A methodology for discriminating phase and amplitude effects on synchronization in tokamak pacing experiments

The control of macroscopic instabilities, such as Edge Localised Modes (ELMs) and sawteeth, is becoming an essential ingredient in the optimisation of scenarios in preparation for the next generation of tokamaks and the demonstrative reactor. Various pacing experiments have been indeed successfully carried out in many devices but various details of their interactions with the plasma remain poorly understood, in particular the assessment of the relative contribution of driver phase and amplitude to frequency synchronization. In this paper, a data analysis methodology for investigating the details of pacing experiments is proposed. The approach is based on the wavelet decomposition of the signals and the following implementation of information theoretic indicators, to determine the basic form of the interactions. The main analysis tool deployed is the conditional mutual information, equivalent to the informational transfer entropy, which can detect actual causal influences and not only statistical correlations between signals. The most flexible type of ELM pacing, the vertical kicks, permits to clearly confirm the potential of the analysis tools developed. In the dedicated experiments to optimise the ELMs pacing with pellets and sawteeth synchronization with ICRH modulation, the main effect is due to the influence of the amplitude of the external perturbations. Some evidence of phase synchronization has been found, in both JET and AUG, which indicates the direction of possible future optimization of the interventions. Indeed, adjusting the phase of the pacing schemes would free density and ICRH power to give more leeway to other feedback loops, an important aspect, particularly for the integrated control of the next generation of devices. The long-term objective of this line of research is therefore twofold. On the one hand, it is expected to contribute to better physical interpretation of the pacing experiments and possibly also of their target instabilities. From an operational perspective, hopefully these insights will help in the development of reactor relevant scenarios, as exemplified by examples of ELM a pacing with pellets carried out in preparation for the DT campaign on JET.