In this paper, we study the nonlinear interaction of a laser beam with a periodic lattice of nanoparticles in the presence of a planar magnetostatic wiggler. The static magnetic field of the wiggler can couple with the electric field of the laser wave and change the electric field intensity of the pumped wave, leading to the formation of a nonlinear force. In consequence, the nonlinear force enhances plasmonic oscillations of the electronic cloud of each nanoparticle causing electron density modulation, which improves self-focusing property of the laser beam propagating through a periodic lattice of nanoparticles. By manipulating a classical microscopic approach into plasmonic oscillations of electronic clouds of the nanoparticles and the well–known perturbative method, a nonlinear dispersion relation describing the evolution of the laser amplitude propagating through the nanoparticle lattice has been obtained. The effect of the wiggler magnetic strength on the evolution of the laser transverse profile has been discussed. It was found that by increasing the wiggler strength, the transverse profile bandwidth shrinks and laser focusing is enhanced. In addition, further numerical results indicated that by increasing the wiggler field strength, the cut-off frequency of the body waves increases.

Significant progress has been made employing plasmas in the free-electron lasers (FELs) interaction region. In this regard, we study the output power and saturation length of the plasma whistler wave-pumped FEL in a magnetized plasma channel. The small wavelength of the whistler wave (in sub-μm range) in plasma allows obtaining higher radiation frequency than conventional wiggler FELs. This configuration has a higher tunability by adjusting the plasma density relative to the conventional ones. A set of coupled nonlinear differential equations is employed which governs on the self-consistent evolution of an electromagnetic wave. The electron bunching process of the whistler-pumped FEL has been investigated numerically. The result reveals that for a long wiggler length, the bunching factor can appreciably change as the electron beam propagates through the wiggler. The effects of plasma frequency (or plasma density) and cyclotron frequency on the output power and saturation length have been studied. Simulation results indicate that with increasing the plasma frequency, the power increases and the saturation length decreases. In addition, when density of background plasma is higher than the electron beam density (i.e., for a dense plasma channel), the plasma effects are more pronounced and the FEL-power is significantly high. It is also found that with increasing the strength of the external magnetic field frequency, the power decreases and the saturation length increases, noticeably.