An image charge problem and the diocotron mode in non-neutral plasmas

Non-neutral plasmas provide important platforms for testing basic plasma theory. Crucial techniques for studies of antimatter also stem from non-neutral plasma experiments. Most commonly, non-neutral plasmas are confined in cylindrical traps with a uniform axial magnetic field. If the center of charge is displaced from the axis of the trap, the plasma exhibits a stable oscillation in which it drifts azimuthally around the axis. This “diocotron” mode is important for measuring the trapped charge in experiments. Undergraduate students can understand the physics behind the mode and how it is used experimentally. Doing so offers them an opportunity to employ the method of images technique from the electricity and magnetism course and to reinforce their understanding of Gauss's law in a context that connects with ongoing plasma physics research.