## 3 New Approach for the Slowing Down Detection and Comparison with On-Line Estimator at AUG
Figure 4 shows instead the spectra during the ELMy phase shown in Figure 3.  
In Figure 4a,b, even if ELMs show a broadband spectrum not peaked at the low frequencies observed by the slowing down of the mode, they cause oscillations in (6) and consequently the indicator  
Figure 4: Illustrative spectra obtained from Bew and Bns for the pulse 30492 that has also been shown in Figure 3. (**a,b**): ELMy spectra without a rotating mode -evaluated averaging the spectra obtained from 4.0 s to 4.5 s with a time window of 50 ms- (**c**) spectra close to the disruption \(t_{disr}\ =\ 7.516\)s (with the same scale of (**b**)) –evaluated averaging the spectra obtained from 7.465 s to 7.515s with a time window of 50 ms.  
Figure 3: Illustrative example for an Edge localized model (ELMy) phase of the pulse 30492. (**a**): Inner divertor shunt current; (**b**) integrated difference of \(\pi\)-opposed coils (ns and ew respectively). follows the averaged frequency evaluated by the FFT. To avoid this bias, a driving sinusoidal functions has been added to the radial measurements Bew and Bns in a post-processing phase:  
\[ \begin{array}{rcl}B_{r}^{\text{{\it ms}},\text{{\it adv}}}&=&B_{r}^{\text{{\it ms }}}+\text{A}_{0}\sin(\omega_{0}t)\\ B_{r}^{\text{{\it ev}},\text{{\it adv}}}&=&B_{r}^{\text{{\it ev}}}+\text{A}_{0} \sin(\omega_{0}t+\psi_{0})\end{array}  \tag{7}\]  
A sensitivity study, has been performed and it suggests to set an amplitude of \(\text{A}_{0}~{}=~{}1 mT\) and a frequency of \(\text{\
u}_{0}~{}=~{}\frac{\omega_{0}}{2\pi}~{}=2.5\) kHz. Figure 5 reports an example of the behaviour of the average frequency (6) of rotation of the mode for the pulse 30735 varying the amplitude \(\text{A}_{0}\). A too small amplitude cannot damp the effects of unwanted perturbations on the magnetics, like \(\text{A}_{0}~{}=~{}0\), while a too high one is almost insensitive to any perturbation, like \(\text{A}_{0}~{}=~{}10 mT\). The main effect of the added sinusoidal function is to lock the average frequency of rotation of the mode (6) to a reference value, \(\text{\
u}_{0}\), when no mode can be observed or when it rotates at a frequency higher than 5 kHz, like in Figure 6, for the pulse 30492. When a mode appears, starts slowing down and growing, the influence in the (4,5) averages of the sinusoidal frequency \(\text{\
u}_{0}\) becomes negligible and the indicator tracks the mode. A clearer drop in frequency with respect to the basic signal, can  
Figure 5: (**a**) Plasma current for the pulse 30735; (**b**, left). Inner divertor shunt current where ELMs can be clearly seen up to the disruption at 7.506 s (**b**, right) zoom, between 6 s and 6.5 s, of the illustrative ELMy phase; (**c**) Mirnov coil spectrogram showing the ELMy phase. (**d**) The averaged frequency estimator obtained with three different amplitudes for the sinusoidal added term. The highest the amplitude, the less sensitive to oscillations the indicator is. A trade-off between robustness and reliability can be achieved using an amplitude of 1 mT. be observed indeed at 7 s and in this case, it is enough for recognizing the slowing down with the estimator suggested. Figure 6: **(a,b)** Exemplificative spectra obtained from Bew and Bns for the discharge 30492 and the averaged frequency indicator evaluated during the whole pulse. **(a)** Same averaged spectra as in Figure 4b, but showing also the frequency of the sinusoidal driving term. Spectra are dominated by the ELMs and the added sinusoidal term locks the averaged frequency estimator around 2.5 KHz as it can be observed in **(d)**. **(b)** Same averaged spectra as in Figure 4c, evaluated in a time window close to the disruption. The effect of the added term becomes secondary and the estimator in **(d)** follows the slowing down of the mode. **(c)** Mirnov coil spectrogram between 6s up to the time instance of the disruption at 7.516 s. A \(n=2\) mode oscillates at a frequency higher than 5 KHz before 7.0 s; from that instant onward an evident activity can be observed also due to \(n=1\).