Brian Joseph Duda

On the mutual interaction between laser beams in plasmas

The nonlinear interaction between light beams in a plasma is studied. In particular, nonlinearities due to relativistic mass corrections and density modulations from a plasma wave wake are considered; but the results can be generalized for other nonlinearities. A simple physical picture using the nonlinear phase velocity of the light wave in a plasma is developed to show that when two laser beams are coherent, the force can be repulsive or attractive, depending on their relative phase. When the two laser beams are polarized in mutually perpendicular directions, the force is always attractive. Using a variational method, a simple analytical expression for this attractive force is derived for Gaussian beams. The centers of the lasers move analogously to point masses under this attractive force with the laser power playing the role of the mass. Under an attractive force, solutions exist where the two lasers can spiral around each other. It is also shown that the plasma wave wake can cause the two spiraling l...

A variational principle approach to the evolution of short-pulse laser plasma drivers

The attractiveness of variational principle approaches for obtaining good approximations to complicated problems is well established. Motivated by this fact, we have developed a variational principle approach to the evolution of short-pulse laser-plasma accelerator drivers. We start with an action of the form /spl part//sub /spl tau//a/spl Lt/k/sub 0/a where the Euler-Lagrange equations of L, the Lagrangian density, give the well established coupled equations of short-pulse interactions, in the weakly relativistic regime: (/spl nabla//sub /spl perp///sup 2/-2/spl part//sup 2///spl part//spl psi//spl part//spl tau/-2ik/sub 0//spl part///spl part//spl tau/)a=(1-/spl phi/)a(/spl part//sup 2///spl part//spl psi//sup 2/+1)/spl phi/=|a|/sup 2//4. We substitute appropriate trial functions for a and /spl phi/ into S and carry out the /spl int/dx/sub /spl perp// integration. The Euler-Lagrange equations of the reduced Lagrangian density provide coupled equations for the trial function parameters, i.e., spot sizes, amplitude, phase, radius of curvature and centroids for both a and /spl phi/. We present an analysis in the paraxial regime, where the /spl part//sub /spl psi///spl part//sub /spl tau// a term is neglected.