  The form of a sheath near a small electrode, with bias changing from below to
above the plasma potential is studied using 2D particle-in-cell (PIC)
simulations. Five cases are studied: (A) an electrode biased more than the
electron temperature ($T_e/e$) below the plasma potential, (B) an electrode
biased less than $T_e/2e$ below the plasma potential, (C) an electrode biased
nearly at the plasma potential, (D) an electrode biased more than $T_i/2e$ but
less than $T_e/2e$ above the plasma potential, and (E) an electrode biased much
greater than $T_e/2e$ above the plasma potential. In case (A), the electron
velocity distribution function (EVDF) is observed to be Maxwellian with a
Boltzmann-type exponential density decay through the ion sheath and presheath.
In cases (B) and (C), the EVDFs exhibit a loss-cone type truncation due to fast
electrons overcoming the small potential difference between the electrode and
plasma. No sheath is present in this regime, and the plasma remains
quasineutral up to the electrode. The EVDF truncation leads to a presheath-like
density and flow velocity gradient. In case (D) an electron sheath is present,
and essentially all ions are repelled. Here the truncation driven behavior
persists, but is accompanied by a shift in the maximum value of the EVDF that
is not present in the negative bias cases. In case (E), the flow shift becomes
greater and the loss-cone moves further into the tail of the EVDF. In this case
the flow moment has significant contributions from both the flow shift of the
EVDF maximum, and the loss-cone truncation.
