Exact results are presented for the first time for the helicon (H) wave and associated Trivelpiece-Gould (TG) wave modes of a cold, uniform, lossy plasma column inside a conducting waveguide. Both Landau and collisional damping are considered. Contrary to expectation, it is found that even in cases of severe damping, the axial propagation constant is modified only marginally, and damping shows up mainly in the radial propagation constant of only one of the two waves (TG or H). A consequence of such damping is that the damped wave does not form a standing wave in the radial direction; it remains a traveling wave, decaying as it propagates inwards from the plasma surface. These traveling waves can be absorbed efficiently near the plasma surface if their radial wavelengths are short, as usually happens with the TG waves. Unlike previous work, however, where only damping of the TG waves has been reported, the present work also reports damping of H waves. An attempt has been made to understand the damping behavior of the different modes in terms of certain “reduced” dispersion relations obtained from a modified Appleton-Hartree equation derived for the present work.

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