## 2 Definition of the Problem  
In the Introduction, it has been stated that the presence of magnetic islands in Tokamaks is quite endemic; in this section a few more details are provided, but a complete treatment is out of the scope of the article. The most common approach to describe the plasma in a magnetically confined configuration is of a charged fluid description called magneto-hydrodynamic (MHD). If the conductivity of the plasma is considered infinite, the approach is ideal, otherwise resistive. Generally, the ideal modes, or instabilities, grow faster than resistive ones and are more difficult energetically to excite [3]. The so called tearing modes then, i.e., magnetic island from now on, appear in both descriptions and are related to the local modification of the magnetic topology. The overall stability is driven by the radial gradient of the equilibrium toroidal current density and the so called resonant surfaces represent poles of the perturbed force equilibrium equation [1,3]. These resonant surfaces are located at the rational values of the safety factor \(q\propto\frac{B_{\phi}}{B_{\theta}}\) and consequently are usually indicated by \(q\propto\frac{m}{n}\), where the integer \"m\" and \"n\" stand respectively for the number of toroidal and poloidal revolutions around the torus that a field line travels before reconnecting to itself [3]. On resonant surfaces it can be demonstrated that even small perturbations of the magnetic field dominate [2,3]. It is the case of the radial component of the magnetic field, defining both the width of the magnetic islands and their growth rate [2,3]. Such perturbations can be due to topological fluctuations of the plasma, but also to external field errors of few Gauss [1,4]. Theoretically, the proximity to the conducting wall stabilizes the mode but, at the same time, induces currents that tend to brake the mode itself [3]. It has been shown both experimentally and theoretically that the slower the rotation of a mode in the reference frame of the laboratory is, the faster its growth and the more dangerous it is. Indeed, the mode rotates with the plasma and both its width and its growth rate \(\left(\tau_{gr}\right)\) depends of the angular frequency of the rotation \(\left(\omega\right)\). If \(\omega\tau_{gr}\gg 1\) the island does not grow fast enough to reach a dangerous level [3] and does not lock. This can be achieved by external sources of momentum, like the injections of neutral particles beams, to facilitate the rotation of the mode, or by increasing locally the electron density. Typically, m/n = [1/1; 2/1] modes are observed both at AUG and JET and the m/n = 3/1 modes are also coupled with the aforementioned islands [6,7]. However, their coupled dynamics is still not completely understood and consequently, a good knowledge of the radial magnetic field is an important element to prevent disruptions to occur. Six saddle coils are currently installed on AUG, as shown in Figure 1, on the high field side to measure the radial perturbation induced by rotating modes: two large saddle coils, each covering half of the torus (SAT\({}_{\text{west}}\) and SAT\({}_{\text{east}}\)) toroidally and four more coils, since 2011 [7], each spanning \(\pi\)/2 of the torus (SATn, SATw, SATs and SATe) toroidally. Once integrated and filtered, the measurements of the two coils systems are used as an indicator to monitor the presence of a locked mode in real time. An anomalous behaviour of such time trace triggers disruption mitigation actions. The four coils are used instead to either induce or measure radial perturbations to the magnetic field for experimental purposes [7,12]. In the latter case, both the amplitude and the phase of the mode can be obtained. The time integrated and calibrated measurements represent the signals of the radial component of the magnetic field collected into the toroidal portion spanned by the saddle coils.