Resonance Cone Interaction With a Self-Consistent Radio-Frequency Sheath

We study the propagation of lower-hybrid-type resonance cones in a tenuous magnetized plasma, and, in particular, their interaction with, and reflection from, the plasma sheath near a conducting wall. The sheath is modeled as a vacuum gap whose width is given by the Child-Langmuir law. The application of interest is when the resonance cones are launched (parasitically) by an ion-cyclotron radio-frequency antenna in a typical rf-heated tokamak fusion experiment. We calculate the fraction of launched voltage in the resonance cones that is transmitted to the sheath, and show that it has a sensitive thresholdlike turn on when a critical parameter reaches order unity. Above threshold, the fractional voltage transmitted to the sheath is order unity, leading to strong and potentially deleterious rf-wall interactions in tokamak rf heating experiments. Below threshold, these interactions can be avoided.