Effects of density gradients and fluctuations at the plasma edge on ECEI measurements at ASDEX Upgrade

Effects of density gradients and fluctuations at the plasma edge on ECEI measurements at ASDEX Upgrade B Vanovac1, E Wolfrum2, S S Denk2, F Mink2,4, F M Laggner3, G Birkenmeier2,4,M Willensdorfer2, E Viezzer2,5, M Hoelzl2, S J Freethy2, M G Dunne2, A Lessig2, N C Luhmann Jr.6, the ASDEX Upgrade Team and the EUROfusion MST1 Team7 1DIFFER - Dutch Institute for Fundamental Energy Research, Eindhoven, the Netherlands 2Max-Planck-Institut f¨ur Plasmaphysik, 85748 Garching, Germany 3Institute of Applied Physics, TU Wien, Fusion@¨ OAW, 1040 Vienna, Austria 4Physik-Department E28, Technische Universit¨at M¨unchen, 85748 Garching, Germany 5Department of Atomic, Molecular, and Nuclear Physics, University of Seville, Seville, Spain 6Department of Applied Science, University of California at Davis, Davis, CA 95616, USA 7See author list of ”H. Meyer et al 2017 Nucl. Fusion 57 102014” E-mail: [email protected] July 2017 Abstract. Electron Cyclotron Emission Imaging (ECEI) provides measurements of electron temperature (Te) and its fluctuations (δTe). However, when measuring at the plasma edge, in the steep gradient region, radiation transport effects must be taken into account. It is shown that due to these effects, the Scrape-Off Layer (SOL) region is not accessible to the ECEI measurements in steady state conditions and that the signal is dominated by the shine-through emission. Transient effects, such as filaments, can change the radiation transport locally, but cannot be distinguished from the shinethrough. Local density measurements are essential for the correct interpretation of the electron cyclotron emission, since the density fluctuations influence the temperature measurements at the plasma edge. As an example, a low frequency 8kHz mode, which causes 10 % to 15 % fluctuations in the signal level of the ECEI, is analysed. The same mode has been measured with the Lithium Beam Emission Spectroscopy (Li-BES) density diagnostic, and is very well correlated in time with high frequency magnetic fluctuations. With radiation transport modelling of the electron cyclotron radiation in the ECEI geometry, it is shown that the density contributes significantly to the radiation temperature (Trad) and the experimental observations have shown the amplitude modulation in both density and temperature measurements. The poloidal velocity of the low frequency mode measured by the ECEI is 3km/s. The calculated velocity of the high frequency mode measured with the magnetic pick-up coils is about 25 km/s. Velocities are compared with the E×Bbackground flow velocity and possible explanations for the origin of the low frequency mode are discussed. 2 1. Introduction H-mode plasmas[21] are the foreseen scenario for the ITER operation[14]. This type of scenario is characterized by steep gradients and the pedestal build-up at the edge of the plasma. Edge Localized Modes (ELMs)[26, 13] lead to periodic relaxations of the gradients including sudden losses of heat and particles into the unconfined region in ∼ 1-2 ms time scale. These periodic bursts can cause intolerable heat loads on divertor target plates and the erosion of plasma facing components. In order to maintain the high confinement of heat and particles, but with no impurity accumulation and without large uncontrollable ELMs, ELMs need to be mitigated. For such a full control the dynamics of ELMs and ELM associated phenomena should be better understood. The Electron Cyclotron Emission Imaging (ECEI) diagnostic, with multiple lines of sight (LOS), where each LOS behaves like a conventional 1D radiometer, measures the radiation temperature and its fluctuations on µs time scales and is specially suitable for 2D or quasi-3D visualisation of MHD phenomena. It can thus help provide more insight into the behaviour of the relative temperature fluctuations associated with the ELM cycle. To date, ECEI has been installed on many tokamaks including: ASDEX Upgrade[3], KSTAR[25], EAST[24], DIII-D[18] and HL-2A[9]. In the case of optically thick plasmas, where optical thickness is proportional to the product of electron density and temperature, the intensity of the cyclotron radiation equals the level of black body emission. In this case, under the condition that the electrons are in a local thermodynamic equilibrium, radiation temperature is equal to the electron temperature. However, when measuring at the plasma edge, where the density and temperatures are relatively low, the electron cyclotron emission no longer equals the black body radiation and the density contribution cannot be neglected. In this case the radiation transport equation is solved in order to obtain the radiation temperatures. It is important to note here that the geometry under which the light is collected plays a very important role. Under perpendicular observation of the plasma, where the line of sight is perpendicular to the magnetic field line, there is no significant parallel contribution of the cyclotron emission and the Doppler broadening can be neglected. In this case, the radial resolution of the system is set by the the band-pass filtering of the intermediate frequency (IF) signal around the central frequency in the second down-conversion process (the IF bandwidth). If, however, the observation angle is slightly oblique, as is the case with the present ECEI system on ASDEX Upgrade, this Doppler broadening must be taken into account. In this case the radial resolution of the system is set by both, IF broadening and Doppler broadening. Another important point is related to hot H- mode plasmas where the relativistically down-shifted emission contributes significantly to the low field side emission. This effect shifts the peak of the resonance towards the higher magnetic field[19]. When all the mentioned effects are taken into account, measurement positions in the case of oblique diagnostics can significantly differ from the cold resonances as shown in[6]. In this work, we examine a particular H-mode discharge during the phase between 3 two subsequent ELM crashes, where the large amplitude density fluctuation alongside the temperature fluctuations are measured. The main question to answer in this work is if and how much of the fluctuating signal measured with ECEI, which is considered a temperature diagnostic, is affected by the variation of the density at the plasma edge. The paper is organized as follows. The ECEI diagnostic is described in more detail in Section 2. Section 3 explains the forward model that is now routinely used for the ECE Imaging at ASDEX Upgrade. Measurements of the temperature fluctuations and the mode analysis by the ECEI is presented in Section 4. Section 5 treats the spatial localization of the mode. Forward modelling of the electron cyclotron radiation with density fluctuations in the steep gradient region is described in Section 6. In Section 7 we compare measured mode velocities with the E×Bvelocity. A summary is given in Section 8. 2. ECEI at ASDEX Upgrade The ECEI diagnostic at ASDEX Upgrade is well suited for measurements of relative temperature fluctuations with two separate arrays looking at two toroidally separated locations inside the plasma under slightly different toroidal angles[4]. Its poloidal extension covers the regions above, across, and below the midplane. The geometry of the ECEI system, configured for the shot #33616, is shown in figure 1. Figure 1(a) shows the q=6 flux surface in toroidal geometry as the grey transparent surface. The q = 6 magnetic field line is shown as a white solid line on top of the q = 6 flux surface. The two red regions are showing the two ECEI systems and its toroidal location. Toroidal separation of two ECEI systems is about ∆φof 10o. Zoomed, the position of the ECEI arrays relative to 1D ECE radiometer is shown in figure 1(b) in Cartesian coordinates. The toroidal separation of 10ofrom figure 1(a) translates into 40 cm in Cartesian coordinates. The black circle (•) corresponds to the location of the ECEI channel used for the comparison with the magnetic measurements. Figure 1(c) shows the poloidal cross section of ASDEX Upgrade indicating the measurement positions for the different edge diagnostics used in this work: ECE Imaging, Li Beam Emission Diagnostic (Li-BES)[23], channels of the 1D ECE radiometer[17] and magnetic pick-up coils (note that the R is defined ad R=px2+y2). The ECE and ECEI are temperature diagnostics, the Li-BES is an edge density profile diagnostic, and the magnetic pick-up coil measure magnetic fluctuations. The ECEI, ECE and Li-BES are positioned in the same sector of ASDEX Upgrade, measuring at very close toroidal locations. The ECEI has a toroidal observation angle. When focused at the edge, array 1 has a launching toroidal angle of 7 degrees and array 2 has an angle of 5.7 degrees with respect to the the 1D ECE. As a consequence of the toroidal observation angle, the Doppler broadening of the emission lines is increased, and therefore contributes to the radial resolution of the diagnostic. In this work we use the data from the array 2 with the IF bandwidth of 390 MHz. Emission of optically thick Maxwellian plasmas, when observed perpendicularly to 4 2.12.15 2.2 −0.2 −0.1 0 0.1 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 x (m) 0.3 y (m) z (m) 1.7 -0.6 -0.4 -0.2 0.2 0.4 0.6 z (m) 0 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 #33616 @7.2 s R (m) Li Beam 1D ECE ECEI B31-14 b) z (m) x (m) y (m) a) c) 1D ECE ECEI 2 ECEI 1 (9,3) Figure 1: a) q = 6 flux surface plotted as a gray shaded area for the shot # 33616 at t 7.2 s. Magnetic field line for this equilibrium is plotted as white solid line. The red surfaces, intersecting the q = 6 flux tube correspond to two ECEI imaging systems. b) Absolute measurement positions of two toroidally separated ECEI arrays in Cartesian coordinates are shown as red crosses (X); edge channels of conventional ECE radiometer are shown as green dots. The ECEI channel of the ECEI 2 array that is used for comparison with the magnetic measurements is marked as black circle (•). c) Poloidal cross section of ASDEX Upgrade indicating the measurement positions of: the Lithium beam diagnostic, ECE Imaging, standard ECE radiometer and magnetic pick-up coil (B31-14). the magnetic field, originates from a radially thin layer as is the case in the standard ECE diagnostic on ASDEX Upgrade. Therefore, for perpendicular propagation, the radial resolution of the system can be well approximated by the IF bandwidth of the system. ECE Imaging has a contribution of Doppler broadened emission on top of the IF broadening. When observing high density H-mode plasmas under the oblique angle, the LOS can be approximated by a straight line for lower density cases, or curved due to the high density gradient. Refraction of the beams causes an ambiguity in the measurement positions. This is of special importance for the channels at the top and the bottom of the ECEI arrays, since they encounter the strong gradients under the largest angle. Also, due to the high temperature of the plasmas, relativistic effects cannot be neglected. Because of the relativistic mass increase of the resonant electrons, the frequency will be downshifted. When combined with the low optical depth at the plasma edge, these effects make the interpretation and the origin of the electron cyclotron radiation complicated and an extended Electron Cyclotron Forward Model (ECFM), including the radiation transport effects, needs to be used as a standard tool for determining the origin of the emitted radiation [6]. 5 3. Forward modelling of the radiation detected by the ECEI In order to get an idea of the diagnostic constraints and characteristics, we describe the forward modelling of the electron cyclotron radiation for an H-mode discharge where we calculate the expected radiation temperatures for a given equilibrium and electron density and temperature profiles. It is important to note that the IF bandwidth is included in this modelling, the beam is approximated with a single ray and possible influence by the O-mode emission is neglected. For given Teand neprofiles, ray tracing, that accounts for refraction effects, is performed for each channel and then the radiation transport equation is solved along the line of sight until it reaches back to the antenna. The input electron density and temperature profiles are shown in figure 2(a). Ray tracing, with an example of 111.6 GHz channels for all 20 lines of sight, is shown in figure 2(b) alongside the CLISTE equilibrium reconstruction[2]. The separatrix position is shown as a thick solid black line, whilst rays are shown as red dashed lines. The characteristics of the emitted radiation as calculated by the ECFM of a single ECEI (111.6 kHz) channel at the midplane are given in figure 3. We distinguish two positions describing a single channel. The cold resonance position is only dependent on the magnetic field. It is shown as a black dashed line. When radiation transport effects are taken into account the emission position changes thus corresponding to a warm resonance position. The warm resonance is given by the peak of the birth-place distribution function Dω, depicted as a blue solid line. Red dashed line corresponds to the peak of Dωfor this channel. Its resolution is determined by the width of the Dωand would correspond to the radial extent of the plasma mostly contributing to the emitted radiation. 0.5 1 0 1 2 3 4 Te (keV) 0.5 1 0 1 2 3 4 5 6 7 8 1.6 1.8 2 2.2 2.4 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 R (m) z (m) ρpol ne (1019 m-3) Figure 2: a) Teand neprofiles used to forward model the radiation transport. b) Ray tracing representing the lines of sight for 20 ECEI poloidally distributed channels. The radiation transport equation is solved for every channel of one ECEI array. The two dimensional distribution of the cold and the warm resonances is shown in 6 figure 4(a). It is observed that the inner most channels are Doppler shifted towards the larger major radius R, therefore lower toroidal magnetic field, whilst the outer most channels (with the cold resonances outside the separatrix) are measuring the signal from the region inside the separatrix. This emission corresponds to the relativistically down shifted radiation. Expected radiation temperatures for ECEI channel mapped onto cold and warm resonance positions are shown in figure 4(b) and 4(c), respectively. It is observed that the measured surface area of the ECEI window, when mapped on the warm resonances, is smaller than when mapped onto a cold resonances, due to the shifts mentioned above. In the SOL region only shine-through emission from the pedestal region can be observed in the steady state conditions. 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Te (keV) Te Dω cold resonances warm resonances 0.9 0.95 1 0 20 40 60 80 100 D ω (m −1 ) ρ # 33616, f= 111.6 GHz Figure 3: Origin of the observed emission (warm resonance) defined by the emitted intensity Dωfor the 111.6 GHz ECEI channel, at the midplane. Corresponding input Teprofile is shown as a black solid line. Warm resonance position is shown as black dashed line and corresponds to a peak of Dω. The cold resonance is labelled as red dashed line and depends only on the magnetic field strength. The radial width of the plasma contributing to the measured signal is determined by the width (FWHM) of the Dω. The above analysis shows the effect of steady state plasma conditions on the ECEI measurements. From this, one can conclude that measurements in the SOL region are not feasible with the ECEI diagnostics during steady state, and all the signal measured by channels in the SOL comes from the pedestal top. However, the presence of transient events, such as filaments, affects the location of the emitted radiation locally, as shown in figure 5. In order to examine the effect of filaments, we use the electron temperature and density distributions, instead of profiles. As the most realistic scenario we chose the distributions from a non-linear JOREK simulation [8] during an ELM crash. It is a simulation with two fluid effects as described in [16], with a single temperature assuming that T = Te= Ti. However, the JOREK distributions are scaled down uniformly for 7 R (m) z (m) a) 2.05 2.1 2.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 R (m) 2.1 2.15 R (m) 2.1 2.15 100 200 300 400 500 600 b) c) Trad (eV) Figure 4: Shot # 33616 at 7.5 s. a) Calculated cold resonances are labelled as red crosses (X) and the warm resonances as black circles (•). The radiation temperature mapped onto positions of the cold resonances (b) and the warm resonances (c). The separatrix position is marked by a black dashed line. about 20 % in order to match with the core electron density and the temperature values at the midplane of the shot # 33195 at time t = 2.5872 s. In this ’hybrid’ simulation the steady state equilibrium for shot # 33195 together with the electron density and the temperature distributions are used as an input for the forward model. As shown in figure 5(a) neperturbation abruptly is crossing the separatrix, whilst Teshown in figure 5(b) is smooth due to fast parallel heat losses on open field lines. Modelled cold and warm resonances for these input distributions are shown in figure 5(c) and 5(d), respectively. In figure 5(c) cold and warm resonances are plotted over the input electron density distribution. As seen, the positions of the outermost measurements match with the positions of the filaments. These outermost warm resonances of the LOSs at the midplane are in the SOL region. This shows that the presence of perturbation influences the measurement position locally shifting them towards the cold resonances. In figure 5(d), resonant positions are shown together with calculated radiation temperature. A shine-through radiation of about 300 eV is observed in the SOL region. This shine-through originates from the filamentary structures crossing the separatrix. Although, as shown, it is possible to probe the SOL in non steady state conditions, both Teand a shine-through is expected in this region. Thus, it is impossible to correctly interpret the measured signal without the knowledge of the local density fluctuations. 8 R (m) z (m) 2.1 2.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0 0.5 1 1.5 2 2.5 3 R (m) z (m) 2.1 2.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 a) b) ne (10 19 m −3)Te (keV) R (m) z (m) 2.1 2.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0 0.5 1 1.5 2 2.5 3 R (m) z (m) 2.1 2.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 100 200 300 400 500 600 700 800 900 ne (10 19 m ) −3 Trad (eV) c) d) Figure 5: 2D JOREK profiles of a) Electron density; b) electron temperature. These profiles are matched to the values of the density and the temperature for the shot # 33195 at time t = 2.5872 s and used as an input for electron cyclotron forward model (ECFM). c) Warm resonance positions as calculated with the ECFM are marked as black circles (•) and the cold resonances labeled as white crosses (X) are mapped onto two dimensional distribution of the input density profile that is color codded. d) Warm resonance positions as calculated with the ECFM (•) and the cold resonances (X) are mapped onto a radiation temperatures obtained with the forward model for the input electron density and temperature profiles shown in a) and b), respectively. 9 4. Observations of the modes between ELM crashes Less violent transient events related to an ELM are inter-ELM modes. They play a crucial role in understanding an ELM cycle and may also be responsible for transport across the pedestal. So far, extensive research on this topic has been reported characterising the dynamics of the temperature fluctuations during the inter-ELM period[5, 1] with ECEI. Magnetic signature also reveal high frequency fluctuations with well defined mode numbers. They are located in the steep gradient region[15] corresponding to the location of the minimum of the edge radial electric field[12]. Evidence of the quasi-coherent mode during an inter-ELM period have been reported in[7]. In order to obtain an ECEI signal capturing ELM and inter-ELM associated phenomena, measurements are conducted during H-mode plasmas, where steep density and temperature profiles are formed (pedestal). However, to obtain reliable measurements, the cut-off density limit is avoided by focusing on moderate pedestal top density discharges. At the same time the auxiliary heating power is adjusted to obtain ELM frequencies below 100 Hz, so that the inter-ELM dynamics of the temperature fluctuations can be measured. From the analysis of the previous section, using the typical H-mode profiles shown in figure 2(a), we conclude that radiation temperature equals the electron temperature Tr=Teand the ECEI system delivers the information on the electron temperature Teand its fluctuations inside the separatrix. In this work we will use the the relative change of the electron temperature δTe/hTeiwith respect to the mean value. Here, δTe is defined as the Te− hTei, and hTeiis the time average. An example of the temporal evolution of δTr/hTritogether with the divertor current as ELM indicator in the time period of 60 ms of the discharge # 33616 is given in figure 6(a) and 6(b). Spectrograms of the ECEI signal and the signal measured with the magnetic pick-up coil B31-14, are shown in 6(c) and 6(d), respectively. The discharge was performed at a plasma current Ip= 800 kA, toroidal magnetic field Bt= -2.52 T (negative sign means the opposite to Ip), core line averaged density ne= 7 ×1019 m−3and with upper triangularity δu= 0.128 and the pedestal top collisionality ν∗ ped ≈1.05. Figure 6(a) shows the temporal evolution of the divertor shunt current that consists of combined contributions of thermoelectric and Pfirsch-Schl¨uter current[10]. The bursts in the divertor current are correlated with the drop in δTr/hTrimeasured with the ECEI channel, shown in 6(b). Recovery of the temperature fluctuations after an ELM crash happens in two steps: fast increase followed by the steady state phase. At the onset of the steady phase, a low frequency (∼8kHz) narrow band mode sets in, see figure 6(c). The duration of the mode is about 10 ms and vanishes just at the onset of an ELM crash. This low frequency mode correlates well in time with the high frequency modes appearing in the magnetic measurements shown in figure 6(d). Both low and the high frequency modes occur after the recovery of the maximum pressure gradient as shown in figure 6(e). In figure 6(e) we shot the temporal evolution of the pressure 16 8. Summary and Discussion In summary, it is shown that SOL measurements with the ECEI are not feasible in steady state due to the shine-through emission in this region. The radiation temperature in the SOL region, which is a region of low optical depth, is down-shifted emission from the electrons in the tail of the Maxwellian originating in the pedestal region. However, the presence of ELM filaments in the SOL region can change the optical depth locally, due to the locally higher density and temperature, therefore both, shinethrough as well as the local emission can be observed simultaneously. In this case it is difficult to distinguish between the two contributions without the local density measurements. In the H-mode discharge examined in this work, a strong 8 kHz mode has been observed with different edge diagnostics between ELMs. The mode is highly correlated with the high frequency (∼200 kHz) inter-ELM modes detected on the magnetic pickup coils since the both branches set in the phase of the clamped pressure gradient before an ELM crash. Another interesting feature is that the high frequency modes are localized at the position where the diagnostics measure low frequency amplitude modulation of 8 kHz. This position matches with the minimum of the radial electric field and the propagation direction of both low and the high frequency modes is in the electron diamagnetic direction, in agreement with the sign of the Er. The magnetic pick-up coils measure multiple modes with well defined toroidal mode numbers whilst the ECEI/ECE/Li-BES measures a single mode at low frequency. The low frequency mode is also seen on the magnetics, but of very low amplitude and its mode numbers remained undetermined. The cross-correlation analysis from the ECEI measurements has shown the poloidal structure of the low frequency mode with the local poloidal wavelength λp= 15 cm. The poloidal mode velocity as calculated from the signals of the ECEI channels distributed along the flux surface is 3 km/s, rotating in the electron diamagnetic direction. With the high spatial resolution of the Li-BES and 1D ECE diagnostics, the peak of the perturbation in the signal amplitude is measured with higher accuracy than the one of the ECEI diagnostic. The same perturbation in between ELMs is observed in the density measurements with the Li-BES diagnostic. Since measurements of the Li-BES are sensitive to the changes in the density it is concluded that nefluctuations contribute to the ECEI measurements. To account for this we used forward model of the electron cyclotron emission by adding a Gaussian perturbation in the pedestal region to mimic the possible density fluctuations in that region. This study has shows that the density fluctuation level can influence the measurements of ECEI and contribute to the measured radiation temperature Tr. Thus, knowledge about the local density values is necessary for correct interpretation of the measured signal. Taking into account the measurement facts and the ambiguities in measurements due to the diagnostics sensitivity, only the hypotheses can be proposed as possible explanation for the appearance of the low frequency mode and those will be further 17 investigated. One hypothesis supports the idea of a non linear interaction between two or more high frequency modes that as a result give the low frequency mode. This resulting mode is non linearly amplified in the low field side region where it is measured by the ECEI. Experimental findings that support this theory have already been reported on different machines. Significant modification of the mode structure due to the non-linear coupling has been reported on TCV [22] and similar amplitude modulation has been observed in KSTAR [11] and explained by a superposition of two modes with different poloidal velocities. In the case studied in this manuscript, the result of the multiple mode interaction would be the wave with a measured group velocity of 3 km/s. Another hypothesis is that the measured mode coexist together with the high frequency modes, at the same position, but very weak in amplitude compared to the high frequency modes. In this case, the E×Bvelocity of 25 km/s and the measured mode velocity of 3 km/s would result in a mode with a large phase velocity vph = 22 km/s, in the ion diamagnetic direction. The third possibility is that the mode is located where the measured velocity of the mode matches the E×Bvelocity. In this case the position of the mode is at the pedestal top and mode has no resolvable intrinsic phase velocity (vph = 0). The mode has well defined structure rotating in the electron diamagnetic direction in agreement with the E×Bat that location. The nature of the mode could be assigned to the density fluctuation at the pedestal top that influences the steepest gradient region, where the diagnostics is most sensitive. To distinguish between the possible explanations on the origin of the mode in near future work we will examine the poloidal velocities of the low frequency modes with a variation of plasma parameters which are known to change the frequency of the high frequency modes, i.e. edge safety factor qand the ion pressure gradient ∇pi. Also, we will compare the dynamics of the fluctuations measured by the ECEI with newest non-linear JOREK simulation comprising an inter-ELM period. Further investigation on the sensitivity of the measurements in the pedestal top region will be conducted. Possible effect of the low frequency mode on transport will also be assessed in the future analysis. The ECEI diagnostic, with its excellent poloidal resolution, is a useful tool for characterizing fluctuations at the edge by means of their poloidal size and velocity. The signal, however, can be dominated by the changes in the density profile and does not necessarily reflect the amplitude of the Tefluctuations. 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