A theoretical analysis was carried out to investigate the characteristics of plasma arc injected transverse to a transverse-alternating magnetic field. Two mathematical models were developed to describe both the oscillating amplitude of the plasma arc root and the heat flux density distribution of plasma arc on the workpiece surface. The characteristic of plasma arc under the external transverse-alternating magnetic field imposed perpendicular to the plasma current was discussed. The effect of processing parameters, such as working gas flux, arc current, magnetic flux density and the standoff from the nozzle to the workpiece, on the oscillation and heat flux distribution of plasma arc were also analyzed. The results show that it is feasible to adjust the shape and heat flux density of the plasma arc by the transverse alternating magnetic field, which expands the region of plasma arc thermal treatment and uniforms the heat flux density upon the workpiece. Furthermore, the oscillating amplitude of plasma arc decreases, and the heat flux density gradient upon the workpiece increases with decrease of the magnetic flux density. Under the same magnetic flux density, more gas flux and more arc current cause the oscillating amplitude to decrease. The researches have provided a deeper understanding of adjusting of plasma arc characteristics.