Effect of External Magnetic Field on Critical Current for the Onset of Virtual Cathode Oscillations in Relativistic Electron Beams

TL;DR

This study investigates how external magnetic fields influence the critical current for virtual cathode oscillations in relativistic electron beams, revealing a decrease in critical current with increasing magnetic field and identifying an optimal magnetic field strength.

Contribution

It provides new insights into the relationship between external magnetic fields and virtual cathode formation, including an analytical relation for strong magnetic fields.

Findings

Critical current decreases as magnetic field increases.

Existence of an optimal magnetic field for minimum critical current.

Behavior explained by electron space charge dynamics.

Abstract

In this Letter we research the space charge limiting current value at which the oscillating virtual cathode is formed in the relativistic electron beam as a function of the external magnetic field guiding the beam electrons. It is shown that the space charge limiting (critical) current decreases with growth of the external magnetic field, and that there is an optimal induction value of the magnetic field at which the critical current for the onset of virtual cathode oscillations in the electron beam is minimum. For the strong external magnetic field the space charge limiting current corresponds to the analytical relation derived under the assumption that the motion of the electron beam is one-dimensional [High Power Microwave Sources. Artech House Microwave Library, 1987. Chapter~13]. Such behavior is explained by the characteristic features of the dynamics of electron space charge in the longitudinal and radial directions in the drift space at the different external magnetic fields.