The physical characteristics of a plasma arc affect the stability of the keyhole and weld pool directly during keyhole plasma arc welding (KPAW).There will be significant change for these characteristics because of the interaction between the keyhole weld pool and plasma arc after penetration.Therefore,in order to obtain the temperature field,flow field,and arc pressure of a plasma arc under the reaction of the keyhole,the physical model of a plasma arc with a pre-set keyhole was established.In addition,the tungsten and base metal were established into the calculated domain,which can reflect the effect of plasma arc to weld pool further.Based on magneto hydrodynamics and Maxwell equations,a two-dimensional steady state mathematical model was established.Considering the heat production of anode and cathode,the distribution of temperature field,flow field,welding current density,and plasma arc pressure were solved out by the finite difference method.From the calculated results,it is found that the plasma arc was compressed a second time by the keyhole.This additional constraint results in an obvious rise of the plasma arc pressure and flow velocity at the minimum diameter place of the keyhole,while the temperature field is impacted slightly.Finally,the observational and metallographic experiments are conducted,and the shapes of plasma arc and fusion line agree with the simulated results generally.