Surface charge diagnostics by multiple internal reflection

We propose to measure the charge accumulating at a plasma-dielectric interface via infrared multiple internal reflection. The negative charge deposited into the plasma-facing dielectric, forming the negative part of an electric double layer (the positive part being the plasma sheath), leads to a change of the reflection coefficient, when the interface is subjected to infrared radiation. Based on the Boltzmann equations for the charge kinetics of the double layer [1] and nonlocal surface response functions to calculate the reflection coefficient, we show theoretically and numerically that a local, Drude-like expression is in fact sufficient to describe the optical response. It contains only the integrated surface charge, enabling thus a straightforward analysis of measured data. To amplify the charge-induced change in the reflectivity, we suggest an experimental setup utilizing the plasma-solid interface as a multi-internal reflection element. Numerical results indicate that in such a setup the magnitude of the wall charge can directly be determined from the change it causes in the transmitivity of the optical element.

[1] K. Rasek, F.X. Bronold, and H. Fehske, Phys. Rev. E 102, 023206 (2020)