SOME PROBLEMS IN THE COMPUTER SIMULATION OF MOBILITY MEASUREMENT EXPERIMENTS AND OTHER ION SWARM EXPERIMENTS

摘要

In cases where it is not expedient to eliminate the first-order or mobility term from the mobility-diffusion equation by a transformation of coordinates, the finite difference approximation, (N - N .)/Ax, of the first-order derivative introduces an artificial second-order or diffusion effect in the difference equation solution of this partial differential equation. It is shown that this effect may be removed by replacing D, the coefficient of the second-order term, by D V/2 (Ax - VΔt), where V is the coefficient of the first-order term. The solution of the modified difference equation is shown to approach the analytical solution asymptotically for an initially closely localized ion distribution, and the ion distribution is shown to have the same variance as the analytical solution throughout the calculation.