Matching conditions for nonlinear RF sheath rectification in three-dimensional geometry

The sheath potentials formed near the material surfaces of plasma facing components are dramatically enhanced by the application of radio frequency (RF) power in the ion-cyclotron and lower-hybrid frequency ranges. Ions accelerated in these enhanced sheath potentials that impact the material surface can lead to the undesired generation of impurities via secondary emission. A self-consistent approach that incorporates three-dimensional geometry and nonlinear sheath boundaries is introduced, allowing the complex spatial structure of the sheath potential to be calculated via analytical and iterative methods. This work generalizes previous studies (i.e., Kohno Comp. Phys. Comm. (2017)), providing robust examples of simplified situations that should serve as benchmarks for RF sheath boundary implementation in three-dimensional geometry.