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 second harmonic electron cyclotron resonance heating experiments in magnetically confined fusion experiments. We use the particle-in-cell code EPOCH to study conversion of a fast X-mode pump wave into a combination of half frequency X-mode and electron Bernstein waves and identify two regimes where PDIs can excite trapped electrostatic waves. Above the second harmonic upper hybrid (UH) density, a PDI known also as a two plasmon decay (TPD) instability excites a pair of UH waves that 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.

中文翻译：

---

具有非单调密度背景的磁化等离子体中参数衰减成俘获波的数值研究

参数衰减不稳定性 (PDI) 激发子波被困在具有非单调密度分布的磁化等离子体中。该研究的动机特别是在磁约束聚变实验中的二次谐波电子回旋共振加热实验期间观察到低阈值 PDI 特征。我们使用细胞内粒子代码 EPOCH 来研究快速 X 模式泵浦波向半频 X 模式和电子伯恩斯坦波的组合的转换，并确定 PDI 可以激发捕获的静电波的两种机制。在二次谐波上混合 (UH) 密度之上，PDI 也称为双等离子体衰变 (TPD) 不稳定性激发我们位于频率和波数空间中的一对 UH 波。在较低密度下，被称为受激拉曼散射的 PDI 可能会产生一个被捕获和一个返回的 X 模式子波，其增长率比 TPD 不稳定性慢得多。在这两种情况下，我们都表明子波的频率间隔以可预测的方式取决于密度。在衰减区域几乎没有损失的情况下，被捕获的子波在二次参数不稳定性 (PI) 方面变得不稳定，导致 UH 光谱的明显不同的相位。与初级不稳定性不同，次级 PI 显示依赖于离子动力学。此外，我们观察到由三次 PI 产生的 3/2 泵浦频率附近的逃逸波与最近提出的磁约束聚变实验期间的反向散射一致。