# Review of Advanced Implementation of Doppler Backscattering Method in Globus-M
## 3 Application Results
### Limit Cycle Oscillations  
The four-frequency microwave DBS system was used to study a variety of limit cycle oscillations (LCO) characteristics (see Table 4 in the end of Section 3.2) on Globus-M. LCOs were discovered in plasma discharges with neutral beam injection (NBI) when the direction of the magnetic field was favorable for transition to H-mode (i.e., the toroidal ion drift was  
Figure 3: Coherence spectrum C(f) and cross-phase spectrum \(\phi\)(f) of two Doppler shift oscillations recorded by reflectometers positioned at poloidal angles \(-30^{\circ}\) and \(45^{\circ}\), (\(\#34504\), time = 170 ms) [44]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Investigated Property** & **Range of Values** & **Notes** \\ \hline Mode of operation & Ohmic heating regime & not detected in H-mode \\ \hline \(f\), kHz & 23–28 (D) \(\sim\)36 (H) & Gao formula, influenced by isotope effect [40] \\ \hline Spectral peak width \(\Delta f\), kHz & 2–6 & consistent with the inverse of the GAM burst lifetime \\ \hline Type & burst & Predator-prey model [41] \\ \hline tlifetime, ms & 0.2–0.4 & determined as the time of damping of the velocity autocorrelation function \\ \hline Modulation frequency\(f_{\text{mod}}\), Hz & 300 & assumption of relation to the evolution of the ion pressure gradient \\ \hline Amplitude, kV m\({}^{-1}\) & up to 3 & exceeds the mean radial electric field \\ \hline Location R, m & 0.56 & related to the sharp decrease in the safety factor values followed by Landau damping [41] \\ \hline Location width, cm & 1 & global GAM eigenmode nature \(\lambda_{\text{GAM}}=\text{L}_{\text{f}}^{\dagger}\hat{p}_{\text{f}}^{\dagger}\)[43] \\ \hline Poloidal structure & m = 0 & Linear dynamics of zonal flow modes [41] \\ \hline Non-linear interaction with turbulences & present & the influence of turbulent Reynolds stress on zonal flows or GAMs [41] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of GAMs in Globus-M.  
directed towards the X-point). LCOs were found in the form of low-frequency (5-9 kHz) oscillations in E \(\times\) B drift velocity with the duration of their existence ranging from 2 to 20 ms [46]. Low frequency LCOs (\(\sim\)6 kHz) led to a transition to H-mode while high frequency LCOs (\(\sim\)8.5 kHz) resulted in the transition to L-mode or even in a disruption. The LCO frequencies in Globus-M are much higher in comparison to medium size devices [47]. A strong radial dependence of LCO frequency was not predicted by the model of limit cycle oscillations induced by a predator-prey coupling of turbulence with zonal flows [48]. However, it is in accordance with the Stringer spin-up mechanism [49]. The multichannel DBS system made it possible to estimate the velocity shear \(\omega_{\rm s}\) of the oscillations at LCO frequency. The amplitude of these oscillations was about 10\({}^{5}\) s\({}^{-1}\), but it increased up to 10\({}^{6}\) s\({}^{-1}\) just before L-H transition in the case of the low frequency LCOs. The transition to H-mode after these LCOs can be caused by an increase in the efficiency of the action of the oscillating velocity shear on the plasma turbulence while decreasing its oscillation frequency [50; 51]. A periodic suppression of the turbulence power was observed as well. However, in the event of the high LCO frequency, the turbulence level would decrease not to zero, but to a certain value, after which it began to increase (standard oscillations). For the lower LCO frequency, the turbulence level decreased periodically to zero. Such bursty dynamics were also observed on TCV [52].