# Review of Advanced Implementation of Doppler Backscattering Method in Globus-M
## 3 Application Results
### Limit Cycle Oscillations
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Investigated Property** & \begin{tabular}{c} **LCO in Discharges with** \\ **H-Mode** \\ \end{tabular} & \begin{tabular}{c} **LCO in Discharges** \\ **without H-Mode** \\ \end{tabular} & **Notes** \\ \hline Additional heating & & NBI & not detected in Ohmic phase \\ \hline \(f\), kHz & \(\sim\)6 & \(\sim\)8.5 & \begin{tabular}{c} the higher LCO frequencies predicted by \\ Stringer spin-up [49] \\ \end{tabular} \\ \hline Spectral peak width \(\Delta f\), kHz & 1.5 & 1.5 & corresponds to the calculation of spectra in a 512 ms window \\ \hline Duration of LCO phase \(\tau\), ms & 2–20 & \begin{tabular}{c} the duration of the LCO phase tends to be \\ closer to the value of 2 ms in discharges \\ with H-mode and to the values of 20 ms \\ without H-mode \\ \end{tabular} \\ \hline Velocity shear, s\({}^{-1}\) & order of 10\({}^{5}\)–10\({}^{6}\) & order of 10\({}^{5}\) & \\ \hline Velocity shear behavior & \begin{tabular}{c} a significant increase before \\ transition to H-mode \\ \end{tabular} & \begin{tabular}{c} no significant changes \\ in behavior \\ \end{tabular} & predator-prey model [48] \\ \hline Turbulence suppression & \multicolumn{3}{c}{present during LCO} \\ \hline Turbulence modulation, \% & 98 & 81 & dependence of the onset of the transition \\ \hline Type & bursty dynamics & \
\begin{tabular}{c} standard oscillations \\ around a certain value \\ \end{tabular} &
\begin{tabular}{c} on frequency corresponds to the transition \\ appearance model developed for the case \\ of the appearance of zonal flows [51] \\ \end{tabular} \\ \hline Nonlinear coupling of turbulence & present & possibly, the significant coupling indicates that LCOs are dominated by zonal flows; similar results were obtained in the HL-2A tokamak in the ‘type-Y’ LCO phase [53] \\ \hline Location \(\rho\) & \(\sim\)0.75 & 2 cm inside the separatrix which is similar to other tokamaks \\ \hline Location width \(\Delta\rho\) & \(\sim\)0.4 & close to the radial wavelength of the zonal flows \(\lambda_{ZF}\sim\sqrt{\rho^{i\mu}}\)[41] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Properties of LCO in Globus-M.  
Auto-bicoherence analysis of the perpendicular velocity demonstrated the nonlinear coupling of the broadband turbulence and velocity oscillations at the LCOs frequency in the case of high frequency LCOs [46]. It is possible to assume that this significant coupling indicates that LCOs are dominated by zonal flows caused by Reynolds stress [41]. Similar results were obtained in the HL-2A tokamak in the 'type-Y' LCO phase [53]. The radial scale of the observed flow is estimated to be 4 cm [42,46]. This scale is close to the radial wavelength of the zonal flows [41]. The maximum of the amplitude profile of the velocity oscillations at LCO frequency was located at about 2 cm inside the separatrix. Moreover, the velocity profile maximum moves from the boundary to the core region during the LCO period. This was investigated by studying phase relations between the perpendicular velocity and turbulence amplitude for two radial positions, which are presented in the form of Lissajous phase diagrams in Figure 4. It was demonstrated that at R = 54.4 cm the clockwise direction in the figure corresponds to a predator-prey model [48], while at R = 56.6 cm the counterclockwise direction was associated with a transition to H-mode in work [53]. Using DBS it was possible to observe both trajectories simultaneously. The calculated autocorrelation and cross-correlation functions of amplitude and perpendicular velocity lead to the estimation of the velocity of the movement to be about 3 km s\({}^{-1}\). Apart from that, it was shown that the amplitude oscillations that occur at different cutoff positions are approximately in-phase. From all the obtained data we could conclude that it is impossible to apply the known 0D predator-prey models to explain the observed differences at different radii. Quasi-coherent fluctuations (QCFs) were also discovered in the spectra of the DBS amplitude fluctuations.