Core transport modelling of the DTT full power scenario using different fuelling strategies

A theory-based integrated modelling work of plasma response to deuterium fuelling in the new Divertor Tokamak Test facility (DTT) is performed, using the 1.5D transport code JETTO with the quasi-linear anomalous transport model QuaLiKiz for the core region. The full power DTT scenario E1 is investigated. It is characterised by 28.8 MW of Electron Cyclotron Resonance Heating, 10 MW of Neutral Beam Injection and 6 MW of Ion Cyclotron Resonance Heating to the plasma. Plasma density and temperature profile evolution is calculated up to the separatrix using two different fuelling methods, gas puffing and pellet injection, and two different seeding gases, argon and neon. To sustain the desired pedestal density level with gas puffing a big amount of neutral flux at the separatrix is needed. The feasibility limits of the pumping system are exceeded, regardless of the type of impurity introduced, thus making the use of pellets mandatory. The simulations performed with pellet injection as fuelling method predict that the pedestal density is well sustained with realistic parameters foreseen for the DTT pellet injector. Strong dependence of the core density on the electron cyclotron resonance (ECR) power deposition profile is found. Trapped Electron Modes dominance, low outward flux and strongly hollow density in the inner core region are foreseen with central peaked ECR power deposition profile. Ion Temperature Gradient modes dominance, inward flux and robust density sustainment on the whole radial interval are predicted for spread ECR power deposition, though with central density close to the ECR cut-off limit and with peaked impurity densities. An intermediate deposition extension is found to sustain the whole density profile and to obtain flatter core densities, as previously predicted for the reference full power DTT scenario by fixed pedestal simulations. The ECR deposition is negligibly modified by refraction changes both during a single pellet cycle and after several pellet cycles, indicating full compatibility between the ECR system and the pellet injection system.

A theory-based integrated modelling work of plasma response to deuterium fuelling in the new Divertor Tokamak Test facility (DTT) is performed, using the 1.5D transport code JETTO with the quasi-linear anomalous transport model QuaLiKiz for the core region. The full power DTT scenario E1 is investigated. It is characterised by 28.8 MW of Electron Cyclotron Resonance Heating, 10 MW of Neutral Beam Injection and 6 MW of Ion Cyclotron Resonance Heating to the plasma. Plasma density and temperature profile evolution is calculated up to the separatrix using two different fuelling methods, gas puffing and pellet injection, and two different seeding gases, argon and neon. To sustain the desired pedestal density level with gas puffing a big amount of neutral flux at the separatrix is needed. The feasibility limits of the pumping system are exceeded, regardless of the type of impurity introduced, thus making the use of pellets mandatory. The simulations performed with pellet injection as fuelling method predict that the pedestal density is well sustained with realistic parameters foreseen for the DTT pellet injector. Strong dependence of the core density on the electron cyclotron resonance (ECR) power deposition profile is found. Trapped Electron Modes dominance, low outward flux and strongly hollow density in the inner core region are foreseen with central peaked ECR power deposition profile. Ion Temperature Gradient modes dominance, inward flux and robust density sustainment on the whole radial interval are predicted for spread ECR power deposition, though with central density close to the ECR cut-off limit and with peaked impurity densities. An intermediate deposition extension is found to sustain the whole density profile and to obtain flatter core densities, as previously predicted for the reference full power DTT scenario by fixed pedestal simulations. The ECR deposition is negligibly modified by refraction changes both during a single pellet cycle and after several pellet cycles, indicating full compatibility between the ECR system and the pellet injection system. a Second main author. * Author to whom any correspondence should be addressed.
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Introduction
The new Divertor Tokamak Test facility (DTT [1]), currently under construction, is aimed at performing studies regarding power exhaust and divertor load, which are considered critical issues to be solved in view of DEMO [2] and of the future fusion power plants. A comprehensive modelling work regarding scrape-off layer (SOL) predictions and design of optimised divertor configurations has been carried out and is currently ongoing [3][4][5]. In parallel, in close feedback with SOL modelling, an intensive integrated modelling work has been performed with reduced quasi-linear gyrokinetic and gyrofluid transport models to predict the performances and the limits of the planned operational scenarios [6,7]. In this framework, the sustainment and the evolution of the plasma density are key topics which need to be deeply investigated, taking into account the peculiarities of the foreseen operational scenarios of this machine. Amongst them, the two most stringent ones are the high density values at the separatrix and the strong radiation by impurity seeding. They are needed to achieve a partial or full detachment condition [4], in order to preserve the compatibility with the divertor and first wall power handling capability, and to avoid the tungsten erosion and the consequent high tungsten influx and core accumulation.
A modelling work regarding the plasma density sustainment and evolution includes many aspects: particle transport mechanisms in the plasma core, particle fluxes across the plasma separatrix and particle sources in the plasma due to ionisation of recycling atoms and to additional fuelling methods. The particle fuelling systems presently used for tokamak plasmas are the neutral gas puffing and the injection of frozen pellets. Neutral beam injection (NBI), mainly aimed for heating and current drive, can also be an efficient source of particles. Among the fuelling methods, pellet injection is considered essential to achieve high density scenarios in present tokamaks [8] and is presently the only option to fuel efficiently the core plasma of future fusion reactors. Several experimental works and theoretical and modelling studies have been carried out in order to investigate the fast transport phenomena following the injection of a pellet into a tokamak plasma. Theoretical descriptions of this dynamic have been recently performed and validated on different machines [9][10][11][12], and prediction works on future devices have been carried out [13][14][15].
Another element which can influence the density profiles is the location of the power deposition of the Electron Cyclotron Resonance Heating (ECRH) system, which has been selected as main auxiliary heating system for DTT. The well-known density pump-out effect [16], which is beneficial for preventing the impurity accumulation in the plasma core, can significantly modify the density profiles [17][18][19]. On the other hand, the electron cyclotron resonance (ECR) power deposition itself can be influenced by the density perturbation due to pellet injection, because of the dependence of the ECR efficiency and location on the plasma density. At the ECR injection frequency planned for DTT and for the densities foreseen for DTT in standard scenarios, issues can rise regarding proper ECR beam localisation. It may become problematic especially in outer plasma regions, which must be carefully reached by ECR beams for Neoclassical Tearing Modes stabilisation [20,21]. In general, high densities mean high plasma frequencies.
If the plasma frequency at some radial point becomes close to the ECR injection frequency, the ECR power can also be totally reflected. At ASDEX-Upgrade, the risk of ECR power reflection at high densities caused by pellet fuelling has been avoided by switching off ECR power during pellet ablation [22]. Initial studies regarding the impact of the density perturbation due to pellet ablation on the ECR power deposition location and efficiency have been performed [23]. The reference full power scenario for the DTT configuration R = 2.14 m sustained by pellet injection has been considered. Good compatibility between the ECR system and the pellet injection has been found.
Finally, the core impurity contamination from seeding and plasma facing component erosion and their mitigation strategies are investigated. In addition, phenomena typical of the plasma pedestal region like the temperature screening effect can have also an impact on the fuelling efficiency, as previously investigated and predicted [24,25]. The advantages due to gas seeding and pellet injection can be combined, provided the Greenwald density (which is defined as n GW : = I p /(πa 2 ), where I p is the plasma current and a is the minor radius) is not significantly overcome [26]. For the DTT reference scenarios, Greenwald fractions lower than 0.5 are foreseen [6,7].
In the work presented fuelling and density evolution are investigated taking into account such elements and their impact using as basis the previous particle transport studies. Indications are given regarding the plasma density pedestal sustainment and the impact of the different fuelling methods on the density and the temperatures of the plasma core region. Possible issues linked to the specific characteristics of the DTT machine are highlighted. An integrated modelling study of the full power DTT (R = 2.19 m, a = 0.70 m, B t = 5.85 T, I p = 5.5 MA) H-mode reference scenario has been performed, starting from the most recent DTT scenarios simulations [7] and the updated SOL investigations [5]. In section 1 the DTT full power reference scenario is briefly summarised, together with the simulation set-up of the previous integrated modelling work. A description of the codes used in this work to self-consistently include the plasma fuelling in the core plasma simulations is then reported. Section 2 concerns the methodology for the reconstruction of the density and temperatures pedestal. The results of the integrated simulations using gas puffing as fuelling method are reported. The investigation focuses on the role that the impurities fluxes and the ECR power deposition location have on the pedestal and core temperatures and on the density evolution. Simulations with pellet injection are then described in section 3. Three cases are reported: the first with central peaked ECR power deposition, as initially foreseen for the reference full power scenario. The others are characterised by wider ECR power depositions, self-consistently calculated in the simulations. An analysis of the plasma core transport as predicted by the simulations is performed, and indications on the pedestal and core density sustainment requirements are given. Finally, discussion and conclusions are reported in sections 4 and 5.

Multi-channel integrated modelling setup for DTT full power scenario
The modelling work here presented has been performed using the 1.5D transport solver JETTO [27], which belongs to the suite of codes JINTRAC [28]. The transport equations for heat, particles and momentum are solved up to the separatrix (i.e. ρ t = 1, where ρ t is the normalised toroidal radius, calculated as squared root of the normalised toroidal flux). Radial profiles of electron and ion temperatures, main density, impurity densities, toroidal rotation, and current density are predicted. The single null, positive triangularity DTT full power reference scenario simulations [7] have been used as basis for this study. As in those simulations, the anomalous transport coefficients are calculated by QuaLiKiz (QLK) [29,30], a reduced gyrokinetic quasi-linear transport model, which is integrated in JETTO. Additional Bohm transport (3%) has been added for numerical stability reasons and in order to compensate the low electron heat transport foreseen in the central region (ρ t < 0.2) by QLK [31]. The neoclassical transport coefficients are predicted by NCLASS [32] for both main particles and impurities. The impurities included in this integrated modelling are argon (Ar) or neon (Ne) as seeding gases, needed to enlarge the radiative dissipation in order to decrease the divertor thermal load. Tungsten (W) which originates directly from the first wall and the divertor surface due to sputtering is also considered. Their density profiles and radiation are modelled by SANCO [33], which solves the continuity equation for all the ionisation stages of the impurities together with the continuity equation for the neutral impurities. Neoclassical and anomalous transport coefficients are included. The penetration depth and the ionisation of the impurities which pass through the separatrix as neutrals are calculated. Null escape velocity and null recycling have been imposed as boundary conditions, to conserve the number of impurity particles. As initial condition, uniform values of effective charge Z eff and impurity density ratio have been introduced (Z eff = 2.2 for Ne and W, with n Ne /n W = 0.004, Z eff = 1.8 for Ar and W, with n Ar /n W = 0.01). Such assumptions are set in order to achieve the impurity concentrations compatible with typical values in tokamaks operating in full detachment and with SOL modelling predictions. The MHD equilibrium is self-consistently solved with the code ESCO [28], while the plasma boundary is provided by the CREATE-NL solver [34] and kept fixed. For the DTT full power scenario 45 MW of total power are planned to be delivered to the plasma. The so-called option E1 is characterised by the following heating mix reference configuration: ∼10.0 MW from the NBI system, ∼6.0 MW from the Ion Cyclotron Resonance Heating (ICRH) system, and ∼28.8 MW from the ECRH system. The parameters of the auxiliary heating systems selected for DTT have been included in JINTRAC as input of the codes for the self-consistent calculation of the power deposition and of the driven current profiles (PION [35] for ICRH, PENCIL [36] for NBI, and GRAY [37] for ECRH). The ICRH system is meant to operate in the frequency range 60-90 MHz, and is divided in modular units, with each module composed of two 3-strap antennas. The NBI negative-ion source delivers power to the plasma through a 500 keV deuterium beam. The synergy between ICRH and NBI is taken into account by the coupling of the PION code with the PENCIL code. PION solves a pitch angle averaged Fokker Plank equation which includes the source of NBI fast ions calculated by PENCIL. Absorption provided by the fast ion population is estimated by PION. The ECRH system is foreseen to operate at 170 GHz in O-mode polarisation, with two different antennas which are hosted in the equatorial and in the upper port of each ECRH sector, with six and two single launchers respectively. The eight launchers of a cluster are independently steerable to improve the flexibility, allowing ECR absorption over a broad range of plasma locations. In JINTRAC up to 20 beams with different steering angles can be used, allowing to obtain both peaked and spread power deposition profiles, despite the high focalisation which characterises the ECR beams [38]. The boundary conditions of electron and ion temperatures T e = T i = 130 eV, electron density n e = 8 × 10 19 m −3 , plasma current I p = 5.5 MA have been imposed at the separatrix and kept constant during the running time. These values have been chosen in order to operate in fully detached plasma conditions [4] based on SOL studies performed for DTT [3][4][5].
In [7] the pedestal values were fixed and previously calculated by a consistent MHD analysis using the model EPED1 [39]. However, it is not possible to use fixed pedestal to model the density evolution self-consistently with fuelling. A comprehensive self-consistent modelling of core-edge-SOL is outside the aims of this study. Thus the pedestal region has been reconstructed self-consistently with the evolution of the plasma core using simplified models (see section 2). For the study of the fuelling methods, the gas puffing has been considered first. The code FRANTIC [40] has been used to model the particle source due to the ionisation of the neutral flux at the separatrix. The model performs a very fast 1D neutral gas transport calculation for tokamak core plasmas, taking into account charge-exchange, ionisation and recombination. With a given specific boundary condition of the neutral influx at the separatrix FRANTIC assumes an exponential decay of the neutral profile towards the core of the plasma. Then calculates a flux surface average for the neutral density. The neutral influx is assumed poloidally symmetric. The study of the impact of the location of the gas pumping on the fuelling efficiency has been performed by the SOL modelling using appropriate 3D-codes [3][4][5]. The work is ongoing and different positions are under investigation. Presently quantitative estimates regarding the recycling of the neutrals particle at the separatrix are lacking, then the worst case for fuelling has been considered, i.e. null recycling regime. Finally, the ablation/deposition code HPI2 [41] has been used to calculate the density perturbation following the pellet injection. It is an 'intermittent pellet' module and provides the final state of plasma profiles taking into account ablation, ∇B-induced drift and homogenisation. It is valid for any magnetic and plasma configuration, any hydrogen isotope pellets and any injection position. Moreover, it includes the fast particles contribution to the ablation process. Simulations performed using HPI2 as a stand-alone application [42] identified the Oblique High Field Side (OHFS) and the High Field Side as the injection positions with the highest fuelling efficiency for DTT. For technological reasons, the OHFS position has been selected to be implemented in DTT, and hence has been integrated in JINTRAC and used in this work. Pellets with a dimension of 1 mm and velocity of 516 m s −1 were indicated as the best realistic compromise between the injection performances and the feasibility constraints using OHFS position.

Self-consistent pedestal modelling and predictive simulations with gas puffing
In order to recover the density and temperatures values previously calculated by EPED1, the anomalous transport has been highly reduced in the pedestal region. The external transport barrier (ETB) has been reconstructed modelling the neoclassical transport and tuning the lower limits for the particle and heat transport coefficients. In addition, the transport due to Edge Localised Modes (ELMs) has been considered. First studies regarding the type-I ELMs, typical of H-mode plasmas, have been performed using existing scaling laws and simplified analytical models [7]. Because of the unavailability of the parameters which characterise such discrete phenomena for the DTT full power scenario, a simple model has been selected: the transport coefficients are increased when the normalised pressure gradient exceeds a critical threshold, spreading the ELM-induced transport almost continuously over time [13]. The pressure gradient threshold and the transport coefficients multipliers have been selected as free parameters in order to reproduce the EPED1 density and temperatures pedestals.
Due to the high separatrix density, the density pedestal calculated by EPED1 is outward shifted with respect to the relative temperatures pedestal. Recent extensive experimental investigations [43,44] have shown that injecting high levels of gas puffing, and then increasing the density at the separatrix, two regimes can be found. They depend on the ratio between the separatrix density (ne sep ) and the density at the pedestal top (ne TOP ). For ne sep /ne TOP > 0.4 the density pedestal is outward shifted and the temperature pedestal is lower with respect to cases with lower levels of gas puffing, because of higher turbulent heat transport in the ETB region. For DTT ne sep / ne TOP ∼ 0.6, with ne TOP = 1.4 × 10 20 m −3 and ne sep = 0.8 × 10 20 m −3 . The density pedestal shift has been reproduced fixing different ETB widths for density and temperatures. The temperature values at the top of the pedestal were recovered by increasing the lower limits for the heat transport coefficient in the ETB region.
To reconstruct the pedestal, analysis of the dependence of the edge particle fluxes on the seeding gas type and on the ECR power deposition location has been performed. More details are reported in section 2.1.
In the first part of the work, simulations have been performed including gas puffing as the only fuelling method. A feedback scheme was used: the particle source switches on every time the electron density at the top of the pedestal drops below the value calculated by EPED1. Scans of the input value of the gas puffing nominal rate have been performed. Higher values than the level needed to sustain the density pedestal have been selected in order to avoid density pedestal oscillations due to numerical iterations and in order to adjust instantaneously the density profile. A good neutral penetration into the plasma is evaluated by FRANTIC: the calculated neutral density rate profile is significant up to ρ t ∼ 0.8. The particle source due to NBI is peaked in the plasma centre, though negligible with respect to the needed amount of particles to sustain the whole density profile. The predicted kinetic profiles are displayed in figures 1-left (for Ne) and l-right (for Ar). Good agreement between the simulations with fixed pedestal and the simulations predicting up to ρ t = 1 is found. The stationary condition is achieved: the pedestal and the core density is sustained by gas puffing. Temperatures are recovered over the whole radius.
The density pedestal of the reference full power scenario with Ne as seeded gas is sustained by an ionisation source rate at the separatrix of ∼4 × 10 21 s −1 . In order to reach it, an average influx of ∼1.4 × 10 22 neutral particles per second is needed through the separatrix for the considered plasma scenario configuration, density pedestal, boundary conditions and assuming no recycling for neutral particles at the separatrix. Similar values have been found using Ar as seeding gas.
In order to give indication about the feasibility of such fuelling method for DTT, a first rough evaluation of the fuelling efficiency can be given by the extrapolation of existing data reported in [6]. To achieve the required neutral flux at the separatrix, the gas puffing system needs to supply ∼0.9 × 10 23 particles/s at the first wall. Though the most conservative case of null recycling is considered, this value stays well above the feasibility limits for the pumping system. It implies that a pellet injection system seems to be mandatory for fuelling the DTT plasmas. To obtain results which more realistically reflect the self-consistent interaction between edge and core of the plasma, a modelling work using a core-edge-SOL coupled suite of codes with a discrete model for reproducing the ELMs should be performed. This is left for future work. with QuaLiKiz as transport model and solving the transport equations until the separatrix with gas puffing as fuelling method (red (green) lines for Ne (Ar)) and with fixed pedestal (black lines, see [7]). Graphs on the left (right) refer to the case with Ne (Ar) as seeding gas.

Dependence of the pedestal reconstruction on impurities and EC power deposition
To recover the pedestal as calculated by EPED1, the effect of the impurities in the edge region has to be taken into account. Not negligible impurity fluxes are predicted in the outer core region, due to high densities in the pedestal region. Figure 2 shows the neoclassical convective velocities of the inward directed main ions, and outward directed Ne, Ar and W impurities, due to temperature screening [24]: the high density at the separatrix gives lower normalised density gradient (DG) with respect to the relative normalised temperature gradient, leading to outward directed neoclassical convection for the impurities. For ambipolarity, the main ions are characterised by inward neoclassical convection. Such neoclassical fluxes are beneficial for the plasma core region, helping to avoid the impurities accumulation and facilitating the fuelling by main ions. The existence of such effects is well known, and they usually scale with the impurity concentration. However, their quantitative impact has to be considered with caution. The inclusion of the realistic ELMs dynamics can favourably or unfavourably modify the impurities fluxes in the edge region [45,46]. In addition, in this work a reduced neoclassical model, i.e. which does not take into account the effect of poloidal asymmetries, is used. However, this last choice can be justified by the absence of strong rotation in the DTT full power scenario [6,7], which would be the main cause for asymmetry generation. Taking into account the above described phenomena, in the simulations of the reference full power scenario a boundary condition for main ions of n i,sep = 0.6 × 10 20 m −3 for Ne (n i,sep = 0.65 × 10 20 m −3 for Ar) has been selected in order to recover an electron density n e,sep = 0.8 × 10 20 m −3 .
In DTT, because of the high level of the ECR power, the well-known density pump-out effect can cause differences in the impurity and main ion fluxes also close to the separatrix, depending on the location and on the radial extent of the ECR power deposition profiles. Figure 3 shows the edge neoclassical convective velocities for the cases of the peaked ECR and W (c), as calculated by the simulations of the DTT full power scenario E1 with solving the transport equations until the separatrix. These data refer to the stationary state recovering the pedestal given by EPED1 and with gas puffing as fuelling method. Red (green) lines refer to simulation with Ne (Ar) as seeding gas. power deposition used in the reference full power scenario simulations [6,7], compared with the values obtained using a spread ECR power deposition (see figure 3-left). Ne has been taken as seeded impurity in both simulations. For spread ECR deposition the outward impurity convections are lower, because of lower density pump-out effect and then lower impurity density at the edge. In the simulations the value of the main ion density at the separatrix has to be increased and the normalised pressure gradient threshold value has to be decreased to obtain the same density and temperature pedestals. Such adjustment is purely numerical, because it refers to the tuning work in order to recover the pedestal calculated by EPED1 for the DTT full power scenario with peaked ECR and W (c), as calculated by the simulations of the DTT full power scenario E1 with solving the transport equations until the separatrix. These data refer to the stationary state recovering the pedestal given by EPED1 and with gas puffing as fuelling method. Red (blue) lines refer to simulation peaked and spread ECR deposition. Solid lines represent the neoclassical convective velocities of simulations which rightly reconstruct the pedestal. Blue dashed lines refer to the case with spread ECR deposition with the same ETB + ELMs coefficients with respect to the peaked ECR deposition case. Right: fixed peaked (red) and calculated spread (blue) ECR power deposition profiles. power deposition. However this investigation highlights that, in the case of high edge density, impurities fluxes can have a not negligible role, and must be taken into account carefully for both core and edge predictions.

Predictive simulations with pellet injection
The simulations with gas puffing as fuelling method have been used as starting point for modelling the plasma response to pellet injection. The parameters for the ETB and the ELM model selected for the reconstruction of the pedestal have been kept unchanged. Recent works highlight possible differences in the pedestal structure fuelled by gas and by pellets [47]. However such discrepancies have not always been recovered by pedestal models. On the other hand, extrapolation studies for the estimate of realistic pedestal values for DTT with pellet injection are presently not available. Then the fuelling method has been directly substituted, switching off the gas puffing and starting to simulate pellet injection . The HPI2 code has been used for the discrete modelling of the particle deposition due to pellet injection, with the pellet injector geometry and parameters as reported in section 1. A feedback model has been used in order to sustain the pedestal, injecting a pellet as soon as the level of the density goes under the desired value. First, simulations have been carried out considering fixed central peaked ECR deposition, as initially foreseen by the full power reference scenario. Then the ECR deposition has been selfconsistently modelled, varying the ECR power deposition location and radial extension. Figure 4 shows the density profiles calculated during a single pellet cycle using Ne as seeding gas. The pellet deposition is located in the outer plasma region, around ρ t = 0.8. An injection frequency of ∼18 Hz is needed to sustain the pedestal. At such frequency the first pellet does not totally relax before the Electron density profiles as calculated by the simulations of the DTT full power scenario E1 with transport model QuaLiKiz, solving the transport equations until the separatrix with pellet injection as fuelling method and with Ne as seeding gas. One pellet cycle is represented (the first and the last temporal slices refer to the time of the pellet injection). The density profile obtained by the relative gas puffing simulation is shown with the black dashed line.

Peaked central ECR power deposition
injection of the subsequent pellet. After one pellet cycle the density profile is lowered with respect to the gas puffing density value in the radial interval ρ t = 0.1-0.6. The core particle fluxes during the pellet cycle of figure 4 have been investigated. The outer core region is characterised by inward flux due to pellet injection, with maximum at ρ t = 0.8 and with decreasing value during the pellet relaxation. The inner core region is also affected by pellet injection: during the pellet relaxation the turbulent regime is Trapped Electron Modes (TEM) dominant, leading to outward particle flux. More details regarding the dominant instabilities carrying such fluxes, together with their drivers, are reported in section 3.3.1.  Electron density profiles as calculated by the simulation of the DTT full power scenario E1 with transport model QuaLiKiz, solving the transport equations until the separatrix with pellet injection as fuelling method and with Ar as seeding gas. The temporal slices of the density profile just before (dashed line) and just after (solid line) the 11th (magenta) and the 25th (violet) pellet are represented. The density profile obtained by the relative gas puffing simulation is shown with the black dashed line. The fixed peaked ECR power deposition reported in figure 5-right has been used in the simulation. Figure 5 shows the evolution of the density profile after several pellet cycles. The pedestal is sustained, nonetheless the inner core is lower and hollower, and a pile-up is rising around ρ t = 0.8. Then, a stationary condition with high core density cannot be achieved. A similar though slower density evolution has been observed when neon is substituted with argon (see figure 6).
More investigations have been carried out, varying the injection frequency, the pellet size and velocity within realistic values intervals, however the above described evolution has always been recovered.
The dominance of TEM in the inner part of the plasma core for the DTT full power scenario is also predicted by gyrokinetic codes [6]. This is essentially due to the big amount of EC power to the plasma (28.8 MW), which is deposited in a restricted region (0.1 < ρ t < 0.3). In this radial interval the electron temperature and the relative gradient achieve high values, while the ion temperature remains lower. With continuous particle sources as gas puffing, a condition of stability is reached; however, if a discrete event like a pellet injection modifies, though slightly, the density and temperature profiles and the relative gradients, this causes outward flux due to TEM. 4.1.1. Core transport analysis. During the pellet cycle transient phase reported in figure 4 the neoclassical transport is at least one order of magnitude lower than the anomalous transport, and thus negligible. Figure 7 shows the ion anomalous flux and the relative convective velocity for the time slices of the pellet cycle.
The ion anomalous transport relative to the gas puffing case, here considered as initial time, is reported in figure 7-left with dashed line: inward and outward fluxes alternate in time and space in the inner (ρ t < ∼0.4) region and compensate each other, negligible fluxes characterise the outer core region.
To ease the analysis the radial interval is divided in four parts, dependently on the sign of the particle flux during the pellet cycle. The central region (ρ t < 0.25), where the flux is nearly null, the inner region (ρ t = 0.25-0.38) with outward flux, the mid-radius region (ρ t = 0.38-0.53), where the flux changes sign from negative to positive, and the outward region (ρ t > 0.53), with negative flux. All the inner and partially the mid-radius regions are characterised by positive convective velocity (see figure 7-right) during the whole pellet cycle. It gives outward flux in the radial interval of hollow density, overcoming the inward contribution given by the diffusive term.
The values of the main drivers of the drift wave instabilities and of the relative anomalous fluxes are investigated during the transient phase of the pellet cycle. Table 1 shows the maximum and minimum values of the normalised logarithmic gradients of the ion density and of the temperatures  Minimum and maximum values of the main drivers of the drift modes destabilisation (i.e. the normalised logarithmic gradients of main ion density R/L ni , ion temperature R/L Ti and electron temperature R/L Te , the ratios between R/L Te and R/L Ti and between the temperatures Te/T i , the normalised collisionality and the magnetic shear) for the three radial intervals with no null main ion particle flux relative to the time slices of the pellet cycle of figure 7. (i.e. R/L α : = −(∂α/∂r)R/α, where α is n i , T i , T e and R is the major radius), together with the temperatures ratio T e /T i , the magnetic shear s, the normalised collisionality ν * (defined as ν ie /ε 2 /3 /(c the qR), with ε = r/R, c the = √ 2T e /m e and ν ie the electron-ion collisionality [48]) in the three radial regions with not null flux. R/L ni is considered because in JETTO the transport equation for the ion density is solved, and the electron density is calculated following the quasi-neutrality condition. R/L ni has low absolute values (R/L ni < 2) in the radial interval ρ t = 0−0.8 because of the high values of the densities and the relatively low density gradient (DG) given by pellet injection. R/L Te and R/L Ti are characterised by higher values for nearly the whole radial profile (R/L Te > 10, R/L Ti > 5). Since R/L T ≫ R/L n we tend to exclude that DG instabilities could be the dominant modes at least in the first pellet cycles. This is the opposite of what has been found in the analysis of experimental profiles as due to pellet injection in AUG or JET, where the density profiles were highly modified by a single pellet [11,12]. The ratio T e /T i reaches values higher than 2 in the inner region, and decreases down to 1 at ρ t = 0.8. The normalised collisionality is characterised by very low (low) values in the inner (mid-radius) region. Magnetic shear is higher than 0.5 on nearly all the radial interval with not null transient flux.
The evolution of the main drivers of the modes together with the density and the temperatures at the various time slices of the pellet cycle are then investigated (see figure 8). The involved linear drift instabilities, which can be identified by the frequencies and growth rates, are illustrated in figure 9 as function of the radial position and of the wave vector spectra. The previously described three radial regions with not null transient flux are considered (a) outer region: 1. time just after the pellet injection (see dark blue line of figures 4, 7, 8 and 9(a), (d)): the ion density increases significantly with respect to the gas puffing case. T e /T i increases for ρ t < 0.7. Regarding the impact on the relative normalised logarithmic gradients, decreasing R/L ni and increasing R/L Ti and R/L Te are found. The outer region is characterised by the coexistence of Ion Temperature Gradient (ITG) and TEM, which causes an inward flux, with maximum value around ρ t = 0.7, due to the negative convective contribution (see figure 7(b)). 2. time of pellet relaxation (see lines from 2nd to 7th of figures 4, 7, 8 and 9(b), (e)): already after one time slice and for the subsequent ones, the deposition due to the pellet starts to relax, R/L ni increases, R/L Ti decreases and the flux is lowered but still inward because R/L ni does not recover the values of the case with gas puffing. ITG are characterised by lower growth rate than the time slice just after pellet injection (see figures 9(b) and (e), where the time slice just before the next pellet is shown). The density accumulates, also because the old pellet is not completely relaxed when a new pellet is injected.  (b) mid-radius region: 1. time just after the pellet injection: the ion density slightly increases and T e /T i increases. Slightly decreasing R/L ni and slightly increasing R/L Ti characterise this region. ITG instabilities dominates, giving low inward flux. 2. time of pellet relaxation: after some time slices, increasing R/L ni and decreasing R/L Ti are found, and the gas puffing condition is recovered, apart for T e /T i and R/L Te /RL Ti which remain higher. TEM becomes the only destabilised modes, then outward fluxes are predicted [49], first at lower radial positions and then, just before the next pellet, until mid-radius. It happens also in the region of hollow density. Although usually inward or null fluxes are foreseen for hollow density profiles [9,11,50], gyrokinetic modelling studies showed that, taking into account R/L Te ≫ R/L Ti , low outward fluxes can be predicted for low negative values of R/L n [51]. The density is then lowered. (c) inner region: 1. time just after the pellet injection: the ion density is practically not affected. Increasing T e /T i and high ratio R/L Te /R/L Ti give TEM dominance, then low outward flux with positive convection (see figure 7(b)) also in the region of hollow density.

time of pellet relaxation: increasing T e /T i and increas-
ing R/L Te /R/L Ti reinforce the TEM dominance and the outward flux.
Such dynamics are found also for the next (see brown lines in figures 4, 7, and 9(c), (f )) subsequent pellets. Figure 10 shows the ion density profile before and after pellet injection for several pellet cycles. The hollow inner region becomes larger and the density accumulates in the outer core region, originating a second outer hollow region. In the end a big hollow zone and a huge external peak are formed, as illustrated in figure 5.

Spread ECR deposition
TEM dominance must be reduced to use pellets as fuelling method. Therefore, a wider ECR deposition profile has been considered (0.05 < ρ t < 0.7), keeping unvaried the total amount of the injected ECR power. The ECR deposition profile has been self-consistently calculated in the JINTRAC simulation using the code GRAY. The needed ECR injection angles have been previously determined by studying the power deposition localisation with the stand-alone version of GRAY. Such work has been carefully performed, because highly focused DTT ECR beams are planned in order to give maximum flexibility to the ECR system. To obtain a spread ECR distribution without spikes and null deposition regions, 20 independently directed beams have been simulated. Poloidal and toroidal injection angle intervals which give maximum deposition width have been selected, with co-current in the region inside the q = 1 location, and counter-current outside the q = 1 location. Such choice for the current direction is made according to very recent studies regarding the EC-driven q profile tailoring on DTT full power scenario [7]. Figure 11 shows the kinetic profiles obtained with varying the ECR power deposition localisation. Monotonic density profile, lower electron temperature and slightly higher ion temperature in the inner core region with a ratio T e /T i closer to 1 have been obtained with spread ECR deposition.
JINTRAC simulations with gas puffing and pellet injection have been carried out following the same strategy described in previous sections. The fixed pedestal simulation has been recalculated with spread EC deposition. Figure 12 shows the electron density profile evolution during a pellet cycle, compared with the initial profile, calculated by using gas puffing as fuelling method. The pedestal is sustained with a pellet injection frequency of 20 Hz, with partial relaxation of the density perturbation due to the pellet injection. After one pellet cycle the density profile is sustained also in the core region. It is caused by the ITG dominance which gives low inward particle flux in the inner core region. In the outer core region a similar behaviour to the peaked ECR deposition case is found. More details regarding the analysis of the particle transport dynamics are reported in section 3.2.1. Figure 13 shows the density profiles after several pellet cycles, together with the relative ECR power deposition. A small density accumulation around ρ t ∼ 0.8 is present in the outer core region. However the ion flux is inward on the whole core region, as it can be argued by the increased density profile. After nearly 40 pellets the density profile in the inner core region is close to the stationary state. It is also very remarkable that the variations of the ECR power deposition location and values are negligible during all the simulation. The local density rise due to the pellet does not perturb significantly the EC deposition.  Electron density profiles as calculated by the simulations of the DTT full power scenario E1 with transport model QuaLiKiz, solving the transport equations until the separatrix with pellet injection as fuelling method and with Ne as seeding gas. One pellet cycle is represented (the first and the last temporal slices refer to the time of the pellet injection). The density profile obtained by the relative gas puffing simulation is shown with the black dashed line.   , (e) and integrated radiated power (with negative sign to underline the power loss) (c), (f ) profiles as calculated by the simulations of the DTT full power scenario E1 with QuaLiKiz as transport model and solving the transport equations until the separatrix with gas puffing as fuelling method with fixed peaked ECR power deposition (solid lines) and with self-consistently calculated spread ECR power deposition (dashed lines). Graphs on the left (right) refer to the case with Ne (Ar) as seeding gas. Figure 14 shows the electron density evolution after several pellet cycles using Ar as seeding impurity. The whole density profile is sustained during several pellet cycles and the stationarity condition is achieved for the plasma in the inner core.
This alternative full power DTT scenario, characterised by wider ECR power deposition profile, is rather different with respect to the reference one. With the achievement of so high densities (with density at the magnetic axis n e,0 ∼ 3 × 10 20 m −3 , and with Greenwald fraction f GW ∼ 0.6, defined as the ratio between the line average density and the Greenwald density) we get closer to the density limit. For DTT it is ∼3.5 × 10 20 m −3 , and it corresponds to the ECR cut-off density, i.e. the threshold density for which the ECR radiation is reflected. Scenarios characterised by such values of f GW are foreseen as possible advanced scenarios for DTT, however they are planned to be obtained with lower plasma current values and with densities well below the EC cut-off density. The decreased pump-out EC effect gives higher Ne and W central densities with respect to the case of peaked central EC power deposition, as shown in figure 15. Core impurities accumulation however causes rather limited increase in radiated power in the inner core region. The radiated power at the separatrix has still the value of ∼15 MW, as planned for the DTT full power scenario [7].
Since fuelling by pellet injection is the only feasible option for DTT, we can conclude that wider ECR power deposition profiles are needed to sustain the density in the plasma core region. In order to recover a safer flatter core density for the main ion and for the impurities, a third scenario is considered, characterised by an ECR power deposition profile with intermediate width, between the peaked and the spread ones.   Minimum and maximum values of the main drivers of the drift modes destabilisation (i.e. the normalised logarithmic gradients of main ion density R/L ni , ion temperature R/L Ti and electron temperature R/L Te , the ratios between R/L Te and R/L Ti and between the temperatures Te/T i , the normalised collisionality and the magnetic shear) for the two radial intervals relative to the time slices of the pellet cycle of figure 12. flux is very low and oscillating, with negative and small anomalous convection (see figure 16 right). It is comparable with the neoclassical flux: the total ion flux is weakly inward in this region, due to the direction of the neoclassical part. Since the second injected pellet (brown line in figure 16) the anomalous flux becomes inward. Outside ρ t = 0.45 the ion flux is inward due to the pellet injection, and it remains slightly inward just before the next pellet. Also in this case the relaxation of the pellet is not complete. Looking at the values of the main drivers of the anomalous transport in the plasma core region, which are reported in table 2, R/L ni is always positive and lower than R/L T . R/L Ti is characterised by higher values and R/L Te by lower values with respect to the case with peaked ECR deposition, and the their ratio is never above 1.6. T e /T i has a peaking value around 1.5. Normalised collisionality and magnetic shear are higher than the previous case (see table 1).
The density and the temperatures evolution during a pellet cycle is analysed. In the outer region everything is similar to the case with peaked ECR power deposition. In the inner region the main ion density is slightly modified by the pellet injection (see figure 17(c)). Looking at the corresponding involved instabilities, ITG are always the dominant modes for ρ t < 0.45, as it is shown in figure 18. Just before the pellet injection (see figures 18(b) and (e)), the presence of TEM is more significant, however almost always together with ITG. The main drivers of the drift instabilities evolve similarly to the previous case during the pellet cycle. At the time just before the next pellet injection, part of the inner region is characterised by lower values of the ratio R/L Te /R/L Ti and of R/L ni than the initial time slice. This, together with the already lower values R/L Te /R/L Ti with respect to the case of peaked ECR deposition, reinforce the ITG dominance also during the pellet relaxation and gives inward anomalous flux at the time slice of the next pellet injection also in the inner region.
After some pellet cycles the inner core density increases significantly, as it is shown in figure 19.  Figure 20 shows the profiles obtained by integrated simulations with gas puffing as fuelling method and selfconsistently calculating an intermediate ECR deposition localisation (ρ t = 0.05−0.5). They are compared with the relative profiles of the reference full power DTT scenario.
The electron density profile during one pellet cycle for the case of Ne as gas seeded is shown in figure 21. Despite the inner core region with density values very similar to the peaked ECR case, the whole density profile is sustained. In order to sustain the pedestal, a pellet injection frequency of ∼10 Hz is needed. The evolution of the outer core region is similar to the previous cases. The inner region is characterised by oscillating anomalous particle flux, significantly higher than the neoclassical contribution, due to the coexistence of ITG and TEM during the pellet relaxation phase. More details can be found in section 3.3.1. Figure 22-left shows the density profile after several pellet cycles. It is characterised by higher values in the outer core region with respect to the gas puffing case because of pellet accumulation. During the time the density increases also in the    inner core region. As for the spread ECR deposition, the inner core density profile tends to achieve a stationary condition. In the outer core region the same density values are recovered at every pellet cycle. As shown in figure 22-right the relative ECR deposition profile is slightly varying during the time, with higher values at ρ t = 0.4, because of not negligible changes in the values of the density.
The density evolution due to several pellet cycles with Ar as seeding gas is similar to the Ne simulation also in this case (see figure 23). However the shape of the profile is different between the Ar and Ne simulations: the density profile with Ar is monotonic, while it is characterised by a small hollow region if Ne is used as seeding gas.
The scenario with intermediate ECR deposition profile is characterised by density values which stay well below the EC cut-off density. In addition, the resultant impurity densities are quite flat and without large peaks in the inner core region (see figure 24). The radiation power is slightly higher than the reference scenario, however the value at the separatrix is close to the reference value of 15 MW. Such scenario represents therefore a valid alternative to the reference one.
Regarding the transport analysis of the three cases of ECR deposition, we can conclude that the density sustainment is mainly due to the type of the dominant drift mode in the inner plasma core. It gives the direction of the corresponding anomalous flux, and it mainly depends on the values of the normalised relative gradient of the temperatures. They vary with varying the localisation and the extension of the ECR power deposition, whatever is the sign of the low normalised relative DG.
The self-consistent calculation of the ECR power deposition has been carried out with a frequency of 4 Hz in the integrated simulation, i.e. every 3-5 pellet cycles. Small changes regarding the local intensity of deposited power have been found after several pellets (see figures 13 and 22). Thus we do not expect any significant effect on EC power deposition  during a pellet cycle. Figure 25 shows the density evolution during a single pellet cycle, simulated with self-consistently calculating the ECR deposition with higher frequency than the pellet cycle: each shown temporal slice corresponds to a new ECR deposition calculation. The equilibrium has been correspondently recalculated with the same frequency.
It confirms the analysis carried out in the DTT configuration R = 2.14 m and reported in [23]: also in this R = 2.19 m configuration the density perturbation during a pellet cycle is not problematic for the EC operation, allowing the accomplishment of all the aims foreseen for the EC system. Figure 26 shows the anomalous ion flux together with the relative convective velocity. Two radial regions are considered. For ρ t > 0.4 the anomalous flux is always inward in the outer core region, following the pellet injection dynamic. In the inner core region (ρ t < 0.4) a very low outward convection is partially compensated by the inward diffusion due to positive DG. The flux is oscillating until the second pellet injection, where weak inward flux is found. In this case the neoclassical flux is negligible with respect to the anomalous flux.

Core transport analysis.
Looking at table 3 in the inner core region the R/L Ti values are slightly lower than the values obtained for the spread EC simulation, while R/L Te values are slightly higher with respect to the case of peaked EC deposition, giving intermediate values of the ratio R/L Te /R/L Ti . R/L ni is significantly lower than the corresponding R/L Ti and R/L Te values, similarly to the previous cases. T e /T i and the normalised collisionality are similar to the ECR peaked case, while the magnetic shear values are closer to the ones of the EC spread case.
Looking at figures 27 and 28, in the outer region the kinetic profiles the drift instabilities and their drivers evolve as the previous cases. The inner region is characterised by dominant ITG just after the pellet injection, and coexistence of TEM and  , (e) and integrated radiated power (c), (f ) profiles as calculated by the simulations of the DTT full power scenario E1 with QuaLiKiz as transport model and solving the transport equations until the separatrix with gas puffing as fuelling method with fixed peaked ECR power deposition (solid lines) and with self-consistently calculated spread ECR power deposition (dashed lines). Graphs on the left (right) refer to the case with Ne (Ar) as seeding gas. Left: electron density profiles as calculated by the simulations of the DTT full power scenario E1 with transport model QuaLiKiz, solving the transport equations until the separatrix with pellet injection as fuelling method and with Ne as seeding gas. The temporal slices of the density profile during a pellet cycle relative to the self-consistent calculation of the ECR deposition are represented. Right: the relative self-consistently calculated ECR power deposition profile.  Table 3. Minimum and maximum values of the main drivers of the drift modes destabilisation (i.e. the normalised logarithmic gradients of main ion density R/L ni , ion temperature R/L Ti and electron temperature R/L Te , the ratios between R/L Te and R/L Ti and between the temperatures Te/T i , the normalised collisionality and the magnetic shear) for the two radial intervals relative to the time slices of the pellet cycle of figure 21. ITG at the maximum pellet relaxation time (see figures 28(b) and (e)). Similarly to the case with spread ECR deposition, at the time just before the next pellet, the ratio R/L Te /R/L Ti and R/L ni do not recover the values of the initial time slice in the inner region, reinforcing the ITG dominance at the subsequent time slices. Figure 29 shows the ion density profile evolution during some pellet cycles, just before and just after the pellet injection. The increased density profile in the outer region leads to lower positive and higher negative R/L ni values in the inner region, which tend to mitigate TEM. This, together with decreased R/L Te /R/L Ti causes ITG dominance in the inner region, then inward flux and higher density in the inner core region too.

Discussion
Some points must be highlighted in order to consider the limitations of this work.
The pedestal has been assumed as prescribed by EPED1, which performs ideal MHD stability analysis, giving then upper limit values for the pressure gradient. In addition, differences in the pedestal structure fuelled by gas and by pellets have not been recovered [46]. This is presently a topic of active research in tokamak physics, and no validated models are yet available for common use.
Regarding the uncertainties associated to the choice of the boundary parameters for this work, we refer to [3][4][5], where the DTT SOL modelling and its assumptions and uncertainties are discussed. A feedback model has been used for including ELMs, though the discrete nature of such phenomena has not been simulated. Their possible impact on the impurity fluxes and on the fuelling efficiency has not been considered. The interaction of fuelling pellets with ELMs has not been investigated. Such interaction might be detrimental, however ELM control techniques are foreseen for DTT. Only very recently studies regarding ELMs predictions for DTT have started for the determination of plausible discrete parameters like frequency and intensity, which are needed to be realistically included in the simulations. A comprehensive modelling with the inclusion of the discrete ELMs is planned in the near future.
Pellet injection for ELM pacing is planned: studies regarding an ad-hoc feasible and optimised injection system and a first analysis of the pellet parameters and their impact on the SOL region are ongoing. The impact of pellet injection for ELM pacing has not included in this work.
Regarding the core region, QLK is presently one of the most sophisticated physics based transport models which has been extensively validated in present devices and against gyrokinetic flux-tube simulations. Coupled with transport codes as JETTO, it has successfully reproduced core profiles of several experiments of different machines, properly capturing the turbulence dynamics [12,50,[52][53][54]. It is worth noting that the predicted transient fluxes reported here are low and their direction leads on the type of the predicted dominant drift mode. Then, in order to verify such predictions, calculations by quasi-linear and nonlinear gyrokinetic codes should be carried out for the specific kinetic profiles. However, recent gyrokinetic modelling predicted TEM dominance in the inner   core region of the reference DTT full power scenario with peaked EC deposition and fixed pedestal [6], in agreement with the findings of this work.
Finally, not including in the simulations the physics mechanism of the sawteeth means losing part of the inner core transport dynamics. Very recent studies foresee significant sawteeth for the DTT reference scenario [7], and also in that case, wider EC power deposition seems to be beneficial to mitigate such instabilities. However, it will be mandatory to include sawteeth in the simulations reported here in order to self-consistently model their impact on the particle and heat transport together with the effects due to the plasma fuelling.
Finally, not including in the simulations the physics mechanism of the sawteeth means losing part of the inner core transport dynamics. Very recent studies foresee significant sawteeth for the DTT reference scenario, and also in that case, wider EC power deposition seems to be beneficial to mitigate such instabilities. However, it will be mandatory to include sawteeth in the simulations reported here in order to self-consistently model their impact on the particle and heat transport together with the effects due to the plasma fuelling.

Conclusions
Predictive simulations aimed at the investigation of the main particle fuelling and density evolution for the DTT full power scenario E1 have been performed. The transport model QuaLiKiz has been used to calculate the transport in the core region. Tuned simplified models for the prediction of the edge region transport have been used in order to recover the temperature and density pedestals as calculated by the EPED1 model.
Edge and core fluxes due to impurities have been included and different ECR power deposition profiles have been considered. Gas puffing and pellet injection have been investigated as possible fuelling methods.
Fuelling the plasma only by gas puffing resulted unfeasible in the full power scenario, because of the huge neutral flux required to sustain the density pedestal. Conversely, pellet injection can sustain the pedestal using workable frequencies (10-20 Hz) and pellets with realistic dimensions and velocities (r = 1 mm, v inj = 516 m s −1 ). Nonetheless, injecting pellets drives small outward particle fluxes in the inner core region, which lower significantly the density profiles, and inward fluxes in the outer core region, causing a density pile up, and then emptying the core plasma region. The transport model QuaLiKiz predicts that the core region becomes TEM dominated in the phase after the pellet penetration and during the relaxation towards the null flux condition. The consequent outward particle flux causes density lowering. TEM dominance has been found mainly due to the central peaked ECR power deposition. Keeping the total injected ECR power fixed while widening ECR depositions increases R/L Ti and decreases R/L Te with respect to the peaked ECR deposition case. It allows ITG or the coexistence ITG/TEM to dominate the inner core region of the plasma. For the DTT full power scenario E1, the turbulence type and the particle flux direction are mainly given by the normalised temperature gradients. The values of the relative normalised DG are significantly lower, also during discrete phenomena like pellet injection and ablation. ITG give inward or null particle flux in the inner core region, allowing then the sustainment of the density on the whole radial interval. An intermediate ECR power deposition profile (ρ t = 0.05-0.5) can be considered as a good compromise: the density is sustained, and the kinetic profiles and the performances of the reference full power scenario are essentially recovered. Finally, the impact of the density perturbation during one pellet cycle on the ECR power deposition has been investigated: negligible effects on the localisation of the ECR beams and small differences in the intensity of the more external deposited power have been found.
Being aware about the limitations discussed in section 4, this work can give first indications about the fuelling efficiency for DTT. More in general it investigates the transport mechanisms in the core region due to discrete events like pellet injection. The impact of the ECR power deposition location and extension, and the presence of lighter and heavier impurities are taken into account. In a tokamak equipped by ECRH as main heating system, and with lower dimensions than the future fusion machines like DTT, the plasma core region can be TEM dominated. Though the TEM dominance can be helpful for avoiding impurity accumulation in the central region, it can be also detrimental in presence of discrete events like pellet injection and ablation. It may significantly lower the main ion density, emptying the inner core plasma region. Varying the extension of the ECR power deposition can change the turbulence type and the associated transport, and thus, give an essential contribution for the whole plasma density sustainment.