The integrands in the dispersion equation are not integrable in general , so we used the asymptotic expansion solution to analyze the behavior of the dispersion relation at the singularity and mapped the dispersion relation curves approximately the system composed of collisionless particles which obey maxwellian distribution or all kinds of degenerate distribution , even in their mixture system , their dispersion relation are analogous 一般来说，色散方程中的被积函数都是难以求积的，本文是用函数逼近法分析色散方程在奇点处的行为，并大致划出色散关系曲线。由无碰撞粒子组成的系统，不管初始分布是maxwell分布还是各种简并分布，甚至是这些分布的混合体，色散关系都是相似的。
2.
In this paper , we focus on the following three topics : ( i ) density distribution of dusty plasma in the low - pressure collisionless positive column the radial density distributions of electron , ion and dust particle in the low - pressure collisionless positive column are investigated with a fluid theory and a self - consistent dust - charging model 本文着重以下三个方面的研究： ( )低气压无碰撞辉光放电正柱区尘埃等离子体密度径向分布本文采用流体模型和自洽的尘埃充电模型，研究了低气压无碰撞辉光放电正柱区的电子密度、离子密度和尘埃粒子密度的径向分布。
3.
( iii ) dust charging and levitation in cathode sheath of glow discharges with energetic electron beam . the dust charging and levitation in a collisionless cathode sheath of dc glow discharges with energetic electron beams released from a plane cathode are investigated with a self - consistent theoretic model ( )尘埃粒子在极板有高能电子束发射辉光放电鞘层中的充电与悬浮采用自洽的鞘层模型和尘埃粒子充电模型，我们研究了在极板有高能电子束发射辉光放电鞘层中尘埃粒子的充电与悬浮。
4.
First , we extended the liberman model of collisionless rf sheath . taking into account elastic collisions and charge - exchange collisions between ions and neutral particles , we established a self - consistent model describing the dynamics of rf sheath driven by a sinusoidal current source . the effects of collisions and rf - biased source power on the instantaneous thickness of the rf sheath and the sheath electric fields were studied 首先将liberman的无碰撞射频鞘层模型进行推广，考虑了离子与中性粒子的电荷交换碰撞效应，建立了描述碰撞射频等离子体鞘层动力学特性的自洽模型，研究了碰撞效应，射频偏压，电源参数等对射频鞘层的瞬时厚度及电场分布的影响。
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We have summarized a set of theoretical approach to this problem and discussed the instability of the gas cloud and the systems composed of collisionless particles in the background of dark matter . linear perturbation theory is the method to solve this problem , in which , we add the perturbation into the equilibrium state and discussed its evolution 本文研究了自引力系统的稳定性问题，总结了解决该问题的一套理论方法。并具体研究了存在暗物质背景时气体云和无碰撞粒子系统中扰动的演化情况。解决稳定性问题的方法用线性扰动理论，即在平衡态中加入扰动，研究扰动在系统中的演化情况。
