This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (Dn) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.
Connection coefficients for cold plasma wave propagation near metallic surfaces