摘要： The motivation of present paper is the investigation of effective permittivity and absorption cross section of cluster nanoplasmas in the interaction of a Gaussian laser beam with a cluster of metallic nanoparticles, in the presence of a helical magnetic undulator. The static magnetic field of the undulator couples with the field of the laser wave, and forms a nonlinear force in the interaction region. As a result, the nonlinear force varies the plasmonic oscillations of the electron of nanoplasmas that leads to electron density modulation, which modifies absorption cross section and effective permittivity of nanoparticles. Using a perturbative method, we analytically derived the nonlinear dispersion waves and dielectric constant of metallic nanoparticles lattice (gold, silver, and copper) in the presence of a helical magnetic undulator. Numerical results indicate that with increasing the undulator magnetic field strength, absorption cross section of cluster nanoplasmas increases and absorption phenomenon occurs at frequencies close to the effective plasma frequency. Besides, with decreasing distance of nanoparticles in the cluster (and with increasing the nanoparticles radius), absorption cross section increases. We also found that the dielectric constant of the cluster nanoplasma medium increases with enhancing undulator magnetic field strength only near the effective plasmonic frequency. This concept opens a path toward new properties of cluster nanoplasmas as quantum dots, diagnostics, and sensors based on magnetic undulator structures.