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 ∂_τa≪k₀a 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: (∇_⊥²-2∂² /∂ψ∂τ-2ik₀ ∂/∂τ)a=(1-φ)a(∂²/∂ψ ²+1)φ=|a|²/4. We substitute appropriate trial functions for a and φ into S and carry out the ∫dx_⊥ 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 φ. We present an analysis in the paraxial regime, where the ∂_ψ∂_τ a term is neglected