  An ideal plasma lens can provide the focusing power of a small f-number,
solid-state focusing optic at a fraction of the diameter. An ideal plasma lens,
however, relies on a steady-state, linear laser pulse-plasma interaction.
Ultrashort multi-petawatt (MPW) pulses possess broad bandwidths and extreme
intensities, and, as a result, their interaction with the plasma lens is
neither steady state nor linear. Here we examine nonlinear and time-dependent
modifications to plasma lens focusing, and show that these result in chromatic
and phase aberrations and amplitude distortion. We find that a plasma lens can
provide enhanced focusing for 30 fs pulses with peak power up to ~1 PW. The
performance degrades through the MPW regime, until finally a focusing penalty
is incurred at ~10 PW.
