Simulations of Three-Wave Interactions in Microwave Heated Fusion Plasmas

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 amplication 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 amplication 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 nonmonotonic density prole, 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.