Five distinct discharge modes are observed in a cylindrically-symmetric hel
icon reactor. Each mode is characterized by its plasma impedance, wave mode
structure, density distribution and floating potential structure. It is sh
own that the lowest two modes are capacitive (E) and inductive (H), while h
igher modes are helicon wave (W) modes. Successive wave modes are found to
correspond to helicon wave cavity resonances of the plasma-filled vacuum ve
ssel, each with a well defined wavevector, density and impedance. Measured
wavevectors and densities are in agreement with the helicon wave dispersion
relation. The first helicon discharge mode is found to be an m = +/-1 mode
, as expected for a double saddle field antenna. Unexpectedly, the second a
nd third helicon modes have an m = 0 azimuthal symmetry.