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.

非单调等离子体密度结构（例如斑点和磁岛）会产生被困上层混合 (UH) 波。满足 Bohr-Sommerfeld 量化的捕获 UH 波可以被认为是腔的本征模式。使用完全动力学的细胞内粒子模拟，我们验证了这些 UH 本征模式的存在，并证明了它们的重要性，因为只有本征频率对三波相互作用变得不稳定。本征模式可以通过 X 模式泵浦波的参数衰减不稳定性 (PDI) 以大约 UH 频率的两倍来激发，就像回旋束穿过磁约束聚变等离子体中的 blob 的情况一样。我们推导出 UH 波的波数的闭合表达式，它在接近 UH 层和电子回旋共振时都是准确的。这允许快速分析非单调结构中的本征模式。非均匀等离子体中 PDI 子波放大的表达式被扩展到衰减区域，其中前几个导数消失。根据对流 PDI 的放大，我们估计了涉及陷波的绝对 PDI 的增长率。我们表明，由于子波的俘获，在我们的模拟中通过 PDI 激发的本征模式确实是绝对的，而不是对流的。此外，我们表明只有本征模式通过 PDI 被激发，并且我们能够预测子波的增长率以及它们如何随泵浦波强度而缩放。这是支持分析理论的基本假设的证据，该假设描述了在二次谐波电子回旋共振加热 (ECRH) 期间磁限制聚变实验中观察到的低阈值强散射。这种低阈值不稳定性会降低 ECRH 的性能，但也为离子加热或诊断提供了新的用途。