Assessing parametric instabilities of trapped microwaves in full spatio-temporal framework

The two-plasmon decay instability of high-power microwaves used for electron cyclotron resonance heating has been observed experimentally in multiple fusion devices. This type of instability is a nonlinear three-wave interaction that can transfer energy away from the cyclotron harmonics. Analytical models quantify exponential growth rates and power thresholds, but typically evaluate the growth as a spatially averaged gain over the interaction region of the instability. This description effectively excludes field inhomogeneities and noise, leaving their impact on the instability growth uncertain. We assess this assumption by solving the full nonlinear system on a spatial grid. Across all cases considered, we find that the instabilities drive the wave fields toward the spatially averaged behaviour. After a transient period that scales inversely with the instability growth rate, the simulated growth converges to the averaged prediction, indicating that the established models are asymptotically valid.