含俘获粒子的绝热非线性波：II。波离散度
Adiabatic nonlinear waves with trapped particles: II. Wave dispersion
摘要：
本文导出了无碰撞等离子体中绝热正弦朗缪尔波的非微分形式的一般非线性色散关系，允许俘获电子的任意分布。线性介电函数的推广，和非线性动力学频移$ω_{\rm NL}$被发现作为一个函数的波振幅$a$解析。平滑分布像往常一样产生$ω_{\rm NL} \propto \sqrt{a}$。然而，束状分布的陷阱电子导致不同的幂律，甚至对数非线性，这是作为相同的色散关系的渐近极限。这样的光束形成时，相速度的变化，因为被困的分布是在自共振，从而从通过分布不同的演变。因此，即使绝热的$ω_{\rm NL}(a)$一般也是非定域的。
英文摘要：
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift $ω_{\rm NL}$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $ω_{\rm NL} \propto \sqrt{a}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic $ω_{\rm NL}(a)$ is generally nonlocal.
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