The 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 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, which show that under the influence of an applied electric field, a beam can be self-focused in a very short time.