ABSTRACT
An approach for describing the evolution of short-pulse lasers propagating through underdense plasmas is presented. This approach is based upon the use of a variational principle. The starting point is an action integral of the form S[a,a(*),straight phi]=integrald(4)x L[a,a(*),straight phi, partial differential(&mgr;)a, partial differential(&mgr;)a(*), partial differential(&mgr;)straight phi] whose Euler-Lagrange equations recover the well-known weakly nonlinear coupled equations for the envelope of the laser's vector potential a, its complex conjugate a(*), and the plasma wave wakes' (real) potential straight phi. Substituting appropriate trial functions for a, a(*), and straight phi into the action and carrying out the integrald(2)x( perpendicular) integration provides a reduced action integral. Approximate equations of motion for the trial-function parameters (e. g., amplitudes, spot sizes, phases, centroid positions, and radii of curvature), valid to the degree of accuracy of the trial functions, can then be generated by treating the parameters as a new set of dependent variables and varying the action with respect to them. Using this approach, fully three-dimensional, nonlinear envelope equations are derived in the absence of dispersive terms. The stability of these equations is analyzed, and the growth rates for hosing and symmetric spot-size self-modulation, in the short-wavelength regime (k approximately omega(p)/c) are recovered. In addition, hosing and spot-size self-modulational instabilities for longer wavelength perturbations (k<
ABSTRACT
Subharmonic resonant beat-wave excitation of nonlinear relativistic plasma waves is studied analytically and in particle-in-cell simulations. We find that if the frequency separation of the lasers, Deltaomega, is 2omega(p) or 3omega(p) ( omega(p) is the plasma frequency), then plasma waves are still excited at omega(p) but they grow exponentially or superexponentially rather than secularly. Both of these subharmonic resonant instabilities saturate due to relativistic detuning. The analytical growth rates and saturation levels agree with the simulation results.
ABSTRACT
Using a variational method, we show that an effective attractive force exists between two Gaussian laser beams in a plasma because of a mutual coupling from relativistic mass corrections. The effective force can be generalized to other nonlinearities. This force can cause two laser beams to spiral around each other with a rotation period that is proportional to the Rayleigh length. These orbits are stable if the ratio of the orbit diameter to the laser spot size d(0)/W(0)
