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

Abstract

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.