Within the framework of the kinetic method, the process of interaction of a rarefied electron plasma with laser beat waves is investigated taking into account the initial spread in the velocities of plasma particles. Using the expression for the spectral distribution function of plasma particles in the presence of laser beat waves, an anisotropic tensor of the plasma dielectric permittivity is obtained. In this case, an expression for the nonequilibrium current density induced by the perturbed field and the constitutive equation connecting the conductivity tensor with the dielectric permittivity are determined. Assuming that in equilibrium the particle distribution function has the form of the Maxwellian distribution function, the dielectric tensor is diagonalized. Analytical expressions are obtained for the longitudinal and transverse components of the dielectric permittivity.
