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

Space-resolved average kinetic energy of ion swarms in a uniform electric field

A pulse of noninteracting charged particles in an unbounded gas, exposed to a low, constant, homogeneous electric field, was studied in both space and time using a Monte Carlo simulation technique. The difference in electrical potential between the leading and trailing edges of the swarm results in the space-resolved average ion kinetic energy becoming a linearly increasing function of space. This Letter analyzes whether the average ion kinetic energy at the leading edge reaches a stationary value during the spatiotemporal evolution of the swarm, as has been considered so far. When the swarm's mean kinetic energy reaches a steady-state value, indicating that an energy balance is established over time, the gains (from the field) and losses (due to collisions) are nonuniform across space. The local power balance is negative at the front of the swarm and positive at the tail. Cooling the ions at the front and heating the ions at the tail results in a decrease in the average ion kinetic energy at the front and an increase at the tail. Thus, it can be concluded that stationary values of average ion kinetic energy do not exist at the leading and trailing edges during the evolution. Instead, they tend to approach the swarm's mean kinetic energy as t→∞.

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.