The investigation of edge-localized modes on the Globus-M2 tokamak using Doppler backscattering

The first results of investigation of edge localized modes (ELMs) in the Globus-M2 tokamak using the Doppler backscattering method are presented in this paper. Specifically, ELMs that are initiated by sawtooth crashes in the H-mode are discussed. The goal of this paper is study plasma turbulence behaviour during ELMs and to showcase what ELM characteristics can be obtained using Doppler backscattering (DBS). An increase of the poloidal rotation velocity during an ELM burst and a decrease in the inter-ELM periods was observed. The effect of ELMs on the plasma turbulence was investigated and estimated to span around 6 cm inside the separatrix. This is to do with the fact that the sawtooth crashes which are responsible for initiating the ELMs take place in the core plasma. Additional experiments with standard reflectometry indicate that ELMs develop 3 cm inside the separatrix where the pedestal region is believed to be in Globus-M2. The direction of the expansion of the ELMs from the inner plasma region to the edge was determined and the velocity was estimated to be around 8 km s−1. During a single ELM burst a series of filament structures were found in the peripheral DBS channels. In an attempt to understand the processes involved modelling of the reaction of the DBS signals to filaments was done using the BOUT ++ and IPF-FD3D full-wave codes, and the cases for both linear and nonlinear scattering were considered. The results show that the presence of nonlinear scattering during ELMs can lead to an overestimation of the measured velocity values in the region of filament existence near the separatrix.

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Introduction
The success of magnetic confinement devices, such as tokamaks and stellarators, depends heavily on their mode of operation and whatever limitations it puts on them.Nowadays, the most favourable results have been achieved in a working regime called the H-mode.Studies in the H-mode have been thoroughly carried out on a variety of different devices [1] as its discovery [2] paved the way toward improved confinement for future fusion devices, the likes of ITER [3].
The H-mode is characterized by an increase of energy confinement time which is an important property that improves the quality of the plasma and effectiveness of a device [1].The main indicators of the transition to the H-mode are the drop in D α emission, a steady increase of the plasma density n e and the formation of an edge pressure pedestal.The phenomenon of edge localized modes (ELMs) is also observed in the H-mode [4][5][6][7].They are periodic disturbances of the plasma edge region that are accompanied by the ejection of heat and particles from the plasma.This can lead to confinement degradation and detrimental consequences to the efficiency and physical state of the working device.For instance, the energy expelled could cause excessive erosion in an ITERscale device [8].ELMs are also seen as potentially beneficial in removing impurities and aiding in limiting plasma density [9].This is why understanding ELM activity and obtaining their characteristics is deemed necessary for the development of future fusion devices.
Research in the H-mode has been done on the spherical tokamak Globus-M2 to investigate the properties and characteristics of the developing ELMs.One feature of some ELMs on Globus-M2 is that they are observed to be synchronized with or initiated by sawtooth crashes [10].Such ELMs developed in the previous Globus-M tokamak and are still regular occurrence for Globus-M2 although ELMs not associated with sawtooth crashes can also now be observed [10].A model explaining the phenomenon of the synchronization has already been proposed [11].It is suggested that there is an interaction between the internal reconnections caused by sawtooth and the ELM burst.The experimental evidence for this, as well as the numerical analysis of the magnetic equilibrium indicate that the internal reconnections can induce excess current density near the separatrix.This in turn destabilizes the peelingballooning (PB) mode which is responsible for ELMs.This connection of the two events that take place in different areas of the plasma is of keen interest and continues to be investigated using different diagnostics.
Apart from conventional methods, such as the D α light, it has been found that the diagnostic of Doppler backscattering (DBS) can also be used to observe and investigate the ELM event on Globus-M/M2 [11].The DBS method is seen as useful in providing local measurements about the plasma turbulence and allows to follow changes in its behaviour.For example, the suppression of the turbulence due to velocity shear in H-mode was also confirmed on Globus-M2 [12].An increase in turbulence activity indicating plasma degradation could also be seen during an ELM burst making it a phenomenon worth investigating.The DBS method is actively being upgraded and new applications of the diagnostic are being investigated.The possibility of using DBS to study ELMs (more specifically filaments during ELMs) has been discussed in previous papers and this work should add to both the understanding of ELMs and expand the range of DBS implementation.Information regarding the turbulence reaction to the ELM event, the correlation lengths of the turbulence, as well as the presence of filaments in the plasma during an ELM burst is presented in this paper.Modelling of the PB mode was also done in an attempt to understand the nature of the reaction seen in the DBS measurements.
The paper is structured as follows.First, the Globus-M2 tokamak and operational regime is presented.This is followed by the characterization of ELMs that develop in experiments with H-mode along with the model for the ELMs initiated by saw-tooth crashes.Next the basic principle of the DBS method is described.Also the results of gyrokinetic modelling regarding the type of turbulence that develops in the tokamak plasma for discharges with the H-mode are discussed.After that, the DBS systems installed on Globus-M2 are described along with their characteristics in the experiments.Then the results of the investigation of the ELM event and any accompanying processes using DBS come next.This is followed by a discussion of the modelling of the DBS signals using the BOUT ++ and IPF-FD3D full-wave code with possible explanations of the observations.Next all the findings are discussed with possible explanations for the phenomena in the Discussion segment.Finally, all the data is summed up in the conclusions.

Edge-localized modes on Globus-M2
On the compact spherical Globus-M2 tokamak (major radius R = 0.36 m, minor radius a = 0.24 m) with a two-fold increase of the toroidal magnetic field B T up to 0.9 T compared to the Globus-M and plasma current I p < 0.5 MA [13] clear transitions to the H-mode can be initiated by neutral beam injection (NBI) with neutral injection power P NBI = 0.5-0.8MW.This can be achieved with varying parameters of the deuterium plasma such as averaged electron density ⟨n e ⟩ = (3-6) × 10 19 m −3 ; electron temperature in the plasma core T e = 0.6-1.1 keV, elongation k ≈ 1.9, triangularity δ ⩽ 0.5.The direction of the magnetic field was chosen so that the toroidal ion drift was directed toward the X-point, i.e. the plasma was in the lower null magnetic configuration.The key indicators of the LH transition were a drop in D α emission, a steady growth of plasma density and peripheral pressure gradients.
In discussed discharges the transition to the H-mode on Globus-M2 was accompanied by the development of ELMs [4].ELMs are observed in the form of periodical bursts on the D α emission.In Globus-M2 different types of ELMs have been seen to develop: those that are synchronized with sawtooth crashes and those that are not [10].In this paper we discuss the ELMs that are characterized by the feature of being linked to sawtooth crashes that take place in the core region [11].It can be proven by the fact that the sawtooth crashes seen on the soft x-ray signals (figure 1(a)) are followed by ELM bursts on the D α signal (figure 1(b)) after a short time delay of about 100 µs.A vertical green line is introduced to the figure to highlight how the two events take place almost at the same time.These types of ELMs can occur in the entire range of considered plasma parameters.The classification and comparison of the ELMs and the operational regimes under which they occur in Globus-M2 is presented in paper [10].A model for interaction between the internal reconnections caused by the sawtooth and the ELM has been proposed [11].It was shown that internal reconnections can induce excess current density near the separatrix which in turn destabilizes the PB instability which is responsible for the ELMs.
These ELMs were investigated using various diagnostics on Globus-M2.For instance, one could also observe MHD activity in the magnetic probe signals in figure 2(c) during an ELM burst.A reaction in the DBS signals to the ELM event could also be found.In figure 2(d) there is a burst in the amplitude of the complex DBS signal at 166.8 ms along with a sawtooth crash in figure 2(a) and the appearance of an ELM in figure 2(b).
The physics of the probing beam with O-mode polarization is that the scattering takes place predominantly in the cut-off layer off plasma fluctuations with selected wave vector values k ⊥ .The k ⊥ values satisfy the Bragg's law for backscattering: where k i is the wave vector of the incident wave in the cut-off region and k s is the wave vector of the scattered wave of electromagnetic radiation (see schematic representation in figure 3) [33].This means that DBS is only sensitive to specific wave vector values.
When the fluctuating plasma moves with a certain velocity, a Doppler frequency shift of backscattered radiation is observed and it can be described by the formula: where ⃗ V is the velocity of the moving turbulence in the measurement frame [34] and − → k ⊥ is the turbulence wavenumber [35].The Doppler frequency shift ∆ω D can be extracted from the DBS measurements as the position of the 'centre of gravity' of the complex DBS signal I(t) + iQ(t) spectral density, or the phase derivative of the complex DBS signal.In magnetically confined plasmas the perpendicular wave vector component is typically much larger than the parallel component, i.e. k ⊥ ≫ k ∥ .This is used to estimate the Doppler shift as ∆ω D = k ⊥ • V ⊥ .The velocity V ⊥ contains two components: the phase velocity V phase and E × B drift velocity V E×B , and can be described by the formula V ⊥ = V phase + V E×B .Both these components can help describe the plasma, for instance, data regarding the V phase and its direction offers information about the type of turbulence present, and the V E×B allows to calculate the values of the radial electric field.
In order to understand the physics behind the DBS measurements on Globus-M2 gyrokinetic modelling using code GENE [36] was performed in a linear local approximation to investigate the V phase in the L-and H-mode in different plasma regions.The results of the simulations are presented in figure 4 for instabilities with positive growth rates.For the middle of the minor radius at normalized minor radius ρ = 0.5 (figure 4(a)), predominately the ion temperature gradient (ITG) and electron temperature gradient (ETG) modes develop in the Lmode.After transitioning to the H-mode, the ITG, ETG and the trapped electron mode are destabilized.The values of the turbulence V phase in both operational regimes at ρ = 0.5 did not exceed 0.3 km s −1 .Simulations in the more peripheral region at ρ = 0.75 (figure 4(b)) showed destabilization of the ITG and ETG in the L-and H-mode.In this case, the V phase of these instabilities were less than 0.2 km s −1 in a wide range of wave vectors ranging from 1 to 100 cm −1 .The values of the V phase in simulations were significantly smaller than the typical measured perpendicular velocities V ⊥ on Globus-M2, which have a value of about 3 km s −1 in the L-mode and reach values of about 10 km s −1 in the H-mode [12,37].From this data we conclude that in experiments under consideration, the main contribution to the measured V ⊥ comes from the E × B drift velocity V E×B .On Globus-M2 the DBS method is used to gather data on the poloidal rotation velocity of the density fluctuations in the tokamak which is used to estimate the radial electric field.Moreover, different oscillatory processes and a multitude of other phenomena were studies using DBS [38].These include Alfven eigenmodes [39], neoclassical tearing modes [40], quasi-coherent fluctuations (QCFs) [41], limitcycle oscillations [42] and geodesic acoustic modes [43].It was also observed that this diagnostic can be used to investigate ELMs and filament structures [44][45][46][47], so research was done in this field and some new developments are discussed in this paper.
Two multi-frequency DBS systems were installed and used to study the ELM phenomenon on Globus-M2 [48,49].Nine different probing beam frequencies allow to make measurements in different plasma regions spanning from the inner plasma to the separatrix.The antennas of the DBS systems can be tilted in both the poloidal and toroidal directions, and in experiments the plasma was probed with O-mode microwaves.An example of the probing beam trajectories for all DBS channels is presented in figure 5.These calculations are performed using a ray tracing code written in the Wentzel-Kramers-Brillouin approximation for the Globus-M2 geometry [50].The code requires Thomson scattering diagnostics measurements of electron density and EFIT data [51] regarding the magnetic field configuration.In figure 3 the poloidal crosssection of the Globus-M2 tokamak is presented with a series of lines that correspond to the trajectories of the probing beams.The two DBS systems are schematically denoted by the two triangles.The first system was located in the equatorial plane of the tokamak and the second one 14 cm below.The blue lines correspond to five probing frequencies 50, 55, 60, 65, 70 GHz of system #1, while the purple ones to four probing frequencies 20, 29, 39, 48 GHz of system #2.The higher frequencies correspond to the deeper position of the cut-off radius.The range of probing frequencies was chosen to cover the detection region with the interval of normalized minor radii ρ = 0.5-1.1 and to detect turbulence with wave vector values k ⊥ = 2.7-11.6 cm −1 for the typical discharges presented in the paper.

Results
ELMs were studied using system #2 from figure 3, as the position of the cut-offs of the probing frequencies 20, 29, 39, 48 GHz with ρ = 0.8-1.0correspond to the pedestal and separatrix region where ELMs develop.The system was located in the equatorial plane for discharge # 38361.A link between the backscattered radiation signal power P DBS and the appearance of ELMs was observed.This is shown in figure 6 where the D α signal figure 6(a) and P DBS of the different channels figure 6(b-e) averaged over a 1 ms time window are presented.Two vertical lines are depicted during ELM bursts at two moments in time.One can see an increase in the signals on all four channels during an ELM with varying degrees of reaction to these bursts.By contrast, during the inter-ELM periods, the amplitude of the signals decreases.
The cross-correlation function (CCF) was calculated for the D α signal and the backscattered radiation signal power P DBS for the 39 GHz probing frequency and is presented in figure 7(a).The period of the CCF fluctuation coincides with the period of ELM bursts.The CCF has the maximum value of over 0.2 at around 0 ms which highlights that the events on the D α signal and P DBS are of the same nature and take place at almost the same time.The CCF remains at almost the same value for a time frame spanning over ten periods of the fluctuations.The CCF for the D α signal and the poloidal rotation velocity V ⊥ for the 39 GHz probing frequency was calculated and presented in figure 7(b).Its behaviour is very similar to the CCF of P DBS .
Spectral analysis was applied to the DBS signals to investigate the dynamics of the turbulence during an ELM event.
The DBS systems from figure 5 were used.An example of that is presented in figure 8 for discharge #41095.A reaction of the turbulence to the ELMs is seen not only in the periphery, but also in the inner plasma region.A change in intensity levels can be noted in the spectrogram of the complex DBS signal of the 50 GHz channel in figure 8(b) during an ELM burst.One may also observe an increase of the spectral power at higher frequencies over 350 kHz is seen during an ELM burst, while there is a decrease in the inter-ELM periods.To highlight this, the D α signal in figure 8(a) is shown along with two vertical lines at ELM bursts.These changes are also demonstrated in the form of the spectral power P DBS for the 50 GHz channel in figure 8(b).One may observe an increase of the P DBS during ELMs burst, and a slight decrease during in inter-ELM periods.This indicates the increase of turbulence activity at those times.Apart from that, the spectrogram centre of gravity was calculated and added to figure 8(b).It corresponds to the poloidal rotation velocity for the 50 GHz probing frequency presented in figure 8(d).The negative values of the velocity or Doppler frequency shift in figure 8(b) correspond to the rotation of the plasma in the direction of the electron diamagnetic drift.The velocity temporal evolution also clearly shows that the ELM event led to a sudden growth of the turbulence velocity.
To investigate the depth of the turbulence reaction CCFs between the rotation velocity (or phase derivative) of the different channels of the DBS systems in figure 3 were calculated.The reference channel was chosen to be the one with the probing frequency of 20 GHz, as ELMs are an edge phenomenon making their detection on this channel most likely.Apart from that, the D α diagnostic used to observe ELMs takes measurements in this area close to the separatrix.The resulting CCFs are presented in figure 9.The CCF values indicate the degree at which the events in different plasma regions are correlated and the time delay values (t = 0 ms means there is no delay between the events) are used to determine how quick the reaction takes place.The periodic peaks are an indicator that a periodic event is taking place in the time period in which the CCF is calculated.In this case, the period of 3 ms corresponds to the ELM frequency in the discharge.The values at the maximum peak at around 0 ms steadily decrease the deeper the second channel, but they remain above 0.6 meaning there is strong correlation between the processes at the plasma edge and the turbulence in the inner plasma region.On the 65 and 70 GHz channels the CCF decreases significantly leading to the conclusion that the turbulence reaction to the ELM event spans around 6 cm inside the separatrix.This also means that the velocity profile (or the radial electric field profile) undergoes changes in this region as well.
Apart from the DBS method, standard reflectometry which entails normal incidence of the probing beam was implemented in a series of experiments.Our antenna system allows us to take measurements either as DBS, or as standard reflectometry, but not using both methods simultaneously which is why a different discharge # 41864 which was similar to # 41095 is analysed.Using these measurements, the CCFs for the phase derivative (referred to as 'velocity' in figure 10) of different probing frequencies were calculated.The 20 GHz channel was chosen as the reference signal.The CCF values decrease much sooner, with there already being no correlation between the 20 GHz and 50 GHz channel, meaning the correlation length decreases to 3 cm inside the separatrix.The behaviour of the phase derivative in the case of standard reflectometry corresponds to the behaviour of the cut-off radius.The An increase of the spectral power and velocity is observed during an ELM burst.main factor responsible for this is the density profile, indicating that it is affected by the ELM event in this region.So, we come to the conclusion that ELMs develop 3 cm inside the separatrix.
A delay between the ELM bursts was observed on DBS signals of different channels.This delay could be used to investigate the expansion of the ELMs. Figure 11 depicts two phase derivative signals for the 39 and 20 GHz channels which correspond to the edge plasma where the ELMs develop.Several ELM bursts are highlighted and numbered in the figure.They have very similar characteristics which allow for the time of their appearance to be compared.One may observe that the ELMs emerge first on the 39 GHz channel and after a several ms delay on the 20 GHz channel.This indicates that ELMs expand from the inner plasma region to the periphery in the radial direction.Correlation analysis also shows such a delay, the value of which was used to estimate the velocity of the expansion to be around 8 km s −1 .

Filaments and edge-localized modes
During inter-ELM periods, more specifically between ELMs initiated by sawtooth crashes, but during smaller bursts on D α (potentially, smaller ELMs) bursts of quasi coherent fluctuations in the DBS signals that periodically appear on various channels were found.These bursts had previously been observed on the Globus-M tokamak and under other conditions that were not necessarily associated with ELMs.They were interpreted as the reaction of the DBS signal to backscattering from filaments [52] travelling close to the cut-off region [44].The temporal evolution of one of the DBS signals Cross-correlation functions for reference 20 GHz channel (corresponding to ρ = 1.0) and other DBS channels with probing frequencies of 29, 39, 50, 55 and 60 GHz (corresponding to ρ = 0.9, 0.8, 0.7, 0.65, 0.6) for discharge # 41095.The CCF values indicate that there is correlation between the events at the periphery (ELMs) and the core. of system 2 from figure 3 positioned in the equatorial plane is presented in figure 12.These bursts sporadically appear in the signals.For example, one such burst of QCF is visible at t = 215.21ms for 20 µs only on the 39 GHz channel, however there is a burst at t = 215.27ms on all the channels.The moments of appearance of the filaments are indicated by vertical red lines.The second burst is most prominent on the 20 GHz channel and barely observable on the 48 GHz channel.This could indicate the radial size of the filaments is different.
It is less than 1 cm in the first case and several cm in the second case.
Quasi coherent bursts were found in DBS signals during an ELM event.This is demonstrated in figure 13.Here the signals are presented in the time interval of a single ELM burst.These filaments differ from those in inter-ELM periods, as they come in series of bursts on the DBS signals (figure 13(b)).They were only detected on the 39, 29 and 20 GHz channels that have cut-offs in the peripheral region, meaning that the filaments associated with ELMs are a purely edge phenomenon.Spectral analysis was applied to the signals, and the spectrogram of the complex DBS signal is presented in figure 13(c).The spectral power increases significantly during the bursts in the signals at frequencies ranging from 1500 to 3000 kHz.

Modelling of DBS reaction to edge-localized modes
Since ELMs are predominantly nonlinear phenomena that perturb the local plasma density, it was necessary to investigate whether the effects of nonlinear scattering on ELMs can influence the results of the experiment.For this purpose, modelling of the development of the PB instability was carried out using the system of equations for 6-field MHD.The system of equations was solved using the finite difference method in the three-dimensional toroidal geometry of the Globus-M2 tokamak.The code was implemented based on the BOUT ++ framework [53].As a result of the calculations, 2D plasma density perturbations were obtained.Their characteristic poloidal size was 5 cm which is much larger than the optimal size of the backscattering fluctuations for DBS systems installed on the Globus-M2.To compare them with experimental data of the DBS, synthetic DBS diagnostics was implemented.The two-dimensional distribution of the density perturbation in the poloidal cross-section, obtained from the BOUT ++ code, was specified as an input parameter for modelling the DBS signal with the IPF-FD3D full-wave code [54].The configuration of the calculations was selected based on the geometry and parameters of the DBS system used to study filaments on the Globus-M2 tokamak.Simulations were carried out for different amplitudes of density perturbations.The maximum density of the disturbance varied from 1% to 50% of the cut-off density for the 20 GHz probing frequency.
The results of the calculations are shown in figure 14.One may observe that low amplitude filaments lead to practically no scattering of electromagnetic radiation (blue line in figure 14).This is manifested in the fact that in the signals of synthetic diagnostics, not only the amplitude has small values, but also the phase almost does not change with time.However, in the case of nonlinear scattering, when the filament amplitude increases to values the order of 50% of the density at the cut-off, a significant change in the phase of the complex signal occurs simultaneously with an increase in the amplitude (pink line in figure 14).The phase derivative of the complex signal is usually interpreted experimentally as the plasma rotation velocity.Therefore, the presence of nonlinear scattering during ELMs can lead to an overestimation of the measured velocity values in the region of filament existence near the separatrix.In the experiment, this region corresponds to the position of cut-offs for probing frequencies of 20 and 29 GHz.Thus, we can conclude that the observed oscillations of the phase derivative of the complex signal on the DBS peripheral channels can potentially be a consequence of both the oscillations of the radial electric field and processes of nonlinear scattering on filaments, or even a superposition of these two phenomena.An indirect indication of the presence of nonlinear scattering could be the appearance of bursts of quasi-coherent oscillations in the DBS signals shown in figure 13, which are sometimes observed during ELMs.Since the size of the filament significantly exceeds the wavelength of the probing radiation, in the case of linear scattering the amplitude of quasicoherent bursts in the signal drops sharply [55] and they do not have an effect on the estimate of the plasma rotation velocity.Peripheral perturbations of the plasma density during ELMs can influence the velocity value estimated using measurements of the peripheral channels, but do not directly affect the signals of deeper DBS channels where no quasi-coherent bursts could be observed.Therefore, the earlier conclusions about the existence of a connection between the inner regions and the periphery of the plasma which is caused by the development of ELMs, as well as the radial expansion velocity of the ELMs do not change even in the presence of nonlinear scattering of electromagnetic radiation on the peripheral DBS channels.

Discussion
DBS measurements highlight a reaction of both the peripheral and inner plasma turbulence to the event of the discussed ELMs in H-mode in Globus-M2.This further solidifies the idea that the ELMs are synchronized with or rather initiated by sawtooth crashes.It is worthy of note that the DBS measurements (see figure 2) show a reaction slightly before the ELM burst on the D α signal.This would indicate that the plasma turbulence becomes more active as a result of the process that also destabilizes the ELMs.As proposed in work [10], the sawteeth can induce excess current density which could lead to the development of MHD activity which may in turn interact with the plasma turbulence [56].The burst on the magnetic probe signal in figure 2(c) before the ELM supports this as a possible explanation.Additionally, the fact that the turbulence in the core region reacts first highlights the fact that the whole process takes place in the inner plasma region initially.Similar turbulence reactions to the event of sawtooth crashes have been observed on other devices in the form of turbulence spreading which plays a role in driving edge flows [57], though the situation on Globus-M2 differs due to the presence of ELMs.Experiments with standard reflectometry were undertaken to investigate the changes in the density profile during an ELM burst.The measurements seem to indicate that the area affected by the ELMs was significantly smaller.This leads us to the conclusion that the area of development of the ELMs is limited to the pedestal region (3 cm inside the separatrix).
The turbulence reaction to ELMs is of interest especially now on the Globus-M2 after the upgrade which led to an increase of the pedestal parameters, specifically the pressure profile.The changes allow for PB mode to be destabilized without internal reconnections [10].A change in turbulence behaviour is expected due to the difference in nature of the ELMs.For instance, the inner plasma regions are expected not to have such a strong reaction to these events, as well as there is potential for the direction of the turbulence response to change.However, experiments with normal incidence should still indicate that the area of ELM development is in the pedestal region.Analysis of DBS measurements with desynchronized ELMs is necessary to answer these questions and this is the subject of future research.
One may expect the DBS diagnostic to be unable to provide accurate information about ELMs as they are a nonlinear phenomenon.For instance, there is a possibility that the peripheral event could still be responsible for the reaction on the inner DBS channels.As remarked earlier, we observe a reaction slightly before the ELM burst itself, meaning that in this case the turbulence behaviour in the core region cannot be simply explained by the nonlinear effect.However, to answer the question of how ELMs and more specifically filaments manifest themselves in DBS measurements, modelling was undertaken to see the effect that the presence of different filament structures could have [58].The results suggest that several factors may indeed impact the signals, such as the size and shape of the structure, as well as the filament amplitude (i.e.linear or nonlinear backscattering).Specifically, the obtained velocities could be either under-or overestimated.However, in the case of the measurements provided the DBS data would seem to be reliable, as the Doppler frequency shift was not used to obtain the presented results.
Also, there exists the issue of the DBS measurements not being reliable due to an angle mismatch [59].This could lead to the data being collected not just from the cut-off meaning that events that occur in other area of the plasma would interfere.Using the calculations made with our ray tracing code we are able to estimate the mismatch angle for both DBS systems available.In the case of the high frequency system located in the equatorial plane the mismatch angle is almost negligible, however the mismatch angle is slightly larger for the low frequency system with is located 14 cm below the equatorial place.This suggests that the 1st system should function properly, while the 2nd system might in some cases be collecting data along the beam trajectory.In the case of the discussed scenarios there is no indicator that the presented results are influenced by this phenomenon, as no direct velocity measurements are used, but instead a reaction of the turbulence is analysed.
The modelling using the BOUT ++ and IPF-FD3D full-wave codes also showcases how filaments of different amplitudes during ELMs can lead to either linear or nonlinear backscattering to take place.This could serve as an indicator that heating using microwave methods could become ineffective during phenomena such as ELMs, however further modelling would be necessary to back up the claim.

Conclusion
The first results of investigation of ELMs that are initiated by sawtooth crashes in the H-mode in the upgraded spherical tokamak Globus-M2 using the DBS method are presented in this paper.All the presented results allow us to come to the following conclusions.
Two DBS systems were used in experiments aimed at studying ELMs.The results include the observation of bursts in the signals of the DBS amplitude and an increase in the backscattered radiation signal power during an ELM event.The link of these reactions to the ELM is proven by calculation the CCF of the D α signal and the backscattered radiation signal power, as well as the poloidal rotation velocity.
Spectral analysis was applied to the DBS measurements which highlighted that the rotation velocity of the plasma turbulence reacts to the ELMs in the peripheral and inner plasma regions.This is seen by an increase of the velocity during an ELM burst and a decrease in the inter-ELM periods.Apart from that, correlation analysis was used to investigate the area of the effect of ELMs on the plasma turbulence.It was estimated to span around 6 cm inside the separatrix.However, experiments with standard reflectometry led to the observation that ELMs develop 3 cm inside the separatrix.Additionally, a delay between the DBS signals was noted which allowed to determine the direction of the radial expansion of the ELMs from the inner plasma region to the edge.The velocity of this expansion was estimated to be around 8 km s −1 .
Quasi coherent bursts in DBS signals were observed both during and between ELMs.These were interpreted to be the reaction of the DBS signal to backscattering from filaments.The filaments could be found in peripheral channels, but could not be observed in the inner plasma region.In inter-ELM periods these bursts appeared more sporadically, but during an ELM series of filaments were detected using the 39, 29 and 20 GHz probing frequencies.
ELMs being a nonlinear phenomenon raised the question whether the effects of nonlinear scattering on ELMs can influence the results of DBS measurements.To investigate this, modelling was performed using the BOUT ++ and IPF-FD3D full-wave code.Simulations were carried out for different amplitudes of density perturbations from 1% to 50% of the cut-off density for the 20 GHz probing frequency.The results show that the presence of nonlinear scattering during ELMs can lead to an overestimation of the measured velocity values in the region of filament existence near the separatrix.unique scientific facility 'Spherical tokamak Globus-M'.The results of the modelling were obtained using computational resources of Peter the Great Saint-Petersburg Polytechnic University Supercomputing Center (www.scc.spbstu.ru).

Figure 2 .
Figure 2. Plasma parameters during an ELM burst for discharge #41152: (a) soft x-ray signal, (b) Dα signal, (c) magnetic probe signal, (d) DBS amplitude.A reaction to the ELM event seen in DBS signals.

Figure 3 .
Figure 3. Schematic of backscattering geometry of a microwave beam incident on the reflection layer indicating launched k i , backscattered ks, and probed k ⊥ wavenumber.

Figure 4 .
Figure 4. Phase velocity values for instabilities on Globus-M2 obtained using gyrokinetic simulations: (a) at ρ = 0.5; (b) ρ = 0.75.The blue lines correspond to the values in L-mode and orange line in H-mode.The values indicate that the phase velocity is not the main component of the perpendicular velocity measured using DBS.

Figure 5 .
Figure 5. Ray tracing for DBS systems on Globus-M2 for discharge #41820.The beam trajectories for the probing frequencies used are introduced.The position of the DBS systems is schematically shown.

Figure 6 .
Figure 6.Temporal evolution of the (a) Dα signal, and backscattered radiation signal power P DBS for the (b) 48 GHz, (c) 39 GHz, (d) 29 GHz, (e) 20 GHz channel.An increase of P DBS during an ELM is observed.

Figure
Figure Cross-correlation function for Dα and (a) DBS power P DBS , (b) rotation velocity for the 39 GHz probing frequency.The CCF values indicate that the events on the Dα signal and DBS measurements are of the same nature and almost simultaneous.

Figure 8 .
Figure 8.(a) Dα signal, (b) spectrogram of the complex DBS signal (the red line corresponds to the spectrogram centre of gravity), (c) spectral power of complex DBS signal, (d) rotation velocity and radial electric field of the 50 GHz probing frequency for discharge #41095.An increase of the spectral power and velocity is observed during an ELM burst.

Figure 10 .
Figure10.Cross-correlation functions for reference 20 GHz probing frequency (corresponding to ρ = 1.0) and other probing frequencies of 29, 39 and 50 GHz GHz (corresponding to ρ = 0.9, 0.8, 0.7) for discharge # 41864 with standard reflectometry.The CCF values indicate that the ELMs effect the density profile in the periphery, suggesting that being the area of their development.

Figure 11 .
Figure 11.Temporal evolution of phase derivatives for: top-20 GHz channel, bottom-39 GHz channel for discharge #41864.The reaction to ELMs is first observed on the 39 GHz and later on the 20 GHz channel, indicating the expansion of the ELM takes place from the inner plasma region to the periphery in the radial direction.

Figure 13 .
Figure13.Temporal evolution of (a) Dα signal, (b) DBS signal, (c) spectrogram of complex DBS signals for the probing frequency 29 GHz (corresponding to ρ = 0.9) during an ELM burst for discharge # 41152.Quasi coherent bursts in DBS signals during an ELM event are believed to be filaments.There is an increase of spectral power during this bursts.

Figure 14 .
Figure 14.Temporal evolution of (a) signal amplitude, (b) phase for the 20 GHz probing frequency.The blue lines correspond to filament amplitude of 1% of density at the cut-off and the pink lines to filament amplitude of 50% of density at the cut-off.The presence of nonlinear scattering during ELMs can lead to an overestimation of the measured velocity values in the region of filament existence near the separatrix.