The impact of fuelling and W radiation on the performance of high-power, ITER-baseline scenario plasmas in JET-ILW

A beneficial effect of operating at a reduced gas fuelling rate with the ELM pacing pellets is an enhancement of the core energy confinement, which is associated with increased toroidal rotation and reduced ion temperature gradient stiffness [23]. A comparison of kinetic profiles averaged over a 2 s period of the ELMy H-mode phase of the 3.5 MA ITER-baseline pulses #94 980 with only gas fuelling and pulse #96 713 with pellets + gas fuelling is shown in figure 2. As stated previously in section 2, these pulses have similar total fuelling rates of $\Gamma_{D2} \sim 2.3 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$, however, the pulse #96 713 has only ∼43% of the gas fuelling rate Γ_D2,gas of #94 980.

These profiles are from an interpretive transport analysis using the TRANSP code [24] based on input kinetic profiles which are mapped onto the radial coordinate $\rho_{tor} = \sqrt{\Phi_N}$, where Φ_N is the normalised toroidal flux using a pressure-constrained, magnetic equilibrium obtained from the EFIT++ equilibrium reconstruction code [25, 26]. More details of the TRANSP run, including the origin of the input data and the assumptions made are given in section 2.2.

It can be seen from figure 2(a), that across the core plasma, both the ion temperature T_i and the toroidal rotation rate $\Omega_{\phi}$ are higher in the pellet + gas-fuelled pulse #96 713 than in the gas fuelled pulse #94 980, on-axis by factors of ∼1.5 and ∼2 respectively. However, at the pedestal top, these parameters are approximately equal. It should be noted that the additional heating power P_in is ∼×1.13 higher in #96 713 than in pulse #94 980.

Average values of pedestal parameters over the high-performance, ELMy H-mode phase for the same 3.5 MA pulses as in table 1 are stated in table 2. Note that, in spite of the ∼×2 higher fuelling rate in pulse #94 980 as in pulse #96 713, the pedestal temperatures for the two pulses are quite similar. However, there are significant differences in the edge rotation and density, with lower $\langle n_{e,ped} \rangle$ by ∼×0.8 and lower relative separatrix density $\langle n_{e,sep} \rangle/\langle n_{e,ped} \rangle$ by ∼×0.9 but higher $\langle \Omega_{\phi,ped} \rangle$ by ∼×1.1 in #96 713 with the pellet + gas fuelling compared to those in #94 980.

Density profiles of the electrons and D⁺ ions are shown in figure 2(b). Although n_e,ped is ∼×1.1 higher in the gas-fuelled pulse #94 980 than in the pellet + gas fuelled pulse #96 713, the line-averaged density $\bar{n}_e$ is the same in both pulses, so the density profile is somewhat more peaked in the pellet + gas fuelled pulse #96 713, with $\bar{n}_e/n_{e,ped} \sim 1.67$ compared to ∼1.35 in #94 980. The effect of the lower pedestal density with the pellet + gas fuelling on the power and momentum deposition from the neutral-beam-injection (NBI) heating is discussed in detail in section 2.2. As a lower n_e,ped increases the beam penetration, this will increase the beam particle source in the core, thereby enhancing the density peaking.

Also shown in figure 2(b) are profiles of the flux-surface averaged total emissivity $\langle \epsilon_{tot} \rangle$ from tomographic reconstructions [27] of multi-chord, bolometric measurements of the total radiation [28]. In the peripheral, 'mantle' region (defined here as $0.7 \leqslant \rho_N \leqslant \rho_{N,ped} \sim 0.96$), we see that $\langle \epsilon_{tot} \rangle$ is $\lesssim \times 1.8$ higher in the pellet + gas fuelled pulse #96 713 than in the gas-only fuelled pulse #94 980, which is consistent with the higher concentration of W in the mantle (see figure 11(a)), which is the dominant radiator in such high-power H-mode pulses in JET-ILW. The effect of this strong mantle radiation on the ion and electron power balances is also discussed in section 2.2.1 (see also section 4 of [8]).

Finally, we see from figure 2(c), that on-axis, the total thermal pressure p_th is ∼×1.5 higher in pulse #96 713 than in pulse #94 980, primarily due to the higher ion temperature T_i,0, which is ∼×1.5 higher in #96 713, while T_e,0 is only ∼×1.23 higher than in pulse #94 980. The average volume-integrated, total stored energies $\langle W_{th} \rangle$ and those of the ions and electrons $\langle W_{e} \rangle$ and $\langle W_{i} \rangle$, obtained from the TRANSP runs for these pulses are stated in table 3, together with the corresponding, averaged pedestal stored energies.

Table 3. Thermal stored energies (total and of either ions or electrons) of the whole plasma and that due to the pressures at the pedestal top, averaged over the period $50.0~\rightarrow 52.0$ s during the high-performance, ELMy H-mode phase of the two pulses (#94 980 and #96 713) for which key parameters are stated in table 1. Also stated are the time-averaged ratios of total ion to electron heating power $\langle{P_i/P_e}\rangle$ and thermal energies of the ions and electrons $\langle W_{i} \rangle/\langle W_{e} \rangle$.

Pulse	${\langle W_{th} \rangle}$	${\langle W_{e} \rangle}$	${\langle W_{i} \rangle}$	${\langle W_{th,ped} \rangle}$	${\langle W_{e,ped} \rangle}$	${\langle W_{i,ped} \rangle}$	${\langle{P_i/P_e}\rangle}$	${\frac{\langle W_{i} \rangle}{\langle W_{e} \rangle}}$
#	(MJ)	(MJ)	(MJ)	(MJ)	(MJ)	(MJ)	(—)	(—)
94 980	6.53 ± 0.02	3.18 ± 0.01	3.35 ± 0.01	2.00 ± 0.04	0.88 ± 0.02	1.12 ± 0.03	1.18 ± 0.06	1.05 ± 0.01
96 713	8.54 ± 0.05	3.71 ± 0.02	4.84 ± 0.03	1.52 ± 0.03	0.64 ± 0.02	0.88 ± 0.02	1.33 ± 0.07	1.31 ± 0.01

From these stored energies in table 3, we see that on-average, the pedestal energy $\langle W_{th,ped} \rangle$ is ∼×1.3 higher in the gas fuelled pulse #94 980 than in the pellet + gas fuelled pulse #96 713, primarily due to the higher n_e,ped in the former. However, the total stored energy $\langle W_{th} \rangle$ is ∼×1.3 higher in pulse #96 713, which has ∼×1.13 higher input power than pulse #94 980. Comparing the ratios of the components of the total thermal energy stored in the ions to that in the electrons, we see that $\langle W_{i} \rangle/\langle W_{e} \rangle \sim 1.3$ is higher in pulse #96 713 compared to ∼1.05 in #94 980.

This relative increase in ion energy confinement cannot be explained solely by an increase in the average ratio of ion to electron heating $\langle{P_i/P_e}\rangle$, which is higher in pulse #96 713 compared to that in pulse #94 980 by a factor ∼1.12. Hence, there is also a relative improvement of the ion energy confinement with the pellet + gas fuelling compared to that with gas fuelling alone. The reason for this is discussed in more detail in section section 2.3, in which the effect of the changes to the fuelling between pulses #94 980 and #96 713 on the ion and electron heat transport and the transport of toroidal angular momentum $L_{\phi}$ across the core plasma is investigated.

In this section, results on the power balances of the ions and electrons and the balance of toroidal angular momentum for the two 3.5 MA pulses: #94 980 with the high rate of gas fuelling alone and #96 713 with a similar total fuelling rate from gas and ELM pacing pellets, are presented and compared.

The primary input data for the transport analysis are the kinetic profiles (T_e , n_e , T_i and $\Omega_{\phi}$), which are obtained by fitting the raw data from the high-resolution Thomson scattering system (HRTS) [29] and the core and edge CXRS systems [30, 31]. The fits use an $\mathrm{mtanh()}$ function to represent the profiles over the pedestal region ($\rho_{N,ped} \sim 0.96 \leqslant \rho_N \leqslant 1$) [32] and a third-order polynomial for the core region. Examples of the raw profiles at 11 s are shown in figures 3(a) and 4(a). As the T_i and $\Omega_{\phi}$ data from the edge CXRS system on JET-ILW is considered more reliable than that from the core system, the outer two points of the core CXRS (not shown) are excluded from the fit.

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Pressure constrained EFIT++ equilibrium reconstructions [26] are used to map the measurement data from major radius to the normalised flux coordinate, i.e. $\rho_{tor}(R_m)$. Using these equilibria for the profile mapping, meaningful results can be obtained in the pedestal region with no additional constraint required to ensure a reasonable value for T_e,sep , which is typically ∼100 eV (see [33]).

For these interpretive transport calculations, time-dependent, radial profiles of flux-surface averaged densities of Be, Ni and W impurities are input to TRANSP, which are obtained from an integrated analysis described in [34], as for similar analysis presented in a previous study [8]. This analysis self-consistently fits bolometric measurements of the total emissivity, multi-channel soft x-ray measurements and a horizontal, visible bremsstrahlung measurement of the line-average Z_eff , taking account of the poloidal redistribution of the impurity ions over the flux surfaces by centrifugal forces due to the toroidal rotation.

These calculations, which assume a radially constant concentration of Be impurities, yield the volume averaged quantities for the principle Be, Ni and W impurities, summarised in table 4.

Table 4. Time-averaged quantities over 10–12 s from the integrated analysis of impurity radiation described in [34] for the two pulses for which interpretive TRANSP analysis has been performed here, stating volume-averages $\langle\ldots\rangle$ of: total Z_eff and Be, Ni and W impurity concentrations C_Z , with their incremental contributions ΔZ_eff to Z_eff and their fractional contributions $\mathcal{F}_{Rad,Z}$ to the total radiated power. The H and ³He minority ion concentrations C_min assumed for the TORIC calculations of the ICRH power deposition are also stated.

Pulse	${\langle Z_{eff} \rangle}$	${\langle C_Z \rangle}\,(\%)$			${\langle \Delta Z_{eff} \rangle}$			${\mathcal{F}_{Rad,Z}}\,(\%)$			Cmin  (%)
#	—	Be	Ni	W	Be	Ni	W	Be	Ni	W	H	3He
94 980	1.6 ± 0.03	3.8	0.02	0.005	0.61	0.11	0.05	3.6	17.3	75.5	1	2.5
96 713	1.6 ± 0.03	2.1	0.04	0.01	0.35	0.23	0.12	1.52	12.9	82.5	3	—

For both pulses the volume-averaged $\langle Z_{eff} \rangle \sim 1.6$. Pulse #94 980 has twice the concentration of Be (C_Be  ∼ 4%) than pulse #96 713 (∼2%). Conversely, the volume-averaged concentrations of the heavy impurities Ni and W, which are $\mathcal{O} (10^{-4})$ are twice as high in pulse #96 713 than in pulse #94 980 and in both pulses the concentration of Ni is ∼×4 that of W. In spite of this, the W radiates ${\gtrsim}75\%$ and the Ni ${\lesssim}20\%$ of the total radiated power in both pulses. Although the Be radiates only a few % of the power, this species makes the largest contribution to Z_eff .

Power deposition profiles from the NBI and ICRH heating systems are calculated using the codes NUBEAM [35] and TORIC [36]. The ICRH heats the bulk plasma by means of the cyclotron resonance of the RF waves with a minority ion species. In pulse #96 713 there is a single H minority at a concentration of ∼3%, while for pulse #94 980 there are both H and ³He minority ions at average concentrations of ∼1% and ∼2.5% respectively. The presence of the heavier ³He minority species is to increase fraction of ICRH power heating to the D⁺ ions.

The neutral D⁰ influx at the plasma boundary, which determines the edge ionisation source, is determined from a horizontal, mid-plane $\textrm{D}_\alpha$ intensity measurement by assuming a ratio of ionisations/photon S/XB = 10. Note that the TRANSP runs, from which the results are reported here, do not account for the particle source from the ablation of the D⁰ pacing pellets, which are injected at the upper-HFS of the main vessel.

In the following discussion, we refer to volume integrated forms of the power and momentum balances, e.g. for the power balance, the corresponding power P_X is calculated from the power density Q_X for quantity X as $P_{X}(\rho_N^{^{\prime}}) = \int_0^{\rho_{tor}^{^{\prime}}} Q_X (dV/d\rho_{tor})\,d\rho_{tor}$ to yield the associated power deposited within or leaving the $\rho_{tor}^{^{\prime}}$ flux surface.

We can define two further powers for the ions: the loss power due to ion heat transport $P_{tran,i} = P_{cond,i} + P_{conv,i}$, where P_cond,i and P_conv,i are the conducted and convected powers, and the total loss power from the ions $P_{loss,i} = P_{tran,i} + P_{cx}$, where P_cx is the CX loss power. Similarly for the electrons: the power due to electron heat transport $P_{tran,e} = P_{cond,e} + P_{conv,e}$ and the total loss power from the electrons is $P_{loss,e} = P_{tran,e} + P_{0,ion} + P_{Rad}$, where P_0,ion is the ionisation loss power and P_Rad the radiated power. The total transport loss power through both channels is then $P_{tran} = P_{tran,e} + P_{tran,i}$.

2.2.1. Results of power balance analysis.

Results from the interpretive, power balance analysis of the high-power 3.5 MA pulse #94 980 with the high gas fuelling rate ($\Gamma_{D2} \sim 2.3 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$) are shown in figure 3. The derived profiles are shown averaged over the period 10–12 s of the ELMy H-mode phase, while the measured raw data in figure 3(a) is shown at 11.1 s.

Components of the radially-integrated ion and electron power balances are shown in figures 3(b) and (c). While T_i only slightly exceeds T_e across the full plasma radius, collisional exchange transfers significant power from the ions to the electrons, i.e. integrated out the pedestal top P_ie  ∼ 6 MW, i.e. about ∼50% of the total ion heating P_heat,i . Consequently, at the pedestal top, similar powers are conducted through the electron and ion channels, with $P_{tran,e} \sim P_{tran,i} \sim 10~\textrm{MW}$, in spite of the fact that at mid-radius the integrated power heating and conducted by the ions are twice those in the electron channel. Almost half of the total loss power through the electron channel P_loss,e is radiated, i.e. $P_{Rad}/P_{loss,e} \sim 40\%$, predominantly by the strong W emission from the mantle region.

Note that on including the heavier ³He ion species in the TORIC calculations, significant ICRH power is deposited to the D⁺ ions, with a ratio of on-axis power densities in (MW m⁻³) of $Q_{i,RF}/Q_{e,RF} \sim 0.15/0.04~\sim 3$, while (wrongly) assuming instead a single H (3%) minority species results in insignificant core ion heating).

Results from the interpretive, power balance analysis of the high-power 3.5 MA pulse #96 713 with the lower gas fuelling rate ($\Gamma_{D2,gas} \sim 1.0 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$) and the f_Pel  ∼ 45 Hz ELM-pacing pellets, with a similar total fuelling rate as pulse #94 980 are shown in figure 4.

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The most striking difference between the kinetic profiles for these two pulses is the much higher (∼×2) toroidal rotation rate of $\Omega_{\phi,0} \lesssim 130~\textrm{krad}\,\textrm{s}^{-1}$ in pulse #96 713, cf ∼70 krad s⁻¹ in pulse #94 980. Also, there is a higher ratio of $T_i/T_e \sim 1.3$ across the core plasma. Quoting values at the pedestal top, the exchange heating P_ie  ∼ 9 MW transfers ∼50% of the total ion heating P_heat,i  ∼ 18 MW to the electrons. In fact, the exchange heating of the electrons P_ei almost equals that from the external electron heating P_heat,e  ∼ 11 MW and equals the radiated power from the electrons P_Rad .

Hence, accounting for the ion-electron exchange power and radiation, the net transport loss power through the ion channel P_tran,i  ∼ 12 MW is similar in magnitude to that transported through the electron channel P_tran,e  ∼ 11 MW. The increased radiation in #96 713 ensures that about 50% of the total electron loss power P_loss,e  ∼ 20 MW through the electron channel is lost by radiation (again quoting values at the pedestal top).

In both pulses, the profiles of power deposition density to the ions and electrons differ in that, whereas Q_i,heat peaks on-axis, Q_e,heat peaks in the mantle region. This is because the fraction of NBI power heating the ions ($Q_{NB,i}/(Q_{NB,i}+Q_{NB,e})$) increases with the ratio of T_e to the injection energy E₀, with $Q_{NB,e}/Q_{NB,i} \gt 1$ for $E_0/T_e \gt 15$. Consequently, the ratio of heating power to the ions relative to that to the electrons $P_i/P_e$ is higher and also more peaked in #96 713 in which $T_i/T_e \gt 1$ than in pulse #94 980, i.e. $P_i/P_e \sim 1.33$ cf ∼1.18. In spite of the fact that this pulse has only H (1%) minority ions, more ICRH power is deposited into the D⁺ ions than into the electrons, with a ratio of on-axis power densities in (MW m⁻³) of $Q_{i,RF}/Q_{e,RF} \sim 1.1/0.4 \sim 2.8$.

The cause of the more peaked power deposition and greater fraction of ion heating in pulse #96 713 with the pellet+gas fuelling is partly the increased density peaking $\bar{n}_e/n_{e,ped}$, mentioned in section 2.1. This, together with the higher overall heating power ∼×1.15 in this pulse compared to that in pulse #94 980 results in higher rotational shear and a higher $T_i/T_e$ ratio. Because of the relatively higher radiated power in pulse #96 713, the ratio of ion to electron heat fluxes $q_{i}/q_{e}$ is close to unity at the pedestal top in both pulses. Transport in these two pulses are compared in section 2.3, revealing modest differences in the heat and momentum diffusivities and hence changes to the prevailing transport mechanisms induced by the difference in fuelling method.

2.2.2. Results of momentum balance analysis.

Results of the interpretive toroidal angular momentum balance analysis using TRANSP for the same two high-power, 3.5 MA pulses #94 980 and #96 713 are shown in figures 5 and 6. Torque densities τ (Nm m⁻³) are shown in (a), radially integrated torques T (Nm) in (b) and gyro-Bohm normalised momentum and ion heat diffusivities in (c).

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The dominant source of input torque $T_{\phi,in} \sim 25$–30 Nm is from the NBI heating. Note that because of the more peaked density profile in pulse #96 713, the torque density profile $\tau_{\phi,in}$ is somewhat more peaked than in pulse #94 980, which is partly responsible for the increased toroidal rotation rate. Note that in both pulses, the rate of change of angular momentum $\dot{L_{\phi}}$ is small, i.e. there is a steady rate of toroidal rotation during the averaging period.

In the gas-fuelled pulse #94 980, in which $T_i \sim T_e$, the momentum and ion diffusivities are very similar, i.e. the Prandtl number $Pr = \chi_\phi/\chi_i \sim 1$ except near the pedestal top. Except in the very core, both the ion thermal and momentum diffusivities are much larger than the ion-NC level, i.e. $\chi_i/\chi_{i,NC}$ and $\chi_\phi/\chi_{i,NC} \sim \mathcal{O} (10)$ across the plasma.

As discussed further in section 2.3, in pulse #96 713 with the pellet + gas fuelling, the ion thermal diffusivity is slightly less than that for the electrons, $\chi_i/\chi_e \sim 0.8$, both remaining ${\sim}\mathcal{O} (10) \chi_\textrm{i,NC}$. However, there is a more significant reduction in $\chi_\phi$, with the Prandtl number below $Pr \lesssim 0.5$, particularly further into the core.

In the pedestal region, CX collisions with cold neutral D⁰ atoms results in a radially-integrated, frictional torque $T_{\phi,CX(net)} \sim \mathcal{O} (10)\,\textrm{Nm}$, which opposes the torque imposed by the NBI. This torque $T_{\phi,CX(net)}$ is ∼×1.5 (and $\tau_{\phi,CX(net)} \sim \times 3$) higher in the gas-fuelled pulse #94 980 than in the pellet + gas fuelled pulse #96 713, primarily because the D⁰ influx at the LFS is higher in the gas fuelled pulse.

The large CX torque density ($\tau_{\phi,CX(net)} \sim \mathcal{O} (1)\,\textrm{Nm}^{-2}$) necessitates a large negative viscous momentum flux $\Pi_{\phi,visc}$ across the pedestal to achieve momentum balance. This implies the presence of a strong momentum 'pinch' that can arise from neo-classical effects [37] and/or be driven by turbulence [38]. While the presence of this momentum pinch is worthy of more detailed study, it is beyond the scope of this paper.

The time-dependent, interpretive TRANSP analysis solves the balance equations for the transport of particles, ion and electron heat and toroidal momentum [24, 39]. The source of kinetic profiles (T, n_e , T_i , $\Omega_{\phi}$ and $\langle \epsilon_{tot} \rangle$) and other input data, the magnetic equilibrium used for mapping the profiles onto normalised radius ρ_tor and other assumptions in setting up the runs, e.g. on the impurity densities, are described in detail in section 2.2.

A comparison of results from the solution of the power balances of the ions and electrons and of toroidal momentum are shown in figure 7 for the pulses #94 980 with gas-fuelling alone and #96 713 with pellet + gas fuelling, where the profile data is averaged over a 2 s period of the ELMy H-mode phase.

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It can be seen from figure 7(a), that across the core plasma the normalised gradients $R/L_{T_e}$, $R/L_{T_i}$ and $R/L_{\Omega_{\phi}}$ are all larger in pulse #96 713 than in pulse #94 980, with $R/L_{T_i}$ and $R/L_{T_i} \sim \times 1.5$ higher and $R/L_{\Omega_{\phi}} \sim \times 2$ higher at mid-radius. This increase is a signature of improved energy and momentum confinement, particularly in the ion channel across the core plasma in the pellet + gas fuelled pulse.

The heat fluxes in the ion and electron channels $q_{i}/q_{i,gB}$ and $q_{e}/q_{i,gB}$, normalised to the ion-gyro-Bohm heat flux q_i,gB are plotted in figure 7(b) ¹⁴ . For pulse #96 713 with gas + pellet fuelling, these normalised heat fluxes are almost equal with $q_{i} \sim q_{e}$ right across the core plasma. In contrast, for the gas fuelled pulse #94 980, while $q_{i} \sim q_{e}$ in the mantle region ($0.7 \leqslant \rho_{tor} \leqslant 1$), deeper into the core plasma q_i progressively exceeds q_e , with $q_{i}/q_{e} \gtrsim 10$ in the core.

The normalised, perpendicular E × B shearing rate $\bar{\gamma_E} = \gamma_E/(c_s/a)$ ¹⁵ , also shown in figure 7(b), is considerably higher in pulse #96 713 than in pulse #94 980, by up to a factor ∼3 at mid-radius. This shearing can suppress the amplitude of ion-scale turbulence when $\bar{\gamma_E} \gtrsim \mathcal{O} (1)$ [41, 42], thereby reducing the associated heat flux. Hence, it is likely that E × B shear plays a more significant role in regulating the level of turbulent ion heat transport in pulse #96 713, in which $\bar{\gamma_E} \lesssim 0.3$ at mid-radius, than in pulse #94 980.

Thermal diffusivities for the ion and electron channels, normalised to the ion-gyro-Bohm thermal diffusivity, $\chi_i/\chi_{i,gB}$ and $\chi_e/\chi_{i,gB}$ are compared in figure 7(c) for the same two pulses, together with the normalised diffusivity of the toroidal angular momentum $\chi_\phi/\chi_{i,gB}$. Also shown is an estimate of the gyro-Bohm normalised, neo-classical (NC) ion thermal diffusivity $\chi_{i,NC}/\chi_{i,gB}$, which is calculated in TRANSP using the NCLASS code [43].

It can be seen from figure 7(c) that for both pulses, in the peripheral mantle region the normalised thermal diffusivities of the ions and electrons are approximately equal, i.e. $\chi_i/\chi_e \sim 1$. For pellet + gas fuelled pulse #96 713 this is also the case right across the core plasma. In contrast, for the gas fuelled pulse #94 980, further into the plasma χ_i progressively exceeds χ_e , with $\chi_i/\chi_e \gtrsim 10$ in the core. In both pulses these thermal diffusivities far exceed the ion neo-classical level, with both $\chi_{i,e}/\chi_{i,NC} \sim \mathcal{O} (10)$. This certainly indicates that ion-scale turbulent transport is by no means fully suppressed in either pulse.

In both pulses, the Prandtl number $Pr = \chi_\phi/\chi_i$ decreases from Pr ∼ 0.5 at ρ_tor  ∼ 0.7 both deeper into the core plasma and outward across the pedestal region, which is an indication that there is some degree of suppression of ion-scale turbulence (which results in stronger viscosity than electron scale turbulence) in the core and peripheral regions.

These results suggest that ion-scale turbulence (ITG or TEM), which can result in both ion and electron heat transport with equal efficacy, is primarily responsible for the core heat transport in both pulses. However, in the higher performance pulse #96 713 with pellet + gas fuelling, at least some of the increased ion pressure in the core may be caused by a modest relative reduction in the efficiency of ion-scale, turbulent heat transport, caused by the increased E × B flow shear across the core plasma.

In spite of the fact that in both pulses the integrated heating power to the ions is approximately equal at mid-radius, the ∼×3 higher χ_i in the gas fuelled pulse #94 980 results in lower core T_i gradient and hence reduced core ion energy confinement than in the pellet + gas fuelled pulse #96 713. This is a consequence of the more peaked ion heating and torque deposition profiles resulting from the reduced pedestal density with the pellet + gas fuelling compared to that with the gas fuelling alone.

In high-power ITER-baseline scenario pulses with ${\gtrsim} 25~\textrm{MW}$ of heating power, a substantial fraction of the input power is radiated from the core plasma, i.e. $\mathcal{F}_{Rad} \sim 30\%$–40%. It has been shown in [8] that these losses are dominated by radiation from W impurities, which accounts for ${\gtrsim} 95\%$ of the total radiation. In such pulses, these impurities are typically localised to the outer 'mantle' region of the confined plasma, e.g. as shown for the 3 MA/2.8 T pulse #92 432 with 32 MW heating power in figure 13(a). The radially outward centrifugal force due to the toroidal rotation localises the heavy W ions to the LFS mid-plane where the total emissivity _m peaks [44]. However, because of the very high parallel electron thermal conductivity $\chi_{e,\parallel} \gg \chi_e$, it is the flux-surface-averaged emissivity $\langle \epsilon_{tot} \rangle$ that is relevant to the electron power balance (see figure 2(b)).

The reason why the impurity ions tend to remain localised to the mantle region in these ITER-baseline pulses is because the density gradient across the core plasma is much weaker than that of the ion temperature, i.e. there is a low degree of density peaking. As is discussed in [8] and references therein, the radial neo-classical convection velocity of impurity ions is proportional to the parameter $\zeta_{NC} = R/2L_{T_i} - R/L_{n_i}$ [45]. Hence, a peaked T_i profile and a flat n_e profile favours outward neo-classical convection, expelling the impurities from the plasma core. The converse is also true and, particularly in 'hybrid' scenario plasmas [1], which operate with a lower pedestal density n_e,ped and consequently with a more peaked n_e profile, this can cause the W impurities to accumulate in the plasma core and lead to radiation collapse.

The evolution of the flux-surface-averaged W impurity density $\langle n_W \rangle$ is shown in figures 8(a)–(c) for the three 3.5 MA ITER-baseline pulses discussed in section 2, from which it can be seen that the W is typically localised to the mantle region, i.e. $0.7 \leqslant \rho_{tor} \leqslant 1$. Only in one of these pulses #94 980 is there a brief period during which $\langle n_W \rangle$ peaks in the plasma core but these impurities are expelled again later.

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Also shown in figures 8(d)–(f) is a comparison of the evolution of profiles of the neo-classical convection parameter ζ_NC . This is calculated from the results of an interpretive TRANSP calculation, which is based on kinetic data provided from fits to electron density n_e and temperature T_e profile data measured by the HRTS [29] and Ne^10 + impurity ion temperature T_i and toroidal rotation $\Omega_{\phi}$ profile data from the core and edge CXRS systems [30].

From these plots it can be seen that, while $\zeta_{NC} \sim \mathcal{O} (-100)$ is strongly negative in the pedestal region (off the colour scale), hence driving the impurities across the pedestal into the confined plasma, it is weakly positive $\zeta_{NC} \gtrsim 5$ right across the core of the plasma. Consequently, once inside the confined plasma, the impurities are screened from the core plasma by outward convection, which concentrates them in the outer mantle region. Note that the convection velocity $V_{NC} \propto Z q^2 D_c\, \zeta_{NC}/R$, where Z is the impurity ion charge and D_c is the collisional diffusivity [45]. Typically, the W ions are in charge states W^{25 − 30 +} in the mantle region (see figure 9(c)), so this convection is very strong for the W ions. Also, the strong polodial asymmetry enhances the convection by a further factor 1/(2 ²) ∼ 5, where the inverse aspect ratio  = r/a [46].

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Note that there are circumstances in these high-power, ITER-baseline pulses in which profile changes following an H- to L-mode transition, triggered by the strong W radiation from the plasma periphery, causes a sudden accumulation of the impurities. This typically leads to termination of the high-performance phase, either triggering a 'pulse stop' or causing a disruption due to radiation collapse. Such a radiation event occurs in the 3 MA pulse #92 432, the phenomenology of which is described in section 2.6.

Note that in pulse #94 915, during the periods of ELM-free H*-mode ¹⁶ , radiative cooling of the mantle region by the increasingly strong W radiation together with a concomitant increase in density, causes stronger outward convection ($\zeta_{NC} \gg 0$), localising the W to the plasma periphery. However, during the subsequent periods with rapid type-III ELMs, the resulting increase in the n_e gradient in the mantle causes this convection to reverse ($\zeta_{NC} \lt 0$), thereby allowing the W impurities to penetrate deeper in to the plasma, although they do not accumulate in the core.

While the W impurities are localised to the mantle region by the outward neo-classical convection, they can be efficiently expelled from the confined plasma by the ELMs. The ELMs typically expel a small fraction of the plasma particles, peeling off part of the edge plasma, causing relative density losses $\Delta \bar{n}_e/\bar{n}_e \sim 5\%$–10%. If the impurities are concentrated in the periphery, the ELMs can 'flush' out a larger relative fraction of the impurity content than that of the main ions.

We define here the flushing efficiency of the W impurities by an ELM as $(\Delta \bar{n}_W/\bar{n}_W)_{ELM}$, i.e. the relative change in the W content of the plasma due to the ELM. Because the total radiation in high-power, JET-ILW pulses is dominated by that from W, this flushing efficiency can be evaluated from fast, bolometric measurements of the total radiation from the confined plasma, as described in detail in the following section 2.5.

An estimate of the efficacy of each ELM at flushing the W impurities from the confined plasma (and also their influx during the inter-ELM periods) can be obtained from an analysis of fast, bolometric total radiation measurements, using a method first applied to JET-ILW plasmas described in [47]. For this analysis we use a fast radiated power signal $P_{Rad}^{Hor}$ calculated from a weighted sum of intensities from a bolometer camera viewing the main chamber horizontally from the LFS [28].

As shown in figure 9(b) for the high-power, 3 MA ITER-baseline pulse #92 432, the total emissivity coefficient of W is reasonably constant over the mantle region ($0.7 \leqslant \rho_N \leqslant \rho_{N,ped} \sim 0.96$), i.e. $\mathcal{R}_{\epsilon} \sim 4.5 \times 10^{-31}\,\textrm{MW}\,\textrm{m}^{3}$, where the W radiates most intensely (see figure 9(a)). Typically, in the mantle region, where T_e  ∼ 1–3 keV, the average charge state $\bar{Z}$ of the impurities is W^{25 − 30 +}. The atomic data shown in figure 9 is from the ADAS database of spectroscopic data [48] and uses total radiated line power ($\mathcal{PLT}$) data for W from [49].

As the W radiates mainly from the mantle region and the emissivity of W is reasonably constant over the relevant temperature range (1–3 keV), the average W density $\bar{n}_W$ in the mantle can be estimated from the expression: $\bar{n}_W \sim P_{Rad}^{man}/(\bar{n}_e \mathcal{R}_{\epsilon} V_{man})$, where $\bar{n}_e$ is the average density over the mantle region and V_man is the volume of the mantle ∼22 m³. We next explain how we obtain a fast enough signal $P_{Rad}^{man}$ quantifying the radiated power from the mantle region to determine the ELM flushing efficiency, which requires a frequency response of order 1 kHz.

The power radiated from the confined plasma $P_{Rad}^{Pl}$ can be calculated from a weighted sum of horizontally viewing, line-integrated measurements of total intensity measured using a multi-chord bolometer system [28]. This system has a sample rate of 5 kHz and uses an adaptive filtering algorithm so as not to smooth fast transients due to ELMs, while having lower bandwidth of typically 0.2 kHz during steady phases. As this calculation relies on assumptions on the symmetry of the emissivity on flux surfaces, it tends to overestimate $P_{Rad}^{Pl}$ by as much as 50% in the presence of highly in-out asymmetric emissivity distributions. Here, we refer to this fast radiated power signal as $P_{Rad}^{Hor}$.

In order to overcome this problem and accurately calculate the radiated power from the mantle region $P_{Rad}^{man}$, we use the total emissivity distribution _m (R, z) obtained from tomographic inversion [27] of the multi-chord bolometer data, which take proper account of the poloidal asymmetry. Reconstructions are calculated at the mid-times of each inter-ELM period, using input data averaged over 5 ms intervals. The resulting distributions are integrated over the volume of the mantle to form a 'slow' radiated power signal we refer to here as $\langle P_{Rad}^{man} \rangle$. Note that in these high-power, ITER-baseline scenario pulses, typically ∼70% of the radiated power is emitted from the mantle region (see figure 10(c)).

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We can correct the fast radiated power signal $P_{Rad}^{Hor}$ to provide a more accurate, fast estimate of $P_{Rad}^{man}$ by scaling it to the more accurate, slow signal $\langle P_{Rad}^{man} \rangle$ obtained from the tomography using a time-dependent scale factor. While this procedure may seem complicated, it is necessary if we are to use the resulting values of $P_{Rad}^{man}$ to estimate the concentration of W in the mantle region.

From both the fast estimate of the radiated power from the mantle $P_{Rad}^{man}$ and a fast measurement of the line-average density $\bar{n}_e$ from the lower, horizontal interferometer channel (#5), which passes through the outer half of the lower plasma cross-section, the ELM W flushing efficiency can be evaluated from the change in the signal $f_{fl} = P_{Rad}^{Hor}/\bar{n}_e$ aka the 'flushing' signal between short averaging periods just before and after the ELM crash, i.e. from the expression $\Delta n_W/n_W \sim (f_{fl}^{\,pre-ELM} - f_{fl}^{\,post-ELM})/f_{fl}^{\,pre-ELM} = \Delta(f_{fl})/f_{fl}^{\,pre-ELM}$.

For our analysis we use pre- and post averaging times of $\Delta t_{ELM} = \left\{-7, -2~\textrm{ms} \right\}$ and $\left\{5, 10~\textrm{ms} \right\}$ relative to the time t_ELM of the peak Be II intensity signal. The post-ELM time period is delayed by 5 ms to avoid the transient increase in radiation that is caused by the ELM-sputtered W influx before the ionisation balance has had time to recover. It is a general phenomenon that when a population of impurity ions has not yet reached coronal ionisation balance, they are able to radiate more efficiently than when in equilibrium [50].

A similar measure, estimating the relative change in the W content between the ELMs, i.e. the relative inter-ELM ingress or 'fluence' of W $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$ can be calculated from the difference between the post-ELM value of f_fl and that prior to the subsequent ELM, i.e. $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM} = (f_{fl}^{\,pre-ELM_{i+1}} - f_{fl}^{\,post-ELM_i})/f_{fl}^{\,post-ELM_i}$. These measures of the ELM W flushing efficiency $(\Delta \bar{n}_W/\bar{n}_W)_{ELM}$ and the relative, inter-ELM fluence $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$ can then be used to calculate net rates of change of the W impurity content, $\gamma_W = (d\bar{n}_W/dt)/\bar{n}_W$ from a time-dependent average, as described in appendix B of [51].

In the case of a group of rapid ELMs, with an inter-ELM period shorter than the pre- and post-ELM averaging times of $\left\{ -7, 10~\textrm{ms} \right\}$, it is only possible to determine the flushing for the group of ELMs, which we choose to split equally between the sub-ELMs, while the inter-ELM fluence is allocated to the last in the group. A property of this ad-hoc method of handling the compound ELMs does maintain valid, time-averaged flushing rates γ_W calculated from the $\Delta \bar{n}_W/\bar{n}_W$ data. Rates of change of the W content due to the ELM flushing $\gamma_W^{ELM}$ and the inter-ELM influx $\gamma_W^{i-ELM}$ are shown in figure 11(c) of section 2.7 below, together with the 'net' rate of change due to the balance between these competing fluences, i.e. $\gamma_W^{net} = \gamma_W^{ELM} - \gamma_W^{i-ELM}$.

By availing of fact that radiation from W dominates the radiated power and that the total emission rate coefficient $\mathcal{R}_{\epsilon}$ of W over the 1–3 keV temperature range in the mantle region is almost constant ${\sim}4.5 \times 10^{-31}\,\textrm{Wm}^{3}$, the average W concentration over the mantle region $\langle C_W \rangle_{man}$ can also be estimated from the expression: $\langle C_W \rangle_{man} \sim P_{Rad}^{man}/(V_{man} \mathcal{R}_{\epsilon} \bar{n}_e^2)$. Typically, $\langle C_W \rangle_{man} \sim 2$–3 × 10⁻⁴ in these plasmas, e.g. as shown in figure 10(a).

An example of the application of this ELM-flushing analysis to the the high-power, 3 MA ITER-baseline pulse #92 432 is presented in the following section section 2.6.

The evolution of the high-power, 3 MA/2.8 T ITER-baseline pulse #92 432 with 32 MW of additional heating power and gas fuelling only at a rate of $\Gamma_{D2} \sim 2.3 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$, is shown in figure 10 both as an example of the application of the ELM W flushing analysis described above but also to illustrate the profound effect that the strong W radiation can have on the evolution of such high-power H-mode pulses in JET-ILW. Note that this 3 MA pulse has the same q₉₅ and plasma configuration as the 3.5 MA pulses discussed here.

Provided the W impurities remain primarily in the outer, mantle region of the plasma, their effect on the core fusion performance is relatively benign and their radiation helps distribute the power exhaust over the vessel walls. For this situation to persist, two criteria must be satisfied: firstly, the ELMs must flush out enough of the W that crosses the separatrix between ELMs to maintain a constant impurity content; secondly, the T_e and n_e gradients in the mantle must stay aligned such that the impurity convection is directed outwards, i.e. $\langle \zeta_{NC} \rangle_{man} \gt 0$, so that the W impurities are screened from the plasma core.

During the early ELMy phase of the pulse (${\lesssim} 10~\textrm{s}$) these conditions are fulfilled, however, later the ELM frequency slows and they then cease at ∼10.2 s. During the subsequent, ELM-free H*-phase, the density $\bar{n}_e$, W content ($\bar{n}_W \propto P_{Rad}^{man}/\bar{n}_e$) and the associated radiation primarily from the mantle increase strongly, to a fraction $\mathcal{F}_{Rad} \gtrsim 70\%$ of the input power (see figure 10(c)). The slowing of the ELMs prior to the H*-phase is caused by an increase in the gas puffing rate by the control system, which is intended to increase f_ELM , i.e. this has the opposite effect to that expected. The phenomenology of these events is discussed further in section 3.

The consequent reduction of the net power crossing the separatrix $\Delta P_{Sep} = P_{l,th} - P_{Rad}^{Pl} - P_{LH}$ below L/H-transition threshold power P_LH [52] triggers a subsequent back transition to L-mode (see figure 10(c)). Note that, the fact that P_LH increases with B_t means that this type of behaviour is more prone to occur in higher-current baseline-scenario pulses with higher B_t , making then more difficult to control.

As shown in figures 10(f) and (g), the resulting peaking of the n_e profile due to the loss of the density pedestal after the transition to L-mode results in a sudden reduction of the neo-classical screening ($\zeta_{NC} \rightarrow 0$). As is evident from the evolution of the total emissivity $\langle \epsilon_{tot} \rangle$ shown in figure 10(d) this reduction in screening then causes sudden accumulation of the W impurities the plasma core, resulting in a reduction of the stored energy W_pl by ∼30%.

The influence of the strong mantle radiation on the electron power balance is evident from figure 10(e), which shows that there is a significant reduction of T_e just inside the pedestal top (at ρ_tor  = 0.9) and a corresponding increase of n_e as the level of mantle radiation increases (see [8] for a detailed discussion of the electron and ion power balance in this pulse).

The resulting changes to the n_e and T_e gradients in the mantle initially causes $\langle \zeta_{NC} \rangle_{man}$ to increase (see figure 10(f)), driving the impurities more strongly outwards. At the H/L-transition at 10.5 s, $\langle \zeta_{NC} \rangle_{man}$ suddenly decreases to ∼0, when the normalised density gradient $R/L_{n_e}$ in the mantle region steepens, causing the W impurities to rush into in the plasma core. This behaviour is evident from the evolution of the total emissivity distribution $\langle \epsilon_{tot} \rangle$, which is shown in figure 10(d).

During the ELMy H-mode phase, as shown in figure 10(a), while the W concentration in the mantle ($\langle C_W \rangle_{man} \sim P_{Rad}^{man}/(V_{man} \mathcal{R}_{\epsilon} \bar{n}_e^2)$) remains quite constant at $\langle C_W \rangle_{man} \sim 2 \times 10^{-4}$, there is a gradual increase in the W content $\bar{n}_W \propto P_{Rad}^{man}/\bar{n}_e$, causing a concomitant increase in the mantle radiation $P_{Rad}^{man}$ (see figure 10(c)). This gradual increase is a result of a delicate balance between the flushing of the W impurities by the ELMs from the confined plasma and their influx across the pedestal between the ELMs.

The relative W flushing efficiency $\Delta \bar{n}_W/\bar{n}_W$ and inter-ELM W fluence $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$ evaluated for each ELM are shown in figure 10(b), together with the net, relative change in the W content over each ELM cycle, i.e. $(\Delta \bar{n}_W/\bar{n}_W)_{net} = (\Delta \bar{n}_W/\bar{n}_W)_{ELM} - (\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$. It is evident that, while ∼5%–10% of the W content is flushed by each ELM, a similar amount is convected across the pedestal from the SOL and re-enters the plasma between the ELMs. The small, net change results in a gradual change on a timescale $1/\gamma_W^{net} \sim \mathcal{O} (1~\textrm{s})$.

In this pulse, ELMy H-mode does resume at the end of the period shown but the high-Z impurities remain in the plasma core and the stored energy does not fully recover to the level prior to the radiation event. The use of ELM-pacing pellets in such pulses alters the characteristics of the ELMs and allows the duration such high-performance, ITER-baseline pulses to be extended. The behaviour of 3.5 MA ITER-baseline, H-mode pulses with ELM pacing pellets is discussed in the following section section 2.7.

In this section, we investigate the ELM flushing and W behaviour in the three 3.5 MA ITER-baseline pulses with different gas and/or pellet fuelling that were discussed previously in section 2. Results of the ELM W flushing analysis for these pulses are presented in figure 11.

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Considering first, the pulse #94 915 with the lower rate of gas fuelling ($\Gamma_{D2,gas} \sim 1.5 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$) alone, we see that this pulse is non-stationary, exhibiting three H*-phases, during which the mantle W radiation increases, just as occurred in pulse #92 432, as described in section 2.6 above. The W concentration in the mantle $\langle C_W \rangle_{man} \sim 2 \times 10^{-4}$ is similar in both of these gas-only fuelled pulses.

The strong mantle radiation does not result in an H/L-transition as in pulse #92 432, instead the H*-phase is terminated by a single large amplitude ELM, which is followed by a sustained burst of small, type-III ELMs (see figure 1(e)). During these phases, the n_e gradient in the mantle region increases, resulting in a reversal of the neo-classical convection from outward to inward, as shown in figure 11(e). This reversal allows the W to migrate deeper into the plasma core, as is evident from the evolution of the total emissivity shown in figure 11(f), however, the impurities do not accumulate in the plasma core.

The combined effect of the few, large and frequent, small ELMs does provide sufficient flushing of the W to maintain a reasonably constant W concentration. However, during the final H*-phase, a strong increase of the total radiated power $P_{Rad}^{tot}$ triggered an early 'pulse-stop', which initiated an increase in the gas fuelling rate. During the ramp-down phase of this pulse, there was a disruption, resulting in vessel forces exceeding 350 T. This non-stationary nature of high-power, ITER-baseline pulses with a low rate of gas fuelling leads to a high fraction of pulses disrupting, which is clearly unacceptable.

Increasing the D₂ gas puffing rate, as in pulse #94 980 ($\Gamma_{D2,gas} \sim 2.3 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$), provides a safe means of controlling the W impurity level, and thereby reducing the disruptivity, but at the cost of decreased energy confinement. The more frequent ELMs induced by the increased gas puffing flush out more W, significantly reducing the W concentration to $\langle n_W \rangle_{man} \sim 1$–1.5 × 10⁻⁴. Note, however, that there is a gradual buildup of the W content due to the increasing $\bar{n}_e$ (see figure 11(a)). The W impurities are also not so well screened from the core because of the reduced core T_i and hence weaker $R/L_{T_i}$, resulting in the neo-classical convection parameter ζ_NC  ∼ 0 in the mantle region.

Comparison of the pedestal parameters shown in figures 11(e) and (f), shows that the increased gas puffing in pulse #94 980 does not significantly reduce T_e,ped , or indeed increase n_e,ped , compared to those in pulse #94 915. There is, however, a significant reduction in toroidal rotation rate $\Omega_{\phi,ped}$ at the top of the density pedestal caused by the increased gas puffing rate in pulse #94 980. In both pulses, the ion temperature T_i,ped , here defined as T_i at the top of the density pedestal ¹⁷ , is significantly higher (∼20%) than T_e,ped .

As already discussed above, the use of ELM-pacing pellets in pulse #96 713 allows the duration of the high-performance phase to be extended without degrading the energy confinement. The main beneficial effect of the pellets is to trigger regular ELMs under conditions which would otherwise result in ELM-free H*-phases, as occur in pulse #94 915. This allows pulse #96 713 to be run with an even lower gas puffing rate ($\Gamma_{D2,gas} \sim 1.0 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$) than that used in pulse #94 915 (${\sim}1.5 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$). The danger with such a strategy is the necessity of reliable pellet injector operation to deliver a regular stream of pellets for the pulse to run without risk of a radiation induced disruption.

Although the total D₂ fuelling rate from gas and pellets, i.e. $\Gamma_{D2} \sim 2.3 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$, is the same in pulse #96 713 as used in pulse #94 980, the performance of the pulse is superior in terms its overall energy confinement. We will see that the origin of this lies not in significantly higher T_e,ped but in increased toroidal rotation and hence rotational shear from the pedestal top, inwards across the core plasma and hence increased core ion energy confinement.

From figure 11(a), we can see that the W concentration of $\langle C_W \rangle_{man} \sim 2.5 \times 10^{-4}$ is in fact as high in pulse #96 713 as in pulse #94 915. As evident from the evolution of the total emissivity shown in figure 11(d), the W is also not as well screened from the plasma core as in pulse #94 915. Averaged over the mantle region, the neo-classical convection parameter is slightly negative $\langle \zeta_{NC} \rangle_{man} \sim -2$ in pulse #96 713, i.e. weakly inwards (see figure 11(e)). However, the full radial profiles shown in figure 8(b), show that $\zeta_{NC} \gt 0$ at mid-radius, hence the N-C convection still acts to screen the W from the core.

Comparison of the pedestal parameters in figures 11(e) and (f), show that whereas T_e,ped is similar in the three pulses, while n_e,ped is slightly lower in the pulse #96 713 with the pellets, there is a significant difference in the ion parameters (T_i,ped and $\Omega_{\phi,ped}$) from the edge CXRS measurements. In pulse #96 713, there is a greater ratio of $T_{i,ped}/T_{e,ped} \sim 1.6$, than in the other two pulses (∼1.4) and the rotation at the pedestal top $\Omega_{\phi,ped}$ is also ∼×1.4 higher.

In section 2.1 above, we showed that this enhanced rotation in the pulse #96 713 with pellets and the lower rate of gas fuelling, in fact occurs right across the plasma from the pedestal to the core. This perhaps arises from reduced CX damping of the toroidal momentum due to the lower D⁰ atomic density resulting from the reduced gas puffing into the main chamber.

In the following section section 2.8, the dependence of the W flushing efficiency $\Delta \bar{n}_W/\bar{n}_W$ on the fractional ELM density losses $\Delta \bar{n}_e/\bar{n}_e$ is investigated, classifying the data according to whether the ELMs are spontaneous or pellet-triggered events.

By identifying whether the ELMs are either spontaneous aka 'natural' or 'pellet-triggered' events, the data for the relative W flushing efficiency $(\Delta \bar{n}_W/\bar{n}_W)_{ELM}$ and inter-ELM fluence $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$ can be classified according to ELM type. This classification is performed by determining whether the occurrence of the ELMs is coincident with the arrival of the pellets at the plasma edge.

Such data is shown in figure 12 for six 3.5 MA baseline-scenario pulses with 30–37 MW of additional heating power, three with only D₂ gas fuelling at rates of Γ_D2,gas  ∼ 1.5, 2.3 and $3.0 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$ and three with both gas fuelling (1–$1.5 \times 10^{22}\,\textrm{e}\,\textrm{s}^{-1}$) and $\phi 2~\textrm{mm}$ ELM pacing pellets (f_Pel  ∼ 35 Hz). The W flushing $(\Delta \bar{n}_W/\bar{n}_W)_{ELM}$ and inter-ELM fluence $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$ data are plotted as a function of the relative ELM density losses $\Delta \bar{n}_e/\bar{n}_e$, which are determined from the decrease at the ELMs of the line-average density $\bar{n}_e$ from channel #5 of the FIR interferometer passing diagonally through the lower, outer half of the plasma cross-section.

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To better quantify the differences in these parameters between the different classes of ELMs, histograms, i.e. PDFs, of the distributions of the data are plotted on the corresponding axis. These histogram plots also show the mean and standard deviation of the data for each class of ELMs. While the 'natural' ELMs typically result in density losses $\Delta \bar{n}_e/\bar{n}_e \sim 5\%$–10%, the density losses due to pellet-triggered ELMs are smaller and some of the pellets result in a small net fuelling.

Note that these ELM-pacing pellets are smaller (∼20% of the particle content) than those used for fuelling, i.e. of $\phi 2~\textrm{mm}$, see $\phi 4~\textrm{mm}$ for the fuelling pellets, and are hence mostly ablated before reaching the pedestal top. Typical particle contents of the pacing and fuelling pellets are ${\sim}4 \times 10^{20}\,\textrm{e}^{-}$ and ${\sim}2 \times 10^{21}\,\textrm{e}^{-}$ respectively.

Average values and standard deviations of the data show in figure 12 are stated in table 5. For the natural ELMs, the average density losses $\langle \Delta \bar{n}_e/\bar{n}_e \rangle \sim -2.6\pm0.2\%$ are similar in both the gas-only and gas + pellet-fuelled pulses. However, for the pellet-triggered ELMs, on-average the density losses are considerably smaller $\langle \Delta \bar{n}_e/\bar{n}_e \rangle \sim -0.7\pm0.1\%$, i.e. there is significant net fuelling of the confined plasma by many of the pacing pellets.

Table 5. Average values of data shown in figure 12 by fuelling source and ELM type for high-power, 3.5 MA/3.3 T ITER-baseline pulses.

Fuelling	ELM type	$\langle \Delta \bar{n}_e/\bar{n}_e \rangle$ (%)	$\langle \Delta \bar{n}_W/\bar{n}_W \rangle$ (%)
—	—	ELM	ELM	inter-ELM
Gas-only	Natural	−2.8 ± 0.1	−0.7 ± 0.3	0.2 ± 0.3
Pel and Gas		−2.4 ± 0.2	−1.4 ± 0.2	1.3 ± 0.2
	Pellet	−0.7 ± 0.1	−2.9 ± 0.4	2.3 ± 0.3
—	All	−2.2 ± 0.1	−1.4 ± 0.2	0.9 ± 0.2

There is a large scatter in the ELM flushing $(\Delta \bar{n}_W/\bar{n}_W)_{ELM}$ and inter-ELM fluence $(\Delta \bar{n}_W/\bar{n}_W)_{i-ELM}$ data for several reasons. Firstly, the measurement method gives only an approximate measure and is prone to error. Also, while some ELMs are followed by ELM-free periods of significant duration, others are followed by the groups of rapid small ELMs, which complicates the measurement. In spite of these difficulties with the measurement, it may well be that some ELMs do result in a net increase in the W content as a result of an interchange component of the ELM instability [53], which could mix some cold plasma from the SOL containing W back into the confined plasma.

There are significant differences in the average ELM W flushing efficiency for the three ELM types. The ELMs in the gas fuelled pulses are on-average, about half as efficient at flushing the W than the natural ELMs in the pellet fuelled pulses, while the pellet triggered ELMs are more efficient at flushing the W than the natural ELMs with either fuelling method. This is not simply a result of change to the the density losses $\Delta \bar{n}_e/\bar{n}_e$, which show the opposite trend with ELM type. Although the pellets result in lower net density losses following the triggered ELM, more W is flushed from the plasma than after natural ELMs.

There are also significant differences in the inter-ELM W fluence data between the natural and pellet triggered ELMs. On average, considerably more W is able to enter the plasma following the pellet triggered ELMs. Also, more W enters the plasma after either ELM type in pellet + gas fuelled pulses than gas-only fuelled pulses. Note that the average magnitudes of the ELM W flushing and inter-ELM ingress are similar, so the net change in the W content of the plasma is a delicate balance between these processes. In section 2.10 below, we investigate how differences between the pedestal and mantle gradient parameters might affect the transport of W in the edge plasma.

Other than affecting the ELM W flushing efficiency and inter-ELM ingress of W into the plasma, the pellets might also affect the sources of impurities sputtered by the ELMs from the PFCs. In this section, we compare relative intra-ELM fluences, i.e. influxes integrated over the duration of the ELM peak in the line intensity signal, of Be and W impurities Φ_Be,W sputtered from the inner and outer divertor targets by the interaction with the ELMs.

A relative measure of these fluences can be estimated from time-integrated Be II (527 nm) and W I (401 nm) line intensities measured by a multi-chord spectrometer viewing the HFS, and LFS divertor targets. The lines of sight of this spectrometer are shown in figure 13(a). Profiles of the Be II (527 nm) and W I (401 nm) line intensities time-integrated over the ELM peak are shown in figure 13(b) as a function of the distance S along the divertor target. The most intense interaction with the ELM is with the top of the inner and outer vertical targets aka 'domes' and also at the strike points [51]. Also shown in figures 13(c) and (d) are the evolution of the Be II (527 nm) and W I (401 nm) line intensities, summed over channels viewing the inner and outer divertor targets, over the duration of a typical type-I ELM, indicating the period over which the intra-ELM fluences are integrated.

Note that the inner strike point is hidden from view in this corner-corner (C-C) configuration in which the both strike points are close to the divertor pumping throats, so these measurements are unable to detect the impurity influxes from the vicinity of outer strike point. It has been shown from the analysis of spectrally filtered, fast-camera imaging data from JET-ILW that the intra-ELM sputtered W⁰ influx is almost an order of magnitude larger than the time-integrated inter-ELM influx from the strike-point regions [54].

In figures 14(a) and (b), relative, intra-ELM Be⁺ fluences $\Phi_{Be}^{ELM}$ estimated (assuming constant ionisations/photon, S/XB) from the time-integrated Be II (527 nm line intensity data summed over the HFS and LFS divertor targets respectively, plotted versus the relative ELM density losses $\Delta \bar{n}_e/\bar{n}_e$. Similar data for the relative W⁰ atomic, intra-ELM fluences $\Phi_W^{ELM}$ are shown in figure 15. Average values of these fluences $\langle \Phi_{Be} \rangle$ and $\langle \Phi_W \rangle$ with their standard deviations are stated in table 6. The bremsstrahlung contribution to the W I line, detected by a LOS viewing through the x-point, which does not view a region of the target with significant interaction with the SOL plasma, is estimated to be ${\lesssim}10\%$ during the intra-ELM periods.

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Table 6. Average values of the relative intra-ELM Be⁺ and W⁰ fluence data $\langle \Phi_{Be} \rangle$ and $\langle \Phi_W \rangle$, classified by fuelling source and ELM type for the data shown in figures 14 and 15 from high-power, 3.5 MA pulses. The sum of these fluences from both HFS and LFS targets is also stated.

Fuelling	ELM type	HFS		LFS		Total
—	—	${\langle \Phi_W \rangle}$	${\langle \Phi_{Be} \rangle}$	${\langle \Phi_W \rangle}$	${\langle \Phi_{Be} \rangle}$	${\langle \Phi_W \rangle}$	${\langle \Phi_{Be} \rangle}$
—	—	(a.u.)	(a.u.)	(a.u.)	(a.u.)	(a.u.)	(a.u.)
Gas-only	Natural	1.15 ± 0.03	2.11 ± 0.07	0.73 ± 0.02	2.02 ± 0.07	1.88 ± 0.05	4.13 ± 0.12
Pel and Gas		1.48 ± 0.03	2.16 ± 0.05	0.52 ± 0.02	1.11 ± 0.04	2.00 ± 0.04	3.27 ± 0.10
	Pellet	1.46 ± 0.03	2.59 ± 0.08	0.60 ± 0.03	1.32 ± 0.07	2.06 ± 0.05	3.91 ± 0.13
—	All	1.38 ± 0.02	2.23 ± 0.04	0.60 ± 0.01	1.42 ± 0.03	1.97 ± 0.03	3.65 ± 0.07

The high degree of scatter in the relative ELM-sputtered $\Phi_{Be}^{ELM}$ and W⁰ fluence data is shown in figures 14 and 15 is due to the similarly large spread in the ELM amplitudes. The averaged values over the whole data set, classified by fuelling source and ELM type, reveal little significant difference between these fluences at the HFS target between these cases, except that the natural ELMs sputter slightly less W impurities (∼×0.8) and the pellet-triggered ELMs slightly more Be (∼×1.15) than the average over all ELMs. This is reversed at the LFS target, where the natural ELMs in the gas-only fuelled pulses do sputter significantly more W and Be (∼×1.2 and 1.4 respectively) than the average over all ELMs.

Values of ionisations/photon (S/XB) for these Be and W lines available from the ADAS atomic database [48], increase with both T_e and n_e , as does the fraction of W⁺ ions promptly redeposited at the surface [3]. Hence, without T_e and n_e data with sufficient temporal ($\mathcal{O} (100~\mu\textrm{s})$) and spatial resolution $\mathcal{O} (1~\textrm{cm})$ measured at the divertor target surface, it is impossible to evaluate absolute influxes from the measured intensities. However, by assuming fixed values of S/XB and assuming that the measured Be⁺ influx is equal to the incident flux at the targets, i.e. assuming a balance between erosion and redeposition, it is possible to calculate an effective sputtering yield for W by Be⁺ ions $\gamma_{Be^{4+} \rightarrow W}$.

For intra-ELM conditions, typical S/XB values at T_e  = 100 eV and $n_e = 10^{19}\,\textrm{m}^{-3}$ of (S/XB)_WI  = 46.7 and (S/XB)_BeII  = 52.5 correspond to an S/XB ratio of 0.89 for the two lines, consistent with that used for a previous measurement on JET-ILW [55]. Resulting values for the intra-ELM sputtering yield lie in the range $\gamma_{Be^{4+} \rightarrow W} \sim 0.5$–1.0. These are consistent with values shown in figure 9 of [55], which were obtained using the same diagnostic, assumed S/XB values and spectrometer on JET-ILW.

In [55], it was shown that such high values for $\gamma_{Be^{4+} \rightarrow W} \sim 0.5$–1.0 are higher than that possible for Be⁺ ions on W from physical sputtering, which has a maximum yield of $\gamma_{Be^{4+} \rightarrow W} \sim 0.4$. Hence, there must be a significant contribution from W sputtering by the incident D⁺ fuel ions during type-I ELMs at the prevailing pedestal temperatures in JET-ILW. Also, conditional averaging of the resulting data reveals no significant difference in the measured sputtering yield $\gamma_{Be^{4+} \rightarrow W}$ by the different classes of ELMs.

We have seen above in section 2.4 that the amount of W in the plasma is a result of a delicate balance between the influx across the pedestal driven by inward neo-classical convection and the flushing of the W by the ELMs. Also, the in the high-power ITER-baseline pulses investigated here, the W is typically localised by outward neo-classical convection to the outer, mantle region, hence mitigating the tendency for this to accumulate in the plasma core.

In this section, we quantify the effect of the ELM pacing pellets on the density and temperature gradients in the pedestal and mantle regions during the inter-ELM periods following the pellet triggered ELMs, comparing the derived quantities ζ_NC and $\eta_e = L_{n_e}/L_{T_e}$ (which govern the neo-classical impurity convection and provide the drive for electron-temperature-gradient (ETG) driven turbulence, respectively) during inter-ELM periods following the pellet-triggered or natural, spontaneous ELMs.

Pedestal characteristics T_e,ped , n_e,ped and p_e,ped and gradient parameters derived from mtanh() fits to n_e and T_e profile data from the high-resolution, Thomson scattering system (HRTS) [29] are shown in figure 16. Values of the gradient parameters $R/L_{T_e}$, $R/L_{n_e}$ and $R/L_{p_e}$ and the derived parameters ζ_NC and η_e are spatially averaged over the pedestal $\langle \ldots \rangle_{ped}$ and mantle $\langle \ldots \rangle_{man}$ regions. In this figure the colour represents the type of the ELM preceding the HRTS measurement, i.e. whether the ELMs are pellet-triggered or natural ELMs in either gas-only or pellet + gas fuelled pulses.

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In order to determine whether the ELM-pacing pellets have any statistically significant effect on the average values of the parameters ζ_NC and η_e over the pedestal and mantle regions, the data shown in figure 16 is plotted in figure 17 in the form of histograms, where the data is distinguished according to the preceding ELM type. Average values and standard deviations of the data (σ_data ), also shown in figure 17, are stated in table 7.

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Referring to the values of $\langle \zeta_{NC} \rangle_{ped}$ in table 7, we see that on-average there is relatively strong inward impurity convection ($\langle \zeta_{NC} \rangle_{ped} \sim -(30$–50)) across the pedestal during the inter-ELM periods. However, the time-resolved data shown in figure 16 shows that, during the first ∼10 ms after the pellet-triggered and natural ELMs in the pellet fuelled pulses (, ) there is some tendency for this convection to weaken (and sometimes even reverse) due to the relatively lower $\langle R/L_{n_e} \rangle_{ped}$ following these ELMs. There is hence some tendency for the pacing pellets to reduce the inward W influx just after the ELMs.

In the mantle region, the overall average value of $\langle \zeta_{NC} \rangle_{man} \sim 0.14$ following all of the ELMs is much weaker than that prevailing in the pedestal region ($\langle \zeta_{NC} \rangle_{ped} \sim -(30$–50)). On-average, there is a somewhat higher, positive value of $\langle \zeta_{NC} \rangle_{man} \sim 0.24$ following the pellet triggered ELMs due to the fuelling at the pedestal top by the pellets reducing $\langle R/L_{n_e} \rangle_{man}$. However, after the natural ELMs in the pellet fuelled pulses, there is a slightly negative average value of $\langle \zeta_{NC} \rangle_{man} \sim -1.1$, driving inward impurity convection. This probably arises because of relatively low level of gas fuelling in the pellet fuelled pulses results in a slightly lower n_e,ped than in the gas fuelled pulses and hence a higher value of $\langle R/L_{n_e} \rangle_{man}$, which favours inward impurity convection. Hence, while the ELM pacing pellets do modify the pedestal gradients on-average such as to slightly increase the convection of W (and other impurities) across the pedestal, they also modify the mantle gradients to reduce the screening of these impurities from the plasma core.

Somewhat as an aside to the topic of this paper, the average values of η_e in the pedestal and mantle regions are worthy of note. As was discussed in [8] with respect to the high-power, 3 MA ITER-baseline pulse #92 432, the value of η_e averaged over the steep density gradient region ($\rho_{N,ped} \leqslant \rho_{tor} \leqslant 1.0$) of $\langle \eta_e \rangle_{ped} \sim 2$ as stated in table 7 for the 3.5 MA pulses are similar to those that were found for pulse #92 432, which may indicate that there may be a degree of stiffness of the electron heat transport in the pedestal, predominantly due to the slab branch of ETG turbulence, which is destabilised at a critical $\eta_e \sim \mathcal{O} (1)$. Note that, on-average, there is also an increase in $\langle \eta_e \rangle_{ped}$ during the first ∼10 ms following the ELMs, providing a stronger drive for turbulent electron heat transport at this time.

Turning our attention now to the mantle region ($0.7 \leqslant \rho_{tor} \leqslant \rho_{N,ped}$), the average value of $\langle \eta_e \rangle_{man} \sim 3$–5 is larger than in the pedestal region, which may be consistent with the higher values of η_e required to destabilise the toroidal branch of ETG turbulence at the relatively low values of $\langle R/L_{n_e} \rangle_{man} \sim 5$–10 prevailing in the mantle compared to those in the pedestal region ($\langle R/L_{n_e} \rangle_{ped} \sim \mathcal{O} (-100)$). For further discussion of this topic see section 4 of [8]).

As mentioned in the introduction, sustained H-mode operation of JET-ILW pulses requires fuelling by gas puffing to mitigate the detrimental effect of W impurities sputtered from the divertor targets, predominantly but not exclusively by the extremely high instantaneous powers deposited by the ELMs. The beneficial effect of the gas puffing on this process is illustrated systematically in figure 18.

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Although the physics underlying each step is not always well understood, the underlying mechanism can be explained as follows:

• (a)  
  Effect of increased gas fuelling on ELMs: More gas fuelling typically increases the ELM frequency f_ELM and reduces the ELM energy losses ΔW_ELM (at approximately constant $\langle P_{ELM} \rangle$), resulting in a lower sputtered W source S_W from the divertor targets. A lower W concentration c_W in the SOL then reduces the impurity influx to the confined plasma between ELMs $\Phi_W^{in}$ and the higher ELM frequency flushes more W out again $\Phi_W^{ELM}$. A lower W concentration in the confined plasma then reduces the radiated power $P_{Rad}^{Pl}$, thereby increasing the rate of increase of stored energy dW_pl /dt between the ELMs. This causes p_e,sep to reach the MHD pressure limit faster, triggering the ELMs earlier and thereby increasing their frequency f_ELM . The chain of causality of the effects of increased gas fuelling are illustrated in figure 18(a).
• (b)  
  Effect of increased gas fuelling on pedestal and confinement: Although the effect of the gas fuelling on the inter-ELM pedestal structure is beneficial in terms of further mitigating the W contamination, it also reduces the energy confinement by degrading the pedestal temperature, which reduces the temperature over the whole plasma due to stiffness of core heat transport. An increase in turbulent heat flux across the pedestal due to changes in its structure caused by the gas puffing is now well established as the most plausible explanation for the low pedestal temperature in JET-ILW pulses [10, 12, 14, 56, 57] and this is illustrated schematically in figure 18(b).Increased gas puffing raises the separatrix density n_e,sep , which decreases the density gradient across the pedestal, increasing $L_{n_e}$ and hence η_i,e across the ETB, providing a stronger drive for turbulent heat transport. With the residual power through the ETB $P_{Sep}^{iELM}$ determined by the heating power, radiation and ELM losses, an increase in the heat turbulent heat diffusivity χ_eff must reduce the pedestal temperature T_e,ped .As a consequence of reducing T_e,ped , a higher pedestal density n_e,ped is required for p_e,ped to reach the peeling-ballooning limit at which ELMs are triggered. The lower T_e,ped and higher n_e,ped increases the effective collisionality $\nu_{eff} \propto n_e/T_e^2$ at the pedestal top. This then reduces the density peaking $n_{e,0}/\bar{n}_e$, which is partly driven by a turbulent particle pinch, thereby reinforcing the higher n_e,ped [58].Conversely, less gas fuelling is required with the pellets, resulting in reduced n_e,ped and higher T_e,ped and lower ν_eff , which favours density peaking. This is then further reinforced by the more peaked beam ionisation source resulting from the reduced n_e,ped , which is known to play an important role in peaking the density profile in JET-ILW [59].
• (c)  
  Feedback loops between gas puffing, ELMs and W behaviour: As indicated in figure 18, there is coupling between the changes to the pedestal structure, the ELM behaviour and the W transport, which reinforce the effects of the gas puffing. Firstly, the higher $L_{n_e}$ reduces the magnitude of the inward convection ζ_NC across the ETB, which reduces the W influx $\Phi_W^{in}$ into the confined plasma. Secondly, the lower T_e,ped and higher n_e,ped reduces T_e at the W targets during the ELM crashes, decreasing the incident ion energies and hence the physical sputtering yield and thereby reducing the W source. Also, more gas puffing typically increases f_ELM , flushing more impurities from the plasma ¹⁸ .

We can try to use this insight into the effect of gas puffing on the pedestal and the W flushing by the ELMs to understand the evolution of the high-power, 3 MA baseline-scenario pulse #92 432, which was discussed in detail in section 2.6. A schematic representation of the causality of the underlying mechanisms is shown in figure 19. A breakdown of this mechanism follows:

• (a)  
  Initially, the rate of gas fuelling was probably too low, causing a gradual buildup of the W content, increasing $P_{Rad}^{Pl}$, decreasing dW_pl /dt and hence causing a reduction of the ELM frequency f_ELM (see figure 10).
• (b)  
  In response to the decrease in f_ELM , the plasma control system initiated an increase in the gas puffing rate $\Gamma_{D_2}$, which had the opposite effect to that desired. More gas fuelling raised n_e,ped , consequently increasing $P_{Rad}^{Pl}$, reducing dW_pl /dt and hence further reducing f_ELM , eventually stopping the ELMs entirely.
• (c)  
  Cessation of the ELMs caused n_e,ped to rise faster, resulting in an even faster increase in mantle radiation $P_{Rad}^{man} \propto \langle C_W n_e^2~\rangle_{Man}$, hence strongly reducing $P_{Sep}^{iELM} = P_{l,th} - P_{Rad}^{Pl}$.
• (d)  
  Once $P_{Sep}^{iELM}$ falls sufficiently, this triggers an H/L-transition, which rapidly reduces n_e,ped and increases $R/L_{n_e}$ in the mantle region.
• (e)  
  The increased $\langle R/L_{n_e} \rangle_{man}$ then causes sudden reversal of the neo-classical convection ($\langle \zeta_{NC} \rangle_{man} \lt 0$), driving the W impurities into the plasma core, causing a reduction in T_e,0, a collapse in W_pl , ending the high-performance phase of the pulse.

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Note that this particular pulse does in fact recover from the W accumulation event. The L-mode phase is followed by another period of ELMy H-mode, albeit with higher P_Rad and reduced energy confinement.

The fraction of radiated power $\mathcal{F}_{Rad}$ is higher in the pellet + gas-fuelled pulse #96 713 compared to that in the gas-fuelled pulse #94 980, in spite of the fact that on-average, the level of inter-ELM Be influx $\langle \Gamma_{Be} \rangle$ from the target is comparatively lower (see figures 1(f) and (g)). Although the level of ELM-sputtered W from the targets is lower in in pulse #96 713, the W concentration in the mantle $\langle C_W \rangle_{man}$ is higher than in pulse #94 980 (see figure 11(a)). This implies that the retention [60, 61] and/or prompt re-deposition [3] of the sputtered W in the divertor is less efficient in pulse #96 713, which has a lower (∼45%) gas fuelling rate than that in pulse #94 980.

The process of prompt redeposition of the sputtered W⁰ is due to singly ionized W⁺ ions being redeposited with their first Larmor orbit onto the target. This occurs because the Larmor radius $\rho_{W^+}$ of the heavy ($m_W/m_p \sim 183$) W⁺ ions can be larger than the ionization length L₀ ¹⁹ of the sputtered W⁰ atoms [3]. The fraction of ions redeposited to the target f_dep decreases with an increase of the ratio of ionisation length to the W⁺ Larmor radius $p = L_0/\rho_{W^+}$ according to $f_{dep} \propto 1/(1+p^2)$ [62]. This ratio p decreases with increasing density n_e,t and electron temperature T_e,t at the target. It is hence difficult to predict the effect of increasing the gas puffing on f_dep without complex modelling, e.g. with the kinetic impurity simulation code ERO [63], and knowledge of how n_e,t and T_e,t respond to the changes in fuelling.

The relatively higher ∼×1.5 concentration of W in the pellet + gas fuelled pulse #96 713 compared to that in the gas fuelled pulse #94 980 might also be a sign of reduced retention of the sputtered W in the divertor. Modelling the transport of W (Z_W  = 74), which has many ionisation states, in the SOL plasma is computationally extremely complex. Some insight into the processes involved can be gleaned from inspection of the parallel force balance on the impurity ions, which is stated as equation (1) of [60]. The relevant terms (where I represents impurity ions) are: (1) $m_i n_i n_I \langle \sigma_i v \rangle (U_{\parallel,i} - U_{\parallel,I})$ representing friction with other ion species; and (2) $\alpha_{I,i} Z_I^2~n_I \nabla_\parallel T_I$ and $\alpha_{I,e} Z_I^2~n_I \nabla_\parallel T_e$ representing thermal forces due to the parallel temperature gradients of the ions and electrons. Here, $U_{\parallel,i/I}$ are the average parallel flow speeds of the respective ions i/I, $\langle \sigma_i v \rangle$ is the momentum exchange rate between ions and impurities and the α_I,i/e are coefficients for the ion/electron thermal forces.

It might be expected that, with an increased gas fuelling rate Γ_D2,gas into the main chamber, that with the increased flow of D⁺ ions through the SOL to the divertor, the parallel friction force (1) might increase, thereby enhancing the retention of the W impurities in the divertor. A higher parallel temperature gradient in the SOL would, however, act to reduce the impurity retention by increasing the thermal forces (2), which are directed away from the target. Without detailed modelling with a SOL transport code, it is not easy to determine how $\nabla_\parallel T_e$ will change along the SOL in response to changes in the fuelling and how these changes will influence the impurity retention.

In conclusion, it may well be that increased W retention and also an increase in the prompt redeposition fraction with a higher n_e,t at higher fuelling rate might explain the lower W concentration in pulse #94 980 cf that in pulse #96 713. Exhaustive modelling, e.g. with a SOL transport code such as SOLPS [64] or the latest ITER version SOLPS-ITER [65], is required to elucidate these effects further.

Finally, it is worth noting that, if there is a balance between the incident Be flux to the target and that sputtered during the inter-ELM periods, the comparatively lower intra-ELM Be influx in pulse #96 713 implies, a lower rate of Be sputtering by the ELMs from the main chamber walls, which are faced with Be tiles. The ELM-sputtered Be influx from the walls might be expected to decrease with a lower neutral gas density in the plasma-wall interspace, resulting from reduced gas puffing into the main chamber in pulses with pellet + gas fuelling.