In the laser and plasma interaction, Wong et al. (2018) and Fuchs et al. (2000) have found that the plasmas present the approximate exponential or exponential decay variation of density in experiments. In the paper, based on their researched results, we investigated beam relativistic self-focusing in interaction of intense laser beam and axially exponential decay underdense inhomogeneous plasma. The results show that the relativistic nonlinear effect gives rise to obvious self-focusing in homogeneous plasma and inhomogeneous plasma, comparing with beam self-focusing in homogeneous plasma, exponential decay inhomogeneous plasma is more benefit to form relatively steady self-focusing. Moreover, plasma inhomogeneity promotes self-focusing. In addition, when the amplitude of plasma inhomogeneity increases, beam self-focusing would obviously strengthen, while with the increase of the degree of exponential decay, self-focusing would slightly decrease.
In this work, influence of intense relativistic influence and plasma nonuniformity on ultrarelativistic laser beam filamentation and filamentation instability has been investigated in homogeneous and inhomogeneous plasma. The results are shown that, in ultrarelativistic laser-plasma interaction, relativistic effect plays a crucial role on beam filamentation and self-focusing, and plasma inhomogeneity further increases beam filamentation, while it also strengthens filamentation instability. To avoid filamentation instability, the research results show that it should try to reduce plasma inhomogeneity in laser-plasma interaction.
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