Two-dimensional analysis of the relativistic parapotential electron flow in a magnetically insulated transmission line oscillator (MILO)

This paper presents a two-dimensional model for studying the relativistic parapotential electron flow in a magnetically insulated transmission line oscillator (MILO). The distribution expressions of the velocity, energy, density, and self-electric and self-magnetic fields of electron flow are derived and then analyzed numerically. Results of the model show that the self-electric and self-magnetic fields and density of the electron flow are quite high near the surface of the slow-wave structure of a MILO where they may reach their peak values. In addition, the formation of the insulated electron flow requires a large current flowing through the inner conductor (cathode) of the MILO, which is identical with the previous works. It is also found that considerable increases in the absolute values of axial and radial velocities of the electron flow occur when electrons approach the surface of the slow-wave structure. The electron flow is mainly along the axial direction in between the surfaces of cathode and slow-wave structure except the regions near the two surfaces. More interestingly, the radial velocity of electron flow ran still be increased but the axial velocity decreased when the electrons go into the region in between the inner and outer radii of the slow-wave structure, where the electron flow is not always dominated by axial flow. The results of the present paper are more realistic than those of the one-dimensional model in describing the parapotential electron flow in a MILO.