长滑行带电粒子束中非线性行波脉冲（孤子）与行波扰动的一维动力学描述
One-dimensional kinetic description of nonlinear traveling-pulse (soliton) and traveling-wave disturbances in long coasting charged particle beams
AI总结：
本文利用一维动力学模型研究长滑行带电粒子束在理想导电圆管中的非线性纵向动力学，推导平均轴向电场表达式，分析行波和孤子解的非线性特性，并考虑水袋分布和BGK类两类分布函数解。
摘要：
本文采用一维动力学模型，研究了长滑行束在半径为$r_{w}$的理想导电圆管中传输时的非线性纵向动力学特性。平均轴向电场可表示为$\rangle E_{z}\rangle=-(\frac{\text{d}}{\text{d}z})\rangle\boldsymbol{\theta}\rangle=-e_{b}g_{0}\frac{\text{d}\boldsymbol{\theta}_{b}}{\text{d}z}-e_{b}g_{2}r_{w}^{2}\frac{\text{d}^{3}\boldsymbol{\theta}_{b}}{\text{d}z^{3}}$，其中$g_{0}$和$g_{2}$为常数几何因子，$\boldsymbol{\theta}_{b}(z,t)=\text{d}p_{z}F_{b}(z,p_{z},t)$为束粒子线密度，$F_{b}(z,p_{z},t)$满足一维Vlasov方程。针对从中等振幅到大振幅束电荷密度调制的宽范围系统参数，本文详细研究了具有时间稳态波形的行波和行波脉冲（孤子）解的非线性特性。文中考虑了两类束分布函数解，分别对应：(a)非线性水袋分布，其中$F_{b}$在$p_{z}$空间的有界区域内为常数；(b)非线性Bernstein-Green-Kruskal（BGK）类解，允许被俘获和未被俘获的粒子分布与自生电场$\rangle E_{z}\rangle$相互作用。
英文摘要：
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric field is expressed as $\langle E_{z}\rangle=-(\partial/\partial z)\langleϕ\rangle=-e_{b}g_{0}\partialλ_{b}/\partial z-e_{b}g_{2}r_{w}^{2}\partial^{3}λ_{b}/\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $λ_{b}(z,t)=\int dp_{z}F_{b}(z,p_{z},t)$ is the line density of beam particles, and $F_{b}(z,p_{z},t)$ satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (a) the nonlinear waterbag distribution, where $F_{b}=const.$ in a bounded region of $p_{z}$-space; and (b) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field $\langle E_{z}\rangle$. .
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