Raman forward scattering of a high-intensity, short-duration, frequency-chirped laser pulse propagating in an underdense plasma is examined. The growth of the direct forward scattered light is calculated for a laser pulse with a linear frequency chirp in various spatiotemporal regimes. This includes a previously undescribed regime of strongly-coupled four-wave nonresonant interaction, which is important for relativistic laser intensities. In all regimes of forward scattering, it is shown that the growth rate increases (decreases) for positive (negative) frequency chirp. The effect of chirp on the growth rate is relatively minor, i.e., a few percent chirp yields few percent changes in the growth rates. Relation of these results to recent experiments is discussed.
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