## 2 Narrow Tearing Modes
### DBS Measurements  
Apart from magnetic probes, the DBS diagnostic was employed to research the characteristics of the tearing mode on the Globus-M2.  
Doppler backscattering (DBS, also referred to as Doppler reflectometry) involves the probing of plasma at oblique incidence by means of microwave beams [13; 14; 15; 16; 17; 18]. It is used to measure the Bragg backscattered process at the cut-off layer. This technique allows for local measurement of the density turbulence and its perpendicular rotation velocity at different turbulence scales. Besides that, coherent MHD modes can be detected in the DBS signals [19]. This diagnostic is installed on many tokamaks and has been used to research different plasma processes on the Globus-M/M2 [7; 8; 9; 10; 11; 20]. Various oscillatory phenomena were thoroughly investigated, such as geodesic acoustic modes (GAMs), limit-cycle oscillations (LCOs), Alfven eigenmodes (AEs) and filaments.  
On the Globus-M2 tokamak two DBS systems were used to detect tearing modes [21; 22]. One of them has four channels with probing frequencies 20, 29, 39, 48 GHz and two steerable antennas which probe the plasma with O-mode microwaves. The detection region of the system covered the interval of normalized minor radii \(\rho\) = 0.7-1.1 for typical discharges presented in the following segments. The 20 GHz channel area of detection corresponds to outside the separatrix region, while channels with higher probing frequencies correspond to the tokamak area inside the separatrix. The second system has four channels that probe the plasma at discrete frequencies 50, 55, 60, 65 GHz, allowing to investigate the inner plasma region of the tokamak with normalized minor radii up to \(\rho\) = 0.5-0.7. Its steerable antenna was installed to probe the plasma with O-mode microwaves in experiments.  
The DBS method involves the recording of two signals, the in-phase (I) and quadrature (Q) signals, which are then formed into a complex IQ signal. The derivative of the phase of  
Figure 1: Globus-M2 plasma parameters for discharge #40420: (**a**) plasma current \(\rm I_{P}\), (**b**) electron density \(\rm n_{e}\), (**c**) \(\rm D_{\rm\alpha}\) signal, (**d**) magnetic probe signal \(\rm U_{MP}\).  
the complex signal (or time dependence of the frequency shift of the scattered signal) can be calculated. Examination of the DBS phase derivative signal leads to the conclusion that it could be used to detect the instability which is similar in behavior to the TM seen on the magnetic probe signal in Figure 1d. To prove this, spectra of the magnetic probe signal and DBS phase derivative at different moments in time were calculated. The obtained results are presented in Figure 2. Three different moments in time were chosen: \(t_{1}\) = 148 ms at the beginning of the tearing mode development, \(t_{2}\) = 156 ms in the middle and \(t_{3}\) = 162 ms at the end. One may note that the main frequency component is the same for both DBS and magnetic probe measurements. Over time the TM frequency decreases from 11.7 to 6.8 kHz. The spectral power behaves similarly for both diagnostics, with it decreasing significantly, especially in the case of DBS measurements.  
Not all DBS channels could detect the tearing mode. In discharge #40420 the TM was observed on only one DBS channel with the 48 GHz probing frequency, as the TM intensity was high enough to be detected above the background. This is demonstrated in Figure 3 where the spectrograms of the DBS phase derivative signals for three neighboring channels with probing frequencies 39, 48, 60 GHz are presented. This highlights that the TM is only observable on the 48 GHz channel and cannot be observed on the other 20, 29, 39, 48, 60 GHz channels. It is found in the spectrogram at 148-165 ms during the same time as the fluctuations on the magnetic probe signal in Figure 1d. The frequency of the TM decreases from 12 to 7 kHz, as demonstrated in Figure 2.  
Figure 2: Spectra of the 48 GHz DBS channel phase derivative and magnetic probe signal for discharge #40420.