Plasma-wall interactions are complex and often determine the overall operating regime of a plasma device. The region bridging the plasma to the wall, where potential and density gradients localize, is called the sheath. Particle-in-cell simulations showed that the sheath may become unstable when secondary electron emission from the walls, induced by energetic primary electrons, is significant. This Letter demonstrates theoretically that these instabilities exist because the secondary electron emission depends on the electron energy, and the electron temperature varies in the sheath. The proposed sheath theory can be widely used in plasma physics, from probe-based diagnostics to plasma-wall interactions in fusion reactors or plasma thrusters. The analysis also suggests future experiments to better characterize these instabilities.

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• Plasma discharges
• Plasma instabilities
• Plasma sources
• Plasma-wall interactions
• Plasma sheaths & surfaces
• Particle-in-cell methods
• Phase space methods