Ph.d.-forsvar af Mads Givskov Senstius: Simulations of Three-Wave Interactions in Microwave Heated Fusion Plasmas

Principal Supervisor

Senior Scientist Stefan Kragh Nielsen, DTU Physics


Professor Roddy Vann, University of York, United Kingdom


Associate Professor Mirko Salewski, DTU Physics

Associate Professor Dr. Bengt Eliasson, University of Strathclyde, United Kingdom

Dr. Carsten Lechte, University of Stuttgart, Germany

Chairperson at defence

Professor Jens Juul Rasmussen, DTU Physics


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A copy of the PhD thesis is available for reading at the department and on request 



Through thermonuclear fusion of light elements, we wish to develop a clean, safe and reliable source of energy. A popular concept for such a fusion reactor is based on confining a hot plasma fuel by subjecting it to a strong magnetic field. Microwave beams are commonly employed to both heat and diagnose the plasma. During the past 20 years, the microwave beam power has increased to a point where reactors may now be equipped with several microwave source capable of producing a MW each. According to traditional estimates, a microwave beam carrying such power should still behave as predicted by linear theory. An exception was known to be in a resonant region of the plasma called the UH layer. At the UH layer, wave amplification can lead to nonlinear three-wave interactions known as parametric decay instabilities (PDIs). PDIs can excite daughter waves in the plasma at the expense of a strong pump wave such as a high power microwave beam. The pump wave may decay into the daughter waves if selection rules are satisfied and the process becomes unstable above a pump amplitude threshold. In spite of being below estimates for pump amplitude thresholds, observations of signatures of PDIs during heating experiments have started to be reported with the increase in microwave beam power. Although the heating beams do not reach the UH layer in those experiments, the UH layer is still believed to play an important role.

In this thesis, we study PDIs near the UH layer numerically using a particle-in-cell (PIC) code. PIC codes are fully kinetic and make only few assumptions about how the fusion plasma behaves. This way, we can uncover which effects are important in reproducing experimental observations without making potentially biased assumptions about them first. The price is that the simulations are demanding and require the use of high performance computing (HPC) clusters.

First, a relatively simple setup of PDI near the fundamental UH layer is investigated. This is relevant, in particular, to a diagnostic known as collective Thomson scattering (CTS) and heating using electron Bernstein waves (EBWs). We show that wave amplification near the UH layer occurs, which helps overcome the PDI pump threshold. Above a threshold we demonstrate that an electron pump wave can excite an ion wave and another electron wave, satisfying PDI selection rules. Additionally, linear mode conversion is shown to take place at the UH layer. It is shown that the wave resulting from the linear conversion also decays through PDIs.

Next, we investigate PDIs into trapped waves in non-monotonic background density perturbations. The trapping mechanism is linear wave conversion at the UH layer. With a non-monotonic density profile, multiple UH layers can form and some waves can be trapped in a perpetual cycle of linear mode conversion. We show that two types of PDIs known as two plasmon decay (TPD) and stimulated Raman scattering (SRS) can excite the trapped waves. The TPD instability is shown to have a higher growth rate than the SRS instability. For the first time, we demonstrate numerically that PDI into trapped waves can occur for parameters relevant to microwave beams in magnetically confined fusion plasmas.

Furthermore, we show that PDI is possible over a range of density shapes and magnitudes. We study the eigenmode nature of the waves trapped in non-monotonic density profiles and demonstrate that PDIs excite trapped waves only at a discrete spectrum of frequencies. Waves at these frequencies satisfy quantization conditions as they traverse their trapping regions. We show that exciting these eigenmodes can absorb a substantial part of the pump wave. The eigenmodes may in turn become unstable to further PDIs involving other eigenmodes and ion waves. With our PIC simulations, we demonstrate that a series of PDIs can produce emissions akin to experimentally observed spectra. This provides unprecedented numerical evidence that microwave beams in magnetically confined fusion reactors may be at risk of PDIs. The emissions produced in the PDIs may damage microwave sensitive diagnostics if they are not properly shielded.


fre 19 jun 20


DTU Fysik


The Technical University of Denmark
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