Filamentation Instability of Electron and Positron Colliding Beams in Storage Ring

Abstract

The filamentation instability of the electron and positron colliding beams in a storage ring is investigated within the framework of the Vlasov-Maxwell equations, and a closed algebraic dispersion relation for the complex eigenfrequency $\omega$ is obtained. It is shown that the typical growth rate of instability is a substantial fraction of the electron plasma frequency ${\omega }_{\mathrm{pe}}$. For parameters characterizing the recent colliding-beam experiments at DESY, the instability threshold is marginally satisfied.