We investigate analytically the nonlinear interaction of two beating laser beams with plasma by considering electron density inhomogeneity in the axial and radial directions. We apply the fluid model coupled with Maxwell equations to obtain a nonlinear equation for studying the plasma wave. We solve this nonlinear equation using the hypergeometric and Airy functions and present the damping and outgoing wave solutions. Our results show that the longitudinal and transverse wakefields generated in the preformed density-ramped plasma channel are much stronger than the inhomogeneous plasma with density-ramped profile.

Analytical equations of terahertz (THz) radiation generation based on beating of two laser beams in a warm collisional magnetized plasma with a ripple density profile are developed. In this regard, the effects of frequency chirp on the field amplitude of the terahertz radiation as well as the temperature and collision parameters are investigated. The ponderomotive force is generated in the frequency chirp of beams. Resonant excitation depends on tuning of the plasma beat frequency, magnetic field frequency, thermal velocity, collisional frequency, and effect of the frequency chirp with the plasma density. For optimum parameters of frequency and temperature the maximum THz amplitude is obtained.

The beat-wave accelerator is a promising candidate for accelerating electrons to relativistic energies in very short distances. Hence, in this paper, based on the fluid model coupled with Maxwell equations and obtaining a nonlinear plasma wave equation, we study the evolution of large‐amplitude wakefield excited by the beating of two laser beams in an axially and radially inhomogeneous plasma channel. We numerically solve the nonlinear wave equation by the finite difference method (FDM) in cylindrical coordinates. We also discuss the excitation of wakefield and the possibility of electron acceleration by taking into account three profiles of preformed density-ramped plasma channels. The results showed that the wakefield amplitude in the preformed plasma channel is much stronger than the inhomogeneous plasma with a density-ramped profile. The results also indicated that the wakefield amplitude in the parabolic-radial density profile and exponential-radial density is, respectively, higher than in the linear-radial density profile.