  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.
