Kinetic features of collisionless sheaths around polarized cylindrical emitters from the orbital motion theory

Abstract

The kinetic features of the sheath around a cylindrical emitter immersed in collisionless plasma at rest are analysed. After finding self-consistently the electric potential by applying the Orbital Motion Theory to the Vlasov-Poisson system, the local distribution functions are reconstructed and the radial profiles of important macroscopic quantities (plasma densities, currents, and temperatures) are then computed. It is found that there can only be three kinds of holes that are bound by three different boundaries-two related to the constraints from orbital effects and the other due to the electric potential barrier. The results are presented for three regimes: negative probe bias with monotonic and non-monotonic potential and positive probe bias with non-monotonic potential. To understand the variation of macroscopic-quantity radial profiles, three diagrams are presented for kinetic features: the l-diagram for the integration domains of the two orbital invariants, the effective potential, and the local distribution function. The envelope in the l-diagram is crucial to identify different orbital behaviours, which can be used as a guideline for analytical analyses and serve as one of the criteria to refine the mesh used in numerical calculations.

Parametrization of current–voltage characteristics and operation domains of cylindrical emissive probes in collisionless Maxwellian plasmas at rest

“…Using the same notation and normalization as those in Appendix A, Appendix B, and Ref. [28], the normalized density is…”

“…We take the opportunity to correct a typo of Ref. [28] that does not affect to its result. In that work we incorrectly wrote dε r dε θ = dv r dv θ instead of dε r dε θ = 2ε α dv r dv θ above its Eq.…”

“…The Vlasov-Poisson system applied to cylindrical emissive probes can be written as the integro-differential equation (find details and the normalization of the variables in Ref. [28]) where σ (φ ) ≡ n i − n e − β n em is the space charge that involves some integrals depending on φ (see Eq. (A.8) below).…”