  Electron sheaths form near the surface of objects biased more positive than
the plasma potential, such as in the electron saturation region of a Langmuir
probe trace. Generally, the formation of electron sheaths requires that the
electron-collecting area be sufficiently smaller ($\sqrt{2.3m_e/M}$ times) than
the ion-collecting area. They are commonly thought to be local phenomena that
collect the random thermal electron current, but do not otherwise perturb a
plasma. Here, using experiments on an electrode embedded in a wall,
particle-in-cell simulations and theory, it is shown that under low temperature
plasma conditions ($T_e \gg T_i$) electron sheaths are far from local. Instead,
a long presheath region (in excess of 70 $\lambda_D$) extends into the plasma
where electrons are accelerated via a pressure gradient to a flow speed
exceeding the electron thermal speed at the sheath edge. This fast flow is
found to excite instabilities, causing strong fluctuations near the sheath
edge.
