Stabilization of magnetic islands in tokamaks by localized heating and current drive : a numerical approach

This thesis deals with the theory of active stabilization of the so-called Neoclassical Tearing modes (NTMs) in fusion reactors. Hot fuel, in the form of a fully ionized gas (referred to as "plasma"), is confined by a magnetic field with the topology of toroidally nested magnetic surfaces. The NTM is a spontaneous break of this magnetic configuration, leading to a non-symmetric topology characterised by a chain of magnetic islands. Within a magnetic island temperature and pressure are flattened. The NTM onset occurs when the plasma pressure exceeds a certain limit. Since the fusion power is proportional to the pressure squared, NTMs limit the performance of the reactor. Active stabilization of such instabilities can yield an enhanced performance of the fusion reactor of up to 50%. For this reason, it is important to study the mechanisms responsible for their growth and achieve a reliable control strategy. Control and suppression of NTMs is achieved experimentally by depositing highly localized radio-frequency power, in the range of electron cyclotron frequency (EC), at the island location. Qualitatively, the effect of the localized EC power on magnetic islands is twofold: it makes the island formation more difficult, and it compensates for the effect of the temperature flattening inside the island region by a local increase of the temperature and by inducing a current inside the island. These effects are referred to as Electron Cyclotron Resonance Heating (ECRH) and Electron Cyclotron Current Drive (ECCD), respectively. The thesis addresses the stabilizing contribution of ECRH and ECCD, on the temporal evolution of a magnetic island. This model relies on the equation for the evolution of the magnetic island width, the generalized "Rutherford" equation (GRE), which depends on the different driving and stabilizing mechanisms. There are three main open questions that this work tries to answer: the relative merits of ECRH and ECCD, the role of asymmetries in the magnetic island topology and finally the determination of a criterion for full NTM suppression. The research focused at first on the relative merits of each method. The conditions determining the relative importance of ECRH and ECCD are found to depend on the product of two factors, the efficiency with which ECRH or ECCD generates a current inside the magnetic island and a geometrical factor showing essentially different scalings for either ECRH or ECCD. For a fusion reactor like ITER the main stabilizing mechanism for a magnetic island is found to be the ECCD, while ECRH becomes relevant in smaller devices. In the following step an extension of the model allowed to treat asymmetries in the island shape and to discuss their effect on the ECCD and ECRH contribution to the island evolution. This study demonstrates that these deformations have a small or negligible impact on the tearing mode evolution. Opposing claims in the existing literature could be shown to be based on inappropriate approximations or comparisons. The last part of the thesis is devoted to the determination of the requirements for the suppression of a magnetic island. This is usually described by the parameter ¿NTM, defined as the ratio between the local driven current density, responsible for the stabilization of the mode and the local bootstrap current density, the drive of the NTM instability. An extensive analysis allowed to formulate a general criterion for the full NTM suppression in the form of a combined criterion for the maximum allowed width of the EC power density profile and a minimum required EC driven current. The results of this analysis have been used to suggest an improvement of the design of ITER-ECRH system. A moderate increase of the angle with which EC waves are injected into the plasma of up to 5¿ from its present design value is shown to reduce the power requirement by up to 25%. In conclusion, the theoretical work presented in this thesis has provided a comprehensive analysis of the stabilization of a magnetic island by means of the localized heating and driven current. The proposed model verifies and improves criteria for the design of ITER-ECRH system. Finally, it provides a sound theoretical basis for the design of NTM feedback control loops