The existence of a new class of longitudinally periodic beams with sharply defined central peak is predicted. The intensity patterns of such beams are well reproduced at the equidistant transverse planes passing through nodal focal points on the propagation axis. The total wave field of the beams is shown to be a superposition of the three-dimensional point-spread functions produced by converging spherical wavelets with the same energies and the amplitude distributions of angular spectra. Beamforming systems are proposed that based on positive refractive lenses and novel high-efficient diffractive multifocal lenses with uniform beam splitting and a naturally spaced on-axis array of foci. The phase function of a diffractive multifocal lens is that of a linear one-dimensional fan-out grating with quadratically transformed argument. Two examples of numerical simulations for beamforming systems with continuous-relief and binary diffractive multifocal lenses are considered.