Modulation-slippage trade-off in resonant four-wave upconversion

Following up on a proposal to use four-wave mixing in an underdense plasma at mildly relativistic laser intensities to produce vastly more energetic X-ray pulses [Malkin and Fisch, Phys. Rev. E 101, 023211 (2020)], we perform the first numerical simulations in one dimension to illustrate amplification of a short high frequency seed through four-wave mixing. We illustrate how parasitic processes including phase modulation and spatial pulse slippage limit the amplification efficiency. Although the regimes studied were not where the optimal efficiencies were expected, these regimes do expose the basic physical processes at play, while still yielding not insignificant spectral power upshift.