A method for solving Poisson's equation in geophysical and astrophysical plasma
Abstract
The Quasi Neutrality (QN) equation is usually solved by an iterative procedure to obtain the electrostatic potential distribution in plasmas. A new numerical method to obtain the same result more efficiently, based on the numerical integration of the differential form of the QN equation, is presented. In the case when the QN approximation fails to be a valid approximation of Poisson's Equation (PE), the latter equation needs to be solved. A robust numerical method to solve PE, with boundary conditions at two different altitudes, is proposed. The method consists of integrating numerically by the Quadrature Discretization Method (QDM) a differential form of PE. For boundary conditions corresponding to the QN solution the result coincides with the QN solution.
 Publication:

Presented at 17th International Symposium on Rarefied Gas Dynamics
 Pub Date:
 1990
 Bibcode:
 1990rgd..symp....8L
 Keywords:

 Earth Ionosphere;
 Earth Magnetosphere;
 Numerical Integration;
 Photoionization;
 Poisson Equation;
 Space Plasmas;
 Approximation;
 Boundary Conditions;
 Differential Equations;
 Ionospheric Electron Density;
 Magnetohydrodynamic Flow;
 Robustness (Mathematics);
 Plasma Physics