Pandya R V, Mashayek F
Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, Illinois 60607, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036405. doi: 10.1103/PhysRevE.64.036405. Epub 2001 Aug 29.
In this paper, we use the direct interaction approximation (DIA) to obtain an approximate integrodifferential equation for the probability density function (PDF) of charge (q) on dust particles in homogeneous dusty plasma. The DIA is used to solve the closure problem which appears in the PDF equation due to the interactions between the phase space density of plasma particles and the phase space density of dust particles. The equation simplifies to a differential form under the condition when the fluctuations in phase space density for plasma particles change very rapidly in time and is correlated for very short times. The result is a Fokker-Planck type equation with extra terms having third and fourth order differentials in q, which account for the discrete nature of distribution of plasma particles and the interaction between fluctuations. Approximate macroscopic equations for the time evolution of the average charge and the higher order moments of the fluctuations in charge on the dust particles are obtained from the differential PDF equation. These equations are computed, in the case of a Maxwellian plasma, to show the effect of density fluctuations of plasma particles on the statistics of dust charge.
在本文中，我们使用直接相互作用近似（DIA）来获得均匀尘埃等离子体中尘埃颗粒上电荷（q）的概率密度函数（PDF）的近似积分微分方程。DIA用于解决由于等离子体粒子的相空间密度与尘埃粒子的相空间密度之间的相互作用而在PDF方程中出现的封闭问题。当等离子体粒子的相空间密度波动随时间变化非常迅速且在极短时间内相关时，该方程简化为微分形式。结果是一个福克 - 普朗克型方程，带有在q中具有三阶和四阶微分的额外项，这些项考虑了等离子体粒子分布的离散性质以及波动之间的相互作用。从微分PDF方程中获得了尘埃颗粒上平均电荷的时间演化以及电荷波动的高阶矩的近似宏观方程。在麦克斯韦等离子体的情况下，对这些方程进行了计算，以显示等离子体粒子密度波动对尘埃电荷统计的影响。
