Theoretical Analysis of Electron Trajectories in a Collisional Crossed-Field Gap

Many applications, including Hall-effect thrusters and high-power microwaves, involve the application of a magnetic field orthogonal to the electric field across the gap. One important property of these crossed-field gaps (CFGs) in vacuum is the Hull cutoff magnetic field, which corresponds to the magnetic field where an electron emitted from the cathode reaches the anode with zero-velocity in the direction across the gap. Theory demonstrated that incorporating ions in such a magnetically insulated CFG increased the distance that an emitted electron traveled from the cathode [1]. Particle-in-cell (PIC) simulations showed the collisions induced by these ions caused all the electrons to eventually cross the gap [2].