Simulations validating the ponderomotive filamentation figure of merit *

The pondermotive force due to a laser propagating through a plasma creates density wells, resulting in a spatially varying index of refraction and causing the laser to self-focus. If the intensity of the laser is sufficiently high, the laser will spray due to the self-focusing of each speckle within the beam profile. This process can result in degraded coupling to targets used in laser-driven experiments. Here, we examine the filamentation figure of merit (FFOM) that estimates the threshold at which the laser will self-focus. Two metrics are developed to assess the degree to which self-focusing is occurring: one associated with the angular dispersion of the beam and the second with the fraction of beam power over five times the average intensity. pF3D simulations of a speckled laser beam generated by a random-phase-plate (RPP) in a background plasma are reported, and the two metrics are determined from the simulations. It is shown that these metrics can diagnose self-focusing and that the predicted thresholds agree with the FFOM. These simulations are then used to assess filamentation of the beam and are extended to include polarization smoothing (PS) and smoothing by spectral dispersion (SSD).