Divertor, scrape-off layer and pedestal particle dynamics in the ELM cycle on ASDEX Upgrade

Figure 4 presents ELM synchronised time traces of the SOL current and the ${{\rm{D}}}_{\alpha }$ emission at the inner and outer divertor target, measured in the studied discharge interval. The SOL current consists of Pfirsch–Schlüter current contributions, ohmically driven currents and thermoelectric currents, that originate from temperature differences of the inner and outer divertor plasma. In the standard ASDEX Upgrade magnetic field configuration, like the investigated plasma was performed in, the current flows through the plasma SOL from the outer to the inner target. For this reason the measurements in the inner and outer targets have opposite signs. The ELM crash appears as large burst in the SOL current and has a duration of approximately 1.5 ms. Then a period of reduced SOL current is observed from 1.5 to 7.0 ms relative to the ELM onset especially at the outer target. During this phase the ${{\rm{D}}}_{\alpha }$ emission at the outer target has a second peak that is of similar magnitude as the observed emission during the ELM crash. This is characteristic for a regime of high recycling [10]. For times larger than 7 ms after the ELM onset the ${{\rm{D}}}_{\alpha }$ emission lowers to its pre-ELM values, indicating an attached divertor plasma as it will be discussed later. At the inner divertor target the ${{\rm{D}}}_{\alpha }$ evolves differently than at the outer divertor. The large pre-ELM ${{\rm{D}}}_{\alpha }$ emission indicates that neutral radiation is already present in front of the target and that the inner target is at least partially detached. During the ELM crash the ${{\rm{D}}}_{\alpha }$ emission is reduced, which can be interpreted as re-attachment of the inner divertor target since a larger amount of hot particles flows to the divertor. Another effect that can also be related to the reduction of ${{\rm{D}}}_{\alpha }$ is the movement of the strike line during the ELM crash. This is presented in figure 5, where the location of the strike line (top) in divertor coordinates (S) as well as j_sat, measured by LPs, for locations between 0.5 and 2.5 cm outside of the strike line position (${\rm{\Delta }}{S}$) in the SOL (bottom) are plotted. The S coordinate increases from the inner divertor target across the dome towards the outer divertor target. The ELM crash induced movement of the strike line in the inner divertor is roughly 4 cm in downward direction, while the movement at the outer divertor is about 2 cm. The movement of the inner strike line can also lead to an reduction of the ${{\rm{D}}}_{\alpha }$ emission at the inner divertor if the radiation front moves out of the view of the ${{\rm{D}}}_{\alpha }$ detector. Nevertheless, j_sat at the inner divertor target indicates enhanced particle fluxes to the target and therefore, re-attachment. After the ELM crash the ${{\rm{D}}}_{\alpha }$ emission in the inner divertor increases (figure 4(a), 1.5–2.5 ms relative to the ELM onset). During this time also the strike line moves back towards its pre-ELM location (figure 5(a)). In this phase the ${{\rm{D}}}_{\alpha }$ emission as well as j_sat is reduced, indicating a post-ELM detachment of the inner target. Then ${{\rm{D}}}_{\alpha }$ decreases slightly while j_sat increases steadily during the high recycling period of the outer divertor, where also enhanced j_sat is observed at the outer target (see figure 5(b)). In this phase the inner target fully detaches and the ${{\rm{D}}}_{\alpha }$ radiation front moves upwards towards the midplane and therefore, out of the lines of sight of the ${{\rm{D}}}_{\alpha }$ detector (see figure 4(a)). Approximately 7.5 ms relative to the ELM onset the ${{\rm{D}}}_{\alpha }$ emission jumps to pre-ELM values indicating, that the radiation front moves quickly towards the target again.

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A more detailed view on the state of the inner and outer divertor targets throughout the ELM cycle is given by divertor LP measurements of n_e and T_e. These are presented in figure 6 as ELM synchronised plots. The data is superimposed for locations between 0.5 cm and 2.5 cm outside of the strike line position (${\rm{\Delta }}{S}$) in the SOL. Before the ELM onset the inner divertor is detached, T_e is below 5 eV. During the ELM crash T_e and n_e are increasing, indicating re-attachment of the inner divertor. After the ELM (between 2.5 and 7.0 ms relative to the ELM onset) the fluxes on the inner divertor target are reduced, limiting an accurate n_e and T_e evaluation. Nevertheless, the reduced fluxes indicate that less plasma is reaching the inner divertor. At the outer divertor target the plasma is attached in the pre-ELM phase and T_e is roughly 15–20 eV. When the ELM crash starts (between 0.0 and 0.5 ms relative to the ELM onset) a pulse of hot plasma ('electron heat pulse'; T_e larger than 30 eV) is observed, that is followed by phase of larger n_e (0.5–2.0 ms relative to the ELM onset). After the ELM crash, the plasma T_e at the outer divertor target is approximately 5–10 eV during the period of high recycling. It is accompanied by relatively high plasma n_e at the outer target, which reaches a similar magnitude as the n_e peak caused by the ELM crash.

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In summary, the divertor conditions of the presented discharge interval evolve throughout the ELM cycle as follows: Prior to the ELM crash, the inner divertor is detached, whereas the outer divertor is attached. During the ELM crash, the inner divertor attaches. Immediately after the ELM crash, the inner divertor fully detaches on similar timescales as the outer divertor moves to a regime of high neutral recycling.

As shown in section 3.1 the ELM crash induces a lot of dynamics to the divertor conditions. Since the divertor plasma is coupled to the SOL plasma at the midplane, the dynamics of the SOL n_e profiles at the HFS and LFS are studied in the following. Further, the timescales of their dynamics throughout are related to the evolution of the divertor conditions. The SOL n_e profiles at the HFS and LFS midplane are measured by reflectometry [30] and at the LFS additionally by the LIB. ELM synchronised profiles are presented for three different time intervals relative to the ELM onset in figures 7 (a)–(c). The superimposed reflectometry profiles, which were measured in the corresponding time interval relative to the ELM onset, are fitted by a spline curve. The LFS reflectometry profiles are shown in dark blue, whereas the HFS profiles are shown in dark red. For comparison the LIB n_e profiles, which are also averaged in the corresponding time interval relative to the ELM onset, are shown in blue. Both independent LFS diagnostics measure similar SOL n_e profiles in all time intervals relative to the ELM onset. In the pre-ELM phase the HFS and LFS SOL n_e profiles are similar and below $2.0\times {10}^{19}\,{{\rm{m}}}^{-3}$. A large asymmetry is found in the post-ELM phase in figure 7(b), when the inner divertor target is fully detached and the HFSHD is present, which in this case reaches up to the midplane causing the strong difference of the HFS and LFS SOL n_e profiles. Similar asymmetries and behaviour of the inner divertor have been found also in L-mode [30]. The HFS-LFS asymmetry decreases, when the HFSHD is reduced as seen in figure 7(c).

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The dynamics of the SOL n_e profiles for HFS and LFS are presented in figure 8. On four radial positions from near to far SOL, n_e is tracked. After the ELM crash the HFS n_e at the tracked positions is larger than the cut-off n_e for the reflectometer. The decay of the HFSHD has a similar timescale as the measurements in the divertor would suggest. During the presence of the high recycling regime in the outer divertor also an increased n_e in the LFS SOL is measured. A similar observation was previously named the SOL n_e shoulder and its formation is suggested to be associated to a change of the SOL transport regime [36].

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In this section it was shown that a large asymmetry between HFS and LFS SOL n_e profile exists at the midplane, when the inner divertor is fully detached. Under these conditions the HFSHD expands up to the HFS midplane. Further, it has been described in detail, that the HFSHD is strongly impacted by ELMs, implying that it is changing throughout the ELM cycle and therefore, not stationary. The evolution of the HFSHD can impact on the inter-ELM recovery of the n_e pedestal, which is studied in the following.

The recovery of the n_e pedestal usually takes of the order of less than 2 ms. This short timescale indicates that lost particles due to the ELM are immediately replaced after the ELM crash. A larger neutral particle source caused by neutralisation of the plasma, which is expelled by the ELM crash, the appearance of the HFSHD or a change of the particle transport in the pedestal are possible reasons to explain the short recovery timescale of the n_e pedestal. Figure 9 presents ELM synchronised frequency histograms of radial magnetic field fluctuations ($\partial {B}_{{\rm{r}}}/\partial t$) at the LFS midplane, LFS midplane neutral fluxes measured by the manometer M 17 (see figure 3), which were temporally shifted by −1.5 ms, n_e and ${\rm{\nabla }}{n}_{{\rm{e}}}$ at four radial positions in the confined plasma. The temporal shift of the neutral fluxes was applied to align the increase of the fluxes due to the ELM crash with the actual ELM onset. Because of the finite volume and the small aperture of the manometer, an intrinsic response delay of roughly 1.5 ms is estimated, in which the gas streams into the manometer and fills its volume.

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The $\partial {B}_{{\rm{r}}}/\partial t$ at the LFS midplane (figure 9(a)) shows low activity between 1.5 and 3.0 ms relative to the ELM onset for all frequencies. During this period the n_e pedestal and, respectively, ${\rm{\nabla }}{n}_{{\rm{e}}}$ in the steep gradient region recover (figure 9(d)). Remarkably, the steepening of the gradient is not solely attributed to a rise of the n_e pedestal but also related to a n_e decrease in the confined region close to the separatrix (figure 9(c)), i.e. at ${\rho }_{\mathrm{pol}}=0.99$. This is an indication for a reduced particle flux across the pedestal region. The neutral fluxes at the LFS midplane (figure 9(b)) stay high while the n_e pedestal recovers. It is unknown, whether in addition to the time delay, also a temporal smearing of the measured neutral fluxes occurs. This would lead to a longer detected period of higher neutral fluxes. However, if present, a similar timescale as the one of the intrinsic response delay could be assumed, which would be in the region of 1 ms. An indication that the fast n_e pedestal recovery is not directly linked to the evolution of the source is that between 3.0 and 5.0 ms relative to the ELM onset, the neutral flux slowly decays. In this period neither ${\rm{\nabla }}{n}_{{\rm{e}}}$ nor the pedestal top n_e evolution are affected by this decrease of the source. For this reason the n_e pedestal recovery is not directly related to the evolution of the source, especially the prompt saturation of the $\max (-{\rm{\nabla }}{n}_{{\rm{e}}})$ at 3.0 ms relative to the ELM onset. This will be studied in detail in section 4.2.

As an asymmetry between HFS and LFS during the ELM crash of the n_e pedestal has been observed on JT-60U [37], the fast recovery of the n_e pedestal could be also caused by a symmetrisation of the HFS and LFS n_e pedestal. Unfortunately, this can not be directly addressed using experimental measurements since the n_e pedestal recovery at the HFS can not be measured because of the presence of the HFSHD in the SOL, which 'obscures the view on the pedestal' for the HFS reflectometer. Nevertheless, the timescale of the symmetrisation process of HFS and LFS n_e in the confined plasma is determined by the parallel connection length and the ion sound speed. For the post-ELM parameters of this discharge interval this timescale is around 200 μs, which is definitively faster than the observed n_e pedestal recovery time.

Temporally correlated to the stagnation of the n_e pedestal recovery is the onset of medium frequency fluctuations in the range of 30–150 kHz approximately 3.0 ms relative to the ELM onset (see figure 9(a)). These fluctuations could cause an additional particle flux across the pedestal, leading to the saturation of $\max (-{\rm{\nabla }}{n}_{{\rm{e}}})$ and causing the high recycling phase in the outer divertor. Roughly 7.5 ms after the ELM onset the $\max (-{\rm{\nabla }}{T}_{{\rm{e}}})$ is clamped and high frequency fluctuations ($\gt 200\,\mathrm{kHz}$) set in. The period between 3.0 and 7.5 ms is also the timescale of the high recycling in the outer divertor and the HFSHD is present. These two effects are not temporally correlated to the establishment of ${\rm{\nabla }}{n}_{{\rm{e}}}$ and the fast recovery of the n_e pedestal, which already takes place before. The experimental data suggest that a reduced particle flux is connected to the fast recovery of the n_e pedestal or vice versa an increased particle flux across the pedestal causes the stagnation of the n_e recovery as well as the second ${{\rm{D}}}_{\alpha }$ peak in the divertor.

A simple estimation of the particle flux (Γ) across the pedestal can be done by applying the continuity equation:

$$\begin{eqnarray}&&\displaystyle \frac{\partial {n}_{{\rm{e}}}}{\partial t}=\displaystyle \frac{\partial {\rm{\Gamma }}}{\partial V}+\alpha {S}_{{\rm{i}}}.\end{eqnarray} \tag{ 1 }$$

The particle flux into the volume ($\partial {\rm{\Gamma }}/\partial V$) and ionisation source (${S}_{{\rm{i}}}$) including the proportionality factor (α) determine the temporal evolution of electron density recovery rate ($\partial {n}_{{\rm{e}}}/\partial t$). The evolution of n_e at certain positions from figure 9(c) can be used to determine $\partial {n}_{{\rm{e}}}/\partial t$. Figure 10(a) presents $\partial {n}_{{\rm{e}}}/\partial t$ at four radial positions in the pedestal region. ${S}_{{\rm{i}}}$ profiles are determined using the 1.5D neutral transport code KN1D [38]. Of course a spatial 1D treatment of the neutral distribution is a very simplistic picture in a toroidal plasma. But the LFS main chamber has been found to be the main region for neutral fuelling [8], especially when the HFSHD is present. The neutral flux at the LFS midplane as shown in figure 9(b) was used as condition at the wall and the n_e profiles of the LIB diagnostic, which are measured at the LFS served as input. Since there are no midplane SOL T_e measurements with the required temporal resolution available, the SOL T_e was parametrised by an exponential decay with a characteristic decay length according to the H-mode scaling for ASDEX Upgrade [39]. With this procedure a possible variation of the SOL T_e throughout the ELM cycle is not considered. Further, the SOL T_i is assumed to be equal to T_e, which is reasonable in the sense that the cross sections of ion-neutral collisions do not have strong dependencies on T_i in the relevant T_i range. Another particle source, providing particles to the confined plasma region is the neutral beam injection, which was applied. The injected particle particle rate was $5.7\times {10}^{20}\,{\rm{e}}\,{{\rm{s}}}^{-1}$, which is roughly a factor of ten smaller than the applied external gas puff. This already points into the direction that the effect of beam fuelling is of secondary order in the presented case. The amount of beam fuelled particles per volume, assuming roughly an equal distribution over the whole plasma volume of $12.5\,{{\rm{m}}}^{3}$, is even two orders of magnitude smaller in comparison to the estimated ${S}_{{\rm{i}}}$ in the pedestal region. The evolution of the ${S}_{{\rm{i}}}$ profiles is presented in figure 10(b). They are mainly determined by the evolution of the midplane neutral fluxes, which strongly increase after the ELM crash between 2.5 and 6.0 ms relative to the ELM onset. When the SOL n_e is higher, e.g. during and shortly after the ELM, only few neutrals can penetrate into the confined plasma region, leading to a reduction of ${S}_{{\rm{i}}}$.

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To adapt the ${S}_{{\rm{i}}}$ profiles, α is utilised. In the pre-ELM phase between −4 and −1 ms relative to the ELM onset α can be determined since $\partial {n}_{{\rm{e}}}/\partial t$ is close to zero and the pedestal gradients are clamped. Therefore, Γ can be chosen in such a way that the diffusion coefficient (D) is in agreement with the ones that are observed in H-mode [35]:

$$\begin{eqnarray}&&{\rm{\Gamma }}=-\displaystyle \frac{\partial V}{\partial {\rho }_{\mathrm{pol}}}\langle {({\rm{\nabla }}{\rho }_{\mathrm{pol}})}^{2}\rangle D\displaystyle \frac{\partial {n}_{{\rm{e}}}}{\partial {\rho }_{\mathrm{pol}}}.\end{eqnarray} \tag{ 2 }$$

The assumption of solely diffusive transport in the steep gradient region is rather rough and based on previous results of modelling the L–H transition [40]. Here, a small pinch velocity could not be excluded, but the transport at the edge was dominantly diffusive. Nevertheless, within this work the assumption of diffusive transport is solely used to determine α. A radially dependent D profile linearly increasing from $0.10\,{{\rm{m}}}^{2}\,{{\rm{s}}}^{-1}$ at the separatrix to $0.25\,{{\rm{m}}}^{2}\,{{\rm{s}}}^{-1}$ at the pedestal top is assumed between −4.0 and −1.0 ms relative to the ELM onset, which results in a continuous profile of α ranging from 1.5 at the separatrix to 15.0 at the pedestal top. Within the applied approach, α also scales ${S}_{{\rm{i}}}$ for effects, which were not incorporated in the neutral modelling, e.g. toroidal geometry or reflected, non-thermal neutrals from the wall, which lead to a higher source towards the pedestal top.

Having α fixed throughout the ELM cycles, the temporal evolution of $\partial {\rm{\Gamma }}/\partial V$, shown in figure 10(c), is determined from the continuity equation (equation (1)) at every timestep. The ELM onset leads to an outward burst of plasma particles. After the ELM crash the particle flux across the pedestal is strongly reduced. During this period $\partial {n}_{{\rm{e}}}/\partial t$ is largest for the pedestal top and no magnetic activity is present in figure 9(a). When ${S}_{{\rm{i}}}$ increases after the ELM crash, then also $\partial {\rm{\Gamma }}/\partial V$ goes up since $\partial {n}_{{\rm{e}}}/\partial t$ is already reduced. This is another indication that the fast recovery of the n_e pedestal is more related to a reduced particle flux in the gradient region than to an increased particle source. When ${S}_{{\rm{i}}}$ decreases roughly 5.0 ms after the ELM onset, $\partial {\rm{\Gamma }}/\partial V$ is also reduced, indicating the strong coupling between these quantities. Since the magnetic activity in the medium frequency range is only slightly reduced in this period, the reduction of $\partial {\rm{\Gamma }}/\partial V$ cannot be related to a change of turbulent transport in the pedestal.