In laser keyhole welding the laser beam generates a hole through the workpiece, and a plasma is formed in this hole. The role of this plasma is uncertain, but it seems probable that it assists in the transfer of energy from the laser beam itself to the molten material of the workpiece. This will be caused in part by thermal conduction in the plasma, but earlier investigations have ignored the effects of absorption, reradiation and scattering within the plasma itself. It is probable that in reality these effects are significant, as they are in, for example, energy transfer in glass furnaces, or in stellar structures. The processes involved in the keyhole are examined and assessed, and related to other phenomena known to be of importance, such as recombination at the boundary. From the point of view of incorporation into theoretical models of keyhole processes, the usual approximations to the theory of radiative transfer present problems near to the presence of boundaries, where there are substantial space gradients of the physical quantities. This problem of an appropriate mathematical representation is considered.

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