An estimation of the axial structure of surface-wave produced plasma column

Abstract

An analytical expression to predict the axial distribution of electron density along the surface-wave sustained plasma column has been derived. The model is based on the square root approximation of the dispersion relation that gives a linear roll-off of electron density distribution in the plasma column. The point is to use a more tractable analytical approximation of dispersion relation of surface waves. An expression of attenuation coefficient, which includes the collisional loss, has been applied in studying the structure of the surface-wave produced plasma column. The derived attenuation model predicts a linear axial attenuation of electron density, as well as a nonlinear relation between the glass permittivity dependent frequency sensitivity and the wavenumber. The nonlinearity arises from non-negligible dielectric thickness. This result is consistent with early Aliev's results of the electron density profile, which correspond to the volume collisional absorption regime of surface wave sustained plasmas. The combined effects of surface-wave amplitude attenuation due to collisions and frequency dependence of group velocity cause an axial decrease in the surface wave axial power flux as the wave moves away from the launcher. A short analysis of the sensitivity of the normalized frequency to the permittivity of the glass based on the quasistatic approximation of the dispersion relation of surface waves is given.