distributed within the beam. Some devices produce Gaussian energy distributions, whereas others can be bimodal. A Gaussian energy distribution can be applied by multiplying the power density by a function like this:, where r is the radial distance from the center of the beam, =beam radius or spot size. Using a temperature distribution instead of a point source assumption allows for easier calculation of temperature-dependent material properties such as absorptivity. On the irradiated surface, when a keyhole is formed, Fresnel reflection (the almost complete absorption of the beam energy due to multiple reflection within the keyhole cavity) occurs and can be modeled by , where ε is a function of dielectric constant, electric conductivity, and laser frequency. θ is the angle of incidence. Understanding the absorption efficiency is key to calculating thermal effects. Step 2 Lasers can weld in one of two modes: conduction and keyhole. Which mode is in operation depends on whether the power density is sufficiently high enough to cause evaporation. Conduction mode occurs below the vaporization point while keyhole mode occurs above the vaporization point. The keyhole is analogous to an air pocket. The air pocket is in a state of flux. Forces such as the recoil pressure of the evaporated metal open the keyhole while gravity (aka hydrostatic forces) and metal surface tension tend to collapse it. At even higher power densities, the vapor can be ionized to form a plasma. The recoil pressure is determined by using the Clausius-Clapeyron equation., where P is the equilibrium vapor pressure, T is the liquid surface temperature, HLV is the latent heat of vaporization, TLV is the equilibrium temperature at the liquid-vapor interface. Using the assumption that the vapor flow is limited to sonic velocities, one gets that , where Po is atmospheric pressure and Pr is recoil pressure. Step 3 This pertains to keyhole profiles. Fluid flow velocities are determined by where is the velocity vector, P=pressure, ρ= mass density, =viscosity, β=thermal expansion coefficient, g=gravity, and F is the volume fraction of fluid in a simulation grid cell. Step 4 In order to determine the boundary temperature at the laser impingement surface, you'd apply an equation like this. , where kn=the thermal conductivity normal to the surface impinged on by the laser, h=convective heat transfer coefficient for air, σ is the Stefan–Boltzmann constant for radiation, and ε is the emissivity of the material being welded on, q