• A new general method for calculation of focal region coherence and spatiotemporal evolution in high power laser beam smoothing. • Focal region evolution using beam smoothing method of induced spatial incoherence with continuous phase plate (ISI + CPP) on broadband laser is analyzed and compared with conventional method on narrowband laser. • New definition of laser bandwidth and correction on smoothing speed. • Latest experimental result using beam smoothing method of ISI + CPP. Beam smoothing effect of induced spatial incoherence combined with continuous phase plate is reported. General theoretical models that can be used to describe the spatiotemporal characteristics of the focal region in beam smoothing is proposed. The focal region evolution using induced spatial incoherence is studied and compared with that of using smoothing by spectral dispersion. The result shows that, when using induced spatial incoherence combined with continuous phase plate for beam smoothing, the focal region spatiotemporal evolution is chaotic and random, and the size of speckle on spacetime is determined by the coherence time of the laser. The comparison shows that the smoothing speed of induced spatial incoherence is higher. Focal spot time-resolved spectrum and focal spot intensity distribution using induced spatial incoherence are measured experimentally. The results show that the beam smoothing method has an excellent ability to obtain the desired low coherence in focal region, and can completely suppress the middle-high frequency nonuniformity of the focal spot. [ABSTRACT FROM AUTHOR]