  Electron sheaths are commonly found near Langmuir probes collecting the
electron saturation current. The common assumption is that the probe collects
the random flux of electrons incident on the sheath, which tacitly implies that
there is no electron presheath and that the flux collected is due to a velocity
space truncation of the electron velocity distribution function (EVDF). This
work provides a dedicated theory of electron sheaths, which suggests that they
are not so simple. Motivated by EVDFs observed in Particle-In-Cell (PIC)
simulations, a 1D model for the electron sheath and presheath is developed. In
the model, under low temperature plasma conditions ($T_e\gg T_i$), an electron
pressure gradient accelerates electrons in the presheath to a flow velocity
that exceeds the electron thermal speed at the sheath edge. This pressure
gradient generates large flow velocities compared to what would be generated by
ballistic motion in response to the electric field. It is found that in many
situations, under common plasma conditions, the electron presheath extends much
further into the plasma than an analogous ion presheath. PIC simulations reveal
that the ion density in the electron presheath is determined by a flow around
the electron sheath and that this flow is due to 2D aspects of the sheath
geometry. Simulations also indicate the presence of ion acoustic waves excited
by the differential flow between electrons and ions in the presheath which
result in sheath edge fluctuations. The 1D model and time averaged PIC
simulations are compared and it is shown that the model provides a good
description of the electron sheath and presheath.
