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.
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