Optimizing Brillouin amplification with flying focus pump beams

Strongly-coupled Brillouin backscatter in plasmas offers a promising route towards the amplification of high-power laser pulses in compact systems. However, the success of this scheme requires control of several parasitic effects, including premature scatter of the pump beam before it meets the seed. Advances in the production and modeling of laser pulses with controllable spatiotemporal structure are offering new strategies to overcome these challenges. Using fully kinetic, multidimensional particle-in-cell simulations, we show that pump beams with a flying focus that follows the propagation of the seed pulse can enable efficient Brillouin amplification over long interaction distances, while suppressing premature scattering instabilities of the pump. Restricting our study to over-quarter-critical plasma densities, where Raman scattering instabilities are suppressed, we obtain scaling relations for peak power and energy transfer efficiency of the amplified pulses as a function of the flying focus pump beam parameters. We present the optimal operating parameters for Brillouin amplification with flying focus pump beams.