Tune feedback in PEP-II

The PEP-II B Factory is a 2.2-km-circumference, storage-ring collider in which 9-GeV electrons in the high-energy ring collide with 3.1-GeV positrons in the low-energy ring. In 2002 we installed tracking loops to measure each ring's horizontal and vertical tunes. (The tune, a critical parameter for beam stability and for luminosity, is the fractional part of the number of oscillations of the beam about the central orbit in one revolution.) Each tracker uses a lock-in amplifier to measure the phase difference between a sinusoidal excitation of the beam and its response. If the drive frequency is swept across the tune resonance, this phase drops by 180 degrees. The tracker continually adjusts the frequency to maintain the phase at the middle of this transition. This drive frequency, normalized to the revolution frequency, gives the fractional tune. Recently these four loops (electron and positron, x and y) have been extended to controlling the tunes, by adjusting combinations of quadrupole magnets. However, at the same time we have increased the luminosity by setting the tunes just above the half-integer resonance, where a misadjustment can quickly lose the beam, and beam-beam forces from collisions make the tune spectra broad and complex. Consequently, we added a few non-colliding bunches to the fill pattern of each ring. Fast gates let us excite and measure only these bunches, and let us stop feedback damping of transverse motion for them.