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The white light propagates through the target, with shorter (bluer) wavelengths arriving first, and longer (redder) wavelengths arriving later. Somewhere in the middle of passing through the target, the x-rays join the party, hitting the target at the same place, but for a shorter temporal duration (~50 fs is typical). This causes the index of refraction of the material to change, and generates an edge in the white light power profile (in time, and therefore also spectrally, due to the chirp). See figure:

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