Non-linear RF rectified sheath based on magnetic scalar potentials in Petra-M

A new formulation to describe the RF induced radio-frequency sheath boundary, which is suitable for a large 3D simulation, is discussed. We start from linear asymptotic, so-called thick sheath, model. In this limit, B_n=0 and D_n = 0, where B_n and D_n are normal component of magnetic field and displacement current. Therefore, it is closely related to the DB boundary recently discussed in other fields. In order to use this non-standard form of boundary condition in a regular RF finite element method based on the H(curl) edge elements, we introduce a magnetic potential to describe curl-free vector field on the sheath-plasma boundary, which is then used to apply an in-homogenous Neuman boundary condition. The sheath potential is obtained by integrating a Poisson equation. This approach is further extended to a non-linear sheath regime, which is characterized by non-zero D_n. Since the sheath potential is already obtained, D_n is readily computed using the Ohm’s law and the non-linear sheath impedance (Myra PoP 2017). This D_n is fed to RF solver through another magnetic scalar potential which is used to define the divergence-free component of magnetic field on the sheath-plasma boundary. An actual implementation in Petra-M RF solver and detail is discussed in the poster presentation.