Solvable Examples of Drift and Diffusion of Ions in Non-uniform Electric Fields

TL;DR

This paper provides analytical solutions for the drift and diffusion behavior of ions in inhomogeneous electric fields with cylindrical and spherical symmetry, considering anisotropic diffusion effects.

Contribution

It introduces solvable analytical models for ion drift and diffusion in symmetric inhomogeneous electric fields, including anisotropic diffusion effects.

Findings

Analytical expressions for ion distribution distortions in symmetric fields.

Effects of anisotropic diffusion on ion cloud shape.

Validation of models with Gaussian ion distributions.

Abstract

The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the distortion can be calculated analytically. We examine the specific examples of fields with cylindrical and spherical symmetry in detail assuming the ion distributions to be of a generally Gaussian form. The effects of differing diffusion coefficients in the transverse and longitudinal directions are included.