This work is devoted to improving relativistic self-focusing of intense laser beam in underdense unmagnetized plasma. New density profiles are introduced to achieve beam width parameter up to the wavelength of the propagating laser. By investigating variations of the beam width parameter in presence of different density profiles it is found that the beam width parameter is considerably decreased for the introduced density ramp comparing with uniform density and earlier introduced density ramp profiles. By using this new density profile high intensity laser pulses are guided over several Rayleigh lengths with extremely small beam width parameter.

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The effects of the polarized incident laser pulse on the electrons of the plasma surface and on the reflected pulse in the relativistic laser-plasma interaction is investigated. Based on the relativistic oscillating mirror and totally reflecting oscillating mirror (TROM) regimes, the interaction of the intense polarized laser pulses with over-dense plasma is considered. Based on the effect of ponderomotive force on the characteristic of generated electron nano-bunches, considerable increasing in the localization and charges of nano-bunches are realized. It is found that the circularly polarized laser pulse have N e /N cr of 1500 which is almost two and seven times more than the amounts for P-polarized and S-polarized, respectively.

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