Signal processing techniques based on singular value decomposition applied to modulated ECH experiments

The analysis and interpretation of perturbative modulated electron cyclotron heating (MECH) discharges for power deposition localization using different diagnostics, such as electron cyclotron emission (ECE) and soft x-ray (SXR) measurements, are presented. In particular, the experimental determination of the MECH power deposition is investigated, which is a fundamental requirement, for example, for heat transport studies. The most important problem is related to the coupling between the MECH and the sawtooth activity of the plasma, which disturbs both ECE and SXR measurements. Several techniques have been adopted to circumvent this difficulty. In particular, the singular value decomposition (SVD) and the generalized singular value decomposition (GSVD) have been tested. However, both methods are incapable of treating the problem correctly, which leads to potential misinterpretation of the results. A new method based on system identification using the SVD (SI-SVD) is developed and applied. This method, within reasonable limits induced by the assumption of linearity, is capable of simultaneously separating the MECH from the sawtooth contributions to both ECE electron temperature measurements and SXR emission measurements. Such a method is in particular applied to a neutral beam injection (NBI) heated ASDEX Upgrade discharge in which MECH is added in order to analyse electron heat transport in a mostly ion-heated plasma. Since the NBI heating is also partly modulated with short pulses which coincide with the sawtooth crashes to improve their stability, both the MECH and the NBI deposition profiles are determined. Moreover, treating the signals with the SI-SVD procedure enables a study of the plasma dynamic response also at higher MECH harmonic numbers.