Helicon normal modes in radially non-uniform plasma column

Helicon discharges are often considered somewhat mysterious, exhibiting experimental behaviors that are challenging to explain, such as abrupt plasma density jumps, hysteresis, and 'blue core' formation, among others. A significant part of the difficulty in modeling helicon plasmas stems from the limitations of simple analytical approaches that rely on approximations, such as constant plasma density or collisionless plasma, which fail to accurately describe helicon wave physics. We developed a semi-analytical approach to determine helicon normal modes in a collisional plasma column with an arbitrary radial plasma density profile. The influence of radial density profiles on modes propagation, and particularly on their energy deposition patterns, is then investigated. Notably, the study shows that sharp density drops at the plasma column edge lead to edge-localized power deposition, whereas gently varying radial plasma profiles (bell shapes) result in axially peaked power deposition. In the former case, the rapid damping of the Trivelpiece-Gould (TG) component of the wave at the plasma edge is clearly responsible for the observed energy deposition profile. As the profile sharpness decreases, as in bell-shaped plasmas, the TG component of the modes becomes less dominant, and the radial power deposition profile is mainly determined by the Helicon (H) component. Overall, this study of normal modes also demonstrates that dominant H modes are expected to experience much less axial damping than predicted when considering constant densities. Finally, it is also shown that smooth radial density profiles allow a new family of modes to propagate, characterized by long axial wavelengths and slightly off-axis energy deposition patterns.