By containing ponderomotive self-channeling, the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel. It is found that ponderomotive self-channeling results in the emergence of a solitary wave and catastrophic focusing, which apparently decreases the region for stable propagation in a parameter space of laser power and the ratio of the initial laser spot radius to the channel radius (RLC). Direct numerical simulation confirms the theory of constant propagation, periodic defocusing and focusing oscillations in the parameter space, and reveals a radial instability which prevents the formation of bright and dark solitary waves. The corresponding unstable critical curve is added in the parameter space numerically and the induced unstable region above the unstable critical curve covers that of catastrophic focusing, which shrinks the stable region for laser beams. For the expected constant propagation, the results reveal the need for a low RLC. Further study illustrates that the channel power-law exponent has an obvious effect on the final stable region and laser propagation, for example increasing this exponent can enlarge the stable region significantly, which is beneficial for guiding of the laser and increases the lowest RLC for constant propagation. Our results also show that the initial laser amplitude has an apparent influence on the propagation behavior.

We study the effect of nonlinearly chirped super-Gaussian (SG) laser pulse on wakefield generation in an inhomogeneous plasma. The different types of nonlinearly chirped pulse are employed, and different kinds of inhomogeneous plasma density are used. The maximum wakefield amplitude as the function of nonlinearly chirped laser pulse and inhomogeneous plasma density in parameter space are obtained. Moreover, the dependence of the maximum wakefield amplitude on the SG laser pulse index is discussed. This shows that a larger wakefield can be obtained when the chirped pulse and inhomogeneous density are in the critical regions. Wakefield generation can be controlled by adjusting the chirped SG pulse and inhomogeneous plasma density parameters. That is, we provide an efficient way for the controlled generation of the wakefield.