A reduced-turbulence regime in the Large Helical Device upon injection of low-Z materials powders

Recently an improved confinement regime, characterized by reduced turbulent fluctuations has been observed in the Large Helical Device upon the injection of boron powder into the plasma (Nespoli et al 2022 Nat. Phys. 18 350–56). In this article, we report in more detail the experimental observations of increased plasma temperature and the decrease of turbulent fluctuations across the plasma cross section, on an extended database. In particular, we compare powders of different materials (B, C, BN), finding similar temperature improvement and turbulence response for the three cases. Modeling of the powder penetration into the plasma and of neoclassical electric field and fluxes support the interpretation of the experimental results. Additionally, we report evidence of the temperature improvement increasing with powder injection rates and decreasing for both increasing density and heating power. Though, plasma turbulence response varies depending on the initial conditions of the plasma, making it difficult to draw an inclusive description of the phenomenon.


Introduction
Stellarators are a promising candidate for a magnetic confinement fusion reactor. The three-dimensional magnetic field is provided entirely by the external coils, allowing it to be tailored to minimize neoclassical transport [1]. Even in this case, turbulent 'anomalous' transport accounts for more than 50% of the energy transport, limiting plasma performance [2]. Turbulence dominates the energy transport in tokamaks as well. While the optimization of the stellarator magnetic field to minimize turbulent transport is possible and is an active area of research, the computational cost of turbulence simulations renders this approach unpractical at this time. Therefore, it is of fundamental importance to find alternative and complementary means to reduce turbulence in order to improve plasma performance in existing and future stellarators.
Recently, during experiments on the Large Helical Device (LHD) featuring boron powder injection for wall conditioning purposes, an improved confinement regime has been observed, characterized by reduced turbulent fluctuations [3]. The decrease of turbulence on a wide portion of the plasma volume led to ion temperature increase of the order of 25%, but up to ∼40% transiently. Electron temperature, stored energy and confinement time were observed to increase as well. The regime was observed for both H and D plasmas, for both directions of the magnetic field and for different heating schemes. The most probable cause for the improvement was judged to be the suppression of ion temperature gradient (ITG) turbulence driven by the modification of the plasma density profile and the increase of the effective charge Z eff . Indeed, this mechanism has been proposed to explain the confinement improvement previously observed in tokamaks upon impurity injection [4][5][6][7][8], and recently obtained even using impurity powder injection [9]. A similar improvement was also obtained transiently with pulsed powder injection in the W7-X stellarator [10]. In LHD, the limited database available in [3] suggested that the ion temperature increase scaled positively with the input power.
In this article, we present experimental observations of this improvement on an extended database of dedicated experiments, aimed at further characterizing the access to this regime and to understand the physical mechanisms underlying. The rest of the article is structured as follows: in section 2 we report an example of performance increase due to turbulence reduction upon boron powder injection. In section 3 we introduce the modeling of powder injection into the plasma with the EMC3-EIRENE and DIS codes, which will be used in the following to interpret the experimental results. In section 4 we compare injection of powders of different materials, namely B, C, and BN, finding similar temperature improvements and turbulence reduction for the three materials. The analysis of transport and fluxes for the experiments in section 4 is described in section 5. The effect of different powder injection rates for B powder is discussed in section 6, showing how the temperature improvement scales positively with the boron concentration. The dependence of temperature improvement upon plasma density and input power are investigated in section 7, finding that the temperature improvement is reduced for increasing density and increasing input power. Finally, in section 8 we summarize the results and discuss the possible physical mechanisms involved.

Temperature increase and turbulence reduction
The impurity powder dropper (IPD) is a device designed and built in Princeton Plasma Physics Laboratory [11] for injection of sub-millimeter powder grains into the plasma under the action of gravity. Controllable amounts of powder are injected on request through the application of a sinusoidal voltage to vibrate piezo blades. Its main application is real-time boronization, where boron B (or boron composites) powder is injected into the plasma with the aim of depositing a B layer on the plasma facing components, reducing wall recycling and intrinsic impurity content and finally accessing lower collisionality and better performing plasmas. This technique has the advantage, over the commonly used glow discharge boronization, of not having to interrupt the plasma operation for boronization, and most importantly for superconducting machines, it does not require the magnetic field to be turned off and on again. Also, no toxic gas such as diborane B 2 H 6 is used. This technique has been tested in several tokamaks [9,[12][13][14][15] where in general positive wall conditioning effects have been shown upon injection of B or BN (boron nitride) powder.
In 2019, the IPD was installed on the LHD in Japan with the aim of assessing the viability of real-time wall conditioning in steady state operation, since LHD is capable of 1 hourlong discharges [16]. A first set of experiments demonstrated the successful injection of B and BN powder in the unique LHD magnetic geometry, and the response of the plasma to the powder injection was characterized [17]. Beneficial wall conditioning effects, such as reduction of recycling and of the intrinsic impurities (C, O, Fe) was observed in LHD both on a shot-to-shot basis and in real time [18]. Finally, during B powder injection experiments in plasmas of duration longer than 5 s, both the electron, ion temperature and stored energy have been observed to increase [3], while the input power and line-averaged electron density n e,av are kept constant. At the same time, the amplitude of the density turbulent fluctuations δn measured by phase contrast imaging (PCI) [19] is decreased across most of the plasma volume, up to a factor of two. The radial profiles of n e , T e , T i and δn are shown for one B powder injection discharge in figure 1 (red lines), compared with an identical reference discharge without powder injection (blue lines). n e and T e are measured by Thomson scattering, and T i is measured by charge exchange spectroscopy (CXS). The radial profiles are expressed in terms of the coordinate r eff /a 99 , where r eff is the effective minor radius of the plasma and a 99 is the minor radius of the flux surface enclosing 99% of the stored energy. We remark how the turbulence amplitude is decreased through most of the plasma volume, at least where measurements are available (no PCI measurement is available for |r eff /a 99 | < 0.4).
The database presented in [3] consisted of only four cases, nevertheless it included discharges with different heating schemes (ECH + ICH, NB, ECH+ perpendicular diagnostic Radial profiles of (a) electron density (b) electron (solid lines) and ion temperature (dashed lines) (c) turbulent fluctuation amplitude measured by PCI, for a boron injection discharge (#167 234, red) and its reference (#167 233, blue), at t = 5.25 s (during injection). For (c), no measurement is available for r eff /a 99 < 0.4. (d) PSD from PCI diagnostic for the same two discharges. NB), both H and D plasmas, and both directions of the magnetic fields. The increase of plasma temperature was of the order of 25%, but with T i increasing up to ∼40% in one case. Transport analysis with the DYTRANS code [20,21] has shown a decrease of energy transport, with the ion and electron thermal diffusivities χ i and χ e being reduced by 40% and 50% for r eff /a 99 > 0.4 and r eff /a 99 > 0.5 respectively. The energy confinement time τ E was observed to increase of ∼20%.
Modeling with the radially local neoclassical code SFINCS [22] shows that the neoclassical heat fluxes are increased during powder injection, due to the steepening of temperature profiles at the edge. This is consistent with the decrease of the turbulent energy flux, so that the sum of the two contributions is constant in time since the input power is unvaried during the discharge. SFINCS simulations also show only a modest change of the ambipolar radial electric field E r , suggesting that an increase of E × B flow and its shear could not explain the observed turbulence decrease.
The most possible cause is instead the suppression of ITG turbulence due to the modification of the the density profiles and/or the increase of effective charge Z eff as the impurity powder is injected. Indeed, even though the line-averaged density is kept constant by a feedback on the gas puff fueling, the powder injection makes the density profiles more peaked in the edge and more hollow in the center, as it can bee seen in figure 1(a), where the density profile is shown. This is in part due to the extra source of electrons provided by the powder, which evaporates close to the last close surface (LCFS) 1 < r eff /a 99 < 1.06 according to coupled EMC3-EIRENE and DUSTT simulations [23,24]. Simultaneously, recycling is reduced in real time by B injection and deposition on the plasma facing components, reducing the density in the divertor and making the density profile even steeper. Spectra of the PCI measurements suggests that turbulence peaks at k ⊥ ∼ 0.3 mm −1 , consistent with ITG-like turbulence [25]. During B powder injection, this peak is substantially reduced, while higher frequency modes are excited, as it is shown in figure 1(d), where the power spectral density (PSD) from the line-integrated PCI signal is plotted for one B injection discharge.
In this article, with the aim of better understanding the physical mechanisms behind it, we extend the investigation of this improved confinement regime with a series of dedicated experiments, featuring scans of density, input power and injected mass rates, and different powder materials. The database includes both hydrogen and deuterium plasmas, both directions of the magnetic fields, and plasmas heated with different heating schemes, featuring electron and ion cyclotron heating (ECH, ICH), tangential neutral beams (NBs) and perpendicular pulsed neutral beams for CXS diagnostic.

Modeling of powder penetration
In this section we describe the modeling of the penetration of powder grains into the plasma, which is instrumental to the interpretation of the experimental results. The 3D distribution of the plasma quantities (density, temperature, flow) are modeled using the EMC3-EIRENE code [23,26]. The simulation parameters such as diffusion coefficients for particles and energy are set to match experimental profiles of electron density and temperature n e , T e measured by Thomson scattering and ion temperature T i measured by CXS. In previous studies, the DUSTT code [27] was used to compute the trajectory of powder grains injected from the IPD position and compute the location where they are evaporated into the plasma releasing neutral atoms [24]. As a result, typically the powder grains crosses the divertor leg, where it is deflected by the plasma flow, but still reaches the main plasma where it is fully evaporated. In this article, we use instead the DIS code for this step [28]. DIS was developed implementing a physical model similar to the DUSTT one, but with the capability of handling 3D, time dependent plasma backgrounds. A comparison carried out on LHD cases has shown how the trajectories computed by DIS differ for less than 6% from the ones computed by the more established DUSTT code [29]. Upgrades to the DIS code have been undertaken with respect to the version described in [28], implementing powder materials relevant for IPD experiments (B, BN, C, B 4 C, Li). Also, a statistical approach on the powder initial position has been introduced: while with the previous DUSTT investigation only a single trajectory is computed, with vertical injection of one powder grain at the nominal IPD position, now 1000 independent trajectories are computed, where the initial conditions are chosen randomly within a distribution. As the vertical position Z 0 is kept fixed, the position on the horizontal plane x 0 , y 0 is given by a normal distribution around the nominal IPD location with amplitude σ x = σ y = 5 mm. The absolute value of the powder grain initial velocity is kept constant v 0 = 6.5 m s −1 , consistent with the free fall of the powder from approximately 2.2 m above the border of the EMC3-EIRENE simulation domain, while the angle with respect to the vertical α is normally distributed with amplitude σ α = 10 • , and the angle β with respect to the x axis in the (x, y) plane is uniformly distributed. The result of such calculations is shown in figure 2(a) for discharge #166 256, where the powder trajectories are shown in red, together with T e resulting from EMC3-EIRENE simulations for three different toroidal angles, and a flux surface. This result qualitatively compares with what can be observed from the visible camera images taken from the top of the plasma at the IPD location, shown in figure 2(c) for the same discharge, showing the powder grains spreading out as they enter the plasma. A top view of the simulated trajectories is plotted in figure 2(b) for comparison. We remark that the parameters σ x , σ y , σ α are chosen empirically to give a qualitative agreement with the visible camera images, while a more in details comparison is foreseen for future works. Even though a few trajectories do not end up in the main plasma, the almost totality of the injected powder is evaporated into the plasma, the residual mass amounting to the 0.6% in this case. Finally, the neutral atoms source released by the powder as it evaporates is remapped on the magnetic equilibrium (figure 2(d)). Consistently with the previous DUSTT investigation [3] the neutral atom source peaks just outside the LCFS 1 < r eff /a 99 < 1.06, though in this case some powder particles reach inside the LCFS. The fraction of evaporated mass above the X-point (in the divertor leg) is ∼0.5% for this case. Even though the neutral atom source is peaking just outside the LCFS, EMC3-EIRENE simulations of the impurity transport including the B neutral source from the powder trajectories calculations suggest that a substantial amount of B ions is transported inside the LCFS, where they are completely ionized.
The three-dimensional distribution of the resulting B ions is investigated with full torus impurity transport simulations, and the results are shown in figure 3. In subplot (a) and (b) the density distribution of B + and B 5+ ions respectively are shown in the poloidal cross section corresponding to the toroidal location of the IPD. As a result, the low ionization states are more localized in the poloidal plane close to the injection location, while higher ionization states penetrate in the closed field line region and are distributed more evenly in the poloidal cross section. This holds true also in the toroidal direction, as shown in subplot c where the volume-averaged density for the different B ionization states is shown as a function  figure 3(c)), while for increasing ionization states the density distribution gets progressively more uniform in the toroidal direction. This is consistent with the fact that EUV [30] and CXS measurements, performed approximately 180 • apart toroidally, representative of B 4+ and B 5+ population respectively, exhibit a similar evolution in time, as previously reported in [17]. Also for this case, most of the B ions reach into the confined region and are completely ionized. However, it is worth noting that EMC3-EIRENE allows only tracing amounts of impurities and no electric field is included, potentially affecting the impurity force balance and therefore their final distribution. We remark how the toroidal distribution of low ionization states in figure 3(c) exhibits 6 peaks and minima. This can be qualitatively understood as an effect of flux expansion. Indeed, low ionization states (for example B + , figure 3(a)) are poloidally peaked around the injection location, which in this case is close to the X-point region. The B ions would stream along the field line in the parallel (mainly toroidal) direction. As the flux tube winds around the torus, the maxima of average density corresponds to the region where the flux tube connected to the injection location is close to the X-point region, expanding poloidally, and the minima correspond to the region where the flux tube is located poloidally halfway between the two X-points, being squeezed on the side of the main plasma. The X-point transits of the flux tube contribute therefore more substantially to the volume-averaged density, with respect to the main plasma side transits, as it can be seen in figure 4, where the poloidal distribution of B + density is shown for the toroidal position of the toroidal maximum of volume-averaged density (a), and at the closest relative minimum (b). As the density of B + ions only extends approximately half torus in both directions from the injection location (due to cross-field diffusion), this results in a 6 peaks structure instead of a 10-fold periodicity as expected from the magnetic structure of LHD.

Comparison of powder materials
Series of experiments have been performed comparing different powder materials. In particular, B powder of 150 µm in size was compared with carbon microspheres (C) of size 120 µm and boron nitride (BN), size 60 µm. We discuss here the case for R ax = 3.6 m, n e,av = 2.7 × 10 19 m −3 , P in = 5.6 MW from both tangential and perpendicular NBs, for which the time traces of relevant plasma quantities are shown in figure 5. The effect of the powder is evaluated at approximately 3 s into powder injection, to avoid initial transients due to an excursion of the line averaged density from the reference level of ∼10%, then recovered by the feedback on the gas puff (figure 5(a), solid lines). We remark that the reference plasma features density profile peaking on the magnetic axis, with the global peaking factor f p = n 0 /⟨n⟩ ∼ 1.37, (figure 5(a), dotted lines), with n 0 the density on axis and ⟨n⟩ the average of density for |r eff /a 99 | < 1. In all cases, the powder injection provides an extra electron source localized in the edge of the plasma, and the density profile becomes less peaked in the center and even hollow. The reduction in central peaking and hollowing of the density profile, as the line averaged density is kept constant by a feedback on the gas puffing, implies that the density profiles become more peaked in the edge of the plasma during powder injection. DIS EMC3-EIRENE simulations of powder penetration show that while the B and C cases are similar, with almost all the powder being evaporated in the main plasma just outside the LCFS 1 < r eff /a 99 < 1.05 (figure 6(a)), for BN almost 60% of the neutral source is located in the divertor leg and the neutral source is more spread out for higher values of r eff /a 99 . This is due mainly to the smaller powder grain size (60 µm diameter against 150 and 120 µm of B and C respectively) and the lower material evaporation temperature. The resulting distribution of B + ions resulting from B and BN powder is shown in figures 6(b) and (c). Even though the low ionization states for the BN case are more spread in the divertor region, finally for both cases most of the B is completely ionized in the main plasma, with spatial distributions of of B 5+ density analogous to the one shown in figure 3(b). We conclude that impurity transport can make up for the difference in source location in between those two cases.
While the extra electron source localized around the LCFS increases locally the electron density, the hollowing of the density profile could be due to an enhanced neoclassical thermo-diffusion due to the increase of T e [31]. Also, turbulence is believed to drive particle flux directed inwards in large stellarators, contributing to making the density profile more peaked [32]. The reduction of turbulence due to powder injection might then in turns reduce this inwards particle flux, rendering the density profile more hollow.  PCI measurements of (a) turbulent fluctuation amplitude radial profile (b) turbulence spectrum for a reference discharge (blue), and discharges with B (red) C (green) and BN (yellow) powder injection. Variations with respect to the reference discharge of (c) Te and T i on axis (d) average turbulence fluctuations amplitude. (e) Variation of Z eff for the powder injection cases (red) compared to reference discharge value (blue). stored energy (figure 5(d)) increase for all different powders. As it is shown in figure 7(a), in all cases powder injection results in turbulence decrease through most of the confined plasma cross section |r eff /a 99 | < 1, even though up/down asymmetry is evident, while turbulence is enhanced outside the LCFS |r eff /a 99 | > 1. The increase of turbulent density fluctuation amplitude in the edge of the plasma can be explained at least in part by the fact that as the density profile becomes more hollow in the center, the density and its peaking are increased in the edge, as already discussed above. The up-down asymmetry could be due to the effect of E × B shear on turbulent eddies. The turbulent spectrum is damped in correspondence of the peak for the reference discharge f ∼ 50 kHz, while turbulence is increased at both lower and higher frequencies ( figure 7(b)). Simultaneously, as turbulence is reduced, a substantial increase ⩾30% of ion and electron temperature on axis is observed ( figure 7(c)). The plasma stored energy W p and energy confinement time τ E also increase by ∼15% for the three powders. For this case, the three different powders produce a similar effect both in terms of change in the turbulence spectrum and plasma performance, with C powder giving better results, even though this might depend on the specific values of the injection rates.
The plasma effective charge Z eff , measured from visible bremsstrahlung radiation [33], is similar for the three cases during powder injection, even if slightly increasing going from B to C to BN. The effect of the powder on the radiated power (figure 5(e)), P rad = 1.1 MW without powder injection, is the same for B and C, where P rad is slightly decreased by 19% and 7% respectively, probably due to a decrease of both oxygen and iron concentration (figures 7(i) and (j)) and of carbon as well during B injection ( figure 7(g)). For BN injection, the decrease of intrinsic impurities is overshadowed by the increase of nitrogen concentration, strongly radiating, which results in doubling P rad with respect to the reference level. The access to the reduced turbulent regime with the high radiating BN powder suggests that the reduction of P rad obtained with B powder is not a prerequisite to access this regime. While one can expect the radiation enhancement in the BN case to be toroidally asymmetric, similarly to what happens in N gas seeding experiments in LHD [34], an in-detail analysis of the toroidal distribution of P rad is reserved for future works.
Analysis of the divertor Langmuir probe measurements shows that during BN injection the peak electron temperature in the divertor is decreased from ∼30 to ∼20 eV. While in this case there is no indication of detachment, the reduction of the divertor plasma temperature upon BN injection while turbulence is decreased and temperature is improved in the main plasma, suggests that BN powder might be promising for integrating an improved core confinement with reduced turbulent reduction with mitigated heat fluxes at the divertor plates.
We consider now the effect of the different powders on wall recycling. As shown in figure 8(a), an initial decrease of H α radiation is observed upon powder injection for the three different powders. This is due to the increase of electron density due to the powder injection itself, and the consequent decrease of gas puff due to the feedback on the density value. In these discharges, the gas puff is eventually set to zero to counter the n e increase, and density control is momentarily lost as discussed beforehand. The decrease of H α is then not due to a decrease of recycling, but to the decrease of the neutral H gas flow into the chamber. After a few seconds, the gas puff is increased again above the reference level, reaching a stationary value, and H α radiation recovers its original value. This, together with the increase of the gas puff to achieve the same line-averaged density can be attributed to a decrease in recycling due to the deposition of a new layer of atoms on the plasma facing components, since H α intensity is in first approximation proportional to both neutral and electron density. While the decreasing in recycling is not surprising for B and BN, it is unexpected for C, and might indicated that the effect on recycling is due to co-deposition rather than to chemical reactions. A more thorough analysis of this phenomenon is reserved for future works.

Transport and fluxes
In this section we present the analysis of transport and fluxes for the same discharges as in the previous section, where different powder materials are compared. The dynamic transport code DYTRANS [20,21] has been used to compute the ion and electron thermal conductivities χ i and χ e from the experimental profiles of the plasma quantities. DYTRANS (dynamic-transport) is part of the integrated transport analysis suite TASK3D-a, computing relevant transport quantities from experimental profiles. A detailed description of this code is presented in [20]. The results are shown in figure 9 for the region 0.4 ⩽ r eff /a 99 ⩽ 0.9, where χ i is reduced by ∼50% with respect to the reference case for the three different powders. χ e is reduced of about 1/3 in the inner region of the plasma, while at the edge the reduction amounts up to 2/3 of the original value. The reduction of the transport coefficients in the edge is consistent with previous results [3] and the steepening of the temperature gradients in the edge region. A similar result was obtained transiently in LHD by injecting C pellet in the plasma [35], where the improvement of confinement and reduction of transport coefficient was found to be correlated with the C concentration in the plasma. Here, the reduction in transport is consistent with the reduction in turbulence level reported in the previous section. To support this point, the sum of the energy fluxes across the flux surfaces for ions and electrons Q i + Q e resulting from DYTRANS is compared with the same quantity resulting from the neoclassical code SFINCS [22], in figure 10. In the powder injection discharges the experimental energy flux is slightly decreased with respect to the reference discharge with no powder injection. As the input power and average density are the same for all discharges and steady state conditions are considered, the decrease in total heat flux in the powder injection shots is to be attributed to a decrease in NB absorption with respect to the reference case. Indeed, the DYTRANS analysis shows that during powder injection the beam absorption is reduced of the same order of magnitude as for the variation of Q in figure 10. The decreased beam absorption can be attributed to the hollowing of the density profiles during powder injection, discussed beforehand. The situation is different for the neoclassical heat fluxes. Indeed, for the reference discharge, the neoclassical heat flux computed by SFINCS is substantially lower than the experimental one computed from DYTRANS, suggesting that turbulence (which accounts for the difference in between the two) dominates the heat transport in this case. In the powder injection cases, the neoclassical heat fluxes are increased with respect to the reference case and can be comparable to the experimental ones, suggesting that the turbulent heat transport is substantially reduced in this case. Though, the absolute level of the heat fluxes depends on the details of the profiles and the values of their gradients, and the value of Z eff , the impurity mix, and variations of quantities within the flux surfaces [36] that are not accounted for in this case. Indeed, for the SFINCS simulations the value of Z eff measured by visible bremsstrahlung radiation is used. The impurity mix is assumed to be He + C for the reference discharge and the C powder injection discharge, while it is He + B + C for the B powder injection discharge and He + B + C + N for the BN powder injection discharge. All the impurity concentrations are assumed to be uniform across the plasma radius. The He/H ratio is estimated from visible line radiation measurements. The C concentration is deduced from He concentration and the Z eff value for the cases without B. For the cases with B and N, the C concentration is deduced by comparison with the reference discharge using the ratio of the CVI line UV radiation in between the two discharges. The B concentration is deduced by difference to recover the Z eff value. For the BN powder case, the B and N concentrations are assumed to be equal. In these simulations, the resulting heat fluxes carried by the impurity ions is negligible with respect to the main ion heat flux.
The radial electric field E r resulting from the neoclassical calculations is shown in figure 11. Consistently with previous results, the ambipolar radial electric field is already negative for the reference discharge, so that the observed increase of confinement can not be attributed to a change from electron root to ion root regime. Furthermore, the change in E r upon powder injection can not explain the increase in confinement since the absolute value of E r is decreased at most radial positions. An increase of E × B shear in the edge of the plasma seems unlikely to justify the observed reduction of turbulence over a wide portion of the plasma cross section as observed by PCI diagnostic and reported in the previous section. More importantly, as there are differences in between the simulated E r for the different powder materials, it appears evident by the comparison of figures 11 with figure 10 and figure 9 that those changes in E r do not correlate with the variation in both neoclassical and experimentally measured transport, which is qualitatively the same for all powder materials.

Correlation with powder amount
Different series of experiments have been conducted keeping all parameters fixed (input power, plasma density) and varying the amount of powder injected. In this section we discuss the results for B powder injected in the R ax = 3.6 m configuration, for which data is more abundant, but partial data is available for R ax = 3.55 m or different powder materials. The results of this investigation are shown in figure 12, where the relative variations of T e , T i and of the average density fluctuation inside the LCFS ⟨δn⟩ are plotted as a function of the intensity of the BV EUV spectroscopy line normalized to plasma density, for five different sets of experiments for different values of n e,av and P in plotted with different colors. Time windows of 0.3 s have been selected for ∆t = 2.5 s from the start of powder injection, to avoid initial transients. In general, for each set, the relative variation of electron temperature ∆T e /T e increases with the amount of B present in the plasma. The relative variation of T i is in general also increased with the amount of B present in the plasma. The energy confinement time τ E is also generally increased by powder injection, and overall increases with the amount of injected powder, as it is shown in figure 12(d). Here, the relative variation of τ E is shown with respect to the reference discharge without powder injection for each scenario. The dependence of turbulence on the amount of B appears to be more complicated; turbulence reduction is scaling positively with the B amount for low power (red lines), at intermediate power (violet lines) ⟨δn⟩ decreases slightly with the injected B amount, and at higher power (yellow, green) the average turbulence amplitude is not affected much by powder injection, even though it decreases in part of the radial profile. We remark that PCI measurements only cover the region |r eff /a 99 | > 0.5, so we do not know how turbulence is affected in the inner part of the plasma. Also, the initial turbulence state of the discharge for each set appears to be different, both in terms of radial profiles of the fluctuation amplitude, and of their spectra, as shown in figures 12(e) and (f ). Here the reference discharges, without powder injection, are plotted. While for low power, turbulence is stronger in the core |r eff /a 99 | < 1, for different power/density turbulence in the edge of the plasma is dominating |r eff /a 99 | > 1. A careful characterization of the turbulence type for each case would be needed but is outside of the scope of the present work. Based on previous LHD experiments where a comparison with gyrokinetic simulations has been performed (e.g. [37]), we can speculate that the higher-frequency part of the PCI spectra in figure 12(e), f ⩾ 80 kHz, could be attributed to TEMs, while lower frequencies could be associated with ITG modes. Similarly, one could speculate that TEMs would rather contribute to the radial profiles in figure 12(d) closer to the edge r eff /a 99 ⩾ 0.8, as the density gradient is steeper in this region, while ITG modes would dominate the inner region of the plasma. The analysis of magnetic probe measurements reveals that MHD activity is generally present in our experiments, the frequency of MHD modes being f ≲ 10 kHz. It is therefore a possibility that MHD activity, which generally increases with powder injection due to the steepening of the pressure profile, could contribute to the lower part of the spectrum of the PCI measurements and to the radial profiles of fluctuation amplitude, used for the analysis presented in figure 12(c) and complicating its interpretation, but also providing a possible explanation for the apparent lack of correlation between the increase of temperature and the reduction of turbulence. For the moment, we can only remark that the response of the plasma in terms of turbulence is different for plasmas dominated by different types of turbulence.
We remark that for the case n e,av = 3.2 · 10 19 m −3 , P in = 1.27 MW (red lines) an additional discharge with bigger B injection rate resulted in the collapse of the plasma, and for the case n e,av = 2.2 × 10 19 m −3 , P in = 6.3 MW (blue lines), for which PCI measurements are not available, an higher B injection rate resulted in the loss of density control. Both cases are not shown in this figure. We conclude that, while in general increasing B injection rate increases the temperature of the plasma, it exist an optimum B injection rate, different for each initial plasma condition, passed which either the benefits of powder injection are reduced, density control is lost and/or the plasma is collapsed. For example, for the red series in figures 12(a)-(c) (D plasma n e,av = 3.2 × 10 19 m −3 , P in = 1.27 MW) a discharge with BV/n e,av ⩾ 7000 resulted in loss of density control and plasma collapse, while this B concentration is tolerable for plasmas with higher P in in the same plot. For the blue series (H plasma n e,av = 2.2 × 10 19 m −3 , P in = 6.3 MW), a discharge with BV/n e,av ⩾ 8500 results in the loss of density control without collapsing. A more in details characterization of the maximum amount of powder tolerable by the plasma as a function of n e,av and B concentration is outside the scope of the present work and reserved for future investigations. Finally, we remark that plotting figure 12 as a function of Z eff (or its variation with respect to the reference discharge ∆Z eff ) instead of BV/n e would produce qualitatively similar results, but with no clearer trend emerging. We prefer therefore to rely on a more direct measurement rather than the derived, higher-uncertainty estimation of Z eff , which sometimes produces unreasonably high or low values for the discharges in our dataset, especially for lower density plasmas.

Trend with density and input power
To try and better understand the mechanism behind the improvement of confinement upon powder injection, we performed dedicated experiments investigating the role of the initial plasma scenario before powder injection. In particular, we performed a series of experiments where the plasma density has been varied systematically. For each plasma density value, a reference shot (without powder injection) is performed, and a second shot is repeated with powder injection. The powder injection rate is the same for all values of density. Similarly, we performed a second series of experiments, where all parameters are fixed except for the input power, which is varied from shot to shot. The results of those experiments are reported in this section. We anticipate that, even though we are able to extract main trends with n e,av and P in , one result is that the initial turbulence state, and therefore the response to the powder injection, depends on the plasma scenario. Then, outlining a general rule for confinement improvement with powder injection is not possible, and each plasma scenario should be evaluated individually.
In figures 13(a)-(c) the relative variations of central T e , T i and ⟨δn⟩ for three different series of discharges with the same input power and powder injection rates are shown, as n e,av is varied. For the first series (orange lines), featuring NBI heated plasmas P NB ∼ 7.6 MW, no PCI measurement is available. For the other two series, the heating scheme is a mix of NBI, ICH and ECH, with relative port-though power of P NB ∼ 7.8 MW, P ECH ∼ P ICH ∼ 2 MW (see figure 14(e)). As a general picture, the increase of central T i , which can be as high as 50% at low density, decreases with n e,av , while no clear trend can be found for the increase in central T e , which is nevertheless positive in all cases. The same consideration holds for the energy confinement time τ E (figure 13(d)), which is in general increased by the powder injection with respect to the reference discharges, except at higher plasma densities, and for which no overall trend can be found. The turbulence reduction though exhibits an opposite trend than for ∆T i /T i : turbulence reduction is the strongest at high density, decreasing for lower density where eventually turbulence is increased instead on the whole plasma cross section, where PCI measurements are available. This is shown in figures 13(e) and (f ), where the radial profile of density turbulent fluctuations normalized to n e,av and the turbulent PCI spectrum is shown for three boron injection discharges with different density (solid lines) and compared with their references (dashed lines). As it emerges from the figure the shape of both PSD and radial profile of turbulence fluctuations before powder injection is different, suggesting that turbulence might be dominated by different modes at different densities, similarly to what has been discussed in the previous section. We also remark that no PCI measurement is available for |r eff /a 99 | < 0.5, so that we do not know if for the low density case, turbulence is increased also inside this region or is decreased instead. While T i is increased in the whole plasma volume, the improvement in electron temperature is indeed localized inside r eff /a 99 < 0.5, as shown in figures 14(b) and (c), so that this hypothesis can not be excluded. In this case, the plasma self-organizes to a completely different state at t ∼ 5.4 s, whit possibly the formation of an internal barrier for electron energy ( figure 14(f )). While it is not clear what the mechanism behind this transition is, it does not appear to be directly related to the powder injection itself, starting at t ∼ 4 s ( figure 14(g)). Indeed, before t ∼ 5.4 s the ion temperature grows gradually as expected for this kind of experiments, and the turbulent spectrum is damped at frequencies typical of ITGs f ⩽ 30 kHz while being increased at higher frequencies ( figure 14(h)), in line with the cases discussed before. Another difference with respect to the previously analyzed discharges [3] is that due to the low density and high temperature, for both the reference discharge and the B injection one, the plasma is in the electron root regime E r > 0 across most of the cross section, as confirmed by E r measurements from CXS. Therefore the impurity transport is expected to be different from the previously analyzed discharges in ion-root regime, possibly further affecting the turbulence response. Detailed analysis of this discharge will be needed for a better understanding of this case, which is beyond the scope of the present article. Finally, we remark that once again the effect of B and C powder in figures 13(a)-(c) is qualitatively the same.
We remark that for this series of experiments, since the powder injection rate is kept fixed, varying the density results also in a variation of Z eff , namely Z eff is expected to decrease with line averaged density. This is indeed the case, even though in this series of experiments the change in Z eff is rather driven by the the change in n e itself rather than by the powder injection: for the lowest density, Z eff = 4.9 already for the reference discharge (without powder injection). While a more in depth analysis is needed for future works, we reckon this value is improbably high for a discharge without powder injection, and the estimation of Z eff is less reliable for low density. The analysis of the impurity radiation still shows BV/n e,av (CVI/n e,av for the C powder injection case) to decrease with n e,av as expected.
In figure 15, the relative variation of T e , T i and ⟨δn⟩ and τ E is reported for series of discharges with the same line averaged density and powder impurity material and injection rate, as a function of injected power P in . In particular, B, BN and C powder injection are compared. Two different injection mass rates are compared for both B and C powder. The mass rates are estimated from the IPD accelerometer data through previously acquired calibration curves. As a result, for all the series of this experiment, the improvement in both ion and electron temperature is decreased with input power, contrarily with what one could extrapolate from the reduced database in [3], for generally lower P in values and mixed values of n e,av . Accordingly, the effect on turbulence seems to decrease for higher input power. Qualitatively, the same trend is observed  Radial profiles of (a) electron density, (b) electron temperature, (c) ion temperature, for a discharge with B powder injection (blue) and its reference (blue). Time traces of (d) line-averaged density (e) input power (f ) electron (solid) and ion (dashed) temperature (g) BV EUV line. (h) Spectrogram from PCI diagnostic.
for the relative variation of τ E , which except for one outlier, decreases with the input power. We remark that, nevertheless, while the relative improvements ∆T i /T i and ∆τ E /τ E decrease with P in , ∆T i /T i > 0 and ∆τ E /τ E > 0 in all cases so that the ion temperature and confinement in general are always increased by powder injection. Once again, while the amount of temperature improvement varies slightly with the powder material and sensibly with the amount of injected powder, the effect of different powder materials is qualitatively the same, with both ∆T e /T e , ∆T i /T i and |∆⟨δn⟩/⟨δn⟩| decreasing with P in for a given powder material and injection mass rate. In this series of experiments, Z eff after powder injection does not vary substantially with P in , being overall 2.9 ⩽ Z eff ⩽ 3.7, the higher value corresponding to the BN powder injection case. For each of the series in figure 15, i.e. for a fixed powder type and injection rate, the variation of Z eff with P in is within errorbars. Though, the variation of Z eff with respect to the reference discharge, ∆Z eff , is stronger for the lowest power case, being Z eff = 2.1 for the reference discharge, while Z eff = 2.8 for the reference discharge with highest P in . This suggests that either powders are assimilated more efficiently for lower power, or impurity confinement is better in this case. Indeed, the normalized boron radiation BV/n e,av (CVI/n e,av for the C powder case) is the highest for the lowest P in .

Discussion
In this paper, we report advances of the characterization of a reduced turbulence regime, first observed on LHD in [3].
Systematic scans of plasma density, input power, impurity powder material and injection rates have been performed. The access to this regime is achieved for a variety of scenarios, with increase of ion temperature that can be up to 40%. While the first result is that the effect of the powder on the plasma turbulence strongly depends on the combinations of all of these variables, and in particular of the initial state of the plasma and the type of turbulence governing it, some general trends can be extracted. First, powders of different materials appear to have a qualitatively similar effect on both the plasma turbulence and the improvement in plasma temperature. While for C powder no reduction in wall recycling is expected, the analysis of H α radiation and gas puff traces suggests that C powder injection has a similar effect to B and BN in this terms. The concentration of O and Fe intrinsic impurities is observed to decrease during powder injection, either because their influx to the plasma being prevented by C (and B) deposition on the wall, or being flushed out by a change in impurity transport. In light of these observations, the access of the reduced-turbulence regime with C powder still can not exclude wall conditioning itself to play a role in this phenomenon. The most likely cause still remains the suppression of turbulence because of the density profile modification driven by the powder injection itself (in all cases the density profiles become more peaked in the edge and hollower in the center), and/or to the increase of Z eff . Both effects have been shown before to reduce plasma turbulence. Modeling with the codes EMC3-EIRENE and DIS show similar powder penetration for the B and C cases, while for BN powder more than half of the injected powder is evaporated in the divertor leg. Though, most of B ions end up completely ionized in the main plasma for both B and BN powder, so that impurity transport makes up for the difference in the impurity neutral source. The temperature increase and turbulence reduction even with BN injection, which causes P rad to double contrarily to the B and C case where P rad is decreased, excludes the reduction of radiation as a prerequisite to access the reduced turbulence regime. The transport analysis performed with DYTRANS shows how the powder injection reduces both χ i and χ e in the edge of the plasma for the three different powder materials. The comparison of the experimental heat fluxes with the neoclassical ones computed by the SFINCS code suggests that turbulent heat fluxes are reduced by the powder injection, consistently with both PCI measurements and previous results.
Secondly, in general the magnitude of the relative increase of plasma temperature, ∆T/T, scales positively with the amount of injected powder. This has been shown here for the B powder injection case ( figure 12), but comparing the more limited database with different powder type (C, BN), the behavior appears to be qualitatively the same ( figure 15). This is true only until a threshold in impurity injection rate is reached, above which either the density control is lost and/or the plasma is collapsed. This threshold depends on the plasma initial state, such as on its density and input power, and should be evaluated on a case to case basis. A similar improvement of plasma performance upon impurity injection was previously reported in LHD using C pellets [35], in which case the improvement also correlated with the amount of injected impurity and also exhibited a threshold behavior. This similarity suggests that the same mechanism could be at play in the two cases.
Third, the increase of ion temperature is in first approximation reduced by increasing the plasma density. Though, the powder is observed to have the opposite effect on turbulence at low density, increasing it instead of decreasing it as observed in other cases. While partial explanations can be found in the partial coverage of the plasma by the PCI diagnostics and the plasma being in the electron root regime in this case E r > 0, this case will need to be analyzed in more details in future works and for now we can only speculate that the different turbulence response is due to a different type of turbulence dominating the transport in this case. Also, as discussed in section 7, in our database n e,av and Z eff are correlated, in the sense that for the same powder injection rate, lower density and lower power plasmas have a larger increase of Z eff . Dedicated experiments with tailored powder injection rates for different densities to keep Z eff constant will be needed to disentangle the dependency from n e from the Z eff one.
While based on the limited database in [3] one could expect an increase of ∆T i /T i with P in , the experiments presented here show that this trend can not be confirmed, and in general ∆T i /T i appears to decrease with P in , for higher values of P in with respect to the database in [3]. Though, T i and the energy confinement time τ E are generally increased by powder injection across the presented database.
As the results presented here advance the understanding of this reduced turbulence regime and its access through impurity powder injection, only approximate general trends can be extracted so far and the plasma response differs from case to case. Gyrokinetic simulations are foreseen for future works to better understand the phenomena behind the turbulence suppression and the resulting increase of plasma temperature.
Finally, we remark that this reduced turbulence improved confinement regime might be relevant to other machines as well. Indeed, a similar temperature improvement has been obtained transiently in W7-X upon pulsed injection of B 4 C powder [10]. Most possibly the same mechanism is at play, and steady-state improvement of confinement would be possible in W7-X as well with a continuous powder flow like the one provided by the IPD. Also, improvement of electron temperature upon B powder injection with the IPD has been observed in the WEST tokamak L-mode plasma as well [9], possibly caused by the same mechanism as in LHD.