BBU instability in rectangular dielectric resonator

TL;DR

This study investigates the beam breakup (BBU) instability in a rectangular dielectric resonator using PIC simulations, focusing on charge losses and mode interactions under relativistic electron bunch excitation.

Contribution

It provides new insights into BBU instability behavior and charge loss limits in rectangular dielectric resonators with specific mode excitation.

Findings

Charge losses due to BBU do not exceed 5%.

Charge losses are unaffected when the repetition period matches other eigenfrequencies.

Mode interactions influence BBU stability in dielectric resonators.

Abstract

Studies were made into the arise and an evolution of the beam breakup (BBU) instability in a rectangular dielectric resonator under excitation by a sequence of relativistic electron bunches. The dielectric resonator is a metal rectangular waveguide $R_{26}$ $(45mm\times 90mm)$ with Teflon dielectric slabs $8.2mm$ thick (dielectric constant $\varepsilon=2.051$) located along the wide side of the resonator. The wavelength of the $LM_{21}$ operating mode having a symmetric profile of the longitudinal electric field component is $53.2mm$. The electron energy of bunches is $4.5MeV$ , the charge of each bunch is $6.4nC$, the bunch repetition period is equal to twice the wavelength of the $LM_{21}$ mode. By the use of numerical PIC simulations, the charge losses of electron bunches on the dielectric plates were investigated as the bunches were displaced relative to the cavity axis. It is found that the charge losses on the dielectric slabs due to the BBU instability do not exceed $5\%$. When the bunch repetition period is changed to a multiple of another eigenfrequency (e.g., the $LM_{11}$ mode), the charge losses of drive bunches do not change appreciably.