含俘获粒子的绝热非线性波：I.一般形式主义
Adiabatic nonlinear waves with trapped particles: I. General formalism
摘要：
本文对无碰撞等离子体中含囚禁粒子的一般非耗散准周期非线性波发展了一种拉格朗日形式。绝热时均拉格朗日密度$\mcc{L}$用单粒子振荡中心哈密顿量表示;一旦找到这些哈密顿量，就可以导出完整的几何光学方程组，而无需参考麦克斯韦-弗拉索夫系统。被捕获的粒子的数量被假定为固定的;特别是，那些可能靠近波捕获势的底部，所以它们永远不会被捕获。然后，它们对波动量和能流的贡献主要取决于作为独立参数的捕获粒子密度和相速度，而不是明确地取决于波振幅$a$;因此，$\mcc{L}$获得了$a$独立项。此外，波的作用一般是不守恒的，因为它可以与捕获粒子密度的共振振荡交换。明确地找到了相应的波包络方程的修正，并导出了新的作用流速。这些结果的应用留给了该系列的其他两篇论文，其中涉及到与被困粒子的波的性质和动力学有关的具体问题。
英文摘要：
A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density $\mcc{L}$ is expressed in terms of the single-particle oscillation-center Hamiltonians; once those are found, the complete set of geometrical-optics equations is derived without referring to the Maxwell-Vlasov system. The number of trapped particles is assumed fixed; in particular, those may reside close to the bottom of the wave trapping potential, so they never become untrapped. Then their contributions to the wave momentum and the energy flux depend mainly on the trapped-particle density, as an independent parameter, and the phase velocity rather than on the wave amplitude $a$ explicitly; hence, $\mcc{L}$ acquires $a$-independent terms. Also, the wave action is generally not conserved, because it can be exchanged with resonant oscillations of the trapped-particle density. The corresponding modification of the wave envelope equation is found explicitly, and the new action flow velocity is derived. Applications of these results are left to the other two papers of the series, where specific problems are addressed pertaining to properties and dynamics of waves with trapped particles.
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