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Steady - State Self Focusing of Gaussian Rippled Electromagnetic Beams in Plasmas: Relativistic Nonlinearity

Ghanshyam, Rajeev K. Verma, Narayan Kumar, Sudesh K. Jayaswal and Bhrigunandan Prasad Singh

This paper presents an investigation into the growth of a radially symmetrical spike, superimposed on a Gaussian laser beam propagating in unmagnetized plasma. Here we consider a collisionless plasma, where nonlinearity arising through the relativistic electron ponderomotive force in addition to the relativistic increase in mass.. The density depression is due to transverse pondromotive force on the electrons is larger than on the ions by the mass ratio. The electrons forced out of the radiation beam region set up an electrostatic restoring force which, on a slower time scale, causes the ions to be expelled. This density depression creates a local increase in the effective index of refraction and acts as an optical guide for the radiation beam. In addition to this self-focusing mechanism, a further reduction in the plasma frequency occurs in regions of high field intensity due to the relativistic mass increase of the electrons in the presence of the radiation beam. The small radius spike on the axis of the main beam grows very rapidly with the distance of propagation as compared to the self-focusing of the main beam. At higher intensities, the saturation effects of nonlinearity become predominant, making the nonlinear refractive index in the paraxial region have slower r dependence, and thus, letting the spike attract relatively less energy from its neighborhood.