Shotorban B
Department of Mechanical and Aerospace Engineering, The University of Alabama in Huntsville, Huntsville, Alabama 35899, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066403. doi: 10.1103/PhysRevE.83.066403. Epub 2011 Jun 10.
Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.
等离子体中由于电子和离子的离散性导致的尘埃颗粒的随机电荷涨落，可以用一个一步过程主方程来描述 [T. 马苏卡斯和 M. 拉塞尔，《应用物理杂志》77, 4285 (1995)]，该方程没有精确解。在本工作中，使用范坎彭的系统规模展开方法并结合线性噪声近似，通过展开主方程得到了一个具有精确高斯解的福克 - 普朗克方程。高斯解具有随时间变化的均值和方差，由两个模拟尘埃颗粒充电非平稳过程的常微分方程控制。通过将其结果与通过数值求解主方程得到的结果进行比较来测试该模型。电子和离子电流通过轨道运动限制理论计算。在充电的非平稳过程的不同时刻，模型结果与主方程结果非常吻合。当电荷的标准差在大小上与平均电荷相当时，偏差更为显著。
