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In this Thesis we explore parametric decay instabilities (PDIs) in the electron cyclotron resonance heating (ECRH) beams at the ASDEX Upgrade tokamak. PDIs are nonlinear phenomena leading to decay of a strong quasi-monochromatic pump wave to two daughter waves once the amplitude of the pump wave exceeds a threshold determined by the interaction strength between the three waves. Due to their reliance on large wave amplitudes, PDIs are found in applications involving high-power wave heating, for instance in connection with ECRH of the plasmas at ASDEX Upgrade to temperatures relevant for fusion of hydrogen isotopes (∼ 100MK) by means millimeter-waves generated by gyrotron sources. Conservation of energy in the three-wave process underlying PDIs requires the daughter waves excited by the instability to have a diﬀerent frequency from the pump wave used to excite them. This is a serious issue, as the ECRH beams at ASDEX Upgrade contain up to 1 MW of power, while the millimeter-wave diagnostics used to determine the plasma properties accept powers in the range of µW or lower. Even the conversion of a minuscule part of the ECRH power to millimeter-waves in the frequency range outside the protective ﬁlters around the ECRH frequency can thus have disastrous consequences for the millimeter-wave diagnostics, and this problem will be further ampliﬁed in a fusion power plant, which will rely heavily on millimeter- wave diagnostics due to their relative resistance to neutron damage. A further concern is that current theories suggest that a non-negligible part of the ECRH power can be converted to power in the daughter wave modes under certain circumstances, resulting in diﬀerent heating and current drive characteristics than those expected from linear ECRH theories, potentially jeopardizing more than the just the diagnostics of a fusion power plant. The studies at ASDEX Upgrade described in this work have been devised to assess the actual impact of PDIs in ECRH beams under fusion-relevant conditions, to avoid the abovementioned deleterious eﬀects, as well as to explore the possibility of utilizing such PDIs in novel diagnostic schemes. Our approach has been both theoretical and experimental in nature. We provide a detailed description of the theory behind PDIs, deriving some new and number of known results. With the developed theory and the ASDEX Upgrade ECRH system, we proceed to investigate PDIs experimentally. Our focus is on PDIs near the upper hybrid resonance (UHR) and its second-harmonic. The PDIs near the UHR occur in connection with injection of 105 GHz radiation for collective Thomson scattering (CTS). Using analog modulation of the ECRH power, a sweep of the toroidal magnetic ﬁeld strength, and the ASDEX Upgrade CTS system, we are able to demonstrate agreement between the experimental PDI threshold and the PDI threshold expected theoretically. Additionally, we are for the ﬁrst time able to characterize secondary and tertiary PDIs near the UHR in a controlled laboratory setting. A simple increase of the toroidal injection angle of the gyrotron beam is found to suppress these instabilities in usual cases. The PDIs near the second-harmonic UHR are investigated in the standard 140 GHz ECRH scenarios at ASDEX Upgrade. These instabilities require the daughter waves to be trapped near the PDI region in order to be accessible at the power levels available with ECRH gyrotrons. They therefore occur when the second-harmonic UHR is located near a local density maximum, e.g., the center of an edge localized mode (ELM) ﬁlament, the O-point of a magnetic island, or the plasma center. PDIs in connection with ELMs are investigated in standard second-harmonic ECRH scenarios and found to be of limited concern to millimeter-wave diagnostics, but of potential diagnostic value. The PDI threshold during the passage of an ELM ﬁlament expected theoretically is found to be is reasonable agreement with the experimental PDI threshold observed during ELM crashes, and the duration of the microwave spikes during an ELM crash are additionally found to be in agreement with the passage time of an ELM ﬁlament through an ECRH beam according to a nonlinear magnetohydrodynamics simulation. The PDIs in connection with magnetic islands and near the plasma center are of more concern, as they have been found to damage mixers of the electron cyclotron emission (ECE) system due to the generation of strong millimeter-wave signals near half the ECRH frequency. For the PDIs in connection with magnetic islands, we have reproduced the original results from the TEXTOR tokamak and additionally shown the occurrence of such PDIs in third-harmonic ECRH experiments for the ﬁrst time; we have also made the ﬁrst observations of PDIs near the plasma center in third-harmonic ECRH experiments. The mere vicinity of an island to the overlap of an ECRH beam and the second-harmonic UHR is, however, found to be insuﬃcient for the generation of strong millimeter-wave signals, highlighting the need for a more detailed characterization of the electron density proﬁle associated with magnetic islands. The PDIs in third-harmonic ECRH scenarios are a potential risk to the ECE system in the early operation phase of ITER. They can, however, be mitigated by minimizing the ability of the ECE radiometers to pick up signals generated in the ECRH beams.
|Place of Publication||Lyngby, Denmark|
|Publisher||Technical University of Denmark|
|Number of pages||140|
|Publication status||Published - 2019|