Nonlinear penetration of an inhomogeneous laser beam in an overdense plasma

This paper presents an analysis of the penetration of an intense electromagnetic beam in an inhomogeneous plasma. It is seen that on account of the electron density gradient created by an intense transversely inhomogeneous beam a region is created in the overdense plasma where the beam can propagate. Typically a C${\mathrm{O}}_2$ laser beam of width $r_0=100\mathrm{}$ μm, power $P=15\mathrm{}$ GW, and $\omega =1.7\mathrm{}\times {10}^{14}$ ${\sec }^{-1\mathrm{}}$ can penetrate to a region where $\frac{{\omega }_p^2}{{\omega }^2}=20\mathrm{}$ in a 500-eV inhomogeneous plasma characterized by $\frac{{\omega }_p^2}{{\omega }^2}=\left(\frac{{\omega }_{p0\mathrm{}}^2}{{\omega }^2}\right)\mathrm{}(1+Bz)\mathrm{}$.