含俘获粒子的绝热非线性波：III。波动力学
Adiabatic nonlinear waves with trapped particles: III. Wave dynamics
摘要：
绝热波的演化与自共振被困粒子描述的拉格朗日模型中开发的文件I，假设这些粒子的作用分布是保守的，特别是，它们的数量在每个波长是一个固定的独立参数的问题。作为一个典型的例子，一维非线性朗缪尔波与深陷电子。对于驻波，从作用量守恒定理的观点解释了隧穿进入过临界等离子体的现象。对于非定常波，根据初始参数$S$，这是被捕获的粒子所携带的能量通量的比，通过粒子进行定性不同的制度实现。在$S < 1/2$处，波是稳定的并且表现出群速度分裂。在$S > 1/2$中，俘获粒子调制不稳定性（TPMI）的发展，与现有的TPMI理论相反，但与一般的边带不稳定性理论一致。值得注意的是，非线性薛定谔方程没有捕捉到这些效应，而薛定谔方程传统上被认为是波自作用的通用模型，但忽略了被捕获粒子的振荡中心惯性。
英文摘要：
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter $S$, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At $S < 1/2$, a wave is stable and exhibits group velocity splitting. At $S > 1/2$, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schrödinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
