The role of Trivelpiece–Gould waves in antenna coupling to helicon waves

Abstract

It is well known that the simple theory of helicon waves, in which the electron mass me is neglected, is valid only if Ez also vanishes, a condition which is not satisfied in experiment. Exact solutions of cold plasma theory with finite me and Ez predict the existence of additional highly damped Trivelpiece–Gould (TG) modes (H-TG theory), which can greatly modify the nature of helicon discharges. However, most experiments have been explained using only the simple theory for which the helicon waves are undamped. In that case, antenna-plasma-coupling calculations predict infinite resonances. To avoid this problem theorists have set Ez=0 and included finite me effects (the TE-H theory). By comparing the TE-H theory with exact (i.e., closed form) solutions for uniform density, the role of TG modes has been clarified. To do so for nonuniform density, a new algorithm is developed to treat the case of high magnetic fields, when the wave equation becomes singular. The results show that, though the wave patterns are not greatly affected by TG modes except at low magnetic fields or near the radial boundary, the kz spectrum and radial profile of the energy deposition are greatly modified. In particular, the peaks in the TE-H-mode spectrum, which lead to predictions of erroneously high antenna loading, are suppressed and broadened by the TG modes which also produce high edge absorption. Both the TE-H and exact theories give maximum antenna loading for 12me(ω/k)2≈10–100 eV, in contrast to several hundred electron volts predicted by the simple theory.