A main limitation for many applications of laser-driven sources of narrowband terahertz (THz) radiation in spectroscopy and particle acceleration is the low optical-to-THz conversion efficiency. Due to power limitations, it is often necessary to use small sizes of the optical pump beam in the range of the THz wavelength to achieve sufficient intensity to effectively drive the nonlinear process. However, diffraction of the THz radiation can then adversely affect the conversion efficiency. Here, we report on an experimental study of the role of self-focusing and the beam size of the pump beam on the down-conversion of lasers in periodically poled lithium niobate using tunable pulse trains. We identify self-focusing as a limiting factor of the conversion efficiency, demonstrate the potential of the pulse-train approach to mitigate this effect and investigate the dependence of the efficiency on the pump beam size.