Numerical simulation of the electromagnetic instability of an intense beam in a quadrupole focusing system.

Abstract

Discrete quadrupole focusing systems are subject to an electromagnetic instability wherein the growing transverse motion of the beam interacts with the quadrupole field and the ${\mathrm{TE}}_{11}$ waveguide mode. We study this via three-dimensional particle simulation. We find evidence of the instability, with growth rates and frequencies in reasonable agreement with theory. The instability is found to saturate at a low amplitude, however, and has no discernable effect on the macroscopic properties of the beam.