Some features of the thermal field in laser heating of metals

An analysis is made of the heating of a metal sample occupying a half-space, by a laser radiation beam. This boundary-value problem is nonlinear as a result of the strong temperature dependence of the rate of energy release during oxidation of a metal. It is shown that, depending on the relationship between the intensity and the radius of the radiation beam, the problem may have two, four, or no steady-state solutions. A bifurcation set that divides the parameter space into regions having different numbers of solutions is plotted. It is observed that the structurally stable boundary-value problem has three parameters–the intensity, beam radius, and heat loss constant. The complete set of stationary states has a "swallow-tail" type of characteristic.