Measurement of coherent beam-beam tune shift under crabbing collision at KEKB

Effective head-on collision and improvement in specific luminosity were established by the installation of crab cavities in KEKB. Tune spectra of a colliding bunch in a crabbing collision were observed by using a spectrum analyzer. The beam-beam spectrum showed strong nonlinear resonance. By taking into account this nonlinearity, the coherent beam-beam tune shift was measured as a function of the bunch current. The vertical beam-beam parameter estimated from the coherent beam-beam tune shift was found to agree with that observed by using a bunch-by-bunch luminosity monitor. The estimated vertical beam-beam parameter is saturated at approximately 0.05; this value is the beam-beam limit. Further, the bunch current corresponding to the beam-beam limit was found to be considerably lower than that used in usual operations. The horizontal beam-beam parameter was not saturated over 0.15. The horizontal beam-beam parameter estimated from the coherent beam-beam tune shift approximately agrees with a calculated beam-beam parameter considering the dynamic beam-beam effect.