Parametric decay instability in high-power microwave beams in the plasma edge of Wendelstein 7-X

In magnetically conned fusion plasmas, high-power microwave beams play a central role in plasma heating and current drive. The efficiency of the microwave system can, however, be affected by excitation of nonlinear parametric decay instabilities (PDI) along the beams if the injected power exceeds a given threshold.

In a PDI process, a strong wave decays into a pair of daughter waves in regions where energy and momentum conservation for the three waves are satised. The power threshold for parametric decay instability (PDI) during second-harmonic electron cyclotron resonance heating (ECRH) becomes accessible to present-day microwave sources if the beam trajectory intersects a non-monotonic density prole, where daughter waves can be trapped.

We investigate excitation of PDI in Wendelstein 7-X (W7-X) stellarator using a heterodyne radiometer with steerable line-of-sight. The radiometer can detect signals produced by daughter waves within approximately 1.2 GHz from the ECRH microwave frequency. The signal is mixed-down in two stages and sampled with a fast digitizer.

The spectral power density is computed with a Fourier transform and the calibration is performed using blackbody sources at different temperatures. We present experimental evidence of PDI in W7-X stellarator in magnetic congurations with a different number of magnetic islands in the plasma edge. In congurations where the O-point of the magnetic island is crossed by the microwave beams, we detect symmetric sidebands around the microwave frequency with a power threshold around 320 kW.

In these cases, PDI in the plasma edge is also supported by strong correlation of PDI-related signals with fluctuations in the island region, known as island localized modes. Signatures of PDI daughter waves is presented also in cases where microwave beams intersect the X-point between a pair of magnetic islands.

A broadband signal, stretching 500 MHz below the ECRH frequency is, here, detected together with symmetric sidebands. We propose a theoretical model for PDI in W7-X when the ECRH beams cross the O-point of an edge magnetic island. The model is developed for the first time from experimental proles of the decay region and shows that the instability can be sustained by trapping of a single daughter wave in the density bump created inside the island.

We predict the spectrum and power of the daughter waves, and provide a value for the instability power threshold of approximately 300 kW. Furthermore, the model predicts a fraction of power drained from the microwave beam in the experiments, around 4% and envisages absorption up to 50% for minor variations of the density bump.

This scenario is particularly alarming for stellarators like W7-X, where the stationary nature of the magnetic islands could potentially induce persistent power absorption for discharges as long as thirty minutes. A deeper understanding of PDI and the conditions necessary to excite it could, therefore, increase the ECRH heating efficiency.

Furthermore, generation of PDI daughter waves must be monitored in order to avoid harmful heat loads on microwave diagnostics and to reduce generation of fast electrons in the edge, potentially detrimental for plasma-facing probes.