At present, the existing researches on magnetic confinement of arc mainly focus on the influence of traditional free welding arc, while the researches on magnetic re-confinement of plasma cut arc which has been constrained by mechanical structure are relatively lacking. In this study, a three-dimensional (3D) electromagnetic model of the confinement device and a 3D plasma cutting arc model based on magneto-hydrodynamics were established. Maxwell and ANSYS co-simulation were adopted to study the distribution of the longitudinal magnetic field (LMF), and the influence of the LMF on the characteristics of the plasma cutting arc was emphasized. The temperature field, velocity field, flow field and arc pressure distribution of plasma cut arc under different LMF intensity in the range of 0 ~ 200 mT were simulated. The results show that the application of LMF is helpful to increase the current density of plasma cutting arc, improve the temperature and straightness of the arc, and thus improve the cutting effect of plasma cutting arc. The research results have guiding significance for the rational design of magnetic re-constraint plasma arc cutting device and process in practical engineering applications.