Helicon theory revisited

Summary form only given. Analysis of experiments on helicon wave discharges have so far relied on a relatively simple formulation in which the electrons are assumed to be massless. Though this approximation is a good one at magnetic fields B above 100 G or so, it fails when applied to results at lower fields. Including the electron mass raises the governing equation to a fourth-order differential equation and gives rise to a new root, sometimes called the helicon-ECR mode, which is related to Trivelpiece-Gould modes. In general, the wave in the plasma is a mixture of the normal high-field helicon mode (Pi) and this low-field mode (β/sub 2/), and this mixture depends sensitively on the boundary conditions. In a plasma-filled conducting cylinder, the amplitude of β/sub 1/ is dominant at high magnetic fields; but β/sub 2/ becomes increasingly important as B is lowered, until for ω/sub c/<2ω, it is the only mode possible. Since β/sub 2/ has short radial wavelength and is highly damped, it is effectively a surface wave. If the conducting boundary is separated from the plasma by a small gap, the two modes become decoupled and can have arbitrary amplitudes. If the conductor is moved to infinity while the plasma is confined by an insulator, the two modes are again coupled, but with a different ratio of amplitudes. This interesting behavior has not yet been verified in experiment but will affect the design of low-field helicon sources being developed for plasma processing.