Relativistic self-focusing in interaction of intense laser beam and exponential decay underdense inhomogeneous plasma

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.