Observation of Vertical Betatron Sideband due to Electron Clouds in the KEKB Low Energy Ring

The effects of electron clouds on positively charged beams have been an active area of research in recent years at particle accelerators around the world. Transverse beam-size blowup due to electron clouds has been observed in some machines and is considered to be a major limiting factor in the development of higher-current, higher-luminosity electron-positron colliders. The leading proposed mechanism for beam blowup is the excitation of a fast head-tail instability due to short-range wakes within the electron cloud. We present here observations of betatron oscillation sidebands in bunch-by-bunch spectra that may provide direct evidence of such head-tail motion in a positron beam.

Figure 1

Two-dimensional plot of vertical bunch spectrum versus bunch number. The horizontal axis is the fractional tune, from 0.5 on the left edge to 0.7 on the right edge. The vertical axis is the bunch number in the train, from 1 on the bottom edge to 100 on the top edge. The bunches in the train are spaced 4-rf buckets (about 8 ns) apart. The bright, curved line on the left is the vertical betatron tune, made visible by reducing the bunch-by-bunch feedback gain by 6 dB from the level usually used for stable operation. The line on the right is the sideband.

Figure 2

Averaged spectra of all bunches with the feedback gain (a) high, (b) low, and (c) set to zero. The vertical betatron peak is visible at 0.588, and the sideband peak can be seen around 0.64.

Figure 3

Effect of changing synchrotron tune on the separation between sideband peak and betatron peak. In (a), the sideband-betatron peak separation is plotted along the bunch train for ${\nu }_s=0.0246$ (solid lines) and ${\nu }_s=0.0234$ (dashed lines). In (b), the difference between the two curves is plotted. Statistical $1\mathrm{\text{−}}\sigma$ error bars are shown.

Figure 4

Example time series of single bunches taken via (a) BPM and (b) PMT. Different bunches are shown for each detector; the data were taken within 1 min of each other. A burstlike behavior is visible in the BPM signal. A fast ramp-up behavior with a similar rise time as the BPM burst is seen in the PMT signal, followed by a gradual ramp-down.

Figure 5

Model focusing wake. The horizontal axis is the longitudinal coordinate in units of the bunch length.

Figure 6

Example mode spectrum for model focusing wake at ${\nu }_s=0.022$ (dashed lines) and ${\nu }_s=0.024$ (solid lines).

Figure 7

Peak heights of maximum-amplitude frequency bins in the sideband region of a bunch spectrum, plotted for the first 100 bunches in the train, for two values of ${\nu }_s$. Error bars are $1\mathrm{\text{−}}\sigma$ statistical error bars.