Evolution over time of daughter wavelength energies in a Brillouin retrodiffusion instability. Applications in particle acceleration experiments using wavelength beating

The asymptotic behavior of the Brillouin instability is studied. In regimes where the instability is of a convective nature, the growth of a perturbation is finite in the case of a plasma of finite length. The reflectivity depends on the level of thermal fluctuations. Two goals are sought in carrying out the calculations: to calculate the Brillouin reflection over time in the event of interactions and to study the level of sonic waves in the areas where the weakening of the pump flux is negligable.