Initial development of ponderomotive filaments in plasma from intense hot spots produced by a random phase plate

Local intensity peaks, hot spots, in laser beams may initiate self-focusing, in lieu of linear instabilities. If the hot spot power, P, contains several times the critical power, Pc, and if the plasma density, n, is small compared to the critical density, nc, then on a time scale less than an acoustic transit time across the hot spot radius, τia, the hot spot collapses, capturing order unity of the initial hot spot power. The collapse time is determined as a universal function of P/Pc and τia. The focal region moves towards the laser with an initially supersonic speed, and decelerates as it propagates. The power of this back propagating focus decreases monotonically until the critical power is reached. This limiting, shallowest, focus develops on a time scale long compared to τia and corresponds to the focus obtained in a model with adiabatically responding ions. For low-density plasma nonlinear ion effects terminate collapse and a bound on the transient intensity amplification is obtained as a universal function of the optics f/number, F, and n/nc. The boundary between thermal and ponderomotive regimes depends upon F and not the laser intensity