In situ observations of the fast solar wind in the inner heliosphere show that minor ions and ion subpopulations often exhibit distinct drift velocities. Both alpha particles and proton beams stream at speeds that rarely exceed the local Alfvén speed relative to the core protons, suggesting the presence of instabilities that constrain their maximum drift. We aim to propose a mechanism that generates an alpha-particle beam through nonlinear Landau damping, primarily driven by the relative super-Alfvénic drift between protons and alpha particles. To investigate this process, we perform one-dimensional, fully kinetic particle-in-cell simulations of a nonequilibrium multispecies plasma complemented by its linear theory to validate the model during the linear phase. Our results provide clear evidence that the system evolves by producing an alpha-particle beam, thereby suggesting a local mechanism for alpha-beam generation via nonlinear Landau damping.