  Plasma-based parametric amplification using stimulated Brillouin scattering
offers a route to coherent x-ray pulses orders-of-magnitude more intense than
those of the brightest available sources. Brillouin amplification permits
amplification of shorter wavelengths with lower pump intensities than Raman
amplification, which Landau and collisional damping limit in the x-ray regime.
Analytic predictions, numerical solutions of the three-wave coupling equations,
and particle-in-cell simulations suggest that Brillouin amplification in
solid-density plasmas will allow compression of current x-ray free electron
laser pulses to sub-femtosecond durations and unprecedented intensities.
