## 1 Introduction  
Plasma arc welding (PAW) is one of the arc welding processes that produces deep penetration and low distortion compared with conventional gas tungsten arc welding [1; 2]. In comparison to laser beam welding (LBW) and electron beam welding (EBW) processes, PAW equipment is cheaper and joint preparation is easier, even though its energy is less dense [3]. Consequently, PAW has been widely applied in industry fields such as aerospace [4], automotive [5], and rail transport [6]. Similar to LBW and EBW, PAW can be operated in keyhole mode (called keyhole plasma arc welding (KPAW)). In KPAW, the material flow around the keyhole is transported backward through both sides of the keyhole, producing a weld pool. The void behind the keyhole must be filled with the molten flow to maintain welding stability. The two necessary conditions for welding stability include: the molten flow on both sides must bridge the gap formed at the rear part by the passage of the keyhole and the molten flow must be supported by the surface tension acting on the back surface of molten pool. To improve the welding stability, the keyhole formation mechanism must be studied considering the material flow behavior of the weld pool. To understand and improve this behavior, mechanisms involving transportation of the convection flow in the weld pool must be studied in further detail. The behavior indicated above is a result of the interaction of forces acting on the surface and inside the KPAW weld pool. As described in a review paper, the four principal forces driving the welding convection flow of welding arc processes include: (i) drag force (shear force), which is created by the plasma flow acting on the liquid surface through the keyhole and plasma flow acting on the weld pool surface; (ii) buoyancy force, which is caused by the temperature difference within the weld pool; (iii) Lorentz force, which is generated by the self-magnetic field of the welding current within the weld pool; and (iv) Marangoni force, which is formed by the temperature gradient on the surface of the weld pool and on the surface along the keyhole wall. These forces are interrelated. They are principally controlled by welding process parameters such as welding current, welding voltage, shielding gas, welding speed, and base metal [7]. Recently, to increase the understanding and the knowledge about this process, many experiments were conducted. To improve the quality of welding joints, [PERSON] et al. observed the influence of welding speed and welding current on the change in the keyhole diameter and the weld pool surface using an insulated gate bipolar transistor (IGBT) power module [8; 9; 10]. Using this module, welding current was controlled in pulse waveform to decrease the brightness of the main arc. When the brightness of the main arc was weak, the keyhole and the weld pool surface were clearly visualized using a high-speed video camera (HSVC). [PERSON] et al. achieved good quality weld joints through controlling keyhole stability [11; 12; 13; 14] by developing a welding current control unit for KPAW process. During the welding process, the keyhole and the weld pool surface were captured in an image and the temperature at the bottom side of the base metal was measured. The main results showed the relationship of welding current and keyhole geometry parameters. To accurately control the position of the welding torch when welding by robot, [PERSON] et al. investigated and developed algorithms for adapting the control of the welding robot through processing the weld pool images to track the weld line based on the boundary between the base metal and the weld pool [15; 16; 17]. During welding process, however, clearly distinguishing the boundary was difficult due to the high brightness of the main arc. To correctly achieve control, a pulsed current wave form was used to cut off the main arc for a very short time. [PERSON] et al. mainly considered the flow velocity distribution inside the weld pool using experiments [18].