Analysis of injected electron beam propagation in a planar crossed-field gap

This paper examines basic crossed-field device physics in a planar configuration, specifically electron beam perturbation and instability as a function of variation in magnetic field, and angle between magnetic and electric field. We perform a three-dimensional (3-D) simulation of electron perturbation in a planar crossed-field system using the full 3-D particle trajectory solver in CST Particle Studio (CST-PS). The structure has a length, height, width and anode-sole gap of 15 cm, 2 cm, 10 cm, and 2 cm, respectively. The anode to sole voltage is fixed at 3 kV, and the magnetic field and injected current varied from 0.01 T to 0.05 T and 1.5 mA to 1 A, respectively. The simulations show that applying a magnetic field of 0.05 T makes the beam stable for a critical current density of 94 mA/cm² for an anode-sole gap of 20 mm. Above this current density, the beam was unstable, as predicted. Introducing a 1^◦ tilt in the magnetic field destabilizes the beam at a current density of 23 mA/cm², which is lower than the critical current density for no tilt, as predicted by our theory. The simulation results also agree well with prior one-dimensional (1-D) theory and simulations that predict stable bands of current density for a 5^◦ tilt where the beam is stable at low current density (<13.3 mA/cm²), unstable above this threshold, and then stable again at higher current density, (>33 mA/cm²).