Sheath structure around particles in low-pressure discharges

Collisionless orbit theory is used to model isolated particles in low-pressure discharges with and without the presence of negative ions. The key results are as follows: (1) Debye–Hückel theory works well for approximating the potential profile around the particle, and (2) the size of the sheath around the particle is determined by a Debye length that results from linearizing the Poisson–Vlasov equation. These results are valid as long as the ratio of particle radius to Debye length is small and the ratio of Debye length to mean free path is small.