First-principle based predictions of the effects of negative triangularity on DTT scenarios

Plasmas with negative triangularity (NT) shape have been recently shown to be able to achieve H-mode levels of confinement in L-mode, avoiding detrimental edge localised modes. Therefore, this plasma geometry is now studied as a possible viable option for a future fusion reactor. Within this framework, an NT option is under investigation for the full power scenario of the Divertor Tokamak Test (DTT) facility, under construction in Italy, with δtop=−0.32/δbottom≃0.02 top/bottom triangularity values at the separatrix. The transport properties of this scenario are studied in this work. Gyrokinetic GENE simulations and integrated modelling using ASTRA with the quasi-linear trapped gyro-Landau fluid (TGLF) model have been performed. The emerging picture from the ASTRA-TGLF runs with boundary conditions at ρtor=0.94 is that, in the L-mode NT option, the larger peaking of the kinetic profiles in the edge region is not sufficient to recover the loss of the PT H-mode pedestal, and reach similar central temperature values. Two additional shapes are also considered, obtained by flipping the triangularity of the scenarios, to single out the effect of the triangularity sign. A negligible ‘direct’ effect of the triangularity is found for the L-mode, while a small beneficial effect is observed for the H-mode. The ASTRA-TGLF results are validated by GENE and TGLF stand-alone at two selected radii. GENE shows ITG dominant micro-instability and explains the small beneficial effect of the NT for the H-mode as due to a strong reduction of the heat fluxes, when reversing the triangularity, with a relatively high Ti stiffness. An improvement of the predicted performances of the NT DTT scenario could come from ρtor≳0.9 , as indicated by some recent experiments at the tokamak à configuration variable (TCV) and ASDEX Upgrade.


Introduction
Tokamaks are axisymmetric devices, where the magnetic geometry is uniquely specified by knowing the magnetic field on a poloidal plane, i.e. at fixed toroidal angle.The projection of the magnetic surfaces on a poloidal plane, up to the last closed flux surface (LCFS), consists in a set of closed curves, eventually collapsing at a single point which represents the magnetic axis.The two-dimensional 'poloidal cross section' of the magnetic field configuration can assume different shapes.The most common choice in actual tokamaks is the 'dee-shape', where the poloidal cross section of the magnetic surfaces resembles a 'D', with the D convexity that points outwards with respect to the torus axis.This shape has various advantages.It allows to achieve larger plasma currents [1] and pressures [2] than plasmas with circular cross section, due to improved magnetohydrodynamic (MHD) stability properties, and it minimises the J × B stresses on the toroidal field coils [3].It is thus possible to achieve high performance plasma conditions in deeshape, and this magnetic configuration is particularly suitable to sustain the H-mode regime [4].
However, the H-mode presents some issues, that are making the fusion community question whether it can be a viable option for future fusion reactors.Indeed, the H-mode is often accompanied by detrimental instabilities in the plasma edge, the so-called edge localised modes (ELMs), which release large amounts of energy and momentum to the tokamak walls, potentially damaging their structural integrity [5].Moreover, if reactors were to be maintained in a detached state [6] to reduce the amount of power that could potentially damage the plasma facing components, it would be easier to operate in L-mode regime than in H-mode as shown for example in [7].These issues could constitute a severe threat to the fusion roadmap, since H-mode levels of confinement are considered necessary for a viable DEMO reactor [8].
Several solutions are under investigation to overcome these obstacles, and one of those consists in modifying the magnetic geometry, reversing the shape of the plasma cross section, from 'dee' to 'reversed-dee', i.e. with reversed D shape, where the D convexity points towards the torus axis.'dee' and 'reversed-dee' shapes are also known with the names of 'positive triangularity' (PT) and 'negative triangularity' (NT), respectively, since the triangularity parameter δ, defined according to [9], is positive when the D convexity points outwards (dee shape), while it is negative when it points inward (reversed-dee shape).The NT option has gained interest throughout the years [7], since experimental evidence has been gained that with NT shape it is possible to achieve H-mode confinement properties staying in L-mode, also avoiding the dangerous ELMs.This is evident if one considers the promising results of recent experiments at various tokamaks such as tokamak à configuration variable (TCV) [10][11][12], DIII-D [13][14][15] and ASDEX Upgrade (AUG) [16], where a clear improvement of the plasma confinement in NT with respect to PT was observed, and it has been ascribed to a beneficial turbulence reduction for NT cases.Given these auspicious experimental evidences, the option of designing a DEMO NT Tokamak (NTT) has been considered in the recent years [17,18].
Within the roadmap to DEMO, the Divertor Tokamak Test (DTT) facility [19] is an experiment that is under construction in Frascati (Italy) and will be devoted to testing alternative designs and materials for the divertor.It will consider the NT among the possible plasma configurations and in particular an NT option is currently under investigation for the DTT full power scenario [20].The goal of this work is to present a detailed analysis of the predicted heat transport properties for such NT scenario.The NT option is here confronted with the reference DTT full power scenario, which features PT.Since DTT is under construction, there are no available experimental results to compare with, therefore the whole analysis is purely numerical.Indeed, in order to interpret the promising experimental performances of NT plasmas, an effort is ongoing in the fusion community to explore the underlying physics by performing theoretical analysis and numerical modelling [21][22][23][24][25].In particular, this work has been carried out within the EUROfusion Theory, Simulation, Validation and Verification (TSVV) Task 2 (physics properties of strongly shaped configurations), under which a broad team of experts is performing theoretical and numerical work with the goal of developing a deeper understanding of the physics of NT and the tradeoffs involved in its implementation in a reactor.
Different numerical frameworks are considered for the fluxes evaluation, in order to improve the reliability of the analysis.The results of the quasi-linear (QL) trapped gyro-Landau fluid (TGLF) model [26] are compared with higher realism gyrokinetic simulations, performed with the GENE code [27,28].Predictive transport simulations, performed with the ASTRA [29] transport solver coupled with TGLF, have been run to compare density and temperature profiles of the PT reference scenario with the NT option, aiming to estimate if the NT L-mode could recover the central values of the PT H-mode, possibly due to a reduced heat and particle transport in NT compared to PT.Then, in order to validate these results at two selected radii, they are compared with the ones obtained with the stand-alone version of TGLF and GENE.Furthermore, in order to single out the effect of the triangularity alone on the results, two additional numerical cases are considered, which are obtained by manually flipping the magnetic equilibria of the two reference PT and NT cases, reversing sign of the triangularity and of its shear.
For the NT DTT scenario, only the radial region that approximately ranges from the magnetic axis to the top of the pressure pedestal of the DTT PT H-mode full power scenario has been modelled.In particular, the NT case has been assumed to be an L-mode.Therefore, all the possible beneficial effects of reversing the triangularity of the DTT PT scenario, coming from the plasma edge and/or from the scrape-off layer (SOL), are here neglected.Indeed, a reliable modelling of the edge-SOL of NT plasmas is presently difficult to perform, as there is currently a lack of well established multimachine scaling laws for the heat flux decay length [30], as it is instead the case for H-mode [31] and partially for L-mode [32] PT plasmas.However, our assumption is a first guess, that gives a lower boundary to the predicted DTT NT scenario performance.An additional beneficial effect of δ < 0, coming from the edge-SOL, would improve the predicted performance compared with the present work, but this is left for future investigation.Nevertheless, for our case, some early simulations of the ideal (infinite-n) ballooning mode at the plasma edge of the DTT NT scenario, indicate that a strong access of the H-mode is inhibited (these simulations are part of an ongoing work about simulating the edge-SOL of the DTT NT scenario, and will be published in a related work).Indeed, recent works show that these instabilities should be the main responsible of limiting the edge pressure gradient of NT plasmas [33][34][35][36], excluding the possibility of destabilising the lowern peeling ballooning MHD modes, which are identified as main responsible for triggering ELMs [37], and also reducing the height of the pedestal to L-mode-like levels.Ultimately, these L-mode-like levels would be influenced by the microturbulence in the edge-SOL.In particular, in the plasma edge, a possible reduction of the micro-turbulence levels for NT compared to PT, could be beneficial for NT plasmas.Indeed, the smaller profile stiffness in the edge compared with the plasma core [38] would allow the pressure profiles to peak, reaching larger gradients in NT if those profiles are less stiff than in PT.Modelling all these effects would need consistent turbulence simulations across the separatrix, up to the tokamak wall, which are out of the scope of this work.
The paper is organised as follows: in section 2 the reference scenarios are introduced.Section 3 contains the ASTRA-TGLF predictive transport analysis.The linear GENE results are compared with TGLF stand-alone in section 4, while the nonlinear results are collected in section 5. Conclusions are drawn in section 7.

Description of the magnetic equilibria
Two DTT scenarios with PT and NT, respectively, and same input power (45 MW: electron cyclotron resonance heating (ECRH) + neutral-beam injection (NBI) + ion cyclotron resonance heating (ICRH)), are compared in this work.The total ECRH, NBI, and ICRH input powers are kept equal in the two scenarios, while the power deposition profiles are computed self-consistently.The PT scenario is the reference full power DTT scenario with B t = 5.85 T/I p = 5.5 MA and neon seeding [39], while the NT scenario is a corresponding NT option that is under consideration with B t = 5.85 T/I p = 4 MA.The plasma current limit of 4 MA for single null (SN)-NT configuration is related to the engineering constraints on the maximum forces on the poloidal field system.This also allows to have similar q 95 .The poloidal cross sections of the PT and NT magnetic equilibria are shown in figures 1(a) and (b).
The LCFS, together with the two surfaces at ρ tor = 0.7, 0.85, i.e. the two radial positions that were chosen to perform the local gyrokinetic/QL analysis, are represented by full lines.Here, ρ tor = √ Φ/Φ edge is the normalised toroidal radius, where Φ is the toroidal magnetic flux.The LCFS shapes were provided by the free boundary CREATE-NL solver [40], while the equilibria inside the LCFS were obtained in ASTRA using the SPIDER equilibrium code [41].An approximation of the ρ tor = 0.7, 0.85 surfaces with the analytic Miller equilibrium [42], i.e. the geometry implemented in the TGLF code, is shown by dashed lines.Indeed, while in the GENE simulations of this work a realistic equilibrium is assumed (see section 4), in the ASTRA-TGLF interface the plasma shape is approximated as a simplified up-down symmetric Miller local equilibrium, only accounting for elongation κ and triangularity δ: where R 0 , Z 0 , a (geometrical minor radius) and κ are defined as in [9], and the triangularity δ is obtained as an average of the top and bottom triangularities.As a consequence, TGLF misses more than half of the top NT absolute value for the DTT NT scenario, since at the LCFS the Miller average triangularity is δ = δ top + δ bottom = −0.15> δ top = −0.32, in addition to missing all the up-down asymmetry of that plasma.Indeed, from inspecting figure 1, it is clear by sight that the ASTRA-TGLF Miller approximation (dashed) is very good for the PT scenario, which is up-down symmetric, while it poorly reproduces the magnetic surfaces for the NT scenario.Two additional numerical magnetic equilibria have been considered, in order to single out the impact of the triangularity alone on the results.They were obtained in the following way: first, the LCFS was flipped, mirroring it with respect to the R = R 0 cylinder, with R 0 the toroidal radius of the magnetic axis; then, the inner equilibrium has been recomputed with the CHEASE [43] MHD solver, imposing the new specular LCFSs but keeping as fixed as possible p ′ (ψ) and T (ψ)T ′ (ψ) when solving the Grad Shafranov equation, where p is the plasma pressure, T the poloidal current flux function and ψ the poloidal magnetic flux.The resulting numerical equilibria are named PT-flipped (obtained by flipping the NT equilibrium) and NT-flipped (obtained by flipping the PT equilibrium) in this work and their poloidal cross sections are shown in figures 1(c) and (d), respectively.
The safety factor q, the elongation κ and the triangularity δ radial profiles are shown in figure 2. In particular, in figure 2(c), the top and bottom triangularities δ top and δ bottom , with δ = (δ top + δ bottom )/2, are shown by dashed and dotted lines, respectively.All these geometric parameters are defined according to [9].q is ∼20%-35% larger for NT compared to PT at 0.2 ≲ ρ tor ≲ 0.95, while it is ∼5%-20% larger for PT compared to NT-flipped at ρ tor > 0.7 (this difference has been checked to have a very little impact on the linear growth rates of the main unstable mode by means of linear gyrokinetic simulations).The elongation is similar for all the four cases.The absolute value of the triangularity is smaller for the NT case compared to the PT one (35% ≲ |δ NT |/|δ PT | ≲ 54% for ρ tor ≳ 0.2), since it is obtained as an average between δ top , δ bottom , where for the NT case δ bottom is positive throughout the radius (δ bottom ∼ 0 at the LCFS), due to the engineering constraints of the DTT tokamak vessel.The two numerical equilibria NTflipped and PT-flipped have, as expected, δ profiles that are with a good approximation specular, with respect to δ = 0, to the PT and NT ones, respectively.These four cases have been numerically modelled, by performing both a radially global predictive transport analysis and a local gyrokinetic and QL analysis at fixed radii.A remark has to be made: while in the local gyrokinetic/QL analysis the four equilibria have been kept fixed and they have been set as input of the simulations (the density and temperature profiles of NT-flipped/PT-flipped cases have been set equal to the ones of PT/NT cases, respectively, to single out the effect of the plasma shape on the results), in the global transport analysis what has been kept fixed is the shape of the LCFS for the four cases, the corresponding heat and particle sources, and the boundary conditions, letting the NT-flipped/PT-flipped equilibria evolve consistently with the corresponding density and temperature profiles.This reflects the fact that the local gyrokinetic analysis is made of gradient-driven simulations, while the radially global transport analysis is intrinsically fluxdriven.The predictive transport simulations are described in the following chapter.

Predictive transport analysis
The transport code ASTRA, coupled with TGLF to compute the heat and particle turbulent fluxes, has been used to predict the density and temperature profiles for the four considered cases.ASTRA has been run in the predictive framework, with imposed heat and particle sources, simulating almost all the plasma radius up to ρ tor = 0.94, close to the top of the PT H-mode pedestal.TGLF has been run with the saturation rule SAT2 [44].For the PT/NT-flipped cases, the PT H-mode pedestal has been computed with the Europed code [45] using the EPED1 model [46], choosing the density at the top of the pedestal in order to have n e,lin /n GW = 0.45, while for the NT/PT-flipped cases in L-mode the n, T boundary conditions at ρ tor = 0.94 have been obtained by simulating the 0.94 < ρ tor < 1 region with JINTRAC-QuaLiKiz [47,48].The values at the separatrix have been set to T e = T i = 60 eV and n e = 7.6 × 10 19 m −3 similarly to what described for the PT cases in [20], with the temperatures scaled down from the PT H-mode case using the two point-model [49] considering a six times increase of the near-SOL conductivity from χ e /χ i = 0.18/0.14m 2 s −1 of the PT H-mode to the χ e = χ i = 1 m 2 s −1 of the NT L-mode.The effect of the triangularity has thus been neglected outside ρ tor = 0.94, both neglecting the possible beneficial effect of NT in the SOL and in the 0.94 < ρ tor < 1 region (since QuaLiKiz uses a non-shaped sα geometry).The heat and particle NBI sources have been computed by JINTRAC and then used in ASTRA.In particular, the ICRH antenna, NBI injectors, and ECRH gyrotrons have been configured within the JINTRAC suite, and their power deposition profiles have been computed by PION [50][51][52], PENCIL [53] and GRAY [54], respectively.The heat sources, i.e. the volume integrals q e and q i of the total electron and ion power densities P e = P OH + P ECRH + P ICRH,e + P NBI,e − P ei − P rad and P i = P ICRH,i + P NBI,i + P ei , are shown in figure 3 for the four considered scenarios.Here P OH , P ECRH , P ICRH,e , P NBI,e , P ei and P rad indicate the power densities corresponding to ohmic heating, ECRH heating, ICRH and NBI powers transferred to electrons, electron/ion heat exchange and radiation power.Similarly, P ICRH,i and P NBI,i correspond to the ICRH and NBI powers transferred to ions.Here, the names Total electron (full) and ion (dashed) heat sources, for the four considered scenarios.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by a vertical dash-dotted line.qe is only shown for ρtor < 0.9, since numerical instability arises in the ASTRA equilibrium solver outside ρtor = 0.9, resulting in spurious Ohmic heating power peaks.q e , q i are chosen to indicate the heat sources.This is made for clarity, since q e , q i will be used to indicate the electron and ion heat fluxes, and the two quantities, neglecting the relatively small (5/2)T e Γ e,NBI convective contribution to the energy flux (with Γ e,NBI the particle flux due to NBI) are equal in the stationary phase of the scenarios, according to the heat transport equation.
The NBI particle source is also computed by PENCIL, while the edge neutral penetration is negligible inside ρ tor = 0.94.Neon and tungsten impurities will be present in the considered DTT scenarios.Ne is a seeding gas used to enlarge the edge radiative dissipation decreasing the divertor power load, while W comes from the divertor.Ne and W have been accounted for in the simulations, and their density profiles consistently predicted using NCLASS [55] and TGLF.The impurities are considered to be in thermal equilibrium with the main ions.The impurity density profiles are shown in figure 4(a) for the four considered cases, while the corresponding effective charge Z eff = ∑ i Z 2 i n i /n e (sum over ion species) profiles are reported in figure 4(b).
Energetic particles (fast ions: FIs) which are generated by both NBI and ICRH are retained in the simulations.Their density and energy profiles are shown in figure 5.
Finally, the plasma rotation that is generated by the NBI injection is calculated in JINTRAC using a semi-empirical model for momentum transport and then used interpretatively in ASTRA.The corresponding toroidal angular velocity profiles are shown in figure 6.More information about the implementation of the coupled ASTRA/JINTRAC modelling setup, regarding the DTT full power scenario with Ne seeding H-mode in PT, can be found in [39].The main results of the ASTRA predictive transport simulations are shown in figure 7. The predicted electron density n e , electron temperature T e and ion temperature T i radial profiles are shown in the first row, while the corresponding normalised logarithmic gradients a/L f = −d log f/dρ tor (herein f = n e , T e , T i ) profiles follow in the second row.Here a = √ Φ edge /π B 0 provides an estimate of the average minor radius of the tokamak, where B 0 is the vacuum magnetic field at the magnetic axis.The T e predictions of the radial region ρ tor ≲ 0.2 should not be trusted for the PT/NT-flipped cases, since very large values of the electron heat diffusivity χ e ∼ 5 m 2 s −1 are predicted by TGLF, which are probably unphysical and should be tested by comparing TGLF with gyrokinetic simulations.However, this is outside the scope of this work.Indeed, the focus of the analysis is the study of the effect of the triangularity on the transport, and δ is expected to only impact the results in the outer core, where its modulus is sufficiently large (see the δ profiles in figure 2).A grey band has been added to figures 7, 8 and 10, covering the T e predictions in the inner plasma region, which are not reliable.
Comparing the reference PT H-mode scenario (red) with the NT L-mode option (blue), the temperatures ((b) and (c)) are larger for PT than NT throughout the radius, since the larger temperature logarithmic gradients that are observed for NT ((e) and (f )) are not sufficient to recover the loss of the PT H-mode pedestal.In fact, the larger edge R/L T values that are found for NT compared to PT, just reflect the fact that the NT case is a L-mode while the PT case is an H-mode, and they are not due to a beneficial effect of δ < 0. Indeed, the larger R/L T values of the NT case are found for the PTflipped case as well, due to the same L-mode boundary conditions.Unlike the temperature profiles, the density is higher for NT than PT at ρ tor < 0.45.As a consequence, if one looks at the electron and ion pressures, which are shown in figure 8, this increase of n e with decreasing radius allows the NT pressures to get a little bit closer to the PT values with decreasing radius, even if they only reach them for ρ tor ≲ 0.2.Therefore, since the NT pressures stay below the PT ones along the most of the plasma radius, this NT L-mode option is expected to have a poorer plasma performance compared to the reference PT H-mode scenario.More quantitatively, the energy confinement time τ E = plasma stored energy/rate of energy loss = 0.36 s/0.21 s for the DTT PT/NT scenarios, respectively, with a ∼−40% lower value for the NT L-mode compared with the PT H-mode.On the other hand, it is possible to single out the effect of the plasma triangularity alone on the density and temperature profiles, comparing PT with NT-flipped (red/orange) and NT with PT-flipped (blue/light blue).The beneficial effect of NT on the density profiles is very small.There is only a non negligible beneficial effect of NT on the electron and ion temperature profiles for the H-mode PT/NT-flipped comparison at 0.7 < ρ tor < 0.9.This effect can be better visualised by looking at the logarithmic gradients in figures 7(e) and (f ).Indeed, the NT-flipped case has larger a/L Te and a/L Ti than the PT case in that radial interval.On the contrary, for the L-mode NT/PT-flipped comparison, the effect of NT is found negligible.Directly looking at the T e , T i profiles instead of their gradients for the H-mode comparison, one sees that only the NT-flipped T e overcomes the PT central values, reaching a 10% higher value, while for T i , the better performance of NTflipped at ρ tor > 0.7 is compensated by a slightly larger a/L Ti for PT at ρ tor < 0.7, leading to similar central T i .Looking at the pressures (figure 8), the effect of NT alone is non negligible only for the H-mode comparison PT/NT-flipped, while for the L-mode comparison NT/PT-flipped a small detrimental effect of NT is observed, mainly due to the larger n e in PT-flipped compared to NT, but this result should not be trusted since it lies in the ρ tor ≲ 0.2 region.
In order to test if the larger effect of NT alone for the Hmode comparison was due to the larger |δ| that the NT-flipped case (orange line in figure 2) features compared to the NT one (blue line in figure 2), an additional ASTRA-TGLF predictive simulation was run for the NT case, keeping all the parameters fixed except for the shape of the LCFS, that was taken from the NT-flipped case instead of NT.The resulting n, T predicted profiles are shown by green lines in figure 9, compared with the results of the NT case (blue).
The results of the new run are very close to the ones of the original NT simulation, indicating a small role for the different shape (and corresponding δ) of the two cases, i.e. the H-mode and L-mode scenarios with NT.A numerical exercise that has been conducted with TGLF, by performing a/L Ti scans of q i for different values of |δ|, indicates that a |δ| ∼ 0.8, approximately nine times larger than the value of the NT case, would be needed to set a sufficiently large T i peaking to recover the loss of H-mode pedestal for ρ tor > 0.7 (where the triangularity is sufficiently large to matter in the considered cases).However, the validity of TGLF for such high |δ| values is not clear.Still, it is evident that larger |δ| values would be required to see an effect in these L-mode cases.
It should be noted that a possible beneficial effect of NT could come from the outer region ρ tor > 0.94, outside the radial box of the ASTRA simulations.An improved heat transport for NT L-mode compared with PT L-mode in the SOL or in the edge (ρ tor > 0.94) would result in proportionally larger core temperatures if a/L T would be similar for the PT/NT Lmodes inside ρ tor = 0.94.Indeed, if two temperature profiles have the same a/L T within a radial domain, their ratio stays constant in that region.In figure 10, the modification of the DTT NT option T e profile, due to a possible beneficial effect of δ < 0 coming from ρ tor > 0.94, resulting in an increase of T e by +30%, is shown.The 'improved' electron temperature profiles in figure 10   L-mode profile is able to reach the same central temperature as the PT H-mode.In this hypothetical case, the beneficial effect of δ < 0 is equally split between a +15% increase of T e at the LCFS, coming from an improved heat transport for δ < 0 in the SOL, and an additional +15% coming from a possibly weaker heat transport for δ < 0 in the 0.94 < ρ tor < 1 region.Despite this picture could seem artificial and unlikely to happen, this is exactly what has been observed in plasmas with DTT shape that have been recently obtained at TCV [56], to test the effect of reversing the triangularity of the DTT full power scenario.A strong beneficial effect of NT, that allows NT L-modes to largely overcome the performance of corresponding PT plasmas, is observed in those TCV pulses, with NT L-modes that reach the central pressure and temperature values of larger power H-modes.A beneficial effect of NT is also observed in similar discharges that have been performed at AUG [57].Therefore, the ASTRA-TGLF analysis of this chapter cannot rule out the possibility of a beneficial effect of NT, coming from the egde-SOL, that could allow the DTT NT full power scenario to have similar core performance to the reference PT H-mode.Moreover, as it has been pointed out in the previous chapter, ASTRA-TGLF adopts an up-down symmetric Miller analytic equilibrium, poorly describing the up-down asymmetric DTT NT geometry.In addition, this way also almost half of the absolute value of the NT of the DTT NT option is lost, due to the average of the top and bottom triangularities that is performed in the ASTRA-TGLF interface to produce the Miller parameters.As a consequence, the beneficial effect of δ < 0 could be underestimated also for ρ tor < 0.94.Summing up, ASTRA-TGLF predict a very small beneficial effect of NT in the ρ tor < 0.94 radial region, for the considered DTT scenarios, with the NT L-mode that is not able to recover the central T i values of the PT H-mode, and the ion and electron pressures that are larger for the PT H-mode than for NT L-mode for the most of the radial domain, resulting in poorer plasma confinement properties for the NT case.A non negligible effect of the triangularity alone is seen for the H-mode case.However, a beneficial effect of δ < 0 could be missing in this analysis, either coming from the edge-SOL of the plasma, or from the incapability of ASTRA-TGLF to fully model the up-down asymmetric DTT NT shape.

Linear GENE and TGLF spectra
In order to validate the predictive transport analysis, together with gaining more insight on the turbulence properties of the considered scenarios, a gyrokinetic flux-tube analysis has been performed at fixed radii.The gyrokinetic modelling of the H-mode comparison PT/NT-flipped has been performed both at ρ tor = 0.85 and ρ tor = 0.7, since the largest effect of NT alone was observed in H-mode in the ASTRA-TGLF modelling, while the L-mode comparison NT/PT-flipped has been only modelled at ρ tor = 0.85, where the triangularity is larger.The gyrokinetic results at ρ tor = 0.85 have also been compared with TGLF, that has been run in its stand-alone version, keeping the same SAT2 saturation model that was set in the ASTRA-TGLF analysis, for consistency.
The gyrokinetic simulations have been run with the GENE code.GENE solves the GK equations, coupled with the Maxwell equations, within a δf approximation.It adopts a set of field-aligned coordinates {x, y, z, v ∥ , µ} in the reduced five-dimensional gyrokinetic phase space.x, y and z are the radial, binormal and parallel (to B) coordinates in configuration space, while v ∥ and µ are the parallel velocity and the magnetic moment.The simulations are carried out in the fluxtube (radially local) limit using realistic magnetic equilibria, reconstructed with CHEASE, taking into account collisions and finite-β (electromagnetic) effects, both from δB ⊥ and δB ∥ fluctuations.Electrons, deuterium, Ne and W impurities have been modelled as kinetic species.The flux-tube version of the code has been used.The finite-size effects (global effects) could potentially affect the relative transport levels for PT/NT plasmas [23,58], but they are expected to be small for the considered cases, due to the large DTT size, that corresponds to ρ ⋆ = ρ s /a ∼ 600-1200 at the radii of analysis ρ tor = 0.7, 0.85, respectively.The linear simulations have been run with a typical grid n kx × n z × n v∥ × n µ = 24 × 32 × 48 × 12, while the nonlinear simulations with grids ranging from n kx × n ky × n z × n v∥ × n µ = 128 × 32 × 32 × 48 × 12 to 512 × 64 × 60 × 48 × 12, depending on the particular case, with x and y box sizes ranging from (L x /ρ s , L y /ρ s ) = (69, 126) to (236, 251).
Here ρ s = c s /Ω i is the sound Larmor radius, where and c s = √ T e /m i the ion sound speed and Ω i is the ion cyclotron frequency.The nonlinear simulations have been run until t max c s /a ∼ 300-800 to collect sufficient statistics, depending on the particular case.Linear and nonlinear convergence tests have been performed.TGLF has been run with the SAT2 saturation rule, for consistency with the ASTRA-TGLF modelling, in the collisional regime, including kinetic impurities.The Miller analytical model has been used to approximate the plasma geometry in TGLF.
The main plasma parameters of the selected cases at the radii of analysis, used as input of GENE and TGLF, are listed in table 1.
In table 1, νc = R 0 ν ei /c s is the normalised electron-ion collision frequency, where R 0 is the major radius of the magnetic axis, β e = 2µ 0 n e T e /B 2 0 is the ratio of the electron plasma pressure to the magnetic pressure, with µ 0 the vacuum permeability, and ŝ is the magnetic shear.
First, in order to characterise the micro-instability regime that sets the turbulence in the considered DTT scenarios, as well as to test if NT has a stabilising effect on the linear modes, the binormal wave number k y spectra of the linear growth rates γ and frequencies ω of the most unstable mode have been computed by means of GENE linear simulations, and compared with TGLF.The results at the larger radius ρ tor = 0.85, where the effect of the triangularity is expected to be larger, are collected in figure 11.To single out the effect of the triangularity alone on the results, the H-mode PT/NTflipped comparison is presented in the first row, while the Lmode NT/PT-flipped cases are confronted in the second row.The micro-instability regime is found to be ITG dominant at the wavenumbers k y ρ s ≲ 1, which mostly contribute to the nonlinear heat fluxes spectra (as will be shown in section 5, figure 15).This can be visualised by looking at the mode frequencies (figures 11(b) and (d)), where positive values indicate modes rotating in the ion diamagnetic direction, consistent with GENE definitions).Micro tearing modes (MTMs) are found at the smaller wavenumbers for the H-mode cases (modes with negative ω, identified as MTMs since they display an electrostatic potential with odd ballooning parity), which contribution to the nonlinear fluxes was found a posteriori to be negligible.For the same wavenumbers, the GENE-TGLF agreement is good (very good for k y ρ s ≲ 0.8, for all the cases except the NT-flipped).TGLF does not predict the low-k MTM branch that can be seen by looking to the GENE linear eigenvalues for the H-mode cases.However, this is not expected to impact the TGLF predictions, since MTMs, as stated before, are not found to impact the heat fluxes in the GENE nonlinear simulations.
The main result of this section is that GENE predicts a larger stabilising effect of NT for the H-mode comparison (GENE: −55% stabilisation of maximum ITG growth rate going from PT to NT-flipped; TGLF: −45% stabilisation), while it predicts a negligible effect for the L-mode comparison (NT γ values: similar to PT-flipped ones within the ITG branch), consistent with the ASTRA-TGLF picture.
The impact of key physics ingredients such as collisions, impurities and finite β e (electromagnetic: EM) effects on the spectra of the linear eigenvalues has been tested for the reference DTT PT and NT cases by repeating the GENE linear k y scans removing one physics ingredient at a time, i.e. in the collisionless regime, without impurities or with β e = 10 −4 ∼ [59], has been studied in detail (see the appendix), indicating that the PT and NT reference β e values are well below the KBM instability threshold.By looking at figure 12, one would be tempted to directly compare the PT and NT growth rates, which are similar, and infer that the NT has no effect.However, this comparison is meaningless, since the two cases have very different parameters in addition to the different triangularities, since the PT case is an H-mode and the NT-case is an L-mode.Therefore, a comparison of the reference PT and NT cases has only sense within a flux-driven full-radius framework, which was indeed followed in the ASTRA-TGLF modelling, looking for a possible effect that allows the NT n, T profiles to overcome the loss of the H-mode pedestal and reach central values that are similar to those of the PT case.The effect of the NT alone on the linear eigenvalues has also been evaluated at the smaller radius ρ tor = 0.7 with GENE for the H-mode comparison, where its impact has been found to be larger then for the L-modes in the analysis at ρ tor = 0.85.The results are shown in figure 13.At ρ tor = 0.7 the microinstability regime is the same as at ρ tor = 0.85, i.e.ITG dominant.A −53% stabilisation of the maximum ITG growth rate going from PT to NT-flipped is observed, comparable with the −55% stabilisation at ρ tor = 0.85, with almost double |δ| values at the larger radius.This result could seem to contradict the negligible effect of NT that was found on a/L Te , a/L Ti at ρ tor = 0.7 when comparing PT with NT-flipped in the ASTRA-TGLF predictive simulations (see figures 7(e) and (f )), but the apparent contradiction will be explained when looking at the T e , T i stiffness in the next section.
Indeed, investigating the effect of NT on the ion and electron heat fluxes at fixed reference parameters, without varying the main driver of the dominant ITG turbulence regime, is not particularly enlightening.In the following section, the ion stiffness, i.e. the degree to which the radial T i profile responds to changes in the applied heat fluxes, is studied, evaluating how much it changes when changing the sign of the triangularity, starting from the reference PT and NT cases.This allows to evaluate the effect of the triangularity on the T i peaking, with a flux-driven point of view that allows to compare the GENE/TGLF nonlinear results with the ASTRA-TGLF predictive modelling, validating it.

Nonlinear heat fluxes
Nonlinear GENE and QL TGLF stand-alone simulations have been run at ρ tor = 0.85, varying the main drive a/L Ti of the ITGs, which are the dominant micro-instability that regulates the turbulence regime.In that way, the ion temperature stiffness can be evaluated for the four considered DTT scenarios and the impact of the NT on the T i peaking assessed.The results of such analysis are shown in figure 14.The E × B shearing due to rotation has been neglected in the simulations, since the corresponding shearing rate has been found much smaller than the maximum linear growth rate at ion scales.Indeed, the normalised E × B shearing rate is equal to γ E = −(ρ tor /q)(∂Ω tor/∂ρtor )(a/c s ) = 0.013, 0.024 for the PT H-mode and NT L-mode, respectively, resulting in γ E /γ max ∼ 5%-10% for all the four considered cases PT/NTflipped/NT/PT-flipped, where γ max is the maximum linear growth rate at ion-scales.
The ion heat flux q i and the electron heat flux q e are shown in (a) and (b), respectively, versus a/L Ti .The PT, NT-flipped, NT and PT-flipped cases are indicated in red, orange, blue and light blue, respectively, following the same colour code that has been kept throughout the work.The GENE fluxes are shown by circles, while the TGLF ones by triangles.The ASTRA-TGLF values at the radius of analysis are also added to complete the picture, and represented by stars.Finally, the ASTRA-TGLF q e and q i values for the reference DTT PT and NT scenarios only are also indicated by horizontal lines, to facilitate the visualisation of the impact of triangularity on the T i peaking.Indeed, these plots have to be observed with a flux-driven perspective: the given q e , q i (horizontal lines), have to be intersected with the GENE or TGLF q e,i vs a/L Ti lines, to obtain the predicted a/L Ti for each of the four considered cases.First, looking at the GENE results, it is clear that a beneficial effect of NT is only observed for the H-mode comparison, with a ∼+36% larger a/L Ti predicted for the NT-flipped case compared with the PT one when looking at q i vs a/L Ti (figure 14(a)).This just slightly underestimates ASTRA-TGLF, which predicts a ∼+43% larger a/L Ti for NTflipped.A larger ∼+80% effect of NT is found by GENE and TGLF stand-alone when looking at q e vs a/L Ti , overestimating the ASTRA-TGLF result, but the disagreement is not so pronounced when looking at figure 14(b) and allowing for a ±10% error bar on a/L Ti .The agreement between GENE and ASTRA-TGLF could be further improved by a fine tuning of other parameters, such as a/L Te , T e /T i , etc. . .; anyway, one should not forget that GENE and TGLF stand-alone have to be compared with ASTRA-TGLF with the caveat that for GENE and TGLF stand-alone only the magnetic equilibrium shape changes from cases with PT or NT, with fixed n, T profiles, while for ASTRA-TGLF only the LCFS shape is flipped when flipping the triangularity, and all the n, T profiles are evolved and consistently predicted.In agreement with the ASTRA-TGLF analysis, a negligible impact of NT is found for the L-mode comparison.TGLF stand-alone predicts a larger increase of the T i peaking compared with GENE, when reversing δ.The GENE/TGLF stand-alone agreement is only qualitatively good for the L-mode.
Even if it is less significant to compare the GENE nonlinear fluxes for the four considered cases at fixed a/L Ti values from DTT PT and NT reference scenarios, it is worth doing that, because the nonlinear flux reduction from PT to NT-flipped in H-mode can be compared with the NT linear stabilisation of the growth rates for the same comparison from the previous section, learning if the stabilisation of the fluxes for NT cases compared to PT ones is a purely linear/QL feature or some more complicated nonlinear physics is at play.Indeed, q i and q e are reduced by −61.5% and −77.5%, respectively, when flipping the triangularity from PT to NT-flipped (compare the PT red circles with the NT-flipped orange triangles in figure 14, for the reference a/L Ti corresponding to the red star).This is more than the ∼ − 50% stabilisation of the linear growth rates that was observed in the linear analysis, indicating that more complicated nonlinear dynamics is at play.The corresponding GENE nonlinear flux spectra, which are shown in figure 15 following the same colour code, show that the beneficial effect of NT is uniformly spread along all the wavenumbers, and not due to the stabilisation of a particular k y sub-interval of the spectrum.
In figure 15 the q i (a) and q e (b) spectra in MW are divided for each case by the spectral resolution ∆(k y ρ s ) for better visual comparison with the integrated values of figure 14, so that the area below the curves is equal to the total fluxes.Turning to the L-mode comparison, when flipping the triangularity from NT to PT-flipped, the nonlinear heat fluxes are almost unchanged (compare the NT blue circles with the PTflipped light blue triangles in figure 14, for the reference a/L Ti corresponding to the blue star), and the same can be inferred by inspecting the corresponding flux spectra in figure 15, within error bars.This reflects the already observed negligible linear γ stabilising effect of NT in L-mode, and also indicates that there is no additional nonlinear mechanism that changes the linear picture in L-mode.
Finally, the ion stiffness analysis has been repeated for the H-mode PT/NT-flipped cases at ρ tor = 0.7.The results are shown in figure 16.The results at ρ tor = 0.85 are reported in grey to help the comparison.By looking at the ion stiffness plots, it is possible to resolve the apparent inconsistency that was found in the linear analysis, where a strong suppression of the growth rate of the most unstable mode was observed when flipping triangularity from PT to NT-flipped, while almost no effect on both a/L Ti and a/L Te was found in the ASTRA-TGLF predictive simulations at ρ tor = 0.7.Indeed, going from PT to NT-flipped at fixed reference a/L Ti (the a/L Ti value Figure 14.Ion temperature stiffness plot for the four considered cases at ρtor = 0.85, comparing GENE with TGLF.The electron heat flux qe and the ion heat flux q i are shown in (a) and (b), respectively, versus a/L Ti , which is the main drive of the ITG dominant micro-instability.The GENE results are indicated by circles (error bars represent the standard deviation of the fluxes time traces over the same time interval that has been considered to compute their averages), while the TGLF stand-alone ones by triangles.Finally, the stars represent the ASTRA-TGLF results (the ASTRA-TGLF qe and q i values for the reference DTT PT and NT scenarios are also indicated by horizontal lines).
corresponding to the red star), there is a strong reduction of q i and q e (q i and q e are reduced by −61% and −71%, respectively, when flipping the triangularity from PT to NT-flipped, similarly to ρ tor = 0.85), but when looking to the ion stiffness, i.e. to the slope of the heat fluxes vs a/L Ti , it is clear that the stiffness of both PT and NT-flipped cases is larger at ρ tor = 0.7 than at ρ tor = 0.85, as expected since the temperature stiffness is usually observed to decrease with increasing radius.This more than halves the a/L Ti improvement when going from PT to NT-flipped at ρ tor = 0.7, compared to ρ tor = 0.85.Within the experimental error bars, it is consistent with the almost vanishing effect that the triangularity flip has on a/L Ti in the ASTRA-TGLF runs at ρ tor = 0.7 (compare the red with the orange stars in figure 16).This smaller effect of the triangularity at ρ tor = 0.7 can be at least partially attributed to the fact that at ρ tor = 0.7 the triangularity parameter δ is almost half than at ρ tor = 0.85.
As a remark, from the nonlinear simulations of the Hmode cases at the two radii of analysis, one can observe that, even with the limited number of available q e,i vs a/L Ti GENE points, the results indicate that the beneficial effect of reversing δ is given by an increase of the a/L Ti threshold, with similar T i stiffness (i.e.slope of q e,i vs a/L Ti ), consistently with previous works [60] and with the emerging common behaviour observed in the simulations performed under the TSVV2.
Summing up, GENE is in good agreement with ASTRA-TGLF at both ρ tor = 0.7 and ρ tor = 0.85, predicting similar improvements of the T i peaking when reversing the triangularity from positive to negative in H-mode and negligible effect on T i for the L-mode, thus validating the predictive transport analysis.The NT L-mode temperature profiles are not able to overcome the loss of the H-mode pedestal and reach central values comparable with the ones of the PT scenario.
The NT pressures, even though are able to reach central values that are comparable to the PT ones, stay below them for the most of the plasma radius, resulting in worse overall performance.The effect of the triangularity alone is non negligible only for the H-mode in a small radial region 0.7 ≲ ρ tor ≲ 0.9, while it is negligible for the L-mode.The GENE-TGLF comparison has been focussed on the heat transport channel.A multi-channel comparison, also including the particle transport, is foreseen as a future work.

Key parameters that determine the beneficial effect of δ < 0 for the H-mode
In order to investigate which are the parameters that mostly influence the different effect that flipping the triangularity has on the heat fluxes for the H-mode and L-mode cases, nonlinear GENE runs have been performed at ρ tor = 0.85, where the negative δ has the strongest stabilising effect for the H-mode cases, starting from the L-mode cases and replacing the parameters with those of the H-modes.The resulting heat fluxes are shown in figure 17(a).The points at the far left indicate the reference L-mode cases (NT and PT-flipped, corresponding to the data of figure 14. with the reference L-mode a/L Ti = 4.45).Starting from the L-mode cases, the simulations have been repeated with replacing only one parameter at a time, taking it from the corresponding H-mode cases (PT and NT-flipped, corresponding to the data of figure 14 with the reference H-mode a/L Ti = 1.95).From the left to the right: R/L Te , the shapes (the shape of the PT-flipped plasma cross section is substituted with the PT one, while the NT shape is substituted with the NT-flipped one), the impurities and finally νc = ν ei R/c s , are taken from the H-mode.It results that only changing νc it is possible to increase the NT stabilisation for the L-mode.Therefore, it would be tempting to identify the normalised collisionality νc as the key parameter impacting the stabilising effect of NT for the considered cases, and its role could be naively interpreted as follows: when increasing the collisionality from νc = 1.28 to νc = 8.10, going from the Hmode to the L-mode, the plasma particles are more de-trapped by collisions, and they are less sensitive to the different geometries of PT and NT.However, since the turbulence is very bursty in the GENE runs for PT, NT and PT-flipped cases, within the numerical 'error bars' given by the fluxes fluctuations over simulation time, it is not possible to quantify the impact of νc on the NT stabilisation.One also notes that, when changing the plasma shape from L-mode to H-mode one, the δ < 0 flux becomes larger than the δ > 0 one.However, when taking into accounts the error bars, this difference becomes very small.
In order to make an independent test of the hypothesis that the different collisionality sets the different strength of the δ < 0 stabilisation for the H-modes and L-modes, a collisionality scan has been performed with GENE nonlinear simulations, starting from PT/NT-flipped H-mode parameters at ρ tor = 0.85 and increasing the collisionality, well beyond the NT/PT-flipped L-mode value.This is shown in figure 17(b), where the ratio of the heat flux of the NT-flipped case and the one of the PT case is plotted versus the GENE collisional frequency parameter ν c (ν c is here reported instead of νc = R 0 ν ei /c s = 4Z eff √ m i /m e ν c to help the reproducibility of the results).This scan has been performed neglecting impurities, to save computational resources, but as can be seen by comparing the results with the one obtained when retaining impurities (crosses) with the nominal collisionality, their impact is small.Reversing the triangularity stabilises q e,i by −70%/−80% for the H-mode even with NT L-mode collisionality (or even much larger).Therefore the collisionality is ruled out as a possible single parameter explaining why the stabilising effect of NT on the heat fluxes is strong for H-mode and vanishing for the L-mode.Therefore, a single parameter explaining this difference has not been identified, and a deeper understanding of the underlying mechanism is left to future work.
Finally, an important remark has to be made.Also a/L Ti changes from a/L Ti = 1.95 to a/L Ti = 4.45 when going from H-mode to L-mode.However it is not possible to only change a/L Ti when performing the reference H-mode runs, taking it from the L-mode, or vice-versa, since the values are so different and T i is so stiff that, when replacing the L-mode a/L Ti with the lower H-mode value, the turbulence is almost stable, while when doing the opposite the transport is so strong that it is tricky to reach numerical convergence with the GENE runs (it was impossible with our available resources).

Conclusions
The transport properties of an alternative option for the DTT full power scenario with neon seeding, featuring NT and Lmode regime, have been studied in this work.The NT option has been compared with the reference DTT full power scenario with neon seeding, which is expected to display PT and H-mode.
ASTRA-TGLF SAT2 predictive transport simulations have been compared and validated at selected radii with GENE gyrokinetic runs.The magnetic shapes of the DTT PT and NT scenarios have been considered, as well as two additional ones, obtained by artificially flipping the triangularity of the LCFS, in order to single out the effect of the triangularity alone on the results.Neon and tungsten impurities, as well as fast ions from NBI and ICRH, have been accounted for.GENE flux-tube simulations have been performed at the two radii ρ tor = 0.7, 0.85, where the absolute value of the triangularity is sufficiently large to impact the results, still being inside the H-mode pedestal.GENE uses realistic magnetic equilibria, differently from TGLF, which uses a Miller analytical equilibrium approximation.GENE runs take into account collisions, full electromagnetic effects, kinetic electrons, Ne and W impurities (gyrokinetic species).
The details about the ASTRA-TGLF and GENE modelling follow, then some final comments and future perspectives are drawn.• Linear growth rates and frequencies of the microinstabilities (GENE and TGLF stand-alone simulations at ρ tor = 0.85): the micro-instability regime is found ITG dominant for all the four cases (δ > 0/δ < 0, H-mode/L-mode).
Flipping the triangularity from positive to negative results in halving the maximum growth rate for the H-mode, while it has a negligible effect for the L-mode.This is found by both GENE and TGLF stand-alone, with a good agreement in the eigenvalue spectrum (both γ and ω), and validates the ASTRA-TGLF transport modelling at ρ tor = 0.85.
Collisions have a similar ∼−20% stabilising effect on the ITG growth rates for the PT H-mode and the NT L-mode.
Impurities have a smaller stabilising effect (∼−14%: NT L-mode, negligible: PT H-mode).Finally, electromagnetic effects are found to be negligible (all cases well below KBM instability threshold, MTMs at small wavenumbers appear linearly but they do not impact nonlinear fluxes).• Nonlinear gyrokinetic and quasilinear fluxes (GENE and TGLF stand-alone simulations at ρ tor = 0.85 and GENE simulations at ρ tor = 0.7): GENE and TGLF stand-alone nonlinear and quasilinear scans of q i and q e vs a/L Ti , which is the main drive of the dominant ITG turbulence, indicate that flipping the triangularity from positive to negative for the H-mode at ρ tor = 0.85 reduces both the absolute fluxes and the T i stiffness (i.e. the slope of q i,e vs a/L Ti ), resulting in a ∼+40% larger a/L Ti for δ < 0 compared with δ > 0, in agreement with the ASTRA-TGLF results at ρ tor = 0.85.ASTRA-TGLF is also verified at that radius by GENE for the L-mode cases, where the effect of flipping δ is found negligible.The δ < 0 stabilising effect for the H-mode heat fluxes is ∼−61%/ − 77%, stronger than the ∼−50% linear effect, implying that some more complicated nonlinear dynamics is also at play.GENE simulations have been also performed at ρ tor = 0.7 for the H-mode, where a similar stabilising effect of δ < 0 is found on the absolute fluxes, but a negligible effect is observed on a/L Ti .This is in agreement with ASTRA-TGLF at that radius, validating it.The negligible effect on a/L Ti is explained by GENE by the higher T i stiffness that is found at the smaller radius ρ tor = 0.7 for both PT and NT-flipped cases.From the nonlinear simulations of the H-mode cases at the two radii of analysis, the beneficial effect of reversing δ is given by a increase of the a/L Ti threshold, with similar T i stiffness, consistently with previous works [60] and with the emerging picture from TSVV2.• Nonlinear GENE scans to identify the key parameters that influence the different strength of the δ < 0 stabilising effect for the H-mode and the L-mode at ρ tor = 0.85: it was not possible to identify a single parameter that explains this difference.The main ITG drive a/L Ti , being different in Hmode and L-mode, could impact the δ < 0 effect.However, it is so different that it is not possible to only vary it to single out its effect, since it would give either stable turbulence or too strong turbulence to be numerically resolved.
To summarise, the main outcome of this numerical analysis, that simulates the actual DTT PT and NT alternatives for the full power scenario up to ρ tor = 0.94, is that, if neglecting a possible beneficial effect of δ < 0 coming from the edge-SOL of the plasma, for the NT L-mode the lack of the pedestal is not balanced by a sufficiently smaller heat and particle transport along the plasma, compared to the PT H-mode.GENE and TGLF predict a negligible effect of δ < 0 for the NT Lmode, that is thus unable to achieve the core performance of the PT H-mode.A plasma cross section with a much larger NT would be needed for the NT scenario to recover the central temperatures of the PT one.A new NT scenario is thus under development, with larger negative top triangularity and reduced volume to satisfy the DTT tokamak engineering constraints.A larger stabilising effect of δ < 0 is observed for the H-mode, but the goal, when designing an NT scenario, is avoiding strong H-mode access, with corresponding ELMs.However, the predictive transport simulations have been performed with boundary conditions at ρ tor = 0.94 and GENE simulations for ρ tor ⩽ 0.85, therefore one cannot rule out possible edge effects coming from ρ tor ≳ 0.9.This is left to future work, since it would need to simulate the PT H-mode pedestal to compare with, which would need more complicated and numerically expensive gyrokinetic simulations.This possibility must be taken seriously, since a beneficial effect of δ < 0 coming from the SOL and resulting in larger n, T at the LCFS when δ < 0 compared to δ > 0 is also reported in recent experimental and numerical works [61,62].Also, the possibility for the DTT NT option to access larger edge pressure gradients than those usually compatible with L-mode regimes is open, still not accessing H-mode-like pedestals due to the inhibited access to the second stability region of high-n ballooning modes for sufficiently negative δ [33][34][35][36], and this could contribute to the possible improvement of the DTT NT scenario performance.
Moreover, recent experiments carried out on TCV [56] and AUG [57], under the EUROfusion WP TE 2022 experimental campaign, reproducing the PT and NT shapes foreseen for DTT, and in similar ITG dominant transport conditions, have shown a more positive picture regarding δ < 0 stabilising effects.TCV shows a strong beneficial effect of NT, that allows NT L-modes to largely overcome the performance of corresponding PT plasmas, reaching the central pressure and temperature values of larger power H-modes.AUG also shows cases where NT plasmas reach central values comparable to PT plasmas with very reduced ELMs.In both tokamaks, part of the better performance of NT seems to be coming from the SOL, resulting in larger n, T at the LCFS.It remains to be understood if a similar effect could be present also in DTT plasmas, which would bring to an improvement of the NT performance with respect to what is calculated in this work.is 38% larger when adapting α MHD to β e .This points out that including this effect would be important to model higher-β cases where the reference/experimental β e value is closer to the KBM threshold.

Figure 1 .
Figure 1.Magnetic equilibrium of the PT reference DTT full power scenario (a), the corresponding NT option (b), and the two numerical cases that are obtained by manually flipping the two equilibria with the CHEASE code, i.e.PT-flipped, obtained by flipping the NT case (c) and NT-flipped, obtained by flipping the PT case (d).The LCFS is shown for the four cases, together with the magnetic surfaces corresponding to the two radii ρtor = 0.7, 0.85 that were considered for the gyrokinetic/quasi-linear local analysis.The dashed lines indicate the analytic approximation of the ρtor = 0.7, 0.85 surfaces with Miller equilibrium (more details can be found in the text).

Figure 2 .
Figure 2. Safety factor q (a), elongation κ (b) and triangularity δ (c) radial profiles, for the reference four considered scenarios.In (c), the top and bottom triangularities δtop, δ bottom are indicated by dashed and dotted lines, respectively.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines.

Figure 3 .
Figure3.Total electron (full) and ion (dashed) heat sources, for the four considered scenarios.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by a vertical dash-dotted line.qe is only shown for ρtor < 0.9, since numerical instability arises in the ASTRA equilibrium solver outside ρtor = 0.9, resulting in spurious Ohmic heating power peaks.

Figure 4 .
Figure 4. (a) Density profiles of the Ne and W impurities, for the four considered scenarios.(b) Effective charge Z eff profiles, for the same cases.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by a vertical dash-dotted line.

Figure 5 .
Figure 5. Density profiles (full lines, left y axis) and energy profiles (dashed lines, right y axis) of the fast ions that are produced by ICRH and NBI.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by a vertical dash-dotted line.

Figure 6 .
Figure 6.Toroidal angular velocity, for the four considered scenarios.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by a vertical dash-dotted line.

Figure 7 .
Figure 7. ASTRA-TGLF predicted density and temperature profiles.The electron density, electron temperature and ion temperature are shown in (a)-(c), respectively, while the corresponding normalised logarithmic gradients are shown in the second row (d)-(f ).The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by vertical dash-dotted lines.The grey band indicates the inner region, where TGLF predictions of Te are not reliable (see the text).

Figure 8 .
Figure 8. ASTRA-TGLF predicted pressure profiles.The radii of the gyrokinetic/quasi-linear analysis are shown by vertical dashed lines, while the upper radial boundary of the ASTRA predictive simulations is indicated by a vertical dash-dotted line.The grey band indicates the inner region, where TGLF predictions of Te are not reliable (see the text).

Figure 9 .
Figure 9. Electron (full) and ion (dashed) density (left y axis) and temperature (right y axis) profiles, for the NT case parameters, with LCFS shape from the NT case (blue) or NT-flipped case (green).It is recalled that TGLF predictions of Te are not reliable for ρ tor<0.2(see the text).
(black lines) are computed as Te (ρ tor ) = Te (ρ tor ) e ´ρtor ρtor a L Te dρ ′ tor , (3)with ρtor = 0.94, 1 and Te (ρ tor ) = T e (ρ tor ) * 1.3, T e (ρ tor ) * 1.15, respectively, corresponding to the solid and dashed black curves, where a/L Te is kept equal to the ASTRA-TGLF output for the DTT NT scenario.We see that the solid black NT

Figure 10 .
Figure 10.Possible beneficial effect of reversing the sign of the triangularity on the Te profile of the DTT NT scenario, coming from ρtor > 0.94.The dashed black curve is obtained by increasing by +15% the Te value at the LCFS and keeping fixed a/L Te inside ρtor = 1 while, for the solid black curve, Te is increased by +30% at ρtor = 0.94 and then, similarly to the dashed one, a/L Te is kept fixed inside that radius.The grey band indicates the inner region, where TGLF predictions of Te are not reliable (see the text).

Figure 13 .
Figure 13.Linear GENE spectra of the growth rate γ (a) and frequency ω (b) at ρtor = 0.7, comparing PT with NT-flipped cases.γ, ω are normalised with cs/a, while ky with 1/ρs.The corresponding results at ρtor = 0.85 are indicated in grey.

Figure 15 .
Figure15.Nonlinear GENE heat flux spectra at ρtor = 0.85.The nonlinear GENE ion and electron heat flux spectra q i (kyρs) and qe(kyρs) are shown in (a) and (b), respectively, divided by the spectral resolution ∆(kyρs), so that he area below the curves is equal to the total fluxes in MW.

Figure 16 .
Figure 16.GENE ion temperature stiffness plot at ρtor = 0.7, for the H-mode PT (red)/NT-flipped (orange) cases.The results at ρtor = 0.85 are shown in grey for comparison.The error bars represent the standard deviation of the fluxes time traces over the same time interval that has been considered to compute their averages.

Figure 17 .
Figure 17.(a) Dependence of the NT stabilising/destabilising effect on the different parameters of H-mode and L-mode cases.The points at the far left indicate the reference L-mode cases.The following points are obtained swapping one parameter at a time, taking it from the H-modes, as is explained in detail in the text.The error bars represent the standard deviation of the fluxes time traces over the same time interval that has been considered to compute their averages.(b) Collisionality scan neglecting impurities: the ratio of the heat fluxes of NT-flipped and PT cases is shown versus the GENE normalised collisionality parameter νc.The reference PT H-mode collisionality is indicated by a vertical red line, while the NT L-mode value by a vertical blue line.The results obtained when considering impurities are shown by crosses for the reference H-mode collisionality.

Figure 19 .
Figure 19.Linear βe scans of the growth rate γ (a) and the frequency ω (b), comparing the results obtained by keeping α MHD fixed (full) with those obtained with adapting α MHD to βe (dashed), for the most unstable linear mode with kyρs = 0.3 at ρtor = 0.85.The PT and NT-flipped cases are compared.The reference βe value for the PT case is indicated by a vertical dashed red line.

Table 1 .
GENE and TGLF stand-alone input parameters at the two radii of analysis ρtor = 0.7, 0.85.
0 (indicated as electrostatic: ES).The results are shown in figure12by dashed lines (collisionless), dotted lines (without impurities) or crosses (ES), compared with the full-physics ones from figure11(full lines in figure12).The γ and ω are reported in physical units, since c s is different for H-mode cases (PT/NT-flipped) and L-mode ones (PT-flipped/NT), due to different T e (see figure7(b)).Collisions have a similar stabilising effect for PT and NT (−19% on the maximum ITG γ) for k y ρ s < 0.8 (mostly contributing to the nonlinear heat fluxes).Impurities have a smaller stabilising effect for the NT case (about −14% on the maximum ITG γ), while they do not affect the PT case.EM effects are negligible, except for the lower k y MTMs, which do not impact the turbulent heat fluxes.The stability of the kinetic ballooning modes (KBMs) Figure12.Effect of collisions, impurities and EM effects on the GENE ky spectra of the growth rate γ and the frequency ω, for the most unstable linear mode.The PT case is in red, while the NT one in blue.The results obtained in the collisionless regime (dashed lines), removing Ne and W impurities (dotted lines) or in the ES regime (crosses), are compared with the ones obtained with full physics (full lines).

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Predictive ASTRA-TGLF simulations: the runs, performed with boundary conditions at ρ tor = 0.94, indicate that the NT L-mode temperature profiles are unable to recover the central values of the PT H-mode, leading to a −40% smaller energy confinement time for NT compared with PT.Inverting the triangularity δ alone improves the temperature peaking for the H-mode cases, while it has a negligible effect on the L-mode ones.Since the PT H-mode has larger average |δ| compared to the NT L-mode (δ LCFS,PT = 0.44, δ LCFS,NT = −0.15),an additional simulation has been run to test if this is the reason of this behaviour, by repeating the NT run substituting the NT L-mode equilibrium with the one obtained by artificially flipping δ from the PT H-mode case, but the results are very close to the original NT ones, indicating that it is not the different |δ| the cause of the different strength of the NT stabilising effect for the H-mode and Lmode cases, but the other different parameters.A numerical exercise that has been performed with TGLF stand- alone indicates that |δ| ∼ 0.8 values, approximately nine times larger than the value of the NT scenario at ρ tor = 0.85, would be needed for T i to recover the loss of H-mode pedestal for ρ tor > 0.7, where the triangularity is expected to matter.