Investigation of fast ion effects on core turbulence in FIRE mode plasmas

Further investigation of fast ion effects on turbulence and transport in the fast ion regulated enhancement (FIRE) mode discharge (Han et al 2022 Nature 609 269–275) was performed in this work as a continuation of a previous study (Kim et al 2023 Nucl. Fusion 63 124001) that showed that the dominant turbulence suppression mechanism by fast ions is the dilution effect in the FIRE mode discharge. The current study includes (i) the impact of the fast ion relevant mode observed in the simulation of thermal energy flux, (ii) dilution effects by fast ions compared to dilution effects by other species, and (iii) fast ion effects on electron-scale turbulence. First, nonlinear gyrokinetic simulation results show that turbulence is significantly suppressed even without the fast ion relevant mode, indicating that the impact of this mode on thermal transport is not significant in this discharge. Second, further analysis on the dilution effects shows the three following results: Turbulence is not completely suppressed by the reduced main ion density fraction effect due to impurities; the reduction in energy flux can be limited by a certain impurity mode that is destabilized by a high impurity density gradient from adjusting the main ion density gradient; electrons can contribute to turbulence suppression through the main ion density gradient change, although this effect is less significant compared to other species. Third, we observe that two fast ion effects can influence the linear growth rate of the electron-scale turbulence mode. The growth rate decreases by an increase in β∗(≡(−8π/B2)dp/dr) and increases by dilution effects, suggesting that fast ion effects on electron-scale turbulence can differ depending on the operation scenario, such as the fast ion fraction. The comprehensive analysis performed in this study can enhance our understanding of fast ion physics, required for burning plasma operation in the future.

Further investigation of fast ion effects on turbulence and transport in the fast ion regulated enhancement (FIRE) mode discharge (Han et al 2022 Nature 609 269-275) was performed in this work as a continuation of a previous study (Kim et al 2023 Nucl.Fusion 63 124001) that showed that the dominant turbulence suppression mechanism by fast ions is the dilution effect in the FIRE mode discharge.The current study includes (i) the impact of the fast ion relevant mode observed in the simulation of thermal energy flux, (ii) dilution effects by fast ions compared to dilution effects by other species, and (iii) fast ion effects on electron-scale turbulence.First, nonlinear gyrokinetic simulation results show that turbulence is significantly suppressed even without the fast ion relevant mode, indicating that the impact of this mode on thermal transport is not significant in this discharge.Second, further analysis on the dilution effects shows the three following results: Turbulence is not completely suppressed by the reduced main ion density fraction effect due to impurities; the reduction in energy flux can be limited by a certain impurity mode that is destabilized by a high impurity density gradient from adjusting the main ion density gradient; electrons can contribute to turbulence suppression through the main ion density gradient change, although this effect is less significant compared to other species.Third, we observe that two fast ion effects can influence the linear growth rate of the electron-scale turbulence mode.The growth rate decreases by an increase in β * ( ≡ ( −8π /B 2 ) dp/dr ) and increases by dilution effects, suggesting that fast ion effects on electron-scale turbulence can differ depending on the operation scenario, such as the fast ion fraction.The comprehensive analysis performed in this study can enhance our understanding of fast ion physics, required for burning plasma operation in the future.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Introduction
Fast ions, generated by external heating or nuclear fusion reactions, play a crucial role in achieving and sustaining the high temperatures required for burning plasma operations in fusion energy development.Nonetheless, the presence of fast ions can induce magnetohydrodynamic modes [1][2][3][4][5], which have the potential to degrade plasma confinement.On the other hand, previous studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] have also suggested that fast ions might improve the confinement by suppressing turbulence.Given this multifaceted impact of fast ions on fusion plasmas, a comprehensive understanding of their effects has become imperative to provide a base for future burning plasma operations.
Previous research in the KSTAR found an internal transport barrier (ITB) mode, which was named fast ion regulated enhancement (FIRE) mode discharge [22].In the FIRE mode discharge, ITB foot location was correlated with a high fast ion fraction generated by neutral beam injection.Because of the ITB, the FIRE mode achieves a level of confinement comparable to hybrid modes [23][24][25] with a neoclassical level of ion heat diffusivity.Furthermore, this mode offers several advantages that address the limitations of traditional ITB modes [26,27], including low impurity accumulation levels and plasma sustainment without sophisticated control for approximately 30 s.
Nonlinear gyrokinetic simulation using the code CGYRO [28] has predicted that thermal energy fluxes decrease significantly due to suppression of turbulence mainly driven by ion temperature gradient mode, as fast ions are added, which is qualitatively consistent with experiment [22].It was also found that the dominant turbulence suppression mechanisms due to fast ions are dilution effects including reduced main ion density fraction and inverted main ion density gradient; details of this analysis are reported in [18].However, additional studies are required to more comprehensively understand the role of fast ions, including the fast ion relevant mode observed in the simulation, the dilution effects of fast ions compared to dilution by other species, and the fast ion effects on electron-scale turbulence.The objective of the current study is to investigate these three aspects.
The linear and nonlinear simulation results in [18] showed the occurrence of a fast ion relevant mode, which might be a type of fast ion driven mode.Understanding fast ion driven modes is of prime importance as these modes can enhance fast ion transport, which can damage the wall and hinder self-sustainment.Fast ion driven modes have been found to decrease thermal energy flux through turbulence suppression by generating zonal flow [15,16], but conversely, these modes have also been found to increase thermal energy flux through damping mechanisms [29][30][31][32].These various aspects of fast ion driven modes motivated us to explore the impact of the fast ion relevant mode on thermal energy transport in the simulation results.
In the FIRE mode, turbulence was found to be suppressed mainly due to dilution effects by fast ions [18].Here, it was found that both dilution effects, namely a reduction of the main ion density fraction and changes in the main ion density gradient, were significant.We note that the main ion density fraction and its gradient can be varied by other species.Therefore, turbulence suppression by dilution can be realized by other species as well.In the current work, to explore the potential to apply the findings of [18] in developing improved confinement modes and to enhance our understanding of dilution effects by fast ions, we performed further investigation of dilution effects by other species.
The electron temperature gradient (ETG) mode [33][34][35], an electron scale drift wave instability, is generally driven by the ETG.It has been reported that the ETG can significantly increase electron transport [36][37][38] by generating a radially elongated streamer [39] and also affect ion-scale turbulence through multi-scale interaction [40][41][42][43][44].To complement the previous study that focused on the fast ion effects on ion-scale turbulence in the FIRE mode [18], in the current study we investigated the effects of fast ions on electron-scale turbulence in the FIRE mode through linear gyrokinetic analysis.
This paper is organized as follows.Section 2 details the gyrokinetic simulation setup including numerical resolution and experimental input parameters.In section 3, the effects of the fast ion relevant mode on thermal transport are discussed.Section 4 compares the dilution effects by fast ions with those by impurities and electrons.Then the fast ion effects on electron-scale turbulence are presented in section 5. Section 6 summarizes and concludes this study.

Gyrokinetic simulation setup
Using CGYRO [28], a local flux tube gyrokinetic simulation code, gyrokinetic analysis was performed to investigate the fast ion effects on turbulence inside the ITB region (ρ = 0.4 with the square root of normalized toroidal magnetic flux, ρ) of the FIRE mode discharge.Electromagnetic simulations were performed with electrostatic potential, δϕ , and vector potential, δA ∥ .The ranges of the poloidal wavenumber, k y , used in this study were k y ρ s ⩽∼ 1.0 and k y ρ s ⩽∼ 52.0 for ion-and electron-scale simulations, respectively.For ion scale simulations, minimum k y ρ s is 0.067, corresponding to toroidal mode number ∼4, where k y ρ s = 0.015 corresponds to toroidal mode number, n = 1.Here, ρ s is the ion sound gyro-radius, defined as c s / (eB/m i c) where c s (≡ √ T e /m i ) is ion sound speed.The range of the radial wavenumber, k x , Table 1.Input parameters for FIRE mode discharge #22663 at ρ = 0.4.Here, q and s (≡ (r/q) (∂q/∂r)) are safety factors and magnetic shear, respectively.a/Lx denotes the inverse gradient length scale defined as −a∇ X/X with minor radius a. β * is defined as dp/dr where b and p are the magnetic field and plasma pressure, respectively.νee and ω E×B (≡ − (r/q) (dω 0 /dr) where ω 0 is angular frequency ) are the electron-electron collision frequency and the equilibrium E × B flow shearing rate in units of cs/a, respectively.Values in parentheses denote the case without fast ions.[45] was used for equilibrium geometry.Electron dynamics was considered by using gyrokinetic equations.The Sugama collision operator [46] was used for considering collisions.
Here, carbon was used as a single impurity species, with flat Z eff (=2, where Z eff ≡ Σ j Z 2 j n j /n e with ion species j) profile assumption.Rotation effects were also included in the simulation.To consider the effects of the plasma flow and its shear, the equilibrium E × B flow profile was estimated from the radial force balance of the impurity species (carbon), based on the experimental toroidal velocity of carbon measured via charge exchange spectroscopy [47] and on the neoclassical poloidal velocity calculated by the NEO code [48].The fast ion species, which is deuterium, was treated as an additional ion species with a Maxwellian distribution [49].Additionally, a finite Debye length was considered for electron-scale simulation.
The numerical parameters for the resolution and simulation domain were obtained by convergence tests.
[n radial , n ξ , n θ , n energy , n tor ] = [216, 16,28,8,16] and [L x , L y ] = [97.72ρs , 93.78ρ s ] were used for the resolution parameters and simulation domain, where n radial , n ξ , n θ , n energy , and n tor are radial, pitch angle, poloidal angle, energy, and toroidal grid numbers, respectively.The experimental parameters shown in table 1 were used as input parameters.Here, q and s (≡ (r/q) (∂q/∂r)) are safety factors and magnetic shear, respectively.a/L x denotes the inverse gradient length scale defined as −a∇ X/X with minor radius a. ν ee and ω E×B are, respectively, the electron-electron collision frequency and the equilibrium E × B flow shearing rate, defined as ω E×B ≡ − (r/q) (dω 0 /dr) with the angular frequency ω 0 .Both parameters are presented in units of c s /a.Here, we note that a/L ni is negative to satisfy the quasi-neutrality condition (Σ j Z j en j = 0 and Σ j Z j e∇n j = 0, where j is the ion and electron species) with the high fast ion fraction and strongly peaked fast ion density profile.A more detailed explanation for the input parameters, numerical parameters, and simulation domain used in this study can be found in [18].

Effect of the fast ion relevant mode in FIRE mode simulations
Instabilities such as fishbone instability [1] or the Alfven eigenmode [2-5] can be excited by interaction with fast ions.Fast ion driven modes can affect not only fast ion transport but also transport of thermal species through zonal flow generation [15,16] or energy transfer by damping mechanisms [29][30][31][32].
A significant reduction in thermal energy flux was observed in the FIRE mode plasma, from 105 for the case with fast ions [18].Here, Q GB is gyroBohm energy flux (Q GB = n e T e c s ρ 2 * ) and ρ * is ρ s /a.We also observed an electrostatic mode having a ballooning structure destabilized in long wavelength region, k y ρ s ⩽ 0.2 in the simulation along with the thermal energy flux reduction by adding fast ions.The fast ion relevant mode has the highest linear growth rate at k y ρ s = 0.133, and its corresponding toroidal mode number is ∼9.In this study, we call this mode fast ion relevant mode since it exists only in the case with fast ions.At this moment, it was inconclusive that the fast ion relevant mode shown in the simulation was destabilized in the real experiment due to the diagnostic availability.This will be clarified in the future.Nevertheless, it is worth understanding the physics related to the fast ion relevant mode in this plasma through the simulation regardless of consistency with experiments since it was found that most of the electron energy flux was driven from k y ρ s ⩽ 0.2 and electrostatic, consistent with the fast ion relevant mode.This suggests that the fast ion relevant mode is related to the electron thermal transport.Therefore, further investigation of the effects of the fast ion relevant mode on thermal transport is required.
In addition, the experimental energy fluxes are Q i [Q GB ] ∼ 0.48 and Q e [Q GB ] ∼ 0.68, higher than the simulated energy flux levels.Although the simulated energy flux levels are not matched with experimental energy flux levels, we note that the main conclusion of this paper will not be altered from the case matching experimental energy flux since this study focuses on the qualitative trend instead of quantitative predictions.

Impact of fast ion relevant mode on thermal energy flux reduction
Figures 1(a) and (b) show the linear stability analysis results consisting of real frequency and linear growth rate with different T f /T i .The (+) and (-) signs of real frequency correspond to the electron and ion diamagnetic direction, respectively.The blue dashed line in figure 1(b) denotes the equilibrium E × B flow shearing rate.In the simulation using experimental parameters, which corresponds to the green line in figures 1(a) and (b), a discontinuous jump in real frequency was observed at k y ρ s ⩽ 0.2.Since this mode does not exist when the fast ion species is not included (not shown here), the mode in the k y ρ s ⩽ 0.2 domain is related to fast ions.It was also observed that this fast ion relevant mode was stabilized as T f /T i decreases, and it was almost suppressed when T f /T i = 5 as shown in figures 1(a) and (b).It can be seen that the linear growth rate is higher when T f /T i = 5 compared to the case with experimental T f /T i (= 9.8).
However, figure 1(c) shows that thermal energy flux levels are already quite low, less than 0.1 Q GB , even without the fast ion relevant mode (T f /T i = 5).The thermal energy flux levels for this case were Q i [Q GB ] ∼ 0.012 ± 0.004 and Q e [Q GB ] ∼ 0.020 ± 0.005.Here, the energy flux levels were quantified as the average values during the saturated phase denoted by the black arrow in the same figure.These levels were much smaller than the levels in the case without fast ions (Q i [Q GB ] ∼ 19.200 ± 7.497 and Q e [Q GB ] ∼ 9.614 ± 4.284) but were agreed with the energy flux levels in the case with fast ions (Q i [Q GB ] ∼ 0.001 ± 0.031 and Q e [Q GB ] ∼ 0.067 ± 0.105) within their uncertainties.This result indicates that the fast ion relevant mode is not necessary to reproduce the thermal energy flux reduction with fast ion addition.This result is attributed to the turbulence suppression by other mechanisms, such as dilution effects.It follows that the impact of the fast ion relevant mode on thermal transport is not significant in the FIRE mode simulation.

Impact of fast ion relevant mode on zonal flow
From the previous section, we can conclude that the impact of the fast ion relevant mode on thermal transport is not significant compared to other fast ion effects, such as dilution, in the FIRE mode discharge studied here.Despite this, to enhance our understanding of fast ion effects, it is beneficial to continue to investigate the fast ion relevant mode impact on transport from various aspects.Figure 2 shows linear and nonlinear gyrokinetic simulation results for real frequency, linear growth rate, energy flux, and zonal flow shearing rate for different a/L ni .The gyrokinetic simulations shown in figure 2 were performed with n f /n e = 0.40, T f /T i = 9.8, β * = 0.075 while varying a/L ni from −1.494 (experimental level) to 1.067 (=a/L ne ) along with a/L nf to satisfy the quasi-neutrality condition.As a/L ni varied from −1.494 to 1.067, the linear growth rate tended to increase except for the k y ρ s ⩽ 0.2 region where the fast ion relevant mode appears.As the linear growth rate was higher than the equilibrium E × B shearing rate when a/L ni = 1.067, the thermal energy flux levels also increased.Interestingly, the zonal shearing rate was not well correlated with the energy flux level.Figure 2(d) shows that the zonal shearing rate was reduced by ∼80% as a/L ni varied from −1.494 to 0, while the energy flux levels were similar in these two cases.We can also see that the zonal shearing rate was slightly increased even with the significant increase in the thermal energy flux levels as a/L ni varied from 0 to 1.067.Instead of the energy flux levels, the zonal shearing rate was indeed correlated with the growth rate of the fast ion relevant mode here.The fast ion relevant mode was suppressed when a/L ni = 1.067, mainly due to the lower a/L nf used in this case (a/L nf = 1.067) compared to the case with a/L ni = −1.494(a/L nf = 3.572).We can also observe a reduction in the linear growth rate of this mode as a/L ni varied from −1.494 to 0. As a result, we can see that the changes in the linear growth rate at k y ρ s ∼ 0.13 or 0.2 are well correlated with the changes in the zonal shearing rate.This suggests that the higher zonal shearing rate shown at a/L ni = −1.494 is mainly due to the fast ion relevant mode, which can contribute to turbulence suppression.However, as discussed in section 3.1, turbulence was already sufficiently suppressed even without the help of the increased zonal flow.Nevertheless, it is worth clarifying the comprehensive effects of the fast ion relevant mode in this discharge.

Increased thermal transport level by highly destabilized fast ion relevant mode
It is known that fast ion driven modes can generate significant thermal energy flux [29][30][31][32]50].Here, the possibility that a highly destabilized fast ion relevant mode could increase thermal transport was investigated.Figures 3(a) and (b) show the linear stability analysis results while varying a/L Tf .As a/L Tf increased, the linear growth rate increased in the k y ρ s ⩽ 0.2 region while it slightly decreased in the k y ρ s > 0.2 region.The changes in the real frequency were negligible.This result shows that the fast ion relevant mode observed in simulation is destabilized by a/L Tf .Figures 3(c) and (d) illustrate that the changes in the thermal energy flux levels are nonmonotonic with a/L Tf , but also that the fast ion energy flux increases monotonically as the fast ion relevant mode becomes more destabilized with a/L Tf .The thermal energy flux levels decreased as a/L Tf increased from 50% of the experimental value to the experimental a/L Tf value.This reduction can be attributed to the zonal flow generated by the fast ion relevant mode.In contrast, thermal energy flux, especially electron energy flux, increased when the fast ion relevant mode became highly destabilized, as shown in the case of a fractional change of a/L Tf greater than 1.This increase in thermal energy flux may be due to energy transfer from the highly destabilized fast ion relevant mode to electron species through a certain damping mechanism [29][30][31][32].The detailed damping mechanism is out of scope in this paper, and will be investigated in the future.This result indicates that a highly destabilized fast ion relevant mode can increase the thermal energy flux by more than its reduction due to fast ion effects.In the experimental case, since the fast ion relevant mode was not highly destabilized, we observed the significant reduction in thermal energy flux.However, we can still observe a higher electron energy flux level (∼0.067Q GB ) compared to the thermal ion flux level (∼0.001Q GB ) in this case, which is likely due to energy transfer from the fast ion relevant mode.

Comparison between dilution effects due to fast ions and other species
Dilution effects can be separated into effects from a reduced density fraction and the effects due to changes in the density gradient to match the quasi-neutrality condition.
Fast ions are known to affect turbulence through dilution effects [9,12,18], i.e. by altering the main ion density fraction and by altering the main ion density gradient, and these dilution effects are mainly responsible for the observed thermal energy flux reduction in the FIRE mode [18].However, both dilution effects can be realized not only by fast ions but also by other species such as impurity or electron.In this section, we investigate the dilution effects due to other species and compare them to the effects from fast ions to find out the advantages and limitations of turbulence suppression by dilution effects due to fast ions.
Figures 4(a) and (b) plot energy flux predicted by nonlinear simulations while varying the fraction of the main ion (n i /n e ) by the addition of fast ions.In these simulations, a/L n of all species is set to 1.07 and β * is fixed to 0.024, which is the level in the case without fast ions.Both ion and electron energy fluxes significantly decreased to near 1 Q GB as n i /n e decreased from 0.8 to 0.6 with the increase of n f /n e from 0 to 0.2, after which they maintained at a similar level with a further increase in n f /n e to 0.4.The similar thermal energy flux levels between the cases with n f /n e = 0.2 and 0.4 are likely due to their low levels, which were already too low to expect further reduction.From the linear stability analysis shown in figures 4(c) and (d), we observed that the linear growth rate of the most unstable mode increased in the k y ρ s < 0.75 region along with a marginal change in the real frequency as n i /n e decreased with higher n f /n e .
The main ion density fraction can also be reduced by increasing the fraction of impurity species.As done in the aforementioned case adjusting the main ion density fraction by fast ions, nonlinear simulations were conducted with reduced n i /n e by increasing the impurity (carbon) density fraction (n c /n e ) while maintaining the density gradient of all species and β * .Figures 5(a) and (b) show that both ion and electron energy fluxes are reduced by ∼60% as n i /n e decreases from 0.8 to 0.6, as expected.However, both ion and electron energy fluxes stayed at similar levels or increased slightly as n i /n e decreased from 0.6 to 0.4.
A linear stability analysis, shown in figures 5(c) and (d), was conducted to interpret the saturated energy flux levels even with the additional significant reduction in the main ion density fraction observed in figures 5(a) and (b).As the main ion density fraction decreased with increasing impurity fraction, we observed relatively small changes in the real frequency of the most unstable mode and its growth rate for k y ρ s < 0.4, while changes in the linear growth rate for k y ρ s > 0.4 were more evident.The linear growth rate increased as the main ion density fraction decreased.The slight changes in the energy flux levels as n i /n e decreased from 0.6 to 0.4 may be due to the increased linear growth rate in the k y ρ s > 0.4 region.These results suggest that thermal transport is reduced by a decreased main ion density fraction due to the addition of impurity species, but this effect can be limited by a certain instability driven by the impurity species as the impurity fraction reaches a certain level.

Main ion density gradient change due to impurity and electron species
The previous study showed significant turbulence suppression by an inverted main ion density gradient due to the addition of fast ions [18].The main ion density gradient can also be varied by other species, such as impurity and electron species.To explore the main ion density gradient as a control knob for turbulence suppression, we investigated multiple cases varying the main ion density gradient by adjusting the density gradient of impurity or electron species.
In figure 6, a/L ni was varied from 1.067 to −1.494 and a/L nc from 1.067 to 11.31 to satisfy quasi-neutrality.In these simulations, the fractions of main ion and impurity (carbon) were fixed to 0.8 and 0.03, respectively.β * was fixed to 0.024, corresponding to the case without fast ions.
The nonlinear simulation results in figures 6(a) and (b) show a significant thermal energy flux reduction as a/L ni inverts with increasing a/L nc .The a/L ni = −0.533case shows negligible thermal energy flux.The effect of main ion density gradient change due to impurity species is consistent with the case using fast ions.When a/L ni = −1.494,although the thermal energy fluxes still showed a negligible level, the electron energy flux increased slightly to 0.2 from 0.07 Q GB as a/L ni varied from −0.533 to −1.494.This marginal increase in electron energy flux was analyzed via linear stability analysis, as shown in figures 6(c) and (d).As a/L ni decreased with increasing a/L nc , the real frequency of the most unstable mode gradually increased, and eventually, the most unstable mode in the whole k y ρ s range propagated to the electron diamagnetic direction when a/L ni < 0, as shown in figure 6(c).The linear growth rate decreased to a level lower than the E × B shearing rate as a/L ni decreased and inverted to −0.533.However, the linear growth rate started to increase as a/L ni became more negative.This is likely due to a certain impurity mode destabilized by the large a/L nc used to generate a large negative a/L ni value.Likewise, the slight increase in thermal energy flux levels shown in figures 6(a) and (b) may be caused by this destabilized mode due to the high impurity density gradient.
As shown in figure 2, the changes in the main ion density gradient due to fast ions can reduce the thermal energy flux levels.However, the fast ion relevant mode can be destabilized as the fast ion density gradient is increased to adjust the main ion density gradient, which limits further reduction in thermal energy flux or maintains the flux levels if they are near negligible levels.The simulation results given in this section also show that the changes in the main ion density gradient due to the impurity density gradient can reduce the thermal energy flux significantly, similar to the fast ion case.However, it should be noted that a significant increase in the impurity density gradient to adjust the main ion density gradient can also result in destabilizing certain impurity modes.
The main ion density gradient can be varied by the electron density gradient as well as the density gradient of fast ions or impurities.Figure 7 shows the simulation results varying a/L ni and a/L ne .When a/L ni decreased, a/L ne decreased together to satisfy the quasi-neutrality condition in this case.When a/L ni and a/L ne both decreased, both ion and electron energy flux monotonically decreased, but still exhibited larger energy flux levels compared to the cases using fast ion or impurity species.Figure 7(c) shows that the real frequency moves to the electron diamagnetic direction as a/L ne decreases.The linear growth rate decreased monotonically with a decrease in a/L ne , as can be seen in figure 7(d).The linear stability analysis results are consistent with the nonlinear simulation results.However, the reduction in the linear growth rate was smaller than the reduction observed in the other cases, such as by adjusting the main ion density gradient through fast ion or impurity species.
Since the electron density gradient should decrease for lower and inverted values of the main ion density gradient, while the gradient of fast ion or impurity species should increase for the same purpose, the reduction in thermal energy flux by changes in a/L ni is not limited by the certain unstable mode found in the cases utilizing fast ion or impurity species.This is consistent with the results in figure 7 showing the monotonic reduction of thermal energy flux as a/L ni moves to negative values.Therefore, electrons can also partially contribute to turbulence suppression by changing the main ion density gradient, although this is less effective compared to the cases using fast ion or impurity species.

Fast ion effects on electron-scale turbulence
Most previous studies on the fast ion effects on turbulence focused on ion-scale turbulence [6][7][8][9][11][12][13][14][15][16][17][18][19], but recently, fast ion effects on electron-scale turbulence were also investigated [10] since electron-scale turbulence can degrade confinement significantly by increasing the electron energy flux.Here, we also performed linear gyrokinetic simulations inside the ITB location (ρ ∼ 0.4, the same location as in the ion-scale simulations) to investigate the fast ion effects on electron-scale turbulence in the FIRE mode plasma.
Figure 8 shows the real frequency and linear growth rate of the most unstable mode for k y ρ s ⩽∼ 56 with varying a/L Te .Since the most unstable mode propagates in the electron diamagnetic direction, and the linear growth rate increases with a/L Te , as can be seen in figures 8(a) and (b), it is most likely that the most unstable mode in the k y ρ s ⩽∼ 56 region is the ETG mode.
We investigated the changes in the linear stability analysis results of this ETG mode depending on possible fast ion effects including increased β * and dilution effects, as shown in figure 9. To consider an increased β * due to fast ions, linear simulation was performed for the case without fast ions but increasing β * to the values in the case with fast ions (increased β * case in figure 9).Both real frequency and linear growth rate decreased with increasing β * compared to the case without fast ions.This result is consistent with previous studies [51,52] showing that the ETG mode can be stabilized with a high β * value or the Shafranov shift effect.Next, to consider other effects including dilution effects, we added fast ion species but with the β * value fixed to the case without fast ions.Since other mechanisms, such as interaction between fast ions and unstable modes and generation of zonal flow, were not considered in this linear simulation, the dilution effects were the main focus of this case, hence the 'Dilution' label in figure 9.
In this case, the linear growth rate increased compared to the case without fast ions while the real frequency stayed at a similar level.It is noteworthy that the reduction in linear growth rate due to increased β * is more significant than the increase due to dilution effects for k y ρ s ⩽ 36.Consequently, when the fast ion species was included, we can see a reduction in the real frequency in all k y ρ s regions and also in the linear growth rate in the k y ρ s ⩽ 36 region, similar to the results expected when both effects are added.Therefore, the changes in the linear growth rate due to the addition of fast ions are the result of competition between the effects of increased β * and dilution.This result suggests that the effects of fast ions on electron-scale turbulence can differ depending on the operation scenario.For the FIRE mode plasmas, which have a high fast ion population, the positive effects due to increased β * are expected to be mitigated or almost cancelled out by the negative effects due to dilution.In the ITER burning plasma operation scenario, alpha particles generated from the nuclear reactions will have a small density fraction (n f /n e ∼ 1%) [53,54] but high temperature, providing high β * .Therefore, β * effects will be dominant and thus favorable to the suppression of electron-scale turbulence.Further investigation using nonlinear simulation will be performed in the future.

Conclusion
A previous study of the fast ion effects on FIRE mode discharge showed that dilution effects were mainly responsible for the thermal energy reduction with the addition of fast ion species observed in simulation [18].Further investigation was conducted in the current study to enhance our understanding of the fast ion effects on turbulence and transport.We discussed the impact of the fast ion relevant mode observed in the simulation on the turbulence, dilution effects of fast ions compared to dilution by other species, and fast ion effects on electronscale turbulence.
Nonlinear gyrokinetic simulations with a reduced fast ion temperature (T f /T i = 5 from 9.8) to suppress the fast ion relevant mode observed in the simulation predicted very low levels of thermal energy flux, similar to the simulation results with the fast ion relevant mode (T f /T i = 9.8 case).This result indicates that the impact of the fast ion relevant mode on thermal transport is not significant in this case, a finding that is attributed to the significant turbulence suppression by other fast ion effects including dilution.Nonetheless, additional analysis showed that the fast ion relevant mode significantly contributes to zonal flow generation.We also observed that the fast ion relevant mode can increase the thermal transport level when this mode is highly destabilized.
Dilution effects due to fast ions were compared to other species since the main ion density profile can be adjusted by other species, such as impurities and electrons.It was observed that the energy flux levels were reduced by the reduction in the main ion density fraction through the addition of an impurity species.However, the thermal energy flux is not reduced further and stays at a higher level compared to the case using fast ions, as the fraction of the main ion is below a certain level with increased carbon density fraction, which can be attributed to the destabilization of the observed mode due to a high impurity fraction.It follows that the reduction in the main ion density fraction by the addition of impurities will be less effective compared to the case using fast ions.Adjusting the main ion density gradient through impurities can suppress turbulence, resulting in almost negligible thermal energy flux levels, similar to the case using fast ions.However, certain impurity modes can be destabilized by a high impurity density gradient, which can limit the further reduction of energy flux levels or maintain low energy flux levels.A similar constraint can be found in the case using fast ions due to the fast ion relevant mode.The electron density gradient should be reduced to adjust the main ion density gradient to lower or inverted values.Therefore, the constraint observed in the cases using fast ions or impurities does not exist in the case using electrons.This result suggests that electrons can contribute to turbulence suppression through changes in the main ion density gradient, although it was observed that its effect is less significant compared to the case using other species.
Fast ion effects on electron-scale turbulence were also investigated.While the linear stability analysis showed that the electron-scale turbulence mode is unstable in the FIRE mode discharge studied here, the impact of this mode may not be critical.It was found that the linear growth rate of this mode decreased when β * increased, consistent with previous studies [51,52], while dilution effects by fast ions increased the linear growth rate.In the FIRE mode discharge studied here, the reduction in the linear growth rate due to increased β * was comparable to the increase in the growth rate due to dilution for k y ρ s > 36, while the increment of the linear growth rate due to dilution was smaller than the changes due to β * in the other region.Consequently, the linear growth rate decreased in the k y ρ s < 36 region as the fast ion species was added in this case.Therefore, competition exists between increased β * and dilution.These results suggest that the fast ion effects on electronscale turbulence can vary depending on the operation scenario.Further investigation of fast ion effects on electron-scale turbulence, including nonlinear analysis, will be performed in the future.
The comprehensive analysis performed in this study can support our understanding and insights on the effects of fast ions on turbulence.The findings here can also be utilized in developing high confinement operation scenarios.

Figure 1 .
Figure 1.(a) Real frequency and (b) linear growth rate of linear stability analysis results with T f /T i = 5 (red) and 9.8 (green).(c) Time series of gyroBohm normalized energy flux for T f /T i = 5.Here, the black arrow denotes the time-averaging range.

Figure 2 .
Figure 2. Linear stability analysis for (a) real frequency and (b) linear growth rate with varied a/L ni .(c) GyroBohm normalized energy flux for ions and electrons as a function of a/L ni .(d) Zonal flow shearing rate (ω zf ) for different a/L ni .All gyrokinetic simulations were performed with n f /ne = 0.40, T f /T i = 9.8 (exp), β * = 0.075, which is the same condition as the experimental parameters except for a/L ni .

Figure 3 .
Figure 3. (a) Real frequency and (b) linear growth rate of the linear stability analysis results with varied a/L Tf .GyroBohm normalized energy flux for (c) ions and electrons, and (d) fast ions as a function of fractional change of a/L Tf .

Figure 4 .
Figure 4. GyroBohm normalized energy flux predicted by nonlinear simulation for (a) ions and (b) electrons with varied n i /ne and n f /ne.(c)Real frequency and (d) linear growth rate of the linear stability analysis results varied n i /ne and n f /ne.Here, a/Ln of all species is set to 1.07, and β * is fixed to 0.024, the level in the case without fast ions.

D. Kim et al Figure 5 .
Figure 5. GyroBohm normalized energy flux predicted by nonlinear simulation for (a) ions and (b) electrons as a function of n i /ne.(c) Real frequency and (d) linear growth rate of the linear stability analysis results with varied n i /ne and nc/ne.Here, a/Ln of all species is set to 1.07, and β * is fixed to 0.024, the level in the case without fast ions.

Figure 6 .
Figure 6.GyroBohm normalized energy flux predicted by nonlinear simulation with varied a/L ni and a/Lnc for (a) ions and (b) electrons.(c) Real frequency and (d) linear growth rate of the linear stability analysis results.Here, nc/ne and β * are respectively fixed to 0.033 and 0.024, the level in the case without fast ions.

Figure 7 .
Figure 7. GyroBohm normalized energy flux predicted by nonlinear simulation with varied a/L ni and varied a/Lne for (a) ions and (b) electrons.(c) Real frequency and (d) linear growth rate of the linear stability analysis results.nc/ne and β * are respectively fixed to 0.033 and 0.024, the level in the case without fast ions.

Figure 8 .
Figure 8.(a) Real frequency and (b) linear growth rate of the linear stability analysis results with varied a/Lte for kyρs ⩽ 56.

Figure 9 .
Figure 9. (a) Real frequency and (b) linear growth rate of the linear stability analysis results for fast ion effects.