Much progress
has been made recently in the area of ultra-high-intensity plasma wakefield
acceleration (PWFA). In this regime, while the wakefields experienced
by the beam are asserted to be linear (linear focusing, acceleration
independent of radial position), the plasma response is highly nonlinear.
The deviation from linear PWFA behavior arises in three notable ways:
field ionization of neutral or partly ionized atoms; relativistic plasma
electron response; and ion motion. The first is seen as a great aid
to current and future experiments, by providing a robust mechanism for
high density plasma creation. Relativistic aspects plasma response gives
rise to a new effect, that of plasma electron snow-plow by the beam?s
electromagnetic field. It is seen that this effect contributes to the
persistence of linear scaling of wakefield amplitude with charge even
in a very nonlinear regime. Finally, we note that for very intense beams,
the plasma ions collapse to form a high density region under the influence
of beam fields. This is precisely the case for the current afterburner
proposal, which is seen to suffer from complete ion collapse and concomitant
beam-degrading nonlinear transverse fields. The negative implications
of this effect on PWFA and laser plasma accelerators is discussed.