Wave modeling in a cylindrical non-uniform helicon discharge

A radio frequency field solver based on Maxwells equations and a cold plasma dielectric tensor is employed to describe wave phenomena observed in a cylindrical non-uniform helicon discharge. The experiment is carried out on a recently built linear plasma-material interaction machine: The magnetized plasma interaction experiment [Blackwell, Plasma Sources Sci. Technol. (submitted)], in which both plasma density and static magnetic field are functions of axial position. The field strength increases by a factor of 15 from source to target plate, and the plasma density and electron temperature are radially non-uniform. With an enhancement factor of 9.5 to the electron-ion Coulomb collision frequency, a 12 reduction in the antenna radius, and the same other conditions as employed in the experiment, the solver produces axial and radial profiles of wave amplitude and phase that are consistent with measurements. A numerical study on the effects of axial gradient in plasma density and static magnetic field on wave propagations is performed, revealing that the helicon wave has weaker attenuation away from the antenna in a focused field compared to a uniform field. This may be consistent with observations of increased ionization efficiency and plasma production in a non-uniform field. We find that the relationship between plasma density, static magnetic field strength, and axial wavelength agrees well with a simple theory developed previously. A numerical scan of the enhancement factor to the electron-ion Coulomb collision frequency from 1 to 15 shows that the wave amplitude is lowered and the power deposited into the core plasma decreases as the enhancement factor increases, possibly due to the stronger edge heating for higher collision frequencies.