The effect of the propagation of a ring-rippled laser beam in the presence of relativistic and ponderomotive non-linearities on the excitation of ion-acoustic wave (IAW) and resulting stimulated Brillouin backscattering in collisionless plasma at relativistic powers is studied. To understand the nature of propagation of the ring ripple-like instability, a paraxial-ray approach has been invoked in which all the relevant parameters correspond to a narrow range around the irradiance maximum of the ring ripple. Modified coupled equations for growth of ring ripple in the plasma, generations of IAW and back-stimulated Brillouin scattering (SBS) are derived from fluid equations. These coupled equations are solved analytically and numerically to study the intensity of ring-rippled laser beam and excited IAW as well as back reflectivity of SBS in the plasma for various established laser and plasma parameters. It is found that the back reflectivity of SBS is enhanced due to the strong coupling between ring-rippled laser beam and the excited IAW. The results also show that the back reflectivity of SBS reduce for higher intensity of the laser beam.

This paper presents a theoretical model for the propagation/growth of a ring ripple, on a Gaussian electromagnetic beam, propagating in plasma with dominant relativistic-ponderomotive nonlinearity. A paraxial like approach has been invoked to understand the nature of propagation of the ring ripple like instability; in this approach, all the relevant parameters correspond to a narrow range around the irradiance maximum of the ring ripple. The dielectric function is determined by the composite (Gaussian and ripple) electric field profile of the beam. Thus, a unique dielectric function for the beam propagation and a radial field sensitive diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple has been taken into account. The effect of different parameters on the critical curves has been highlighted and the variation of the beam width parameter with the distance of propagation has been obtained for the three typical cases viz of steady divergence, oscillatory divergence and self-focusing of the ripple.