Electron Cycloidal and Brillouin Flows in a Two-Dimensional Planar Crossed-Field Gap

In crossed-field devices, Brillouin flow is regarded as the prevalent equilibrium flow
¹
. One-dimensional (1-D) theory and particle-in-cell (PIC) simulations demonstrated the universality of the near-Brillouin (nB) state, which corresponds to Brillouin flow superimposed upon a turbulent background
^2,3
. The collapse of cycloidal flow to nB flow occurs for sufficiently high injection current density
$J^{2}$
. This transition is also sensitive to external perturbations, such as superimposing a small AC voltage on the gap
²
or adding a small series resistance
³
.