Study of a longitudinal coupled-bunch instability in the Fermilab main ring

One goal of the Fermilab Main Ring accelerator is to keep the longitudinal beam oscillations as small as possible, since beam coalescing efficiency is greatly influenced by this motion. It is found that when the proton beam intensity reaches a certain value, longitudinal beam oscillations rapidly grow. This motion can be explained by the phenomenon of longitudinal beam instability. The dominant driving source for this instability is shown to be the impedance from the radio-frequency (RF) cavities. To understand impedance distributions in an RF cavity, a measuring technique using a network analyzer is applied. The result shows that there are two higher order modes of interest. The mode at 225 MHz has enough impedance to drive this instability. An experiment was carried out to observe the beam behavior. The beam had {dollar}2times 10sp{lcub}10{rcub}{dollar} particles per bunch with an energy of 150 GeV. The whole ring was only partially filled with a train of 10 to 15 bunches out of a possible 1113. The traditional theories about coupled bunch instability are not useful with this bunch spacing. Due to wake fields produced by the charged beam in the cavities, motions of different bunches are correlated. The longitudinal wake fields for higher order modes decay away quickly on the scale of one machine revolution. Then the head bunch no longer feels the fields after one turn, making it stable. But other bunches still feel wake fields produced by all previous bunches, which can make them oscillate. The longitudinal oscillation amplitudes depends on the beam intensity and impedance. After performing a Fourier transform on the longitudinal beam distribution, its spectrum is obtained. The 225 MHz signal in the spectrum confirms the impedance measurements. In addition, a simulation program was written to understand this process. By making comparisons, it is concluded that the observed beam behavior can be fully explained. It is possible to damp this beam instability by greatly reducing the higher order mode longitudinal impedance. An active feedback system will also help to reduce its severity.