Analysis of plasma dynamic response to modulated electron cyclotron heating in TCV tokamak

The need of durable, economically acceptable and safe energy sources continues to stimulate studies in a field of thermonuclear fusion. The most successful solution for controlled magnetic fusion is the tokamak. The improvement of tokamak performance depends on the optimization of pressure and current density spatial distributions which can be modified by means of an auxiliary heating and a current drive. Electron cyclotron heating, in particular is a very important tool for the study and control of basic physical processes governing plasma confinement and stability, particularly because it allows the injection of highly localized intense power. ECH power deposition location plays a crucial role in sawtooth control and suppression, it is also important for tearing mode stabilization, and for implementation of closed loop systems for automatic control/suppression of magnetohydrodynamic activity. A part of the ECH power can be modulated (MECH), and used to identify where the ECH power has been deposited, and can also be useful in the experimental analysis of the electron transport in general. Nevertheless, despite the goal of MECH being a diagnostic and analysis tool, MECH can couple to plasma oscillations, such as sawteeth. MECH-sawtooth phase coupling adds significant complications in ECH deposition location and transport analysis, in some cases making the interpretations of results misleading. This is why it is important to get an insight into the phenomenon of MECH-sawtooth interaction, and to establish the boundaries where conventional types of modulation analysis can be successfully implemented. This thesis presents the analysis and interpretation of perturbative MECH experiments performed in the TCV tokamak with particular attention paid to the non-linear phase coupling of heat waves. TCV is equipped with a very flexible and high power ECH system. Two independent ECH systems permit MECH to be deposited at two different spatial locations, with two different types of modulating signals. This set-up was used to study simultaneous propagation of heat waves induced by MECH in non-sawtoothing plasmas, and in discharges with sawtooth activity. A new analysis method for the characterization of the plasma non-linear dynamic response to modulated heating was developed on the basis of Higher Order Spectral Analysis (HOSA) technique. This method applied to signals from different diagnostics, such as electron cyclotron emission and soft X-ray measurements, was extensively used to quantitatively characterize the effect of nonlinear phase coupling. In sawtooth free discharges a detailed analysis of the propagation of heat waves demonstrated that their phase coupling is solely related to properties of heat sources. It was demonstrated that if two heat waves are induced by non-coupled power sources (multi-beam MECH) then no phase coupling occurs. In the opposite case, when a source of perturbation (MECH) contains coupled harmonics, the corresponding heat waves demonstrate phase coupling. It was shown that these coupled heat waves loose their phase coherence while propagating in plasma. The dissipation of phase coupling is due to different phase velocities of heat waves and their diffusive damping. The new type of ECH power modulation accompanied with bicoherence analysis was proposed as a candidate for a reliable identification of EC power deposition location in a case of high frequency and low modulation depth MECH, including multi-beam heating. This type of MECH can be particularly important for real time control applications. In cases when MECH is applied to sawtoothing plasmas a direct experimental evidence of MECH-sawtooth non-linear phase coupling has been demonstrated using HOSA techniques, in particular bispectrum and bicoherence profiles. The detailed analysis presented here demonstrates a direct proof of periodic modification of sawtooth behavior by modulated ECH. It was shown that a simple diffusive model for the perturbed electron temperature with MECH source term can not be used for transport analysis in the presence of MECH-sawtooth coupling. Self-consistent time dependant transport simulations including a sawtooth relaxation model is capable of properly reproducing the effect of MECH-sawtooth phase coupling and can be used for transport analysis. On the basis of these simulations, an hypothesis for MECH-sawtooth coupling based on periodic modifications of magnetic shear was proposed. Additional information provided by HOS analysis enabled a correct interpretation of the plasma dynamic response to modulated heating in the presence of MECH-sawtooth coupling.