Raman Scattering of Intense, Short Laser Pulses in Modulated Plasmas

We examine the exponentiation of the Raman forward scattering instability in modulated plasma channels computationally and analytically. An evolution equation for the complex phases of the Raman scattered waves treating the spatial localization and discrete nature of the channel modes is derived. Simulations with WAKE [P. Mora and T. M. Antonsen Jr., Phys. Plasmas 4, 217 (1997)] verify the theory in the linear growth regime and provide insight into the nonlinear stage of the instability when cascading and pump depletion play a role. We find that the exponentiation in modulated channels depends on two factors: the increase in coupling due to the increased plasma wavenumber in the high-density regions of the channel and a decreased coupling due to the reduced longitudinal spatial coherence. For the parameters considered, simulations show that the finite extent of the pump pulse is more significant in determining the exponentiation than phase mixing due to the transverse variation of the channel. Both the theory and simulations confirm that modulated channels allow for the stable guiding of longer pulses than nonmodulated channels.