I-mode pedestal relaxation events at ASDEX Upgrade

I-mode pedestal relaxation events at ASDEX Upgrade D. Silvagni1,2, T. Eich1, T. Happel1, G. F. Harrer3, M. Griener1, M. Dunne1, M. Cavedon1, M. Faitsch1, L. Gil4, D. Nille1, B. Tal1, R. Fischer1, U. Stroth1,2, D. Brida1, P. David1, P. Manz1,2, E. Viezzer5, the ASDEX Upgrade teamaand the EUROfusion MST1 teamb 1Max-Planck-Institut f¨ur Plasmaphysik, Boltzmannstr. 2, 85748 Garching, Germany 2Physik-Department E28, Technische Universit¨at M¨unchen, James-Franck-Str. 1, 85748 Garching, Germany 3Institute of Applied Physics, TU Wien, Fusion@¨ OAW, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria 4Instituto de Plasmas e Fus˜ao Nuclear, Instituto Superior T´ecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal 5Dept. of Atomic, Molecular and Nuclear Physics, University of Seville, Avda. Reina Mercedes, 41012 Seville asee author list of H. Meyer et al. 2019 Nucl. Fusion 59 112014 bsee author list of B. Labit et al. 2019 Nucl. Fusion 59 086020 E-mail: [email protected] Abstract. The I-mode confinement regime can feature small edge temperature drops that can lead to an increase in the energy deposited onto the divertor targets. In this work, we show that these events are associated with a relaxation of both electron temperature and density edge profiles, with the largest drop found at the pedestal top position. The relative energy loss is about 1 %, and is thus lower than that of type-I ELMs for the same pedestal top collisionality. Stability analysis of edge profiles reveals that the operational points are far from the ideal peeling-ballooning boundary. Also, we show that these events appear close to the H-mode transition in the typical I-mode operational space in ASDEX Upgrade, and that no further enhancement of energy confinement is found when they occur. Moreover, scrape-off layer transport during these events is found to be very similar to type-I ELMs, with regard to timescales (≈800 µs), filament propagation, toroidally asymmetric energy effluxes at the midplane and asymmetry between inner and outer divertor deposited energy. In particular, the latter reveals that more energy reaches the outer divertor target. Lastly, first measurements of the divertor peak energy fluence are reported, and projections to ARC – a reactor that could potentially operate in I-mode – are drawn. 1. Introduction The I-mode is an attractive operational regime for magnetically confined fusion reactors. It is characterized by the high-energy confinement of H- mode and the relatively poor particle confinement of L-mode [1, 2]. As a consequence, a temperature pedestal is formed at the plasma edge, while density edge profiles remain similar to those in L-mode. In this way, the I-mode simultaneously combines the desired properties of L-mode and H-mode plasmas, namely reduced impurity and helium ash accumulation in the plasma core, and large fusion energy production. Moreover, the I-mode is free of type-I edge localized modes (ELMs), as its pedestal is ideal peelingballooning stable [3, 4]. It is generally recognized that a large number of type-I ELMs will not be acceptable for ITER and next-step fusion devices [5]. Hence, for these reasons the I-mode is considered as a possible operational regime for a fusion power plant. However, I-mode can feature small edge temperature drops that can ultimately lead to a consistent increase in the energy deposited onto the divertor targets. These I-mode “ELM-like” events were first observed in Alcator C-Mod [3]. Similar events were also seen in DIII-D [6] and more recently in ASDEX Upgrade (AUG). Understanding the appearance and the amount of energy expelled by these events is fundamental for the I-mode candidature as an operational regime in a fusion power plant. It is worth clarifying that these events exhibit macroscopic differences with respect to the previously studied I-mode bursts in AUG [7, 4]. Unlike the others, the events considered here exhibit ELM-like timescales, a characteristic frequency of appearance, and an ELM-like divertor signature. In addition, they cause a full relaxation of edge profiles, observed in both the electron temperature and electron density (no statement can be made with regard to the ion temperature due to diagnostic time resolution restrictions). For these reasons, we will hereinafter refer to them as I-mode pedestal relaxation events (PREs). In this work, we carry out an extensive investigation of the I-mode pedestal relaxation events that have recently been observed in AUG, shedding light on their appearance, characteristics and divertor heat loads. In section 2, an illustrative I-mode discharge with two phases – one with and another without PREs – is shown. The appearance of I-mode PREs in the typical AUG I-mode operational space (Ip= 1 MA, Bt=−2.5 T) is also discussed. In section 3, the temporal evolution of the edge profiles during I- mode PREs is presented, along with their associated energy and particle losses. This section also features a MHD stability analysis of edge profiles during these events. A broad analysis of scrape-off layer (SOL) transport during PREs is carried out in section 4. In particular, the characteristic SOL temporal evolution, filament propagation and their toroidal asymmetric origin are discussed. In section 5, divertor transient heat loads induced by PREs are investigated, with a focus on energy deposition asymmetries between inner and outer divertor targets and divertor peak energy fluence measurements. In this section, projections to ARC [8] are also drawn. Lastly, in section 6, the main conclusions are outlined. 2. Appearance in the typical AUG I-mode parameter range I-mode plasmas are commonly achieved by using magnetic configurations with the ion ∇Bdrift pointing away from the active X-point, i.e. the socalled unfavorable configuration in terms of H-mode access. In AUG, plasma discharges in the unfavorable configuration are more frequently performed in the upper single null (USN) configuration. This is because the upper divertor tiles are not toroidally tilted, allowing more flexibility in the magnetic field line direction (see e.g. [9]). Figure 1 shows an I-mode USN discharge where PREs occur. This plasma is in the typical AUG I-mode parameter range, i.e. Ip= 1 MA, Bt=−2.5 T and with a line-averaged core electron density of about 5 ×1019m−3(see panel (c)). The plasma is heated via a constant 1.5 MW of electron cyclotron resonance heating (ECRH) power and (modulated) co-current neutral beam injection (NBI) power (see panel (a)). The NBI power is ramped linearly until t= 2 s when the NBI feedback control on the βpol value takes over (panel (b)), similarly to [10]. The βpol is defined as p/(B2 pol/2µ0), where pis the average plasma pressure and Bpol is the average poloidal magnetic field strength. At t= 2.02 s the transition from L to I-mode occurs, which is seen from the sudden increase in the electron temperature at ρpol = 0.95 and from the increase in H98, i.e. the energy confinement time normalized to the IPB98(y,2) scaling law [11] (panel (d)). In addition, the weakly coherent mode (WCM) – a characteristic feature of I-mode edge turbulence [12, 13, 14, 15] – appears in the spectrogram of the radiation temperature (panel (e)) measured at ρpol = 0.99 from electron cyclotron emission (ECE). Simultaneously, as the measured βpol becomes larger than the requested one, the NBI power is reduced to match the two values. This reduction in the NBI power is crucial for achieving stationary NBI-heated I-mode plasmas in AUG, as has already been shown in [10]. Later in the discharge, the request value of βpol is increased in a stepwise manner; both βpol and the pedestal top electron temperature rise accordingly, 2 Figure 1: Appearance of I-mode PREs in the typical AUG parameter range. (a) ECRH (blue) and NBI (black) power. (b) Requested βpol (red) and measured value (black). (c) Line-averaged core electron density. (d) Electron temperature at ρpol = 0.95 (purple) and H98 (black). (e) Spectrogram of ECE radiation temperature measured at ρpol = 0.99. (f) Radiation measured by a diode bolometer with line of sight in the upper divertor region. (g) Heat flux onto the upper outer divertor target. Panels (h), (i) and (j) show a magnification of the pedestal top electron temperature, divertor radiation and outer divertor heat flux, respectively, in two different time windows with and without PREs. Panels (k), (l) and (m) show a magnification of the pedestal top electron temperature, the ˙ Bθand ˙ Brsignal measured by magnetic pick-up coils during an I-mode PRE. 3 Figure 2: Left: Electron temperature vs. electron density (both evaluated at ρpol = 0.95) of AUG L-mode, I-mode and H-mode discharges at Ip= 1 MA and Bt=−2.5 T. For n95 e≈4×1019 m−3, I-mode PREs appear just before the I-H transition. Dashed lines indicate isobars. Right: H98 against electron pressure at ρpol = 0.95. I-mode discharges with and without PREs can reach H98 = 1. while the electron density stays constant. At t= 4.3 s the transition to H-mode takes place, which can be seen from the simultaneous rise of both the pedestal top electron temperature and the line-averaged electron density. Also, the WCM disappears from the edge electron temperature spectrogram when the H-mode begins. In AUG, I-mode PREs appear before the I-H transition (in this case when βpol ≈0.58 −0.61). This can be seen by looking at the radiation measured with an AXUV diode bolometer [16] having a line of sight in the upper divertor region (panel (f)). The radiation is characterized by several spikes in this phase and the heat flux onto the upper outer divertor inferred from infrared cameras [17] exhibits transient rises (panel (g)). Also, when I-mode PREs appear, larger low frequency fluctuations (<50 kHz) w.r.t. a typical I-mode without PREs (see e.g. #36233 at 2.5 s) are observed in the spectrogram of the edge radiation temperature. A clearer view of I-mode PREs is shown in the magnification in the bottom right panel of Fig. 1. The pedestal top electron temperature drops during these events (panel (h)). The plasma expelled from the confined region enters the SOL and reaches the divertor region, causing a strong increase in the radiation signal (panel (i)). Ultimately, it hits the divertor target, leading to a substantial increase in the divertor heat fluxes (panel (j)). For comparison, a magnification of the same time traces of an I-mode without PREs is shown in the bottom left panel of Fig. 1. The pedestal top electron temperature is rather constant and does not exhibit large drops. This is reflected in the divertor radiation and heat flux values that do not change substantially. Additionally, panels (l) and (m) show the temporal derivative of the poloidal and radial component of the magnetic field measured by magnetic pick-up coils during an I-mode PRE. After the PRE onset (indicated by a vertical dashed line), both the poloidal and radial component of the magnetic field are perturbed. Moreover, no precursor oscillations are detected by magnetic pick-up coils before the onset of PREs, marking a difference with type-I, type-II and type-III ELMs, which are characterized by detectable magnetic precursors [18, 19, 20]. Figure 2 (a) shows the AUG I-mode discharges obtained at Ip= 1 MA and Bt=−2.5 T in the Te-neoperational space. Also L-mode and H- mode discharges obtained at the same plasma current and toroidal magnetic field are plotted. Electron temperature and density at ρpol = 0.95 have been obtained through integrated data analysis (IDA) [21], which combines different diagnostics measurements (such as edge and core Thomson scattering, electron cyclotron emission radiometers and DCN interferometry). I-mode with PREs appear only in a small portion of the Te-nediagram, namely around the isobar at 4 kPa for 3 ×1019 < n95 e<5×1019 m−3. This isobar lies very close to the I-H transition. Figure 2 (b) shows the same database plotted in the H98-p95 espace, where p95 eis the electron pressure at ρpol = 0.95. When I-mode PREs appear, no substantial enhancement of H98 is observed with increasing p95 e, i.e. I-mode discharges with and without PREs can reach high H98 (≃0.8 −1.0). This indicates that in AUG stationary and high-confinement I-mode plasmas without PREs can be regularly achieved. At this stage, it is not clear whether PREs are present in I- mode at higher densities. For n95 e≈2.4×1019 m−3, which is close to the lowest n95 eachieved in I-mode 4 (n95 e= 2.0×1019 m−3), I-mode PREs have not been found at 1 MA/2.5 T. Density and current dependence of I-mode PREs will be subject of future research at AUG. 3. Edge profiles evolution, losses and stability 3.1. Temporal evolution Thanks to the βpol NBI feedback control, stationary I-mode discharges with several PREs have been obtained. Figure 3 shows the time trace of different quantities during such an I-mode discharge (an USN plasma with Ip= 1 MA and Bt=−2.5 T, see e.g. [4]). The heating power (panel (a)) is a mixture of constant ECRH power and modulated NBI power, with the latter feedback controlled on the requested βpol value (in this case 0.61, see panel (b)). Both the core and edge line-averaged electron density (panel (c)) are constant in this phase. The WCM is present during the entire I-mode and it peaks at around 75 kHz, as can be seen in the spectrogram of the reflectometry signal [22] detected at ρpol ≃0.98 (panel (d)), which is a measure of electron density fluctuations. The divertor radiation measured by diode bolometers with line of sight in the upper divertor region is used in this work as a PRE monitor, as it shows a clear peak during each PRE event (panel (e)). The frequency of occurrence of I- mode PREs ranges between 100 and 400 Hz (panel (f)) in this discharge. The constant plasma parameters and PRE behavior found in this I-mode discharge allowed us to obtain the conditionally averaged temporal evolution of edge electron temperature and density profiles during PREs. Fast measurements of electron density were obtained from DCN interferometry [23] and lithium beam emission spectroscopy (Li-BES) [24, 25], while the electron temperature was measured with electron cyclotron emission (ECE) radiometers [26]. These diagnostics measurements were combined through integrated data analysis (IDA) [21], which reconstructs electron temperature and density profiles in the framework of Bayesian probability theory with a time resolution of 0.1 ms. The reconstructed IDA temperature profiles have separatrix temperatures around 60 −80 eV, which is the typical I-mode separatrix temperature at AUG measured by the edge Thomson scattering (TS) system [27]. Similar separatrix temperatures are also obtained applying the two-point model [28]. In this work, Li-BES data during each PRE were corrected by subtracting the enhanced passive radiation observed during the PRE phase, with the same method used in [29] to analyze the type-I ELM cycle. For details refer to [29]. Hereinafter, the time synchronization of each PRE was obtained using a diode bolometer channel with line- Figure 3: Stationary I-mode discharge with PREs. (a) ECRH (red) and NBI (gray) heating power. The solid black line is the averaged NBI power. (b) Requested βpol (red) and measured value (black). (c) Line-averaged core (black) and edge (red) electron densities. (d) O-mode reflectometry homodyne signal spectrogram caused by density fluctuations at ne= 2.4 ×1019 m−3, i.e. ρpol ≃0.98. (e) Radiation in the upper divertor region. (f) Frequency of PREs. of-sight in the upper divertor region, as it has been found to be the best PRE monitor signal in USN plasma discharges. Then, different plasma quantities were conditionally averaged using the above-mentioned time synchronization in the time window between tstart = 5.5 s and tend = 6.47 s. Only PREs occurring when Li-BES was switched on are considered, giving a total number of 105 PREs. Figure 4 shows the time evolution of conditionally averaged electron temperature, density and pressure evaluated around the temperature pedestal top position, i.e. ρpol = 0.94. Error bars represent the 50% confidence interval of the 105 events analyzed. All quantities are normalized to the value assumed at the PRE onset. The relative drop of the electron density is about 7 %, whereas the electron temperature reduces by 12 %. As a consequence, the electron pressure decreases by about 18 % during the PRE. The relative drop of the pedestal top electron temperature and density during I-mode PREs in #36247 is lower than the corresponding reduction during type-I ELMs, which ranges between 20 and 50 % (for the electron temperature) and 5 Figure 4: Temporal evolution of conditionally averaged electron density (a) temperature (b) and pressure (c) at ρpol = 0.94 (i.e. around the electron temperature pedestal top position). Each quantity is normalized to its value at the PRE onset. between 10 and 40 % (for the electron density) across different devices [29, 30, 31, 32]. It is also worth noting that the electron temperature and density exhibit different recovery times: 2.5 ms after the PRE onset, the electron density is back to its value before the PRE, while the electron temperature has not recovered yet. The different recovery time of pedestal top electron density and temperature is a typical feature of the type-I ELM cycle, as reported in [33, 31, 29] and it has been shown to be related to the different recovery times of the electron temperature and density pedestal gradients during the ELM cycle. Figure 5 shows a comparison of the electron density (panel (a)), temperature (panel (b)) and pressure (panel (c)) radial profiles before and 0.6 ms after the PRE onset. The envelopes around each profile represent the 50 % confidence interval of the averaged profiles. The error envelopes of the electron density profiles are larger at the pedestal top because at that position the lithium beam signal is weaker. After 0.6 ms the electron density profile shows a decrease in the edge density gradient, with the density for ρpol <0.98 reducing and the SOL density increasing. This results in the formation of a pivot point around ρpol = 0.99. The electron density at the pivot point is approximately equal to half of the density at ρpol = 0.95. Both the aforementioned features are similar to what happens during type-I ELMs in AUG [34]. The reconstructed IDA electron temperature radial profile during PRE suffers from the so-called ECE “shinethrough” effect at the plasma edge [35], which makes the evaluation of electron temperature edge gradients around the separatrix challenging in this particular case. For this reason the pivot point of the electron temperature profiles cannot be evaluated. Nonetheless, outside the “shine-through” region (shaded gray area in Fig 5 (b)), ECE data are reliable, as they display very good agreement with TS data. In this region (ρpol <0.98), the electron temperature shows a clear reduction after the PRE onset, as it is observed for the density. Additionally, the bottom panels of Fig. 5 show the radial profiles of the electron density (panel (d)), temperature (panel (e)) and pressure (panel (f)) collapses, defined as the profile difference before and after the PRE. The electron density, temperature and pressure collapses show their maximum around ρpol = 0.95, i.e. around the I-mode electron temperature pedestal top position. From Fig. 5 the PRE profile affected depth can be evaluated, i.e. the distance between the pivot point and the inner radial point where no substantial difference between before and after PRE profile is detected. The PRE affected depth is about 0.2 in terms of normalized poloidal flux radius and 10 cm in terms of radial distance, similar to the ELM affected depth in AUG [36], JET [37], D-IIID [38] and JT-60U [39]. 3.2. Energy and particle losses Knowing the radial profiles’ temporal evolution, the I- mode PRE energy and particle losses can be calculated, as can the convective and conductive components of the energy loss. The PRE energy and particle losses are defined as: ∆WPRE =3 2Z∆pdV(1) ∆NPRE =Z∆nedV. (2) Energy losses are normalized either to the total energy content of the plasma WMHD (which is evaluated from the reconstructed MHD equilibrium) or to the pedestal energy content, defined as Wped = 3/2ppedVplasma. Particle losses are usually normalized to the pedestal particle content, defined as Nped =ne,pedVplasma. A previous multi-machine study on type-I ELMs revealed that the relative ELM energy losses scale with the pedestal collisionality [40], which is defined as: ν∗ ped =Rq95−3/2(λe,e)−1(3) where is the inverse aspect ratio and λe,e= 1.7 ×1017 T2 e,ped (eV)/[ne,ped (m−3)lnΛ] is the electronelectron Coulomb collision mean free path at the pedestal. The Coulomb logarithm lnΛ is evaluated here following the classical formula for electron-electron collisions [41] and using pedestal plasma parameters. The energy loss can be further broken down into 6 Figure 5: Top: Conditionally averaged radial profiles of electron density (a), temperature (b) and pressure (c) before and 0.6 ms after I-mode PREs. The shaded gray area indicates the ECE “shine-through” region. Bottom: difference between the before PRE and after PRE radial profiles of the electron density (d), temperature (e) and pressure (f). two contributions, termed conductive and convective energy losses (∆Wcond and ∆Wconv), which are defined as: ∆WPRE ≈3 2kZn∆TdV+ZT∆ndV= = ∆Wcond + ∆Wconv,(4) where the cross-term is neglected, as it is of second order. Breaking down the energy loss into a conductive and convective term is important, since these two contributions may behave and scale differently in larger devices. Indeed, for type-I ELMs it has been shown that convective ELM energy losses have a weak dependence on pedestal plasma parameters [38], while conductive ELM energy losses show clear trends with pedestal quantities such as ν∗ ped. In this subsection, first estimations of the above-mentioned quantities for I-mode PREs will be shown. The PRE particle loss is calculated directly from the measured ∆neshown in Fig. 5 (d). In the analyzed discharge, the PRE particle loss is 8.6×1018 m−3, which is about 2 % of the pedestal particle content Nped. This percentage is close to the lower range of observed values for ∆N/Nped during ELMs, which varies between 2 % and 13 % in AUG [36] and JET [40]. To calculate the energy losses, the ion contribution also needs to be considered. As no fast measurements of Tiand niwere available to temporally resolve PREs, assumptions need to be introduced. In this lowimpurity content discharge, ni=neis assumed. Also, since in I-mode discharges at AUG the pedestal top ion and electron temperature are very close [4], Ti=Te is considered. Moreover, it is also conjectured that ∆ne= ∆niand ∆Te= ∆Ti. While the first equality has been proven to hold at different collisionalities for type-I ELMs [32], the second one can be broken at low collisionalities for type-I ELMs [32], with ∆Ti<∆Te. Therefore, the following energy losses should be regarded as an upper limit. Considering the above-mentioned assumptions, the conductive and convective energy losses during I- mode PRE are 4.2 kJ (3.3 % of Wped) and 3.2 kJ (2.5 % of Wped), respectively. For the same pedestal collisionality, ELM conductive and convective relative losses range between 6 −11 % and 6 −18 % [38], respectively, and are thus larger than the I-mode PREs losses. The PRE energy loss obtained from Eq. 1 is 7.2 kJ, which is 1.8 % of WMHD and 5.7 % of Wped. This quantity is compared to the energy loss calculated from 7 Figure 6: Relative energy loss against pedestal collisionality for type-I ELMs and I-mode PREs. I- mode PREs exhibit relative energy losses lower than those of type-I ELMs. conditionally averaging the WMHD signal, which yields ∆WMHD/WMHD ≈1.1 % and ∆WMHD/Wped ≈3.3 %. This discrepancy may be explained by the assumptions made on the ion contribution, which lead (as expected) to an overestimation of the relative energy loss. Figure 6 shows the relative energy loss (normalized to WMHD) of I-mode PREs and type-I ELMs against the pedestal collisionality. I-mode PRE energy losses are calculated carrying out a conditional average of the WMHD signal during I-mode PREs for different I-mode discharges. I-mode PRE relative energy losses are on average around 1 %. Type-I ELM data used for the multimachine study in [5] are reexamined here. For the same pedestal collisionality, type-I ELM relative energy losses range between 3 −10 %, and are thus larger than those of I-mode PREs. 3.3. MHD stability Figure 7 shows the peeling-ballooning pedestal stability diagram calculated with the MISHKA code [42] for an AUG discharge with I-mode PREs that later enters H-mode. The MHD stability is parameterized here in terms of the maximum normalized edge pressure gradient αmax [43] and flux-surface averaged edge current density hjtori. The lines show the stability boundary defined with the criterion used in [44] for both I-mode and H-mode. Above the stability boundary, peelingballooning modes are unstable and type-I ELMs occur. The H-mode pedestal is close to the stability boundary and this agrees with the observation of type- Figure 7: Ideal peeling-ballooning stability diagram of the I-mode pedestal with PREs (black cross) and the H-mode pedestal with type-I ELMs (purple diamond) in #34549. The black and purple lines represent the stability boundary in I-mode and H-mode, respectively. The I-mode pedestal with PREs is ideal peelingballooning stable. I ELMs in the analyzed discharge. On the contrary, the I-mode pedestal with PREs is far from the ideal peeling-ballooning stability boundary, which is usually the case in I-mode [3, 4]. This shows clearly that I- mode PREs are not type-I ELMs. 4. Transport in the scrape-off layer 4.1. Characteristic temporal evolution The energy lost during PREs from the confined region enters the SOL and is transported both along and across the open magnetic field lines, i.e. both in the parallel and perpendicular direction. The combination of parallel and perpendicular transport in the SOL sets the characteristic temporal evolution of different SOL plasma quantities and of the energy reaching the divertor targets. The temporal shape and duration of the latter quantity is not only important to understand how energy is transported in the SOL, but is also crucial for the assessment of divertor thermal loads [45, 46] and for extrapolation to larger devices. Figure 8 shows the conditionally averaged temporal evolution of the outer midplane SOL electron density and temperature (top panel) and of the divertor radiation (bottom panel) during I-mode PREs. The conditional average was carried out over the same 105 PREs analyzed in section 3. In Fig. 8 three time instants are marked: the PRE beginning time tbeg (green), the PRE ending time tend (gray) and the time instant of the maximum value tmax (magenta). In this work, the PRE ending time is defined as the time instant when 8 Figure 8: Top: Conditionally averaged temporal evolution of electron temperature (red) and density (blue) at the outer midplane in the SOL (ρpol = 1.024) measured by the helium beam diagnostics during I- mode PREs. Bottom: Conditionally averaged divertor radiation during I-mode PREs measured by a diode bolometer. The line of sight (LOS) of the diode bolometer is depicted in the upper right corner. The dashed line is the fit of the data using Eq. 5. Green and gray markers represent the beginning and ending time of the PRE, respectively. the peak value decays by 1/e, following the definition given in [47] for type-I ELMs. The beginning time is defined as the time instant when the analyzed quantity takes 1/(10 e) of its peak value. From these quantities, the decay time τdecay =tend −tmax and rise time τrise =tmax −tbeg are calculated. The SOL electron density and temperature have been measured by the helium beam system [48] installed at AUG with a time resolution of 17 µs. The radiation is measured in the upper divertor region by a diode bolometer with a time resolution of 2.5 µs. This highly temporally resolved signal is used as a proxy for the energy deposited onto the divertor target plates. IR cameras provide a direct measurement of the energy deposited onto the divertor targets, however their time resolution (about 0.6 ms) is not high enough to measure the characteristic power temporal shape. The drawback of using the radiation measurements is that the line of sight of the diode bolometer (which is depicted in the bottom panel of Fig. 8) crosses both the outer and inner divertor region. Therefore, the radiation temporal evolution shown here should be considered as an “integral” of both inner and outer divertor radiation. The top panel of Fig. 8 shows that electron temperature and density exhibit a different temporal behavior. While their rise time is almost equal (τrise,n/T ≈0.3 ms), their decay time differs substantially (τdecay,T = 0.38 ms and τdecay,n = 0.67 ms). This may be due to the fact that conductive transport takes place on a faster timescale than the convective one, i.e. χD, thus giving rise to a faster temperature decay than the density one, as also predicted by the “free-streaming-particle” model [49]. The bottom panel of Fig. 8 shows that the divertor radiation exhibits the typical temporal evolution of the power deposited onto the divertor targets during type-I ELMs [50]: After an initial sharp rise, a slow exponential decay is present. This characteristic temporal evolution has been successfully modeled in [49] assuming that a Maxwellian distribution of plasma particles (released over a short time δ(t) compared to the parallel transport times and in a short parallel distribution length δ(s) compared to the parallel connection lengths to the target) propagates in a “force-free-way” along the SOL parallel direction. The heat flux reaching the divertor targets can be thus described by the following equation: q(t) = 2E 3√π1 + τ t2τ t2exp −τ t2+qBG,(5) where Eis the total energy reaching the divertor, τis the characteristic decay time and qBG is the background heat flux. Equation 5 closely corresponds to the divertor radiation data (∝kW/m2) (see dashed curve in the bottom panel of Fig. 8). Hence, the I-mode PRE power temporal evolution in the SOL does not substantially differ from the type-I ELM one. This points to the universality of energy transport during any pedestal relaxation event. In addition, Fig. 8 shows that the average PRE deposition time (defined as τdep =τrise +τdecay) is about 0.8 ms. This marks a difference with respect to the previously analyzed I-mode density “bursts” in AUG, which showed turbulence timescales (of the order of µs) both in the confined region and in the SOL [7, 4]. These longer “type-I-ELM-like” timescales reduce the divertor transient thermal load when compared to the shorter turbulence timescales, as they cause a smaller surface temperature rise for the same deposited energy fluence [45]. 4.2. Filament propagation Perpendicular transport in the SOL is dominated by perpendicular advection associated with coherent structures known as filaments. The name comes from the fact that these structures are extended along the magnetic field lines, thereby forming 3D helical filaments [51, 52, 53]. Filaments carry particle and energy towards the plasma facing components of the main chamber and the divertor target plates [54, 9, 55], and are thus a concern for next-generation tokamaks. 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