The possible interactions between plasma waves and relativistic charged particles are considered. An electromagnetic perturbation in the plasma is formulated as an elliptically polarized wave, and the collisionless plasma is described by a distribution in phase space, which is realized in cylindrical coordinates. The linearized Vlasov equation is solved in the semi-relativistic limit, to obtain the distribution function in the rest frame of the observer. The perturbed currents supported by the ionized medium are then calculated, so that an expression can be written for the total amount of energy available for transfer through the Landau mechanism. It is found that only certain modes of the perturbed current are available for this energy transfer. The final expressions are presented in terms of Stokes parameters, and applied to the special cases of a thermal as well as a nonthermal plasma. The thermal plasma is described by a Maxwellian distribution, while two nonthermal distributions are considered: the kappa distribution and a generalized Weibull distribution.