Quasilinear theory of laser-plasma interactions

The interaction of a high intensity laser beam with a plasma is generally susceptible to the filamentation instability due to nonuniformities in the laser profile. In ponderomotive filamentation high intensity spots in the beam expell plasma by ponderomotive force, lowering the local density, causing even more light to be focused into the already high intensity region. The result--the beam is broken up into a filamentary structure.;Several optical smoothing techniques have been proposed to eliminate this problem. In the Random Phase Plates (RPS) approach, the beam is split into a very fine scale, time-stationary interference pattern. The irregularities in this pattern are small enough that thermal diffusion is then responsible for smoothing the illumination. In the Induced Spatial Incoherence (ISI) approach the beam is broken up into a larger scale but non-time-stationary interference pattern. In this dissertation we propose that the photons in an ISI beam resonantly interact with the sound waves in the wake of the beam. Such a resonant interaction induces diffusion in the velocity space of the photons. The diffusion will tend to spread the distribution of photons, thus if the diffusion time is much shorter than the e-folding time of the filamentation instability, the instability will be suppressed.;Using a wave-kinetic description of laser-plasma interactions we have applied quasilinear theory to model the resonant interaction of the photons in an ISI beam with the beam\u27s wake field. We have derived an analytic expression for the transverse diffusion coefficient. The quasilinear hypothesis was tested numerically and shown to yield an underestimate of the diffusion rate. By comparing the quasilinear diffusion rate, {dollar}\gamma\sb{lcub}D{rcub}{dollar}, with the maximum growth rate for the ponderomotive filamentation of a uniform beam, {dollar}\gamma\sb{lcub}f\sb{lcub}max{rcub}{rcub}{dollar}, we have derived a worst case criterion for stability against ponderomotive filamentation: {dollar}{dollar}{lcub}\gamma\sb{lcub}f\sb{lcub}max{rcub}{rcub}\over \gamma\sb D{rcub} \sim .5 {lcub}\tilde f\sp5/\tilde D\sp5\over \vert \tilde E\vert\sp2 \tilde\omega\sbsp{lcub}0{rcub}{lcub}2{rcub}\tilde N\sp6{rcub}\ll 1.{dollar}{dollar}The tildaed quantities are scaled to the following fusion relevant reference values; laser intensity: {dollar}\vert E\vert\sp2{dollar} = 10{dollar}\sp{lcub}15{rcub}\vert\tilde E\vert{dollar} Watts cm,{dollar}\sp{lcub}-2{rcub}{dollar} focal length: {dollar}f = 30\tilde f{dollar}m, width of each ISI echelon: {dollar}D = .75\tilde D{dollar} cm, laser carrier frequency: {dollar}\omega\sb{lcub}0{rcub} = 7.5 \times 10\sp{lcub}15{rcub}\tilde\omega\sb0{dollar} s{dollar}\sp{lcub}-1{rcub}{dollar}, and the number of ISI echelons: {dollar}N = 20\tilde N{dollar}