Conservation of energy analysis of collisional cross-field diffusion

Summary form only given. Cross-field diodes are instrumental in the operation of high-power microwave sources in relativistic magnetrons, magnetically insulated transmission lines for pulsed power systems, and Hull thrusters in space propulsion. These diodes are magnetically insulated in order to prevent electron migration across the gap. In spite of this insulation, many electrons still move towards the anode which leads to pulse shortening and/or excitation of undesired modes. It has previously been shown that the presence of ions in a crossed-field gap increases the electrons excursion toward the anode region. Further work has shown that both electron-electron scattering and ionization of the background species exacerbate this crossed-field migration. In this work, we show that an electron, once scattered or created through an ionizing collision, will move according to the Lorentz force equation and conservation of energy. Using a 1D PIC code we will show that these electrons scattered or created midgap have total energies greater than those injected at the cathode; thus, they are able to penetrate farther into the gap.