Pellet-fueled I-mode plasmas in ASDEX Upgrade

This letter reports on the efforts carried out at the ASDEX Upgrade tokamak to integrate I-mode plasmas with pellet fueling and to increase the I-mode Greenwald fraction fGW , two important requirements for any DEMO operational scenario. For the first time, stationary I-mode plasmas have been achieved with pellet fueling and the core Greenwald fraction has been increased up to 0.8. Larger fGW were not achieved due to technical constraints rather than to a physics-based limit. Pellet-fueled I-mode plasmas exhibit enhanced core and edge density, while core and edge temperature are reduced. Nonetheless, edge normalized gradients remain I-mode-like, namely shallow for the density and steep for the temperature. The I-mode energy confinement time is found to obey two distinct density dependencies: for fGW<0.4 it rises with increasing fGW , while for fGW>0.4 the energy confinement time plateaus with increasing fGW , or even decreases with fGW for the pellet-fueled plasmas. Similarities with Ohmic and L-mode energy confinement time dependency on density are discussed.


Introduction
The improved confinement mode (I-mode) is an attractive operational regime for fusion reactors based on the tokamak a See Stroth et al 2022 (https://doi.org/10.1088/1741-4326/ac207f) for the ASDEX Upgrade Team. * Author to whom any correspondence should be addressed.
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concept. I-mode plasmas feature an enhanced energy confinement time, while the particle and impurity confinement times remain similar to those of low-confinement mode (L-mode) plasmas [1][2][3]. The separation of energy and particle transport channels is reflected in the I-mode edge profiles: a temperature pedestal is formed, while the edge density profile is L-modelike. In this way, the I-mode couples the desired properties of high-confinement mode (H-mode) and L-mode plasmas, namely high energy confinement and reduced impurity accumulation in the core. Moreover, the I-mode pedestal is far from the ideal peeling-ballooning stability boundary and, hence, is free of type-I Edge Localized Modes (ELMs) [4,5]. These are magnetohydrodynamic instabilities which should be avoided in a fusion power plant, due to the high transient energy load that they induce on the divertor target plates [6]. For these reasons, the I-mode is considered as one candidate for the operational regime of the EU-DEMO reactor [7].
I-mode plasmas are typically achieved in the so-called unfavorable configuration, i.e. when the ion B × ∇B drift points away from the active X-point. In this configuration the H-mode power threshold increases, and an operational window for the I-mode opens up. In this way, the I-mode has been achieved in several devices (Alcator C-Mod [2], ASDEX Upgrade (AUG) [8], DIII-D [9], EAST [10], KSTAR [11]), with different fueling species (deuterium, hydrogen and helium) [12,13] and in a wide range of plasma parameters, such as edge safety factor, triangularity, pedestal top collisionality and plasma beta poloidal [14]. Nonetheless, the I-mode still needs to be proven to be compatible with the strict requirements of a DEMO operational scenario. In particular, any DEMO scenario will need to be fueled with pellets [15][16][17], i.e. mm-sized solid bodies composed of frozen fuel, as this is most likely the only way to efficiently fuel devices with large major radius and with a Scrape-Off-Layer opaque to neutrals [18,19]. Moreover, the candidate DEMO scenario will need to achieve high line-averaged plasma densities [7,20], n, normalized to the Greenwald density [21,22], n GW = I p /(π a 2 ) where I p is the plasma current in MA, a the plasma minor radius in m, and n GW is expressed in 10 20 m −3 . This is required to maximize fusion energy production. The I-mode is typically achieved at Greenwald fractions f GW = n/n GW < 0.5 [14] and, as yet, has never been obtained in combination with pellet fueling.
In this work, we report on the experimental effort recently carried out at the AUG tokamak to obtain stationary Imode plasmas with pellet fueling and to increase the I-mode Greenwald fraction.
The paper is organized as follows. In section 2, the experimental route pursued to achieve pellet-fueled I-mode discharges with stationary density is described. In section 3, the properties of high-density I-mode plasmas are analyzed in detail, while in section 4, the main conclusions are outlined.

Experimental set-up
AUG is a medium-sized divertor tokamak (major radius R 0 = 1.65 m, minor radius a = 0.5 m) equipped with a versatile set of auxiliary heating systems: neutral beam injection (NBI, up to 20 MW), electron cyclotron resonance heating (ECRH, up to 6 MW) and ion cyclotron resonance heating (ICRH, up to 6 MW). Moreover, AUG is equipped with a pellet fueling system which is able to fire pellets into the plasma from the High Field Side (HFS) [23,24], maximizing pellet fueling efficiency [25]. The system consists of a cryostat, where deuterium ice is prepared and stored prior to the discharge, an accelerating centrifuge [26], and a curved guiding tube connecting the centrifuge to the tokamak HFS. The system is able to generate pellets with particle content m p of either 1.4, 2.8 or 4.3 × 10 20 deuterium atoms, and to launch pellets with speed v p in the range 240 m s −1 < v p < 1050 m s −1 and with a frequency up to 83 Hz. This considerable flexibility in pellet choice allows a step-wise integration of I-mode plasmas with pellet fueling.
As outlined in the introduction, I-mode plasmas are obtained in the unfavorable configuration, i.e. when the ion B × ∇B drift points away from the active X-point. Considering that the direction of ∇B is fixed in a tokamak geometry, i.e. pointing towards the central solenoid, a change of the ion B × ∇B drift direction is obtained by changing the toroidal magnetic field, B t , direction. The unfavorable configuration can be obtained in AUG both in the Lower Single Null (LSN) and in the Upper Single Null (USN) configuration. The signs of the I p and B t directions for both the USN and LSN unfavorable configurations are shown in figure 1. The B t and I p directions in USN-unfavorable configuration are the same as in the LSN-favorable case, i.e. the so-called 'standard' directions. With this I p -B t combination the ion B × ∇B drift points towards the lower divertor. On the other hand, the B t and I p directions in LSN-unfavorable configuration are both reversed w.r.t. the 'standard' directions, and therefore they are named 'reversed'. In this way, the ion B × ∇B drift points towards the upper divertor, and the magnetic field line helicity at the lower divertor target is kept constant to avoid the formation of leading edges.
As shown in figure 1, pellet injection is possible in both USN and LSN configurations. In terms of density control, the LSN configuration has an advantage over the USN configuration, since both the cryo-pump and the turbomolecular pumps are located in the lower divertor region. In terms of reliability of pellet generation, the USN-unfavorable configuration has an advantage with respect to the LSN-unfavorable configuration, since the ice cutter used to create pellets relies on a permanent magnet which was optimized for the 'standard' toroidal magnetic field direction, i.e. the B t direction in the USN-unfavorable configuration. Moreover, in AUG, LSNunfavorable configuration plasmas are rarely studied, since reversing the plasma current limits the usage of the NBI system, which injects counter-current and, hence, enhances ion orbit losses. For these reasons, pellet fueled I-mode plasmas were first developed in the USN configuration and then, with the acquired knowledge, further studied in LSN. Figure 2 shows the time evolution of several plasma parameters in an USN I-mode discharge fueled with pellets. The plasma current and toroidal magnetic field are 1 MA and −2.5 T, respectively. The plasma is heated with NBI, which is feedback controlled on the beta poloidal β pol , similarly to experiments described in [27,28]. ECRH is not used in this case, to avoid wave cut-off at the higher core density which could be achieved with pellets. The requested β pol (red in panel (b)) is initially linearly increased to enter the Imode, and then kept constant at β pol = 0.5 to maintain a stationary I-mode. At around t = 2.5 s several indications of a L-I transition occur: The pedestal top electron temperature, i.e. the temperature measured by Electron Cyclotron Emission (ECE) [29] at ρ pol = 0.95, increases at almost constant heating power, see panel (e); the thermal energy confinement time, τ th , increases, see panel (d); the line-averaged electron density measured by interferometry [30] stays approximately constant, see panel (f ); and, the Weakly Coherent Mode (WCM)-a typical feature of I-mode edge turbulence [31,32]-becomes prominent in the spectrogram of the phase derivative measured by reflectometry at the plasma edge [33]. Note that the WCM is present also in the L-mode phase preceding the I-mode, as has been recently reported in [27,34]. Due to the β pol feedback control, the I-mode is kept stationary between t = 2.9 s and t = 3.5 s. In this phase, the deuterium gas puff, which is feedback controlled on the requested value of line-averaged density, is turned off to keep the plasma density constant. This is a typical feature of USN discharges in AUG, where the upper divertor is not pumped and, therefore, wall recycling is usually enough to maintain constant density. At t = 3.6 s small pellets (m p = 1.4 × 10 20 deuterium atoms) are fired into the plasma at a speed of v p = 548 m s −1 and with a frequency of f p = 14 Hz. This corresponds to a pellet particle flux of Γ p = m p × f p = 2 × 10 21 e/s, as shown in panel (c). Both the line-averaged density and the core electron density increase linearly in this phase. The core density has been evaluated with Integrated Data Analysis (IDA) [35] combining measurements from core Thomson Scattering (TS) [36] and interferometry. To compensate for the typical reduction of pedestal top temperature observed during injection of cryogenic pellets [37], the requested value of β pol is linearly increased as well. In this way, the pedestal top electron temperature is kept approximately constant in the pellet fueled I-mode phase. Interestingly, the WCM signature at the plasma edge changes during pellet injection. This change is related to the fast edge temperature drops induced by pellets, see panel (e). These drops-and their recovery-affect the central WCM frequency [38], which in turn leads to an apparent WCM broadening. However, on fast timescales, the WCM does not seem to become less coherent.

USN experiments
At t = 5.03 s the plasma enters H-mode, as the applied heating power was large enough to trigger an I-H transition. Note that the so-called Pedestal Relaxation Events (PREs)-i.e. small ELM-like events that typically appear in I-mode before the I-H transition [39,40]-did not occur in this case and in any other pellet-fueled I-mode. After the H-mode transition, the discharge ramps down without any radiative collapse. In the time window 3.6 s < t < 5.0 s a stable I-mode plasma entirely fueled by pellets was achieved. However, the lack of a pump in the upper divertor did not allow density control in these discharges. Therefore, to obtain pellet fueled I-modes with stable and controllable plasma density, experiments in LSN were carried out. Figure 3 shows a LSN I-mode discharge with pellet fueling. The discharge was carried out with 'reversed' I p and B t directions, and absolute values of 0.8 MA and 2.5 T, respectively. The plasma was heated with constant 2 MW of ICRH and with NBI heating, the latter being feedback controlled to reach the desired values of β pol . The addition of ICRH heating was required in LSN plasmas, to decrease the amount of NBI power used and, hence, to reduce ion orbit losses. The requested β pol was initially linearly increased, to enter the Imode and then kept fixed at β pol = 0.58, see panel (b). At about t = 2.4 s the plasma enters I-mode, as can be seen from the increase of the pedestal top electron temperature, the constant line-averaged density, and the appearance of the WCM in the spectrogram of the phase derivative measured by reflectometry at the plasma edge. Note that the L-I transition occurs while the heating power is increasing, and the thermal energy confinement time exhibits only a very mild increase during the transition. This is due to the power degradation of L-mode and I-mode energy confinement time [8,[41][42][43], which would have caused τ th to decrease if no L-I transition had occurred. At t = 3.5 s small pellets (m p = 1.4 × 10 20 deuterium atoms) are fired into the plasma at a speed of v p = 547 m s −1 and with a frequency of f p = 23 Hz. This corresponds to a pellet particle flux of Γ p = m p × f p = 3.2 × 10 21 e/s, as shown in panel (c). As soon as pellets are injected into the plasma, both the line-averaged density in panel (f ) and the core plasma density in panel (g) increase and maintain a steady level at n e = 6 × 10 19 m −3 and n e,core = 8 × 10 19 m −3 , which is about f GW,core = n e,core /n GW = 0.8. Note that the deuterium gas puff is turned off when pellets are injected, as it was controlled in feedback on the line-averaged density. During pellet injection, the pedestal top electron temperature and τ th decrease. Since the NBI power is feedback controlled on β pol , the applied heating power needs to increase to maintain the requested constant β pol when confinement reduces. The energy confinement time dependency with density and power will be further discussed and analyzed in section 3. The WCM signature at the plasma edge remains visible also during pellet injection, see panel (h). The WCM frequency reduces at around t = 4 s following the decrease of T e,ped , in line with a recent scaling of the WCM frequency found at AUG [38]. In this phase, a steady pellet-fueled I-mode plasma with stationary density and f GW,core ≈ 0.8 was achieved. This phase lasted until the end of the current flat-top.

LSN experiments
The electron density, electron and ion temperature profiles during pellet fueling are plotted in figure 4 and compared to the previous phase where the plasma was fueled only via gas puff. The profiles have been evaluated via IDA [35,44], which combines different diagnostics in the framework of Bayesian theory. Interferometry and TS data are combined for the electron density, ECE and TS measurements are used for the electron temperature, while core and edge charge exchange recombination spectroscopy (CXRS) measurements [45,46] are employed for the ion temperature. The ion temperature profile in the pellet-fueled phase is known up to ρ pol = 0.95, as edge CXRS measurements were not available in this phase.
During the pellet-fueled phase, both core and edge electron density increase due to the larger deuterium fueling. Furthermore, the density profile exhibits different gradients around ρ pol ≈ 0.7, which is due to the different neutral source between the two phases. Indeed, the pellet burn out location is on average at ρ pol = 0.68 with a standard deviation of ±0.04. The pellet burn out position has been evaluated by mapping the measured pellet self-emission profile on the magnetic configuration and assuming the pellet travelling along its designated injection path with its initial speed [47]. The small variation Electron density (a), electron temperature (b) and ion temperature (c) profiles in the pellet-fueled phase (5.85 s < t < 6.05 s-orange) and gas-fueled phase (3.20 s < t < 3.50 s-blue) of the I-mode discharge #38 684. Circles represent ECE and CXRS data, squares TS data, while solid lines are the profile fits from IDA averaged over the time window in the pellet penetration depth can be mainly attributed to the nonidentical mass of each pellet, which can slightly deviate from the maximum value of m p = 1.4 × 10 20 atoms. The additional source of neutrals around ρ pol = 0.68 is, therefore, causing the density gradient to vary at that location.
When cryogenic pellets are injected into the plasma, both electron and ion temperature reduce across the whole plasma radius. However, the relative reduction of T i is smaller than that of T e in the plasma center. This is likely due to a combination of several effects: The change in plasma collisionality with pellet fueling, which allows a better coupling between ions and electrons at high plasma densities; the increase of NBI heating during pellet fueling, which could change the electron and ion power deposition profiles; and an increase of electron cooling when pellets are injected, as ablation is typically dominated by collisional heat transfer from electrons. Looking at core gradients, while the ion temperature gradient (ITG) is mainly unchanged between the two phases, the electron temperature gradient slightly reduces at around ρ pol ≈ 0.7 in the pellet-fueled phase. Figure 5 shows the sum of ion and electron pressure profiles in the two phases under analysis. Since the plasma is feedback controlled to have constant β pol , i.e. volume-averaged plasma pressure, the pressure profiles are similar between the two phases. However, the profile shapes differ: While in the gas-fueled phase, the pedestal top pressure is lower and the core gradient steepens around ρ pol = 0.7, in the pelletfueled phase, the pedestal top pressure is larger and the core gradient steepens around ρ pol = 0.5. A possible explanation of the discharge temporal dynamic could be the following: when pellets are fired into the plasma, the pressure gradient is relaxed around ρ pol = 0.7 and, consequently, the volumeaveraged plasma pressure reduces. Then, the feedback control increases the heating power to raise β pol ; however, due to profile stiffness in the core, this additional energy feeds the pedestal top, which is far from ideal magnetohydrodynamic limits [5,28] and, hence, can increase. The shallower core gradient at ρ pol ≈ 0.7 observed during pellet injection is an indication that confinement reduction is (at least partially) due to a decrease of core confinement. To clarify whether pedestal confinement is also affected during pellet injection, an experiment with constant applied heating power is required.

Properties of high-density I-mode plasmas
Here, plasma properties of high-density I-modes are analyzed in more detail. Typically, to show the proximity of the plasma to the density limit [22], the line-averaged density is normalized to the Greenwald density. However, it is well known that the tokamak density limit is determined by the edge density [48][49][50][51], and, indeed, pellet-fueled plasmas can exceed f GW = 1 [37,52]. For this reason, it is interesting to compare the plasma density at different positions of the profile shape, while normalizing it to the Greenwald density. Figure 6(a) shows the core Greenwald fraction f GW,core = n e,core /n GW versus the edge Greenwald fraction evaluated at ρ pol = 0.9, f GW,90 = n e,90 /n GW , for the entire AUG I-mode database. Electron density profiles have been evaluated via IDA [35], and the core density is evaluated at the innermost radial measurement position of the TS system, that is at ρ pol = 0.2. Overall, both core and edge Greenwald fractions extend over a wide range of values; however, while the edge Greenwald fraction is always lower than 0.5, f GW,core reaches higher values (f GW,core = 0.8). Moreover, for the same edge Greenwald fraction, LSN pellet-fueled I-mode plasmas were able to achieve larger f GW,core than gas-fueled I-modes. Figure 6(b) shows f GW,core versus the separatrix Greenwald fraction f GW,sep = n e,sep /n GW for the entire AUG I-mode database. Overall, the I-mode database at AUG never reaches f GW,sep > 0.25, while the core Greenwald fraction can be increased up to 0.8. The relatively low values of f GW,sep reached in AUG I-mode plasmas is one reason for the difficulty in integrating I-mode with divertor detachment [53,54]. Figure 6(b) clearly shows the effect of the presence of a pumped divertor on the I-mode separatrix density. For the same f GW,core , LSN pellet-fueled plasmas (with a pumped divertor) reached lower separatrix Greenwald fractions than USN pellet-fueled plasmas (without a pumped divertor). Therefore, in AUG, switching divertor configuration can be used to lower the separatrix density while keeping the core density unchanged.
The maximum Greenwald fraction achieved in the core was limited by technical capabilities of the pellet system in LSN-unfavorable configuration. As outlined in section 2, the Electron temperature vs electron density maximum edge normalized gradient for L-mode (purple pentagons), gas-fueled I-mode (gray circles), pellet-fueled I-mode (orange squares) and H-mode (blue triangles). Pellet-fueled I-mode plasmas exhibit L-mode-like edge density normalized gradients and H-mode-like edge temperature normalized gradients, as do gas-fueled I-mode plasmas.
AUG pellet system was optimized for operation in the 'standard' B t direction; hence, when B t is reversed, the generation of frozen pellets is hindered, in particular at higher frequency of injection f p . This did not allow reliable pellet operation with f p > 23 Hz, preventing the core Greenwald fraction to go beyond 0.8. Figure 7 shows the maximum edge electron temperature and density normalized gradients for different AUG confinement regimes, including pellet-fueled I-mode plasmas. Edge profiles have been fitted with a modified hyperbolic tangent function, and gradients have been evaluated in the real space coordinate R. As already shown in previous studies [2,28], L-mode plasmas exhibit shallow edge density and temperature normalized gradients, while H-mode plasmas have steep density and temperature normalized gradients due to the presence of the edge transport barrier. I-mode plasmas are instead characterized by L-mode-like edge density normalized gradients and H-mode-like edge temperature normalized gradients. Pellet-fueled I-mode plasmas, despite the presence of a high edge density, still exhibit shallow edge density normalized gradients, i.e. no density pedestal. Moreover, in spite of the edge temperature cooling due to pellet injection, pelletfueled I-mode plasmas maintain steep edge temperature normalized gradients. Therefore, edge normalized gradients of pellet-fueled I-mode plasmas are not substantially different to those of gas-fueled I-mode plasmas.
In the previous section, it was shown that τ th decreased when pellets were fired into a high-Greenwald-fraction I-mode plasma. In order to thoroughly study the I-mode energy confinement time dependence with density, a restricted I-mode database is analyzed. It is composed of I-mode plasmas with constant B t = 2.5 T, with elongation κ = 1.66 and average triangularity δ = (δ up + δ low )/2 = 0.21, where δ up and δ low are the upper and lower triangularity, respectively. The total number of I-mode plasma phases is 331, of which 233 are in USN and 98 in LSN configuration. The only varying engineering parameters are: the plasma current, which ranges between 0.6 MA and 1.0 MA; the line-averaged core electron density n e , which varies between 2.0 × 10 19 m −3 and 7.3 × 10 19 m −3 ; and, the loss power P loss , which spans the range between 1.0 MW and 4.4 MW. The loss power is defined as P loss = P heat − dW/dt, where P heat is the absorbed heating power taking into account the heating losses, and W is the plasma energy. The variation in n e and I p corresponds to Greenwald fractions f GW = n e /n GW between 0.2 and 0.59. The thermal energy confinement time has been calculated as τ th = (W MHD − W fi )/P loss , where W MHD is the plasma stored energy from magnetic equilibrium reconstruction and W fi is the fast-ion energy content evaluated as in [55].
With this database, a regression of τ th on the engineering parameters I p , P loss and f GW has been carried out. The function chosen to fit the data on the log-log scale has the typical linear dependence for I p and P loss , while it depends quadratically on f GW . The resulting function on log-log scale is: ln(τ th ) = ln(C) + αln(I p ) + βln(P loss ) where C, α, β, γ and δ are fitting constants. On linear scale equation (1) reads: The regression result is given by: The covariance matrix of this dataset reveals that I p weakly correlates with P loss , while f GW exhibits a modest correlation (0.4) with P loss . The latter correlation mainly stems from high-density discharges, as it can be seen e.g. in figure 3 where heating power and density are changing simultaneously. Exclusion of high-density data reduces the cross-correlation between P loss and f GW , and yields a similar P loss exponent to that in equation (3). This increases confidence in the validity of the P loss dependence found in equation (3). The regression reveals that the I-mode energy confinement time depends on the plasma current with a positive exponent, in line with previous findings from Alcator C-Mod [56,57], while it depends on the loss power with a negative exponent, similarly to what was previously found at AUG [8] and EAST [43]. What is particularly interesting here is the dependency of τ th with f GW , shown in figure 8(a), where τ th has been normalized to the I p and P loss power terms found in equation (3). The I-mode energy confinement time has a twofold dependency with f GW : for f GW < 0.4 the thermal energy confinement time of I-mode increases with the Greenwald fraction, a desired feature for a future reactor where core density will need to be maximized. This characteristic of I-mode plasmas is well known and has been previously reported in AUG [8] and Alcator C-Mod [56]. However, when the lineaveraged density is further increased, more precisely when f GW > 0.4, the thermal energy confinement stays constant with density, or even decreases with density for the pellet-fueled Imode plasmas.
The twofold dependency of τ th with density is reminiscent of that of Ohmic energy confinement, which scales linearly with plasma density [58] up to a certain point, above which confinement stays constant or even decreases with density, see [59] and references therein. These two regimes are called Linear Ohmic Confinement (LOC) and Saturated Ohmic Confinement (SOC). The transition from LOC to SOC is associated with a change of core turbulent transport, which at low density is dominated by Trapped Electron Modes (TEMs), while at high density is dominated by ITG modes. When density increases in Ohmic plasmas, the rise of collisionality stabilizes TEM-driven turbulence [60]. At the same time, electron-ion coupling improves and, hence, a larger fraction of heat is transported by ions, increasing ITG-driven turbulence [61]. At higher densities, when electrons are fully coupled to ions, energy confinement is mainly set by ion transport, which is strongly stiff [60] if the impurity content does not change substantially [61]. Consequently, the Ohmic energy confinement time no longer increases with density.
L-mode plasmas also exhibit an increase of energy confinement time with density [41,42], which occurs again for the increase of ion heat transport with density [62] and is associated with a change of turbulence characteristics (ITG modes becoming more dominant) [63]. A similar effect could take place in low-density I-mode plasmas as well, and explain part of the observed dependencies. Indeed, figure 8(b) shows that low-density I-mode plasmas have a larger fraction of direct electron heating, which could result in a plasma dominated by electron heat transport (i.e. TEMs) due to the poor electronion coupling at low density. When density rises, TEMs could be stabilized and a larger fraction of heat could be transported by ions, which could cause confinement to increase until electrons and ions are fully coupled. To further investigate this hypothesis, detailed modeling would be required which is left for future work.
The twofold dependency of I-mode τ th with f GW cannot be captured by a simple power function. Instead, it can be modeled with the log-quadratic expression, as shown in figure 8. In particular, the τ th dependency with f GW is not symmetric around the line f GW = 0.4, i.e. τ th decreases for f GW > 0.4 at a slower rate than it increases for f GW < 0.4. A similar parametrization of the τ th density dependence was proposed in [64] for H-mode plasmas, giving the regression law termed ITERH06-IP(y,dd), which is expressed in ITER units [65]. The equivalent scaling expressed in MKS units [66] led, for consistency, to a minor correction of the constant corresponding to the ITER point prediction for standard operation as defined in [65]. This type of parameterization was proposed to capture the decrease of the H-mode τ th with Greenwald fraction, which in H-mode occurs for f GW > 0.8 [37]. Figure 9 shows how various existing τ th H-mode scalings perform in predicting the I-mode energy confinement time dependence with f GW . Three scalings are compared: the IPB98(y,2) [67] and ITPA20-IL [68] regressions, which give τ th,98 and τ th,20 respectively, and the already mentioned ITERH06-IP(y,dd) scaling, which provides τ th,06 . In this work, τ th,06 has been calculated with the expression in [64] multiplied by 280/290 to account for the correction of the constant mentioned previously. The H-factors in figure 9 represent the normalization of the I-mode τ th to each regression law prediction. Therefore, a good prediction of the I-mode τ th dependency with f GW would translate into a flat trend of the H-factor with f GW . The two scalings with a density power dependency, i.e. IPB98(y,2) (τ th,98 ∝ n 0.41 ) and ITPA20-IL (τ th,20 ∝ n 0.147 ), cannot reproduce the I-mode τ th dependency with f GW . On the other hand, the scaling with a density log-quadratic dependence, i.e. ITERH06-IP(y,dd) (τ th,06 ∝ f 0.11−0.22ln( f GW ) GW ), better predicts the I-mode τ th dependency with f GW . Therefore, this plot should encourage researchers to normalize I-mode τ th to the ITERH06-IP(y,dd) regression in future studies to better capture the I-mode τ th density dependence.

Conclusions
In this work, the integration of pellet fueling with I-mode plasmas has been investigated. Stationary pellet-fueled I-mode plasmas have been obtained both in USN and LSN configurations, demonstrating the compatibility of I-mode plasmas with pellet fueling. Moreover, LSN experiments allowed achievement of stationary density owing to the presence of an actively pumped divertor. In this configuration, the core density was increased up to 0.8 of the Greenwald density, broadening the typical I-mode operational window in AUG (i.e. core Greenwald fractions typically lower than 0.6). The core Greenwald fraction could not be raised beyond 0.8 due to technical constraints rather than to a physics-based limit.
When pellets are injected into I-mode plasmas, core and pedestal top temperatures reduce, while core and edge densities increase. Nevertheless, edge density and temperature normalized gradients remain in the typical I-mode range, i.e. shallow for the density and steep for the temperature. In a pellet-fueled I-mode discharge, a reduction of pressure gradient has been observed at ρ pol ≈ 0.7 which corresponds to the pellet burn-out location.
The thermal energy confinement time of I-mode plasmas, τ th , is found to follow a twofold dependency with the Greenwald fraction. For low f GW , τ th rises with increasing Greenwald fraction, up to f GW = 0.4. After this value the energy confinement time stays constant with increasing f GW or even decreases with f GW for the pellet-fueled discharges. A regression of the I-mode energy confinement time has been introduced, which finds τ th to scale log-quadratically with f GW , i.e. τ th,sc ∝ f −1.94−1.07ln( f GW ) GW , similarly to H-mode [64]. In the analyzed dataset, low-density I-mode plasmas are characterized by a large fraction of direct electron heating. This, combined with the rise of electron-ion coupling with increasing density, could lead to an increase of ion heat transport and possibly explain part of the observed τ th dependencies with density.
The plateauing or reduction of τ th with increasing f GW is a negative feature when scaled towards future fusion reactors, which will need to operate with both high Greenwald fraction and high energy confinement. However, a physics-based understanding of the I-mode confinement saturation with density is pivotal and should be pursued in the future, as it will allow reliable extrapolations of the energy confinement time towards future fusion reactors.