NUMERICAL SOLUTION OF TWO-DIMENSIONAL POISSONnEQUATION:THEORY AND APPLICATION TO ELECTROSTATIC- ION- ENGINE ANALYSIS

摘要

A numerical solution of the two-dimensional Poisson equation for mixed boundary conditions is presented, and the theory and application to an electrostatic-ion-engine analysis are discussed.nThe Poisson equation is solved by a method of successive approxima¬tions. The first approximation to the space-charge density, which is obtained from the Laplacian solution, gives rise to an over-space-charge-limited case. The use of a suppression factor to remove this restriction is discussed, and a method of estimating the value of this factor is suggested.nA method of solution is developed in which the differential equation is replaced by finite difference equations, and the properties of the re¬sulting matrix are studied. The Cyclic Chebyshev Semi-Iterative Method is described, and an estimate of an optimum overrelaxation factor is given.nDetailed calculations of the ion trajectories together with the space-charge-density function are presented. Also included is the pro¬gram for an IBM 704 computer that was used for solution of a numerical example of an ion rocket engine being tested at the Lewis Research Center.