We report on a model of highly efficient static, pulsed K DPAL [Zhdanov et al, Optics Express 22, 17266 (2014)], where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams are assumed. The model shows good agreement between the calculated and measured dependence of the laser power on the incident pump power. In particular, the model reproduces the observed threshold pump power, 22 W (corresponding to pump intensity of 4 kW/cm2), which is much higher than that predicted by the standard semi-analytical models of the DPAL. The reason for the large values of the threshold power is that the volume occupied by the excited K atoms contributing to the spontaneous emission is much larger than the volumes of the pump and laser beams in the laser cell, resulting in very large energy losses due to the spontaneous emission. To reduce the adverse effect of the high threshold power, high pump power is needed, and therefore gas flow with high gas velocity to avoid heating the gas has to be applied. Thus, for obtaining high power, highly efficient K DPAL, subsonic or supersonic flowing-gas device is needed.