## 3 New Approach for the Slowing Down Detection and Comparison with On-Line Estimator at AUG  
For real time applications the new methodology herein suggested to track the slowing down of a mode is based on the fast Fourier transform (FFT) of the signals and is described in Section 3.1. Section 3.2 illustrates how the estimator can be applied to detect the presence of a mode rotating so slow to be considered as locked. Before describing the approach however, it has to be recalled what stated in the previous section. At AUG, the two coil system, composed by the SAT\({}_{\rm west}\) and SAT\({}_{\rm east}\) saddle coils, is used to evaluate a mode lock indicator for real time application (MAX:DISRTRIG). Two different thresholds are set in order to trigger different actions in real time and consequently to prevent a disruption to occur. The lower threshold (0.25 V) is used in the feedback network in control room (CR) to start a controlled ramp down for a safe landing of the pulse; the higher one (0.35 V) instead, in case the previous actions have not given the desired results, is used to open the mitigation valves. From now on, the previously mentioned thresholds of the indicator used in CR will be labelled as DISRTRIG25 or DISRTRIG35, respectively. Alternative Approach for Real Time Tracking of the \(n=1\) Modes and Aithomated Offline Detection of It's Locking  
Without any rotating mode, the measured radial perturbation are expected to be around zero and the FFT spectra of \(B_{F}^{\text{ns}}\) and \(B_{F}^{\text{ev}}\) show basically the effect of the intrinsic noise on the measurements. When a mode rotates, then slows down before eventually locking, it dominates the spectra. The slower and the wider the mode, the higher the amplitude of the spectrum at low frequencies. Consequently, the first step is the evaluation of the weighted average frequency of rotation of the mode for each measured radial perturbations:  
\[f_{\text{ev}}(t) = \frac{\sum\ f_{\text{f}}l_{\text{ev}}(t,f_{i})}{\sum\ l_{\text{ev} }(t,f_{i})} \tag{4}\] \[f_{\text{ns}}(t) = \frac{\sum\ f_{\text{f}}l_{\text{ns}}(t,f_{i})}{\sum\ l_{\text{ns} }(t,f_{i})} \tag{5}\]  
Spectra are evaluated considering the signals in a sliding time window of 50 ms previous to the time instance considered. In (4), (5) \(f_{i}\) is the i-th frequency of the spectrum and \(I_{\text{ns},ev}(t,f_{i})\) stands for the intensity at the frequency \(f_{i}\) at the time instance t.  
It is then possible to evaluate an average frequency of rotation from (4) and (5) as:  
\[f(t) = \frac{1}{2}f_{\text{ev}}(t)+\frac{1}{2}f_{\text{ns}}(t) \tag{6}\]  
An example of the different behaviours of the spectra at two different time instances is reported in Figure 2: one at which there is no mode or at which it rotates at a frequency higher than half of the inverse of the sampling rate of the coils (5 kHz) in Figure 2a, and another one 50 ms before the time instance of the disruption in Figure 2b. It should be stated that the higher limit for the detection of the rotating modes is 5 kHz instead of 10 kHz because of the Nyquist theorem. The sampling frequency of the measurements at 10 kHz is also due to the actual damping induced by the wall, shielding the coils and behaving \"de facto\" as a low-pass filter. In Figure 2a, the spectra are almost flat and the average frequency is around 2.5 kHz, while in Figure 2b spectra are indeed dominated by the slowing down mode. Considering what stated in the previous section, (6) cannot filter any influence of instabilities like the edge localized mode (ELMs). The dynamics of ELMs is linked to a relaxation process of the plasma and their influence on magnetic perturbations has been experimentally observed [3]. Figure 3b shows an example of a ELMy phase on the signals derived from the coils. As consequence of the currents flowing through Scape off Layer field lines and the conducting divertor itself, ELMs can be clearly observed as strong spikes [12] in the measured inner divertor shunt current, as shown in Figure 3a.