ pe ⟩ was normalised to the poloidal gyro-radius with m D the deuterium ion mass. The regression result was The normalisation as well as the chosen function parameterisation ensure that at low values of α t the well-known ITPA multimachine regression dependence [37] is obtained and the term including α t resembles a broadening.
Here, we perform a regression analysis using the same function parameterisation for the present data set with the majority of points from highly shaped plasma discharges. We include all data points from section 2, notably with the full available range of plasma current and toroidal magnetic field and for both type-I ELMy and QCE regimes. Using the same functional as equation (11) we get with significantly less broadening in the available α t range compared to equation (11). However, this regression has a low coefficient of determination R 2 = 0.28. Figure 9(a) shows the data set as well as the two scaling laws using α t . The data points in the type-I ELMy phases exhibit a large scatter with respect to α t , but are equally represented with both regressions due to the limited range of α t , see figure 9(b). However, it is observed that the scaling by Eich et al, equation (11), obtained from inter-ELM intervals in type-I ELMy phases, clearly overestimates the broadening with α t in the present data set consisting of QCE phases at α t > 0.55. Moreover, a dependence on q cyl remains, visible in the colorcoding of figure 9(a).
We find a better representation of the data set using the edge collisionality with an improved, but still low, R 2 = 0.46. The scaling with ν * e,edge with a linear q cyl dependence captures the data better than the one with α t with a quadratic q cyl dependence, see figure 9(c).

Power fall-off length in the near scrape-off layer
A broadening of the power fall-off length in the QCE regime was first reported in [8]. Here, we expand the data set and analyse the dependence of the broadening on edge density n e,edge , edge pressure p e,edge and turbulence control parameter α t . We focus on time points in QCE, hence, without data from inter-type-I ELMs. A set of the data points is assembled, including 9 discharges in which IR data for the outer divertor target are recorded. All discharges are at I p = 0.8 MA and B tor = −2.5 T.
The IR data analysis follows the routine analysis in ASDEX Upgrade [22]. Data is recorded in a sub-window mode allowing an increased frame rate of 1.5 kHz. Camera jitter is corrected and a line profile is extracted from the 2D data. Heat flux is calculated using the implicit implementation [38] of the THEODOR code [39]. A time average of 21 profiles is applied (14 ms) to average out the fast filamentary structures typically observed in the QCE regime [8,16]. These profiles are fitted with the 1D diffusive model presented in [40]. To ensure reliable fitting result, a selection of data points is applied, keeping only values where the target value of power fall-off length λ q is below 30 mm and where λ q > S, with S being the divertor broadening. The measured λ q is mapped to the outer mid-plane taking into account the poloidal flux expansion f x for each time point, with f x ≈ 5 for the data set.
The power fall-off length λ q as a function of edge electron density n e,edge , separatrix electron pressure p e,edge and turbulence control parameter α t is shown in figure 10. For the figure a further rolling average of 200 time points (133 ms) is applied. The corresponding standard deviation is around 15%. A strong correlation of λ q with n e,edge and p e,edge is observed, while α t yields no clear trend. The increase of λ q with n e,edge and p e,edge Figure 10. QCE power fall-off length mapped to the outer mid-plane λq as a function of (a) edge density n e,edge , (b) edge pressure p e,edge and (c) turbulence control parameter αt. The horizontal line represents the ITPA multi-machine scaling law, equation (14). The color-coding represents individual discharges. The diamonds represent three time points used in [8] with the red one being inter-type-I ELM and the blue and green ones in QCE.
is described as a linear trend starting with an offset corresponding to the ITPA multi-machine scaling law [37] λ q = 0.63 · B −1. 19 pol,OMP .
The poloidal magnetic field at the outer mid-plane for this data set is B pol,OMP = 0.32 T leading to the multi-machine scaling law prediction of λ q = 2.43 mm. Note here, this data set is taken at a fixed plasma current and machine size, hence, no scaling with poloidal magnetic field B pol is performed. Within this data set, no distinction between density and pressure dependence is possible due to the small variation in edge temperature.
In addition, three time points are shown that were used in [8] where the broadening of λ q in QCE was investigated for the first time. It is observed that the time point marked with the red diamond is below the blue line. This time point is recorded in-between type-I ELMs. It is speculated that the enhanced filamentary transport of the QCE regime is leading to the broadening. A similar broadening of the scrape-off layer width with increasing density is found in a theory-based scaling law for L-mode conditions [41].
Future studies will be needed to reveal if other quantities such as current or machine size enter the broadening and to investigate the influence of plasma shaping. It was shown in TCV L-mode that high triangularity can be beneficial for a broad fall-off length [42]. The effect of B pol could not be studied here and will need further attention as well as a multi-machine comparison to investigate potential major radius dependencies of the broadening.

Edge parameters and confinement
The access to the QCE regime is linked to a high turbulence control parameter and/or high edge collisionality, both achieved at high edge density. High edge density due to strong fuelling is correlated with a lower pedestal top pressure and a loss of confinement in type-I ELMy phases [43,44]. This trend is also seen in the present data set. We investigate the consequences on confinement due to the operation in the QCE regime and the link to α t . Figure 11 shows the normalised energy confinement time H 98y2 as a function of (a) edge density n e,edge and (b) turbulence control parameter α t for the full data set of section 2, including all I p and B tor values. H 98y2 decreases with both increasing n e,edge and α t . QCE phases are at higher α t compared to type-I ELMy phases and expose a reduced normalised energy confinement time. It has to be noted that at similar α t no separation is observed and that close to the transition between type-I ELMs and QCE both regimes have H 98y2 = 0.8-1.0. At very high α t and high n e,edge , the achievable normalised energy confinement time drops significantly, in line with previous observations in type-I ELMy H-mode [19].
In the following paragraph, we pay close attention to the vertical scatter in H 98y2 of figure 11. For this, the data set is restricted to B tor = −2.5 T and I p = 0.8 MA as in section 4. Figure 12(a) presents the sub-set using color-coding for the total input power P tot . It is observed that for a given α t the highest normalised energy confinement time is achieved at lowest P tot . Looking for the absolute value of the energy confinement time in figure 12(b), a strong P tot dependence is observed. Thus, the power degradation in this data set is stronger than predicted by the scaling law.
In order to investigate whether the change in confinement stems from the core or the pedestal region, the pedestal top pressure is now investigated. Looking into the pedestal top pressure instead of the normalised energy confinement time reveals a similar trend. Figure 13 shows the pressure at the pedestal top, taken at ρ pol = 0.9, as a function of the turbulence control parameter α t for the data set with B tor = −2.5 T and I p = 0.8 MA and for QCE phases only. The highest pedestal top pressure is achieved at lowest α t . Both, increasing n e,edge or decreasing T e,edge increases α t and lowers the pedestal top pressure. In addition, at constant α t a higher pedestal top pressure is achieved at higher heating power. HELENA calculations show that both pedestal top and foot are close to the ideal ballooning limit in QCE. High pedestal top pressure is achieved when the steep gradient region in-between is in the 2nd stability region [14].
As a conclusion, a high α t value is penalised by a reduced normalised energy confinement time. As the pedestal top pressure shows a similar trend, we conclude that the change in confinement is mainly pedestal driven. It is shown that QCE and   type-I ELM phases have the same connection between edge parameters and energy confinement. The QCE phases with the highest normalised energy confinement time are close to the boundary to type-I ELMs.

Scenario performance
In the previous sections, it was shown that the QCE regime occurs at high edge density and large values of the turbulence control parameter α t . Its advantageous aspects, the suppression of type-I ELMs and a longer power fall-off length, are bought with a moderate confinement loss. In this section, the QCE scenario is further developed in terms of its reactor relevance.

Route towards low edge safety factor
Low edge safety factor q 95 operation is expected for a viable reactor solution with high fusion gain. In a future reactor-sized tokamak, low q 95 ≈ 3-4 is envisaged [45]. Contrary to that, it was shown that the QCE regime is more readily available at elevated q 95 . This can be explained by higher q 95 increasing α t and ν * e,edge . Hence, less pressure or density at the plasma boundary is needed to reach the necessary access conditions.
The edge safety factor range of the QCE regime in ASDEX Upgrade was successfully lowered to q 95 ≈ 3.3. Figure 14  (a) Plasma current Ip (black) and toroidal magnetic field Btor (red) are ramped up and down, respectively. This reduces the edge safety factor q 95 as displayed in (b). Core tungsten concentration cw is shown in (c). In (d) the ELM proxy Eprox is shown. The QCE is interrupted during the Ip ramp when type-I ELMs re-appear. The QCE regime goes back to a type-I ELMy H-mode at 5 s. In (e) the deuterium gas flux Γ is shown. Heating and radiated power is shown in ( f ). X3 ECRH is applied during the H-mode entry and plasma shaping ramp until 2.5 s before Btor is ramped down. Phases with type-I ELMs are marked in grey.
shows time traces of the final discharge of a series of four consecutive discharges with step-wise lowering the toroidal magnetic field and increasing the plasma current while adjusting the fuelling level. The plasma start-up into the final shape is performed at B tor = −1.8 T with central wave heating until the ELM-free QCE phase is fully established. In order to lower the safety factor the toroidal magnetic field is ramped during the discharge towards B tor = −1.5 T starting at 2.5 s ( figure 14(a)). The final value is slowly approached at 5.5 s due to the large inductance of the coils. At these levels no central wave heating is available in ASDEX Upgrade. After 2.5 s the central X3 ECRH is switched off and compensated by increasing the neutral beam power, shown in figure 14( f ). The tungsten concentration in the core is counteracted by MHD activity appearing at 4.0 s in this discharge. The plasma current is increased from 0.8 MA to 0.94 MA at 3.0 s ( figure 14(a)). With higher plasma current, more fuelling is applied to prevent type-I ELMs from emerging as shown for previous QCE studies [6]. This is also seen by the re-appearance of irregular type-I ELMs after 5.0 s showing that the chosen fuelling amount is marginal for the given safety factor. The type-I ELMs re-appear later in the presented discharge compared to the preceding discharge with lower fuelling level. With additionally increased fuelling level the onset of type-I ELMs might be further delayed or suppressed. An increased plasma shaping might also improve the access window of QCE. The time point of the type-I ELM re-appearance coincides with q 95 ≈ 3.3 and marks the end of the QCE phase.

Low tungsten core concentration
The QCE scenario provides good intrinsic impurity control in all of the exploited operational range. Figure 15 shows the core tungsten concentration c w for the data set of section 4 with B tor = −2.5 T and I p = 0.8 MA. Central wave heating is used for the majority of data points, which is typically applied for ASDEX Upgrade tungsten operation [46]. The core tungsten concentration correlates with both the ELM proxy max(E prox ) and the turbulence control parameter α t . A reduced level of core tungsten is observed in QCE compared to type-I ELMy H-mode. This correlates with the reduction of the impurity source due to the absence of sputtering during type-I ELMs.
A correlation of lower tungsten concentration with increasing α t is observed. It is speculated that the particle and impurity outward transport at the edge of the plasma is increased by the local ballooning modes. The two branches visible for the QCE regime are due to a change in T e,sep . A lower tungsten concentration is observed at lower T e,sep values in phases with lower heating power.

Avoiding large ELMs from start to end of a discharge
While in ITER transient phases with type-I ELMs-at reduced plasma current or mitigated through reduced pedestal top pressure-might be acceptable regarding divertor power load [47], DEMO studies often focus on regimes without any type-I ELMs [45]. We investigate in this section the feasibility of entering the QCE regime without any transient type-I ELM phase. Furthermore, in the previous sections only plasma discharges without seeding are discussed. Here, we show that QCE discharges can transit into a nitrogen seeded, partially detached steady state phase at high normalised energy confinement time.

Overview of the discharge
We focus on ASDEX Upgrade discharge # 37164. For the first time a double feed-back controlled discharge was achieved by using neutral beam injection to control β pol and nitrogen seeding to control the divertor electron temperature T div . Figure 16 shows time traces of the most important parameters of this discharge. Panel (a) shows the plasma current and stored energy. The plasma current is ramped up from I p = 0.6 MA to I p = 1.0 MA in the QCE phase, resulting in q 95 = 4.6 in the flat-top. The discharge starts at low current and the density is increased already in L-mode to very high levels. H-mode is entered at these high densities and low currents, so that already the initial H-mode phase is a phase without ELMs. Subsequently, both current and heating power are simultaneously increased together with the gas puff. This is a delicate path through the operational space, as only slight misalignments lead to the occurrence of ELMs. Our way to Figure 15. Core tungsten concentration cw as a function of (a) the ELM proxy max(Eprox) and (b) the turbulence control parameter αt. QCE phases (Eprox < 1) exhibit low core tungsten concentrations. temperature estimate from shunt current T div , measured (black) and feed-back request (red). (e) ELM proxy Eprox derived from the divertor shunt currents. ( f ) Fuelling levels, deuterium fuelling is provided by gas valves in the divertor D div and main chamber D main . The nitrogen flux N flux from the divertor is feed-back controlled by T div . (g) Heating and radiated power levels, a constant ICRF power P ICRF is applied together with the feed-back controlled neutral beam power P NBI . The radiated power P rad is estimated from bolometric reconstruction.
achieve this successful discharge was to program the gas fuelling feed forward and additionally employ dual feedback: on β pol to control the heating power and on T div to keep the edge cool and the edge collisionality high. The β pol (c) and T div (d) controllers are active from 2.3 s and 2.5 s, respectively. A constant β pol = 1.3 is requested. The T div request value is slowly lowered from 15 eV at 2.5 s to 10 eV at 3.0 s. This allows to avoid large variations in the nitrogen flux which can lead to controller oscillations. Two flat-top values are programmed, T div = 10 eV (3.0-5 s) and later T div = 6 eV (5.3-7.0 s). Deuterium is puffed both from the divertor volume as well as main chamber positions in a feed-forward waveform, increasing during the I p ramp as shown in panel ( f ). The feed-back controlled nitrogen gas puff increases sharply at the start of the T div = 10 eV request. The requested nitrogen seeding rate then reaches a near constant level with a slow decline, a typical behaviour due to the increased amount of nitrogen stored in the wall throughout a discharge [48].
As shown in panel (c), the maximum neutral beam heating power of P NBI = 12.0 MW that was set for the controller is not sufficient to keep β pol = 1.3 when approaching T div = 6 eV. With the additional seeding the line averaged electron density approaches the Greenwald density and a reduction of the energy confinement time is observed, leading also to a drop of the normalised energy confinement time from H 98y2 = 0.9 to 0.75, shown in panel (b). The drop of β pol at constant heating power is reflected in the reduction of W MHD . Figure 17 shows time traces of the initial L-mode phase and the entry into H-mode. Panels (a) and (b) show the evolution of the stored energy and the density, respectively. In the grey area of panel (b) the density signal is perturbed by a MARFE [49], propagating up-and downwards on the high field side. This indicates that the fuelling and the separatrix density are very close to the maximum achievable value before leading to an L-mode density limit in ASDEX Upgrade [50,51]. The necessary fuelling level to stay away from the disruptive density limit depends on the machine conditions. The appearance of the MARFE is not needed for the transition to the QCE phase and should be avoided. In the future, a feed-back controlled fuelling trajectory in this phase is envisaged, similar to the H-mode density limit avoidance of [51].

Initial discharge phase and H-mode entry
The H-mode is achieved with the first step in neutral beam power. In this phase, the plasma current is low and q 95 = 7.8. The high q 95 allows an easier access to the type-I ELM free QCE regime [1,6]. After the L-H transition the stored energy increases, reaching a flat-top when low-amplitude filaments appear. The transition to the close to double-null shape is initiated after the L-H transition. A ramp-up in plasma current is done after achieving the close to double-null shape. Figure 18 shows Langmuir probe (LP) measurements from the outer divertor target in order to study the divertor state and the influence of the enhanced pedestal foot transport onto the divertor conditions. The grey dots represent single LP measurement time points, whereas the blue and red lines correspond to the lower envelope (0.05 quantile) to represent the value in-between filaments and an average (median, 0.5 quantile) over 30 ms, respectively. It is shown that the introduction of nitrogen leads to a partially detached outer divertor. A strong reduction of particle flux and electron temperature in-between filaments is observed. It is found that the filaments lead to an increase in particle flux and are dominating the overall particle flux to the target after nitrogen is introduced.

Influence of nitrogen seeding on divertor conditions
In the following paragraphs we discuss the evolution in detail. Figure 18(a) shows the integrated ion saturation current J tot = 2π R´j sat ds along the outer divertor target coordinate s. Both curves show a clear reduction by ramping up the nitrogen puff level at 3.0 s. The lower envelope (blue line) decreases significantly, J tot = 20 kA to 5 kA. The median value (red) decreases only moderately, J tot = 25 kA to 19 kA. While J tot in-between filaments reaches very low levels, the average value slowly decays towards a final value, J tot ≈ 10 kA. Figure 18(b) shows the peak electron temperature along the outer divertor target probes T e,tgt together with the T div feedback request trajectory in black. The control in such QCE discharges in ASDEX Upgrade works successfully, as the timeaveraged peak temperature from the LPs and the T div request agree reasonably. The time-averaged peak electron temperature at the outer divertor falls below 10 eV, however, single filaments clearly exceed this value. The peak temperature inbetween filaments (blue line) drops with the start of nitrogen seeding to T e,tgt ⩽ 5 eV. The temperature during filaments is likely over-estimated. The estimation of T e,tgt using triple probes assumes equal plasma parameters at all three probe locations which is potentially not given. Figure 18(c) shows the floating potential of one LP at ρ pol = 1.03. The floating potential is linked to the electron temperature but measured at a single location, thus, capable of resolving spatially small structures. It reaches about zero after 3.0 s and the filaments do not lead to a significant excursion.
It is conclude that the divertor is in a detached state in-between filaments and on average partial detachment is reached. However, single filaments still lead to a high ion saturation current, while the divertor temperature is ambiguous and needs further analysis.

Projection to ITER-like plasma parameters
In this section a projection to ITER-like parameters is performed. Limits for the achievable separatrix density, turbulence control parameter α t and collisionality ν * e,edge are derived using estimates of the separatrix conditions and varying assumptions of the fall-off lengths. These values are then compared to the conditions in which at ASDEX Upgrade the QCE regime is found.
We take ITER parameters, major radius of R geo = 6.2 m, minor radius of a geo = 2.0 m, elongation of κ = 1.8, averaged triangularity of δ = 0.49, toroidal magnetic field of B tor = 5.3 T, plasma current of I p = 15 MA and edge safety factor of q cyl = 3.0. Additionally, it is assumed that the power crossing the separatrix is P SOL = 100 MW and Z eff = 1.5-2.5 at the separatrix [52]. For the power fall-off length three values are taken. The smallest value of λ q = 0.9 mm corresponds to the extrapolation by Eich et al [40]. The largest value of λ q = 3.6 mm corresponds to the value chosen for the SOL/divertor simulations for ITER by Kukushkin et al [11]. Recent gyrokinetic simulations predict an even larger value [53]. A  medium value of λ q = 1.8 mm is added. Temperature, density and pressure fall-off length are estimated self-consistently with the chosen power fall-off length by using λ ne /λ Te = 3/2. Furthermore, assuming Spitzer-Härm electron heat conduction being the dominant heat transport channel gives λ Te /λ q = 7/2 and λ pe /λ q = 21/10. These relations are shown to be consistent with measurements in ASDEX Upgrade [25,26,36,54] and JET [36,55]. Note, poloidally averaged values are a factor 16/9 larger than the values at the outer mid-plane [40]. We use Spitzer-Härm electron heat conduction to estimate the separatrix temperature, equation (5). For the given gradient and estimated temperature, we calculate the density n IBM e,edge for which the ideal ballooning mode limit (IBM, α MHD = α crit , see equations (8) and (9)), is reached. With this density, we calculate the turbulence control parameter α IBM t , equation (7), and the edge collisionality ν * ,IBM e,edge , equation (6). The choice of focusing on the ideal ballooning mode limit is because it allows a self-consistency check of fall-off length with n IBM e,edge , α IBM t and ν * ,IBM e,edge . HELENA calculations confirm that an ITERlike pedestal with steep gradients is likely ballooning unstable at the pedestal foot supporting the existence of QCE at ITERlike parameters [14]. Further limitations outside the scope of this analysis are posed by avoiding H-L back transitions as well as excessive degradation of the pedestal pressure. Table 3 shows the calculated values for the three power falloff lengths taking Z eff = 2.0. For the smallest value of λ q = 0.9 mm, the maximum n e,edge given by the ideal ballooning limit is very low, leading together with the high T e,edge to an α IBM t = 0.13 and ν * ,IBM e,edge = 4. At this value of α t and/or ν * e,edge a type-I ELMy H-mode is always observed in ASDEX Upgrade. The situation gets more relaxed with a broader λ q through the increased achievable n e,edge , α t and ν * e,edge . With λ q = 1.8 mm a larger α IBM t = 0.55 and ν * ,IBM e,edge = 18 is calculated. This value of α t and/or ν * e,edge is sufficient to obtain QCE for the ASDEX Upgrade data set. For the largest value, λ q = 3.6 mm, the ideal ballooning limit for n e,edge is above the Greenwald limit n IBM e,edge / n GW = 1.5. This is interpreted that the actual limit is not set by ideal ballooning modes but rather by other effects. Not reaching the ideal ballooning limit but still having α t > 0.55 and/or ν * e,edge > 14 shows in ASDEX Upgrade the access to QCE but not reaching the highest pedestal top pressures.
So far we chose a fixed Z eff = 2.0. A variation in Z eff will lead to a modest change in the parameters. Taking the middle value of λ q , the influence of Z eff is presented in table 4. A variation from Z eff = 1.5-2.5 does not change the conclusions of the previous paragraph. A lower Z eff = 1.5 leads to a 4% higher n IBM e,edge and a 16% lower α IBM t and ν * ,IBM e,edge . A higher Z eff = 2.5 leads to a 3% lower n IBM e,edge and a 15% higher α IBM t and ν * ,IBM e,edge . As a conclusion, very small values of λ q are only selfconsistent with a low edge density due to the ideal ballooning mode limit. Reaching QCE with ITER-like plasma parameters seems plausible with a λ q broader than the empirical extrapolation by Eich et al [40] and at elevated edge densities. Indeed, a broadening is observed when increasing the density in the presented study in ASDEX Upgrade.

Access to detachment and seeding
We have shown that nitrogen seeding is compatible with the QCE regime in ASDEX Upgrade. However, in this initial experiments filaments are not buffered, e.g. still leading to an increased particle flux to the divertor target. This is a potential obstacle for the QCE regime as reactor-relevant alternative. Experiments as well as modelling will be needed to investigate if the filamentary heat and particle flux can be buffered along the open field lines in the scrape-off layer and-if buffering is possible-how to control the dynamic radiation/detachment state in the divertor.
The QCE filaments are thought to originate close to the separatrix. Thus, the ion temperature is of the order of the separatrix temperature. Low amplitude type-III ELMs were successfully buffered in JET [13] demonstrating that ions with such energies interact with the divertor plasma and are able to dissipate part of their energy. Future research has to address the particle flux due to the QCE filaments and verify if they can be buffered sufficiently to achieve low material erosion.
Furthermore, the increased cross-field transport in QCE leads to a density shoulder in ASDEX Upgrade. It was shown that the first wall loading increases with increasing α t [56]. Future studies have to assess if the first wall loading and the associated sputtering is acceptable for a reactor-sized tokamak.

Summary and conclusions
In the present contribution, the operational limits of the QCE regime are analysed and expanded. The transition from type-I ELMs to QCE is gradual. The definition of an automatic ELM proxy using the shunt currents measured at the divertor target allows to distinguish phases with type-I ELMs from QCE phases. The absence of type-I ELMs is correlated with high values of the edge collisionality of ν * e,edge > 14 and of the turbulence control parameter of α t > 0.55, where edge refers to the area 1 mm inside the separatrix.
The concept of a separatrix operational space was presented in [20], showing that H-mode conditions have different boundaries to L-mode, density limit and ideal ballooning limit. These boundaries are shown to also apply towards very high density for discharges in the QCE regime with high plasma shaping. An additional boundary is added for the transition from type-I ELMs to QCE by α t > 0.55.
The loss of type-I ELMs is attributed to a change of turbulence near the separatrix as characterised by α t and/or ν * e,edge . The impact of this change on transport was also studied. The pressure fall-off length at the pedestal foot measured by Thomson scattering is smaller than that predicted by the inter-ELM H-mode scaling of [19]. A regression analysis reveals that the broadening is better described by the linear q cyl dependence of ν * e,edge instead of the quadratic dependence of α t . The power fall-off length measured by infrared thermography is significantly wider in QCE compared to the ITPA multi-machine, inter-ELM scaling [8]. For the available data set, at fixed I p and B tor , the increase is best described by a linear correlation with n e,edge and p e,edge . Other dependencies need to be shown in the future, e.g. by multi-machine approaches.
The near separatrix parameters also affect core confinement. The normalised energy confinement time decreases with increasing n e,edge and α t in the presented data set, consistent with previous works in type-I ELMy H-mode [43,44]. QCE and type-I ELMy phases at similar α t exhibit similar H 98y2 values. At the highest pedestal top pressure the edge is close to the ideal ballooning mode limit, consistent with previous HELENA calculations [14].
The boundary parameters not only influence the plasma core, but also determine the interaction with the wall and the source of impurities. In QCE the tungsten concentration in the core plasma is lower than in type-I ELMy phases, correlated with the increased α t .
Two major steps for the reactor-relevance of the scenario are achieved. First, the QCE regime is successfully demonstrated for a low edge safety factor of q 95 = 3.3. Second, the access to QCE is possible in a demonstration discharge (i) without transient phase with large type-I ELMs, (ii) with a transition to a partially detached divertor and (iii) with high normalised confinement. This is achieved by a double feed-back on β pol and T div used for the first time in ASDEX Upgrade.
We propose a potential route to a safe start-up of a large scale tokamak: we showed that the operational space in terms of separatrix density is significantly larger than previously anticipated, e.g. in [36]. Hence, it is possible to start with very high separatrix density and sacrificing partially confinement. After learning to operate the machine in a safe way one then can reduce the separatrix density close to the border between QCE and type-I ELMy phases within a power exhaust solution to recover the necessary confinement but still operate without large scale transients. It is hence not critical to extrapolate the exact point between type-I ELMy phase and QCE for a larger machine but it is very critical to confirm the large operational density window also in larger machines.