Improved understanding of the hot cathode current modes and mode transitions

Hot cathodes are crucial components in a variety of plasma sources and applications, but they induce mode transitions and oscillations that are not fully understood. It is often assumed that negatively biased hot cathodes have a space-charge limited (SCL) sheath whenever the current is limited. Here, we show on theoretical grounds that a SCL sheath cannot persist. First, charge-exchange ions born within the virtual cathode (VC) region get trapped and build up. After the ion density reaches the electron density at a point in the VC, a new neutral region is formed and begins growing in space. In planar geometry, this 'new plasma' containing cold trapped ions and cold thermoelectrons grows towards the anode and fills the gap, leaving behind an inverse cathode sheath. This explains how transitions from temperature-limited mode to anode glow mode occur in thermionic discharge experiments with magnetic fields. If the hot cathode is a small filament in an unmagnetized plasma, the trapped ion region is predicted to grow radially in both directions, get expelled if it reaches the cathode, and reform periodically. Filament-induced current oscillations consistent with this prediction have been reported in experiments. Here, we set up planar geometry simulations of thermionic discharges and demonstrate several mode transition phenomena for the first time. Our continuum kinetic code lacks the noise of particle simulations, enabling a closer study of the temporal dynamics.