Third-order transport coefficients for localised and delocalised charged-particle transport

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.

Third-order transport coefficient tensor of charged-particle swarms in electric and magnetic fields

Third-order transport coefficient tensor of charged-particle swarms in neutral gases in the presence of spatially uniform electric and magnetic fields is considered using a multiterm solution of Boltzmann's equation and Monte Carlo simulation technique. The structure of the third-order transport coefficient tensor and symmetries along its individual components in varying configurations of electric and magnetic fields are addressed using a group projector technique and through symmetry considerations of the Boltzmann equation. In addition, we focus upon the physical interpretation of the third-order transport coefficient tensor by considering the extended diffusion equation which incorporates the contribution of the third-order transport coefficients to the density profile of charged particles. Numerical calculations are carried out for electron and ion swarms for a range of model gases with the aim of establishing accurate benchmarks for third-order transport coefficients. The effects of ion to neutral-particle mass ratio are also examined. The errors of the two-term approximation for solving the Boltzmann equation and limitations of previous treatments of the high-order charged-particle transport properties are also highlighted.