The cathode erosion rate, arc root velocity and output power of a well-type cathode (WTC), non-transferred plasma torch operating in air are studied experimentally in this paper. An external solenoid to generate a magnetically driven arc and a circular swirler to produce a vortex flow structure are equipped in the studied torch system, which is designed to reduce the erosion rate at the cathode. A least square technique is applied to correlate the system parameters, i.e. current, axial magnetic field and mass flow rate, with the cathode erosion rate, arc root velocity and system power output. In the studied WTC torch system, the cathode erosion has a major thermal erosion component and a minor component due to the ion-bombardment effect. The cathode erosion increases with the increase of current due to the enhancement in both Joule heating and ion bombardment. The axial magnetic field can significantly reduce the cathode erosion by reducing the thermal loading of cathode materials at the arc root and improving the heat transfer to gas near the cathode. But, the rise in the mass flow rate leads to the deterioration of erosion, since the ion-bombardment effect prevails over the convective cooling at the cathode. The most dominant system parameter to influence the arc root velocity is the axial magnetic field, which is mainly contributed to the magnetic force driving the arc. The growth in current has a negative impact on increasing the arc root velocity, because the friction force acting at the spot due to a severe molten condition becomes the dominant component counteracting the magnetic force. The mass flow rate also suppresses the arc root velocity, as a result of which the arc root moves in the direction against that of the swirled working gas. All system parameters such as current, magnetic field and gas flow rate increase with the increase in the torch output power. The experimental evidences suggest that the axial magnetic field is the most important parameter to operate the straight-polarity WTC plasma torch at high output power with a limited cathode erosion rate. This emphasizes the importance of an external magnetic field on a WTC torch system for reducing the erosion at the cathode.