Precise Approximate Solution for the Bohm Sheath Potential

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Martin, P.^1,2 ; Cortés-Vega, L.^3 ; Maass-Artigas, F.^1

Physics Department, Antofagasta University, Casilla 170, Antofagasta, Chile^1

Physics Department, Simón Bolivar University, Apartado 89000, Caracas

1080A, Venezuela^2

Mathematics Department, Antofagasta University, Casilla 170, Antofagasta, Chile^3

关键词: Analytic solution;    Approximate solution;    Approximated solutions;    Nonlinear differential equation;    Transition regions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012107/pdf
DOI  :  10.1088/1742-6596/574/1/012107

来源: IOP

【 摘 要 】

The Poisson equation for the plasma sheath potential near a wall, leads to a nonlinear differential equation, whose analytic solution is not known. The usual approximation taking only the first non-null term does not give good accuracy. Other approximations taken two additional terms are better, but they fail to give good accuracy in the intermediate region. Here a new analytic approximated solution is presented with much higher accuracy, and more precise results, not only near and far away of the wall, but also in the transition region. Two figures showing these new analytic solutions as a function of the relevant parameters are presented. The advantages of the present solution compared with those of pervious works are shown.