Analytic model of near-field radio-frequency sheaths. I. Tenuous plasma limit

An analytic model is derived for electromagnetic radio-frequency (rf) wave propagation in a waveguide filled by a tenuous plasma with a slightly tilted equilibrium magnetic field $B$⁠, i.e., $by=By/B⪡1$⁠. The calculation includes the self-consistent coupling between the rf fields and the sheaths at the sheath-plasma interface and can be used to describe antenna sheath formation in the ion cyclotron range of frequencies. The sheaths are treated as thin vacuum regions separating the plasma and metal wall. It is shown that (i) the launched fast wave is coupled parasitically to the slow wave by the magnetic field structure when $by≠0$ and by the sheath boundary condition, (ii) the sheath voltage $Vsh$ is dependent on the wave parity (the “antenna phasing”), and (iii) integrating the vacuum rf fields, $Vvac=−∫dzE∥(vac)$⁠, gives an overestimate of the sheath voltage. An expression for the self-consistent $Vsh$ including plasma effects and satisfying the Child–Langmuir law is obtained.