Applications of variational principles in laser-plasma interactions.

摘要

In this dissertation, variational principle techniques are used to study the three dimensional, whole-beam behavior of a laser interacting with a plasma. Effects due to the near forward scattering processes of short-pulse (Raman) and long pulse lasers (Brillouin) are considered. It is found that for each of these processes, the laser can undergo 3 basic modes of instability: a hosing instability—involving modulations to the centroid of the laser, a symmetric spot-size self-modulation in stability, and an anti-symmetric spot-size self-modulation instability. The details of these modes are given for each of the two scattering processes, and a comparison is made between them where applicable. For the case of the short-pulse instabilities, dispersion is included in the analysis, so as to include the effects of direct Raman Forward Scattering (RFS). It is found that RFS couples directly and exclusively to the symmetric spot-size self-modulation instability. The de tails of the interplay between these processes are given, and the modifications to the growth rates of hosing and anti-symmetric spot-size self-modulation due to dispersion are also considered. For the case of the long-pulse instabilities, it is found that the peak growth rate occurs at the resonance of the laser—or the Rayleigh length, rather than the ion-acoustic frequency. This is in contrast to the Short-Pulse instabilities, where the plasma resonance determines the wavenumber for the peak growth rate. In addition to the analytical results just described, simulation results on the anti-symmetric spot-size self-modulation instability are presented, and good agreement between the asymptotic spatial-temporal theory and the simulations is found. Simulations on hosing are also presented, at it is found that the final non-linear state of the laser is dominated by a long-wavelength hosing instability. A possible explanation for this is given using variational techniques. In the final section of this dissertation, we consider nonlinear effects. Specifically, we construct a fully nonlinear Lagrangian amenable to the use of trial-functions and apply this Lagrangian to generalize the weakly-nonlinear results for hosing to the case of arbitrary intensity. Last, the weakly-relativistic, non-linear hosing equations are used to demonstrate the possible existence of a hosing sub-harmonic at ω_p/2.