Dynamics of Gaussian spikes on Gaussian laser beam in relativistic plasma A. SINGH, 1 M. AGGARWAL, 1 AND T.S. GILL 2 1 Department of Physics, National Institute of Technology Jalandhar, Punjab, India 2 Department of Physics, Guru Nanak Dev University, Amritsar, India (RECEIVED 24 October 2008; ACCEPTED 20 May 2009) Abstract In the present paper, we have investigated the growth of a Gaussian perturbation superimposed on a Gaussian laser beam. The nonlinearity we have considered is of relativistic type. We have setup the nonlinear differential equations for beam width parameter of the main beam, growth and width of the laser spike by using the WKB and paraxial ray approximation. These are coupled ordinary differential equations and therefore these are simultaneously solved numerically using the Runge Kutta method. It has been observed from the analysis that self-focusing/defocusing of the main beam and the spike determine the growth dynamic of the spike. Keywords: Gaussian; Growth; Relativistic; Ripple; Self-focusing 1. INTRODUCTION The most important problem in the laser driven fusion is the efficient coupling of the laser beam with the plasma, so that the plasma can be heated to high temperature. In the exper- imental situation, where an intense laser beam, traveling through nonlinear self-focusing media, results in multiple filament formation, there is a one-to-one correspondence between filaments and intensity spikes riding with incident laser beam (Abbi & Mahr, 1971). The plasma is one of such nonlinear media. Model used to study the growth dynamics of intensity spikes was proposed as ripple model by Sodha et al. (1976) and later on developed to study laser plasma related physics by a number of researchers (Singh & Singh, 1991a, 1991b; Gill & Saini, 2007; Purohit et al., 2008). Filamentation of the electromagnetic beam in the plasma has been investigated theoretically as well as experimentally in considerable details (Drake et al., 1974; Bingham & Lashmore-Davies, 1976, 1979, 1984; Herbst et al., 1980, 1981; Joshi et al., 1982; ZhiZan et al., 1983; Willi et al., 1984; Young et al., 1988; Rankin et al., 1989). The origin of filamentation instabilities may be due to small scale density perturbation or small scale intensity spike associated with the main beam. The physics of the per- turbation, growing at the cost of the main beam is relevant to the inertially confined fusion plasmas. Direct or indirect evi- dence concentrate on the intensity of the filaments just after its threshold is crossed, and do not go into intermediate details of its growth dynamics. The whole beam self- focusing of laser beam may arise on account of a variety of nonlinearities e.g., from ponderomotive force, collisional non-uniform heating, relativistic effects, etc. Several non- linear processes occur due to self-focusing effects as observed in a number of recent experiments (Torrisi et al., 2008; Faenov et al., 2007). Further dynamics of ponderomo- tive channeling in underdense plasma has recently been reported in the experimental observation of large amplitude electric and magnetic fields (Borghesi et al., 2007). In theor- etical work on the laser-plasma interaction, it is yet to be understood how the development of the intensity in filaments control its growth dynamics. When a high power laser beam is involved, then it can cause an electron oscillatory velocity comparable to the velocity of light, which modifies the effec- tive dielectric constant of the plasma, and hence affects the self-focusing of the beam. The self-focusing is due to the relativistic mass increase of plasma electrons. Relativistic laser-plasma interaction has been studied in detail by many authors, both theoretically (Kruer, 2000; Osman et al., 1999) and experimentally (Tanaka et al., 2000; Fuchs et al., 1999; Monot et al., 1995), and reviewed thoroughly (Umstadter, 2003; Gibbon & Forster, 1996). Nonlinear pro- cesses, playing key role in the generation of new ion sources has been recently reported (Laska et al., 2007; 587 Address correspondence and reprint requests to: Arvinder Singh, Department of Physics, National Institute of Technology Jalandhar, Punjab, India. E-mail: arvinder6@lycos.com Laser and Particle Beams (2009), 27, 587–593. Copyright # Cambridge University Press, 2009 0263-0346/09 $20.00 doi:10.1017/S0263034609990309