Weld bead profile and other weld properrties depend on algorithm of energy input. Firstly, it is energy per length (power of heat source and velocity of moving). But for pulsed modes, parameters of pulses (energy, duration, friquency) have greate influence. Plasma affects welding process during continuous modes, during pulsed modes it also depends on parameters of pulses. Furthermore, shielding gases (composition, directions of flows, flows rate) affect results.

In fusion welding, the shape of the weld pool depends on two non-dimensional numbers, Marangoni number and the Prandtl number. Please see the two attached papers. The origin of the shape is the pattern of liquid metal flow and heat transfer driven mainly be Marangoni force. This driving force originates from the spatial variation of surface tension owing to temperature variation on the surface of the molten pool. Very diverse weld pool shapes and curvatures of the boundaries have been reported, all of which can be explained based of numerical models of heat transfer and fluid flow.

T. DebRoy

http://www.matse.psu.edu/modeling/