Third-order transport coefficients of ion swarms

Mobility and diffusion coefficients are generally extracted from experimental measurements of ion arrival time distributions using tensors of ranks one and two, i.e., in terms of the diffusion equation that is equivalent to Fick's second law. The theory is extended here to tensors of rank three. It is shown that under customary circumstances, the generalized diffusion equation only contains a single third-order transport coefficient. This equation is used to generate synthetic data for ions moving through a pure gas. The mobility and diffusion coefficients and third-order transport coefficients inferred from these data are compared with values used to simulate the arrival time distribution. Finally, an existing computer program has been modified in order to compute one component of the third-order transport coefficient, and this program has been applied to Li⁺ in He.