Maximum depth of keyhole melting of metals by a laser beam

A calculation is reported of the maximum depth and diameter of a narrow crater formed in a stationary metal target exposed to high-power cw CO₂ laser radiation. The energy needed for erosion of a unit volume is assumed to be constant and the energy losses experienced by the beam in the vapor–gas channel are ignored. The heat losses in the metal are allowed for by an analytic solution of the three-dimensional boundary-value heat-conduction problem of the temperature field in the vicinity of a thin but long crater with a constant temperature on its surface. An approximate solution of this problem by a method proposed earlier by one of the present authors was tested on a computer. The dimensions of the thin crater were found to be very different from those obtained earlier subject to a less rigorous allowance for the heat losses.