Study of coexisting stimulated Raman and Brillouin scattering at relativistic laser power ASHISH VYAS, RAM KISHOR SINGH, AND R.P. SHARMA Centre for Energy Studies, IIT Delhi, India (RECEIVED 29 May 2014; ACCEPTED 7 October 2014) Abstract This paper presents a model to study the stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) simultaneously at relativistic laser power. At high intensity, the relativistic mass correction for the plasma electrons becomes significant and the plasma refractive index gets modified which leads to the relativistic self-focusing of the pump beam. This filamentation process affects the scattering processes (SRS and SBS) and at the same time the pump filamentation process also gets modified in the presence of the coexisting SRS and SBS due to the pump depletion. We have also demonstrated that the pump depletion and relativistic filamentation affects the back-reflectivity of scattered beams (SRS and SBS) significantly, for the coexistence case. Keywords: Relativistic nonlinearity; Self-focusing; Stimulated Brillouin scattering; Stimulated Raman scattering 1. INTRODUCTION Due to availability of the high power lasers, laser plasma in- teraction at higher intensity (10 18 –10 21 W/cm 2 ) becomes an important nonlinear phenomenon in recent years. The prop- agation of an intense laser beam through the plasma results into various instabilities namely, self-focusing, filamenta- tion, stimulated Raman scattering (SRS), stimulated Bril- louin scattering (SBS), two plasmon decay, etc. (Krall et al., 1973; Kruer, 1974; Liu et al., 1994; Guérin et al., 1998). These instabilities play a very important role in many areas like fast-ignitor thermonuclear fusion (Deutsch et al., 1996), compact laser-driven accelerators (Tajima et al., 1979), X-ray lasers (Li et al., 2011), laboratory astrophysics (Remington et al., 1999), and many more (Tajima et al., 2002), where laser plasma interaction takes place. In particular, SRS corresponds to the decay of the incident electromagnetic wave into a scattered electromagnetic wave and an electron plasma wave (EPW), while during SBS the incident electro- magnetic wave decays into a scattered electromagnetic wave and an ion acoustic wave (IAW). In this paper, we are mainly concerned about SRS and SBS because due to these in- stabilities, a large fraction of the high power laser energy is not efficiently coupled with plasma as well as modification of the intensity distribution takes place which affect the uniformity of energy deposition (Kruer, 1974; Liu et al., 1994; Lindl et al., 2004; Omatsu et al., 2012). Apart from SRS and SBS, the self- focusing of the laser beam is also a crucial problem in high power laser plasma interactions. For the propagation of a non- uniform intense laser beam inside the plasma, both pondero- motive nonlinearity and relativistic nonlinearity can lead to the self-focusing process. The relativistic self-focusing occurs because at such higher intensities the field associated with the light wave becomes very high which accelerates the plasma electrons at relativistic velocities and hence the relativ- istic mass correction must be taken into account. This relativis- tic change in the electron mass modifies the dielectric constant of plasma ε = 1 − ω 2 pe /γω 2 0 , where ω pe =(4πN e e 2 /m 0 ) 1/2 is the plasma frequency, ω 0 is the laser frequency, N e is the plasma electron density, e and m 0 are the charge and rest mass of the electron, respectively, and γ is the relativistic Lo- rentz factor. Therefore, plasma refractive index (  ε √ ) seen by the intense laser beam becomes γ dependent which leads to the relativistic self-focusing and breakup of the laser beam into intense filaments (Umstadter, 2003). On the other hand, ponderomotive nonlinearity modifies the refraction index by expulsion of the electrons from the higher intensity region. However, these nonlinearities are operative at different time scales according to the inequalities (1) τ < τ pe or (2) τ pe < τ< τ pi ; here, τ is laser pulse duration, τ pe is the electron plasma period, and τ pi is ion plasma period. In case (1), the rel- ativistic nonlinearity is set up (almost instantaneously) while for case (2), both the nonlinearities (relativistic and 657 Address correspondence and reprint requests to: Ashish Vyas, Centre for Energy Studies, IIT Delhi, India 110016. E-mail: ashishvyas.optics@gmail. com Laser and Particle Beams (2014), 32, 657–663. © Cambridge University Press, 2014 0263-0346/14 doi:10.1017/S0263034614000688