Anomalous Capacitive Sheath with Deep Radio Frequency Electric Field Penetration

A novel nonlinear effect of anomalously deep penetration of an external radio frequency electric field into a plasma is discribed. A self-consistent kinetic treatment reveals a transition region between the sheath and the plasma. Because of the electron velocity modulation in the sheath, bunches in the energetic electron density are formed in the transition region adjusted to the sheath. The width of the region is of order $V_{T}/\omega$, where V_{T} is the electron thermal velocity, and $\omega$ is frequency of the electric field. The presence of the electric field in the transition region results in a cooling of the energetic electrons and an additional heating of the cold electrons in comparison with the case when the transition region is neglected.