This paper presents a theoretical and experimental investigation of the self-focusing of a laser pulse in a photorefractive medium on a nanosecond time-scale. For times shorter than the dielectric recombination time, we analyze the space-charge field build-up with respect to time and space and provide strong hints on the short time self- focusing of a narrow powerful beam. In order to validate our theoretical and numerical analysis, systematic investigations were performed on a Bi12TiO20 crystal, to show the effect of the external applied electric field, the intensity of the laser pulse and the beam waist.