Helical and chiral plasma structures are ubiquitous, especially in nuclear fusion devices and space plasmas. However, the spontaneous formation of helical structures has rarely been noticed in non-equilibrium cold plasma jets that have wide applications in biomedicine and material science. Recently the chiral plasma plume without any notable asymmetry has been discovered. Under the specific parameters of pulsed discharges, the plasma bullets that at the beginning propagated in the straight lines spontaneously turn into 3-D helical discharge trajectories. Here, the electromagnetic mechanism for the chiral plasma plumes is clarified by the numerical investigation of the 3-D electromagnetic field. According to the specific standing-wave mode with the periodic poloidal component in simulation, a type of plasma plume which shows the apparent poloidal rotation only at the periodic position of the tube and moves nearly in a straight line at other positions is revealed. These findings are relevant to the development of high-voltage active electromagnetic media for artificial 3-D optical meta-material devices and precise 3-D materials processing involving helical and chiral patterns in diverse fields.