The apparent or integrated energy absorbed by the welding or drilling cavity subject to a focused beam is investigated in this paper. The cavity is assumed to be paraboloid of revolution and the incident flux is considered to be a Gaussian distribution specified by the divergence angle, focal spot size and focal location. Accounting for multiple specular and diffuse reflections of the beam propagating in the cavity, but neglecting absorption and scattering within the plasma in the cavity, the results show that the absorbed energy flux calculated by the analytical model agrees well with the Monte Carlo method for a deep cavity. Regardless of dimensionless cavity depths, spot sizes and divergence angles the apparent absorptivity increases and decreases as the focal spot is lowered from infinity through the workpiece surface to the cavity base. Apparent absorptivity exhibits a relatively minimal value as the focal spot is near the cavity base. Further lowering of the focal spot below the cavity base slightly increases and then decreases the apparent absorptivity. In instances of the incident energy completely entering the cavity, apparent absorptivity is increased by increasing divergence angle, focal location, and spot size.
