Temporally Growing Raman Backscattering Instabilities in an Inhomogeneous Plasma

We derive the equations describing the decay of an intense, coherent electromagnetic wave into a backscattered electromagnetic wave and a plasma wave in an inhomogeneous plasma. The plasma wave and scattered electromagnetic wave are trapped in the vicinity of their cutoffs near ${\omega }_p=\frac{{\omega }_0}{2}$. The resulting temporally growing instabilities may explain the strong heating and the blowoff observed in recent computer simulations of Raman scattering.