Particle-in-cell simulations of high-power cylindrical electron beam diodes

Abstract

Particle-in-cell (PIC) simulations are presented that characterize the electrical properties and charged-particle flows of cylindrical pinched-beam diodes. It is shown that there are three basic regimes of operation: A low-voltage, low-current regime characterized by space-charge-limited (SCL) flow, a high-voltage, high-current regime characterized by a strongly pinched magnetically limited (ML) flow, and an intermediate regime characterized by weakly pinched (WP) flow. The flow pattern in the SCL regime is mainly radial with a uniform current density on the anode. In the ML regime, electrons are strongly pinched by the self-magnetic field of the diode current resulting in a high-current-density pinch at the end of the anode rod. It is shown that the diode must first draw enough SCL current to reach the magnetic limit. The voltage at which this condition occurs depends strongly on the diode geometry and whether ions are produced at the anode. Analytic expressions are developed for the SCL and ML regimes and compared to simulations performed over a wide range of voltages and diode geometries. In the SCL regime, it is shown that many of the results from planar diodes provide reasonably good estimates for cylindrical diodes. In the ML regime, it is found that the critical current formula provides a better fit to the simulations than the parapotential and focused flow models. An empirical fit to the I–V characteristic was developed from the simulations that smoothly transitions from the SCL regime, through the WP regime, and into the ML regime.