Instability, collapse, and oscillation of sheaths caused by secondary electron emission

The Debye sheath is shown to be unstable under general conditions. For surface materials with sufficient secondary electron emission (SEE) yields, the surface's current-voltage characteristic has an unstable branch when the bulk plasma temperature (T_e) exceeds a critical value, or when there are fast electron populations present. The plasma-surface interaction becomes dynamic where the sheath may undergo spontaneous transitions or oscillations. Using particle-in-cell simulations, we analyze sheath instabilities occurring in a high T_e plasma slab bounded by walls with SEE. As the plasma evolves, whenever the sheath enters an unstable state, its amplitude rapidly collapses, allowing a large flux of previously trapped electrons to hit the wall. These hot electrons induce more than one secondary on average, causing a net loss of electrons from the wall. The sheath collapse quenches when the surface charge becomes positive because the attractive field inhibits further electrons from escaping. Sheath instabilities influence the current balance, energy loss, cross-B-field transport and even the bulk plasma properties. Implications for discharges including Hall thrusters are discussed. More generally, the results show that common theories that treat emission as a fixed (time-independent) "coefficient" do not capture the full extent of SEE effects.