The laser scans the powder layer; the melt pool (orange) and solidified track (blue) form behind. Adjacent tracks overlap depending on hatch spacing and layer thickness.
$$\mathrm{VED} = \frac{\eta\,P}{v\,h\,t}, \qquad \dot V = v\cdot h\cdot t$$
Volumetric energy density VED and build rate $\dot V$. η is absorptivity, P is laser power, v is scan speed, h is hatch spacing and t is layer thickness. The process window for most alloys sits in 30–80 J/mm³.
$$\mathrm{Pe} = \frac{v\,d}{2\,\alpha}, \qquad \alpha = \frac{k}{\rho\,c_p}$$
Melt-pool Peclet number and thermal diffusivity α. d is beam diameter, k is thermal conductivity, ρ is density and cp is specific heat. The larger Pe is, the more comet-shaped the melt pool becomes.
$$w \approx d\sqrt{1+0.5(\mathrm{VED}-30)/30}, \qquad D \approx t\sqrt{\mathrm{VED}/60}$$
Empirical correlations for melt-pool width w and depth D (Rosenthal model with experimental corrections). Expect a ±20% error on real machines because the powder layer behaves very differently from a solid.