Nonlinear electromagnetic plasma eigenmodes and their stability to stimulated Raman scattering

Transverse mode structure of nonlinear laser eigenmodes in underdense and overdense plasmas has been obtained by numerically solving the wave equation under relativistic and ponderomotive nonlinearities. The mode structure closely resembles a Lorentzian with half width scaling inversely as the axial intensity of the laser. The threshold condition for laser penetration in an overdense plasma turns out to be γ0≡(1+a02/2)1/2≥2n0/ncr-1, where n0 is the equilibrium electron density, ncr is the critical density at laser frequency, and γ0 is the electron Lorentz factor due to the laser of normalized axial intensity a02. The nonlinear laser eigenmode, in a low density plasma, is unstable to stimulated Raman backscattering off a copropagating space charge reactive quasimode. The growth rate increases with laser intensity as a0 rises up to a0∼1. Beyond this value, growth rate decreases with a0, due to the enhancement of electron mass and depletion of electrons from the axial region. Geometrical effects also reduce the growth rate