An external magnetic field applied in arc welding process results in electro-magnetic stirring (EMS) welding. The added longitudinal magnetic field (LMF) provides an effective method to control the arc behavior and affect the resultant welds. However, few studies have addressed arc behaviors in LMF-TIG hybrid welding, i.e., tungsten inert gas arc (TIG) hybrid welding with an external LMF; the LMF direction is the same as or parallel to the symmetric axis of welding arc. In this paper, a three dimensional (3D) multiphysics field model was established to analyze arc behavior in LMF-TIG hybrid welding. This model is formed by fluid dynamics equations coupled with Maxwell equations. The fields of temperature, velocity, and electric current field were obtained from this model through numerical simulation using the finite volume method (FVM). It was found that the arc changes from its free to strong electromagnetic field controlled status in three stages. After the applied electromagnetic field exceeds a critical value, mutation is induced in the arc resulting in an arc behavior completely different from that of the normal free arc. The arc pressure and temperature distributions shift their centers, where the peak pressure and temperature occur, from the tungsten axis. In addition, the arc exhibits negative pressure (i.e., anti-gravity gradient behavior) below the cathode and a tornado-style behavior. The arc plasma flow reverses, a circular area occurs, and a lowtemperature zone forms in the center of the arc. The highest flow speed takes place on both sides of the arc symmetry axis.The unique appearance of the negative arc pressure and its formation mechanism are discussed.Keywords Tungsten inert gas arc welding . Longitudinal electromagnetic field . Arc behavior . Negative pressure Nomenclature r Axial direction (m) z Radial direction (m) T Temperature (K) P Pressure (Pa) v r Radial component of the speed (m/s) v z Axial component of the speed (m/s) ρ Density of argon plasma (kg/m 3 ) μ Viscosity coefficient of argon plasma k Heat transfer coefficient of argon plasma (W/(m*K)) C p Specific heat capacity of argon plasma (J/(kg*K)) σ Conductivity of argon plasma (S/m) J r Axial component of the arc plasma current density (A/m 2 ) J z Radial component of the arc plasma current density (A/m 2 ) k B Boltzmann constant (J/K) S R Radiative heat loss (J) S 0 Source term of the radial momentum equations in the group of momentum equations (kg m/s) S Z Source term of the axial momentum equations in the group of momentum equations (kg m/s) φ Potential (V) μ 0 Vacuum permeability (T*m/A) A r Radial magnetic vector potential (V*s/m) A z Axial magnetic vector potential (V*s/m) B θ Self-inductance magnetic field intensity (T) R Radius of tungsten cathode top (mm)