  A plasma model is presented for the formation of ``cathode spots'' and
subsequent crater development near field emission sites on a copper surface in
the presence of a strong dc electric field. Adding to previously published
models, we propose that the two-stream plasma instability relates the plasma
density to its dimensions. Arguments are presented that suggest that the
formation and dynamics of such plasma spots are essentially the same phenomenon
for both dc and rf fields. A consequence for accelerating structures is that,
when such plasma spots are present, they erode the copper surface at a rate on
the order of 300 micrograms per Coulomb of ion bombardment current. This
erosion rate can have a measurable effect on the rf properties of an
accelerating structure after processing at high gradients for a few hundred
hours.
