We present novel experimental evidence of parametric decay instability of microwave beams in the plasma edge of Wendelstein 7-X stellarator. We propose that the instability is sustained by trapping of only one daughter wave in the non-monotonic density profile measured with high spatial resolution within a stationary magnetic island. The power levels and spectral shapes of the detected microwave signal are reproduced by numerical modelling and a theoretical power threshold is predicted around 300 kW, comparable with observations. We predict a fraction of power drained by daughter waves around 4% in the experiments, potentially increasing above 50% for minor modifications of the density bump. Such absorption levels could significantly reduce the efficiency of the microwave heating and current-drive system in tokamaks and stellarators.

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Parametric decay instabilities (PDIs) exciting daughter waves trapped inside a magnetized plasma with a non-monotonic density profile are investigated numerically. The investigation is motivated in particular by observations of low threshold PDI signatures during 2nd harmonic electron cyclotron resonance heating (ECRH) experiments in magnetically confined fusion experiments. We use the particle-in-cell (PIC) code EPOCH to study conversion of a fast X-mode pump wave into a combination of half frequency X-mode and electron Bernstein waves (EBWs), and identify two regimes where PDIs can excite trapped electrostatic waves. Above the 2nd harmonic upper hybrid (UH) density, a PDI known also as a two plasmon decay (TPD) instability excites a pair of UH waves which we locate in frequency and wavenumber space. At lower densities, a PDI known as stimulated Raman scattering may produce one trapped and one returning X-mode daughter wave with a much slower growth rate than the TPD instability. In both cases, we show that the frequency separation of the daughter waves depends on the density in a predictable manner. With little loss from the decay region, the trapped daughter waves become unstable with respect to secondary parametric instabilities (PIs), leading to distinctly different phases of the UH spectrum. Unlike the primary instability, the secondary PIs are shown to depend on ion dynamics. Furthermore, we observe escaping waves near the 3/2 pump frequency resulting from tertiary PIs in agreement with recently proposed backscattering during magnetically confined fusion experiments.

Non-monotonic plasma density structures such as blobs and magnetic islands give rise to trapped upper hybrid (UH) waves. Trapped UH waves which satisfy Bohr–Sommerfeld quantization can be thought of as eigenmodes of a cavity. Using fully kinetic particle-in-cell simulations, we verify the existence of these UH eigenmodes and demonstrate their significance as only eigenfrequencies become unstable to three-wave interactions. The eigenmodes can be excited through parametric decay instabilities (PDIs) of an X-mode pump wave at approximately twice the UH frequency, as could be the case for a gyrotron beam traversing a blob in a magnetically confined fusion plasma. We derive a closed expression for the wavenumber of UH waves, which is accurate both close to the UH layer and to the electron cyclotron resonance. This allows for fast analysis of eigenmodes in a non-monotonic structure. An expression for the amplification of PDI daughter waves in an inhomogeneous plasma is extended to a decay region where the first several derivatives vanish. From the amplification in a convective PDI, we estimate the growth rate of the absolute PDI involving the trapped waves. We show that the excitation of eigenmodes through PDIs in our simulations are indeed absolute rather than convective due to the trapping of the daughter waves. Additionally, we show that only eigenmodes get excited through the PDIs, and that we are able to predict the growth rates of the daughter waves and how they scale with the pump wave intensity. This is evidence supporting a fundamental assumption of analytical theory describing low threshold strong scattering observed in magnetically confined fusion experiments during second harmonic electron cyclotron resonance heating (ECRH). Such low threshold instabilities can degrade ECRH performance but also offer novel uses for ion heating or as diagnostics.

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