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One of perhaps the most spectacular applications of the novel high power laser facilities is particle acceleration via the longitudinal electric fields generated during nonlinear propagation of intense laser pulses through plasma. But when Lorentz factor of electron quiver motion becomes of the order of few hundreds, radiation reaction effects should also come into play. We study the impact of radiation reaction on propagation of a high intensity electromagnetic pulse through the cold plasma and identify a novel mechanism of longitudinal plasma field generation based entirely on radiation reaction. The regime for which this mechanism dominates over the conventional ponderomotive one is clearly revealed by numerical simulations.We also present a simple analytical model, which can be used to optimize the conditions for plasma wave generation and electron acceleration in a regime when radiation reaction becomes essential.