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Dynamical aspects of tearing mode suppression by electron cyclotron heating and current drive in tokamak plasmas

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  1. Tez No: 402322
  2. Yazar: BİRCAN AYTEN
  3. Danışmanlar: PROF. DR. A. J. H. DONNE
  4. Tez Türü: Doktora
  5. Konular: Nükleer Mühendislik, Nuclear Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2013
  8. Dil: İngilizce
  9. Üniversite: Technische Universiteit Eindhoven
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 131

Özet

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Özet (Çeviri)

In a tokamak, the hot plasma required for efficient energy production by nuclear fusion is confined in a magnetic field. In the ideal case, the topology traced out by the field lines of this magnetic field forms a set of toroidally nested surfaces. Since the transport along field lines is very fast, these magnetic surfaces are also surfaces of constant pressure. Across the magnetic surfaces the transport is strongly inhibited due to the gyro-motion of the charged constituents of the hot plasma. Magnetohydrodynamic (MHD) instabilities can break up this magnetic topology. One of these instabilities is known as the tearing mode: it tears the magnetic field on the resonant surface, where the magnetic winding number equals the ratio of poloidal mode number to the toroidal mode number, to form magnetic islands. Inside a magnetic island, the temperature and pressure profiles are flattened as a consequence of the fast transport along the magnetic field lines. This leads to a loss of particle and energy confinement. Large islands are even observed to result in a disruptive termination of the tokamak discharge. Thus, developing effective strategies to suppress the magnetic islands is of high importance for future fusion reactors. Tearing mode suppression experiments have been performed successfully using both electron cyclotron heating (ECH) and electron cyclotron current drive (ECCD). Both of them are based on depositing highly localized radio-frequency power in the form of electron cyclotron waves at the island location. In the case of ECH, the heating inside the island reduces the resistivity, and consequently, increases the inductively driven current density. ECCD induces a current inside the island non-inductively. In both cases does the additional current inside the island result in suppression of the island. A theoretical description for the results of current experiments and their extrapolation to future fusion reactors is provided by the generalized Rutherford equation (GRE). This equation describes the time evolution of the width of the magnetic island. It consists of several terms expressing different stabilizing and destabilizing mechanisms. This thesis addresses the dynamical aspects of tearing mode suppression by ECH and ECCD from a theoretical point of view. In the first part of this thesis, experiments on tearing mode suppression by ECH and ECCD performed on the TEXTOR tokamak are modeled. The generation of the tearing mode was achieved in the experiment by the Dynamic Ergodic Divertor (DED) in a very controllable way. The theoretical model is based on the GRE in which the magnetic perturbation from the DED has an effect that is qualitatively very similar to the term responsible for the drive of the neoclassical tearing modes in high beta tokamaks. Satisfactory agreement was found between the modeling and the experimental data. Moreover, it was observed that these experiments can be well modeled with only the ECH term and using the parameters derived from the experiments. This confirmed the experimental observation that in TEXTOR heating is the dominant suppression mechanism for tearing modes above that of current drive. In conclusion, the modeling of the TEXTOR experiments provide a good benchmark for the stabilizing term arising from ECH in the GRE. 121 As localized current drive is the dominant suppression mechanism over localized heating for future fusion reactors, in the rest of the research the focus was on the stabilizing term originating from the current drive in the GRE. Conventionally, this is obtained by averaging the EC driven current density obtained from a linear calculation over an island rotation period. In this thesis this traditional approach was advanced in a first step by removing the averaging over the island rotation period and in a second step by studying the conditions for and effects of a nonlinear ECCD efficiency. The former may be of interest in case of relatively slow rotation as is the case for the next generation fusion devices, like ITER. We investigated the oscillations in the stabilizing term from ECCD in the GRE that arise from the rotation of the island through the power deposition region. This included the study of the dependence of these oscillations on the different parameters characterizing the problem: the collisional time scale on which the driven current is generated/ decays, the rotation period of the magnetic island, the island size, and the power deposition width. Moreover, the consequences for the island growth or the stabilization were analyzed. As a result of the linearity of the ECCD efficiency, for a constant island width the time averaged effect is identical to the effect of the rotation averaged current density profile. A net effect of these oscillations can only come from the time evolution of the island width during a rotation period. In this case we observe a slight increase in the stabilizing effect of ECCD and thus, a small reduction in the minimum power required to fully suppress an island. In a linear calculation, the EC driven current is simply proportional to the absorbed power density, with the constant of proportionality defining the current drive efficiency. However, due to the smallness of the volumes associated with the flux surfaces around the O-point of the magnetic island, the EC power density inside the magnetic island can exceed the threshold for non-linear efficiency as derived previously by Harvey et al., Phys. Rev. Lett., 62 (1989) 426. For this reason, in the last part of this thesis the non-linear ECCD efficiency is studied through bounce-averaged, quasi-linear Fokker-Planck calculations in the geometry as created by the magnetic islands of the tearing mode. These calculations show the possibility of significant non-linear effects on the ECCD efficiency, in particular, in the case of locked islands or when the magnetic island rotation period is longer than the collisional time scale. We studied a typical case from an NTM stabilization experiment on ASDEX Upgrade where the rays propagate tangential to the flux surfaces in the power deposition region. As a result, the whole power from a single ray is absorbed over a very narrow range of flux surfaces. This study shows that the non-linear effects result in an overall reduction of the current drive efficiency for absorption of the EC power on the low field side of the electron cyclotron resonance layer. This observation is explained by the quasi-linear flattening of the distribution function around the resonant velocities reducing the local absorption, which results in a further penetration of the power to regions in the plasma where the current drive efficiency is lower. As a consequence of the non-linear effects, also the stabilizing effect of the ECCD on the tearing mode will be reduced from the linear expectations. In conclusion, this thesis expands our knowledge on the physics of tearing mode suppression by ECH and ECCD by relaxing the assumptions made in the theoretical modeling and by investigating aspects that had not been touched on before.

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