Sheaths tend to form when immersing metallic objects in plasmas. As it avoids the need to capture the sheath details, which occur on the Debye length scale while antennas are typically various orders of magnitude larger, the sheath boundary condition due to D'Ippolito and Myra (2006 Phys. Plasmas13 102508, 2008 Phys. Plasmas15 102501) offers antenna designers a major reduction in the numerical problem size they face. The sheath boundary condition was derived by making a number of simplifying assumptions to enable finding an analytical approximation of the conditions rapidly oscillating waves have to satisfy beyond the sheath that forms close to such objects. This paper discusses the solution of the cold plasma wave equation for sheath relevant density profiles, e.g. highlighting the role of the orientation of the static magnetic field and of oblique incidence, and underlining the impact the density profile has on the wave physics. It illustrates that the cross-talk between the waves impinging on and those excited at the wall and in the sheath sensitively depends on a number of parameters. The 2 × 2 connection coefficient matrix that is numerically obtained captures the sheath region fast time scale wave physics for a given density profile. When supplemented with a satisfactory model for the slow time scale variation it is a numerical tool that permits upgrading the realism of the fast time scale wave physics contained in the sheath boundary condition and that can help delimiting the range of applicability of simplified models, and assessing if a sufficiently general set of boundary conditions to describe the effect of the sheath can at all be constructed.
Sheath constraints on turbulent magnetised plasmas