The kinetic nonlinear dispersion relation, and frequency shift ␦ srs , of a plasma wave driven by stimulated Raman scattering are presented. Our theoretical calculations are fully electromagnetic, and use an adiabatic expression for the electron susceptibility which accounts for the change in phase velocity as the wave grows. When k D տ 0.35 ͑k being the plasma wave number and D the Debye length͒, ␦ srs is significantly larger than could be inferred by assuming that the wave is freely

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... g. Our theory is in excellent agreement with 1D Eulerian Vlasov-Maxwell simulations when 0.3Յ k D Յ 0.58, and allows discussion of previously proposed mechanisms for Raman saturation. In particular, we find that no "loss of resonance" of the plasma wave would limit the Raman growth rate, and that saturation through a phase detuning between the plasma wave and the laser drive is mitigated by wave number shifts.